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Presenting worked examples and solutions leading to practice questions, this helps students to learn maths. It features sample past exam papers for exam preparation, and includes regular review sections. It includes a CD ROM which contains what students need to motivate and prepare themselves. Synopsis: Edexcel and A Level Modular Mathematics C4 features: *Student-friendly worked examples and solutions, leading up to a wealth of practice questions. *Sample exam papers for thorough exam preparation. *Regular review sections consolidate learning. *Opportunities for stretch and challenge presented throughout the course. *'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. *Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. *Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary
CalcPlot3D, an Exploration Environment for Multivariable Calculus Using CalcPlot3D to Visually Verify Homework in Multivariable Calculus One way to use CalcPlot3D, a versatile Java applet, is to demonstrate new concepts during multivariable calculus lectures. I often develop a new concept on the chalk board first and then take a couple minutes to make the concept come to life using the applet. Students find these demonstrations helpful and fun, and they bring variety to my presentations, helping students process the new concepts in a new way. An even more exciting way to use CalcPlot3D in class is to engage in a visual exploration of new concepts using "What if…" types of questions. An example of a topic for which I find this approach works especially well is exploring the variety of possible parameterizations of a plane/space curve, paying special attention to the behavior of the velocity and acceleration vectors. Using these sorts of visual demonstrations in class improves student learning, but to fully engage students in the exploration and discovery process and give them the best chance of learning the geometric nature of the calculus concepts, I feel it is vital to give students opportunities to "play" with the concepts visually themselves. This article focuses on one way this can be done: by requiring students to visually verify solutions to particular homework problems and turn these in for a grade. [Another way this project supports student engagement and "play" is with the guided explorations being developed for various concepts. See the main project website to explore these. At this writing, there are explorations for Dot Products, Cross Products, Velocity & Acceleration Vectors, and Lagrange Multiplier Optimization.] Below is a list of example topics where I often assign this type of visual verification exercise to my students to get them to begin using the applet on their own. Once they start using the applet in this way (because they have to), students often report using the applet more often on their own to explore additional exercises they complete from the textbook and on other assignments. Before giving a visual verification assignment involving new skills with the applet, I always demonstrate using CalcPlot3D to visually verify a similar problem we worked on the board. Once students have seen one example using the applet, most have little trouble completing the exercise on their own. Without further discussion, let's look at some examples of how this can be done! As you develop your own examples, please send them along to me! I would love to develop a library of useful ways to use this applet.
Number Systems Real Numbers Euclid's division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. Proofs of results – irrationality of root 2, root 3, root 5 , decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals. Algebra 1. Polynomials Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients. 2. Pair of Linear Equations in Two Variables Pair of linear equations in two variables. Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be... [continues]
Course starts out easy and then suddenly gets difficult. The math isn't too tough but there are a LOT of formulas to memorize. We didn't need the book at all for the class as we used StatsPortal (a service you need to purchase) but that has an ebook on it.
Numerical analysis is the study of algorithms for computing numerical solutions to mathematical problems. The course provides an introduction to the ideas of numerical analysis via simple problems in analysis and algebra. We will study the efficiency of the algorithms as well as their implementation. . Topics and reviews Representation of floating point numbers, their implementation on the computer, loss of significance.
College Trigonometry Study Guide Our Trigonometry Study Guide is online, available 24/7, and is very affordable. There is no software to download or install. Students can work through the study guide at their own pace and master the types of questions that give them the most trouble. We provide an explanation for each answer, so students can learn how the correct answer is reached. In addition to practice questions, Northstar Workforce Readiness includes diagrams, graphs, and other study aides to help students understand the material. Our study guide covers College Trigonometry curriculum (typically a 1-semester course). It includes 12 topic modules with lessons, and practice questions with explanations.
Discovering Math: Advanced Number Concepts DVD This program addresses various number concepts, including consideration of different systems of numbers, exponents, roots and logarithms, and discrete structures. Develop student understanding with the Discovering Math series. This program addresses various number concepts, including consideration of different systems of numbers, exponents, roots and logarithms, and discrete structures.
Since they are fundamental to the study of linear algebra, students'understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible. show more show less List price: $61.99 Edition: 4th 2012 Publisher: Pearson Education, Limited Binding: Trade Cloth Pages: 576 Size: 8.50" wide x 10 Linear Algebra and Its Applications - 9780321385178 at TextbooksRus.com.
This CD has been created by our institute with the aim of improving the mathematics ability of the college student. It has the following topics : Factors, Simultaneous Equations, Indices, Logarithms, Geometrical Constructions and Sets. Exercises the student can solve alone are included in the CD.This is suitable for the students of grades 9,10 and 11 while and the students of grades 6,7,8,9 and 10 can use this CD to learn further.
Mathematics is the bridge between the arts and the sciences and is used across the whole curriculum. We aim, therefore, to give all pupils a good understanding and appreciation of the four areas of Number, Algebra, Geometry and Measure and Statistics. We hope to spark the pupils' imagination, as well as develop their knowledge, spatial awareness and use of logical thought. Mathematics has a spiral curriculum and so the textbooks we use help us to revise and extend prior subject knowledge. This is complemented by a wealth of other resources, enabling us to extend and encourage as appropriate. In the First Year pupils are taught in their Form groups for Mathematics, enabling us to get to know each child's mathematical ability fully before they are placed in sets in the Second Year and the Third Year. There is movement between sets, if and when this is felt appropriate, and each set is taught the same material. Each teaching group is usually made up of between fifteen and twenty pupils. In the Fourth and Fifth Year (Year 10 and Year 11), pupils are placed in four sets and follow the 2 tier linear specification for IGCSE with the Edexcel examination board. All sets start by following the Higher Tier specifications and the decision of which tier each student is entered at for public exams is made after the mock examinations in the January of the Fifth Form. Our International Centre students also follow the Edexcel IGCSE course in a year. There is an option for the most able pupils to study OCR Additional Mathematics in Year 11 as an extra-curricular activity. Mathematics is a popular subject choice for Sixth Formers at Ackworth. In the Lower Sixth we have three groups following Mathematics AS using the OCR MEI Mathematics course and there is an average of about ten students in each group. The Further Mathematics group of between ten and fifteen students follows the OCR MEI Mathematics modules that lead to an AS in Further Mathematics. The Upper Sixth has two sets of between twelve and fifteen students following A2 Mathematics, continuing with the MEI modules. There is also a Further Mathematics group of about twelve students taking MEI modules to complete the Further Mathematics A2 qualification. Some of our gifted students study extra modules to gain further additional Advanced Level qualifications. Some students enter a Sixth Term Entrance Paper (STEP) or an Advanced Extension Award (AEA) in Mathematics when this is felt appropriate or is necessary for their further studies. Extra-curricular activities within the Mathematics Department include the UK Maths Challenge, which is entered by students throughout the School. There is a puzzle and board games club, open to all students, where different aspects of Maths are investigated. Workshops are available for anyone needing extra help from First Year up to and including the Sixth Form. There is also a club for students who enjoy code-breaking and ciphers. We also enjoy participating in the UKMT team challenge and the Leeds University pop quiz.
Online Math Center Mission Statement The mission of Whatcom Community College's Online Math Center is to provide free access to a wide range of resources related to mathematics, its application, technology, and mathematics education. Design Tied to Mission To this end, the Online Math Center has been designed around two main themes, Teaching and Learning Math, as well as the ancillary themes of Math Resources, Calculators, and Math Events. Learning Math Under Learning Math, there is an on "growing" set of topics. There are links to tutorial sites on the Web as well as on campus. Users have access to Web help pages and may find information about Math Placement and Math Classes, scholarships and other forms of financial aid. Teaching Math Here you will find applications to math from A to Z. Use LiveMath resources to visualize vectors, imaginary roots, three dimensional surfaces. The Math Calendar can locate the birthdays of mathematicians for any day of the year as well as provide information about many different calendars. Teaching Resources from prepared lesson plans to graph paper, and Real Data that can be used for mathematical modeling are also found under Teaching Math. To locate a WCC Math faculty member or find a text publisher, use the links provided under this section. Math Resources Found under Math Resources are Math Software Reviews, ERIC Resources, as well as The Online Math Center Library with links to math oriented web libraries, references, and journals. To locate professional mathematics organizations online, visit our Organizations page. To visit the homepage or math department homepage of many community colleges and four year universities try our Colleges page. Calculators Information about the specifications and operation of Casio, Texas Instrument, and Hewlett Packard graphing calculators and data gathering devices may be found on the Calculator page. There are links to tutorials and to sites from which programs may be downloaded to specific models of graphing calculators. Math Events For mathematical puzzles and contests, current research, and professional meetings, visit the Math Events page. The creation of the Online Math Center was funded through the U. S. Department of Education Title III Grant PO31A980143.
books.google.co.uk - This comprehensive three-part treatment begins with a consideration of the simplest geometric manifolds - line-segment, area, and volume as relative magnitudes; the Grassmann determinant principle for the plane and the Grassmann principle for space; classification of the elementary configurations of... mathematics from an advanced standpoint.
Elementary Statistics: A Step by Step Approach "Elementary Statistics: A Step by Step Approach" is for general beginning statistics courses with a basic algebra prerequisite. The book is non ...Show synopsis"Elementary Statistics: A Step by Step Approach" Minitab, and the TI-83 Plus and TI 84-Plus graphing calculators, computing technologies commonly used in such courses Elementary Statistics: A Step by Step Approach Easy to follow book. Very well prepared for an individual not knowledgeable in using Excel for statistics. I love the step by step Procedure Tables that show the process and the numerous
User bethany - MathOverflowmost recent 30 from by Bethany for What to do with antique math books?Bethany2012-03-16T05:00:00Z2012-03-16T05:00:00Z<p>If you haven't sold all of these books, i might be interested in purchasing some of them from you. I am a math major in college and planning on getting a PhD in Math. Currently i am building a library of math books. Thanks!</p>
CalcuEx 1.0 CalcuEx - The calculator that allows enter expressions using a mathematical notation This program is a calculator that allows enter expressions using a mathematical notation. It has functionality of an engeneering calculator, i.e. it can operate with addition, substraction, multiplication, division, raising to a power, roots, logarithms and trigonometric functions. You can use this program with applications, that supports OLE objects (such as Word or Excel), also, you can save expressions in graphic format
Factoring: Polynomials/Trinomials The learner will be able to factor polynomials, difference of squares and perfect square trinomials, and the sum and difference of cubes. Strand Scope Source Factoring Master NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.14 Radicals: Simplifying The learner will be able to simplify square roots and cube roots that have monomial radicands which are perfect cubes or perfect squares. Strand Scope Source Radicals Master NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.11 Radical Equations: Solve The learner will be able to obtain solutions to radical equations with one radical. Strand Scope Source Radicals Master NM: Content Standards, 2002, Grade 9-12, pg 44: AFG.13 Quadratic Formula: Roots The learner will be able to apply the quadratic formula (and/or factoring techniques) to find out if the graph of a quadratic function will intersect the x-axis in zero, one, or two places. Strand Scope Source Quadratic Equations/Formula Master NM: Content Standards, 2002, Grade 9-12, pg 45: AFG.12 Quadratic Equations: Represent The learner will be able to represent real world problem situations using quadratic equations. Strand Scope Source Quadratic Equations/Formula Master NM: Content Standards, 2002, Grade 9-12, pg 46: AFG.1 Quadratic Equations: Apply The learner will be able to use quadratic equations in the solution of physical problems of various types. Strand Scope Source Quadratic Equations/Formula Master NM: Content Standards, 2002, Grade 9-12, pg 45: AFG.13 Exponents: Comprehend/Rules The learner will be able to comprehend the rules of exponents. Strand Scope Source Exponents Master NM: Content Standards, 2002, Grade 9-12, pg 46: AFG.11 Exponents: Apply Rules The learner will be able to apply the rules of exponents.
GraspMath Learning Systems Trigonometry (16) DVD Series Please Note: Pricing and availability are subject to change without notice. This Trigonometry video tutor series consists of 16 video segments, each segment is approximately 25-30 minutes in length and on its own DVD. Topics include angles, degrees and radians, trigonometric functions of general angles, graphing trigonometric functions, proving trigonometric identities, inverse trigonometric functions, right triangle applications, law of sines, law of cosines, polar coordinates, DeMoivre's Theorem, and nth roots of complex numbers. Segments included in this series: Angles, Degrees and Radians. This segment covers definitions for angles and their measures as well as the circular arc length formula and problems for conversion of angle measure for radians to degrees, degrees to minutes and vice-versa. Introduction to Trigonometric functions. This segment covers the definitions of the trigonometric functions of acute angles using right triangles, as well as special angles of 30, 60 and 45 degrees. Trigonometric Functions of General Angles. This segment covers the definitions of trig functions for general angles using rectangular coordinates, standard position and terminal side. The reciprocal, quotient and Pythagorean identities are covered. Evaluating Trigonometric Functions. This segment covers reference angles and their use in computation of trig functions of general angles. Graphing Trigonometric Functions I. This segment covers the reciprocal relations, the Pythagorean identities, evenness and oddness for trig functions and demonstrations of some simple trig identity problems. Graphing Trigonometric Functions I. This segment covers the reciprocal relations, the Pythagorean identities, evenness and oddness for trig functions and demonstration of some simple trig identity problems. Trigonometric Identities III. This segment covers the double-angle and half-angle formulas and their use in calculations as well as in solution of trig identities. Inverse Trigonometric Functions. This segment covers inverse functions for sine, cosine, and tangent functions as well as computations involving trig functions of an expression containing an inverse trig function. Trigonometric Equations. This segment covers the use of trig identities for solving trigonometric equations. Right Triangle Applications. This segment covers the use of trig functions to solve right triangles from partial information, and applications. Law of Sines. This segment covers the use of the law of sines to solve triangles from partial information. Law of Cosines. This segment covers the use of the law of cosines to solve general triangles from partial information, as well as applications. Polar Coordinates. This segment covers polar coordinates as well as the use of sine and cosine to transform from polar to rectangular coordinates and the tangent function for converting from rectangular to polar coordinates.
... read more Customers who bought this book also bought: Our Editors also recommend: Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figuresPoint Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 Algebraic Topology by Andrew H. Wallace This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.Algebraic Geometry by Solomon Lefschetz An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition. Product Description: and axiomatic approach for easier accessibility. Includes exercises and a
Holt McDougal Mathematics The new Tables of Contents for Holt McDougal Mathematics for Grades 6, 7, and 8 math textbooks reflect a new focus on concepts that are taught in depth. Holt McDougal Mathematics textbooks implement the Standards for Mathematical Practice into student learning and teacher resources, resulting in a deeper understanding of math strategies and concepts. Embedded Response to Intervention resources within the Grade 6–8 math textbooks ensures every student gets the help they need. More than just a print edition, our Grade 6–8 math textbooks are also available as an online textbook and eTextbook, downloadable on any mobile device. Teacher and student resources are available in print, online, and mobile—providing the kind of anytime/anywhere access to resources that today's teaching environment demands and today's students deserve. You can even customize your book to the distinct needs of your school or district. No other math program empowers students to develop the core skills they need like Holt McDougal Mathematics does. A new era and a new approach for reaching all students!
Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time, as viewed by distinguished historians of mathematics from the past and the present. This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. This self-contained work introduces the main ideas and fundamental methods of analysis at the advanced undergraduate/graduate level. It provides the historical context out of which these concepts emerged, and aims to develop connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. A concise yet comprehensive compendium of formulas, functions, symbols, constants, and conversions, Mathematical and Physical Data, Equations, and Rules of Thumb is a treasure trove of data for everyone from electrical hobbyists to engineers. Consistent with the plan-English writing that's made top science writer/author Stan Gibilisco's books consistently popular, this handy guide provides you with crystal-clear explanations. 'There is no other information retrieval/search book where the heart is the mathematical foundations. This book is greatly needed to further establish information retrieval as a serious academic, as well as practical and industrial, area.' Jaime Carbonell, Carnegie Mellon University; 'Berry and Browne describe most of what you need to know to design your own search engine. Their strength is the description of the solid mathematical underpinnings at a level that is understandable to competent engineering undergraduates, perhaps with a bit of instructor guidance. Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition. This volume features key contributions from the International Conference on Pattern Recognition Applications and Methods, (ICPRAM 2012,) held in Vilamoura, Algarve, Portugal from February 6th-8th, 2012. The conference provided a major point of collaboration between researchers, engineers and practitioners in the areas of Pattern Recognition, both from theoretical and applied perspectives, with a focus on mathematical methodologies. This book contains several contributions on the most outstanding events in the development of twentieth century mathematics, representing a wide variety of specialities in which Russian and Soviet mathematicians played a considerable role.
MATH& 141Precalculus I• 5 Cr. Department Division Emphasizes graphs and polynomial functions. Other topics include the theory of equations and rational, exponential, inverse, and logarithmic functions. Either MATH& 141 or MATHY 138 may be taken for credit, not both. Fulfills the quantitative or symbolic reasoning course requirement at BC. Prerequisite: Placement by assessment or MATH 099 with a B- or better. Outcomes: After completing this class, students should be able to: Demonstrate knowledge of College Algebra from and Elementary Functions approach in preparation for Calculus I, II, and III. Build and demonstrate knowledge of using a graphing calculator and utilizing it as an aid in understanding as well as solving College Algebra and Pre-calculus concepts and exercises. Solve 1st degree inequalities including double inequalities and absolute value inequalities. Solve 1srt degree and 2nd degree and rational equations including Quadratic formula and apply it to solving 2nd degree and 3rd degree and rational inequalities using the Test Value Method. Solve related inequality application and to interpret the solutions and make inferences. Demonstrate knowledge of Rectangular Coordinate System graphing by plotting. Apply Distance and Midpoint Formulas into learning of the equations for circles. Identify symmetry in a graph and recognize its associated advantages and limitations. Recognize functions in symbolic, graphical, and tabular formats. Identify Domain and Range in each of these formats. Use Functional Notation and evaluation leading to sketching functions. Identify graphs as decreasing or increasing. Build functions to describe various Application Problems and interpret the results and make inferences. Graph functions in general including utilizing the properties of shifting, stretching, and reflecting and recognize its advantages over point. Given the initial and the final graphs describe symbolically which effect were used. Use a graphing calculator to identify these general properties easier. Identify and contrast Even and Odd functions, as well as Piece-Wise defined functions including the Greatest Integer Function. Recognize 2nd degree or Quadratic Functions and their associated Parabolic Graphs. Find the Vertex from the Vertex Form and/or by Formula and apply it in graphing Parabolas. Use the Quadratic Formula to find the zeros of a Quadratic Function. Combine functions utilizing operations of Addition, Subtraction, Multiplication, Division, and Composition and find the new Domain for each, with the functions being given symbolically, graphically or by a table. Solve related Applications using the Composition Operations. Identify Inverse Functions and One to One functions. Verify two functions are inverses by using composition. Find Inverse Functions given the original function symbolically or graphically or by table. Analyze and Graph Polynomials of Nth degree utilizing general properties of Polynomials and locate the zeros and find and plot test points between and beyond the zeros. Solve related Application Problems and to interpret the solutions. Identify Complex numbers and Add, Subtract, Multiply, and divide. Find and describe complex roots using conjugates after factoring or using the Quadratic Formula. Divide Polynomials, and show knowledge of Synthetic Division. Recognize the connection between Synthetic division and the Reminder and Factor Theorems. Apply the Theory of Equations including the Fundamental Theorem of Algebra, factored form of polynomials, multiplicity of zeros, and bounds on real zeros to graph polynomials and compare and contrast different polynomial graphs. Recognize the Complex roots come in pairs. Find Rational zeros using the Rational Roots Theorem and to reduce to the Quadratic level for future solving. Solve related Application Problems and to interpret the solutions. Analyze and graph Rational Functions through a multi-step process including finding all Intercepts, Domain, all Asymptotes, and plotting a couple of relevant test points. Identify and find Vertical, Horizontal, and Slant Asymptotes. Solve related Application Problems and to interpret the solutions and make inferences. Analyze and graph Exponential and Logarithmic functions. Solve related Applications and to interpret the solutions. Identify the Natural Exponential and the Natural Logarithm Functions with base "e", and utilize them to solve and interpret solutions to Compounded Interest and Continuously Compounded Interest Applications as well as making inferences in Population, Radioactive Decay, Drug level and other applications.
Provides Internet resources that will help improve the teaching and learning of mathematics for all students, professional development for teachers of mathematics, Standards-based resources for classroom use and helps communicate the vision of Standards-based mathematics teaching and learning. Computer program for data management and basic statistical analysis of experimental data. Developed primarily for the analysis of data from agricultural field trials, but many of the features can be used for analysis of data from other sources.
CentAUR: Central Archive at the University of Reading Accessibility navigation The 'algebra as object' analogy: a view from school Colloff, K. and Tennant, G. (2011) The 'algebra as object' analogy: a view from school. Proceedings of the British Society for Research into the Learning of Mathematics, 31 (3). 4. ISSN 1463-6840 Text - Published Version · Restricted to Repository staff only · The Copyright of this document has not been checked yet. This may affect its availability. · Please see our End User Agreement before downloading. 205Kb Abstract/Summary Treating algebraic symbols as objects (eg. "'a' means 'apple'") is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, "3a + 2a = 5a" to year 7 pupils. Results included the notion that the 'algebra as object' analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not 'supposed' to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an'algebra as object' approach. Year 7 pupils did not explicitly refer to 'algebra as object', although some of their responses could be so interpreted. In the main, year 10 pupils used 'algebra as object' to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of 'algebra as object' in pupils' thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.
Help Coming for UNM's Math Challenged Students Math pro­fi­ciency has long been a con­cern of UNM aca­d­e­mic lead­er­ship. Approx­i­mately 2,300 stu­dents per year attempt inter­me­di­ate alge­bra (Math 120) with a pass rate of less than 50 per­cent. Since Math 120 is one of the gate­way courses for UNM stu­dents, address­ing the low pass rates is cru­cial for stu­dent success. Mark Peceny, dean, Col­lege of Arts & Sci­ences, and fac­ulty in the Depart­ment of Math­e­mat­ics, began research­ing and plan­ning a pilot project over the last aca­d­e­mic year to redesign con­tent deliv­ery that replaces lec­tures with time in a learn­ing lab where stu­dents use self-paced, computer-based resources to learn and be assessed. The project is an exper­i­ment that will attempt to improve the low pass rates for Math 120. "The Uni­ver­sity of New Mex­ico and the Col­lege of Arts and Sci­ences is com­mit­ted to help­ing the Depart­ment of Math­e­mat­ics and Sta­tis­tics deliver a qual­ity math­e­mat­ics cur­ricu­lum to all under­grad­u­ate stu­dents at UNM," said Phillip Gan­der­ton, asso­ciate dean, Col­lege of Arts and Sci­ences. "MaLL is a sig­nif­i­cant step in achiev­ing the goal of pro­vid­ing a flag­ship uni­ver­sity edu­ca­tion to the emerg­ing Amer­i­can majority." This method is in place at many insti­tu­tions across the U.S. and is prov­ing to be suc­cess­ful in improv­ing stu­dent learn­ing and pass rates for inter­me­di­ate alge­bra, as well as a num­ber of other courses. The Math Learn­ing Lab (MaLL) will be staffed with teach­ers, grad­u­ate stu­dents and select under­grad­u­ates who will assist stu­dents indi­vid­u­ally as they move through the mate­r­ial. The pilot project for the MaLL begins this fall, and involves a rel­a­tively small num­ber of stu­dents uti­liz­ing an exist­ing com­puter classroom. "Dean Peceny is con­vinced that start­ing with this pilot project, the Col­lege can quickly develop this ini­tia­tive into an inno­v­a­tive model for improv­ing stu­dent suc­cess and grad­u­a­tion," Gan­der­ton said. To achieve the goal of hav­ing all Math 120 stu­dents use this new course deliv­ery model com­menc­ing in the spring 2013 semes­ter, the math depart­ment, Arts and Sci­ences, Uni­ver­sity Libraries, cam­pus plan­ning and Infor­ma­tion Tech­nolo­gies con­ducted an exten­sive eval­u­a­tion of cam­pus space and deter­mined that the learn­ing lab will be located on the south­east side of the main level of the Cen­ten­nial Sci­ence and Engi­neer­ing Library (CSEL). It will be equipped with 125 com­put­ers for instruc­tional pur­poses and a test­ing lab with 15 addi­tional com­put­ers. When the MaLL com­put­ers are not in use by math stu­dents, they will be avail­able for gen­eral CSEL usage.
Book Description: The first book to discuss fractals solely from the point of view of computer graphics, this work includes an introduction to the basic axioms of fractals and their applications in the natural sciences, a survey of random fractals together with many pseudocodes for selected algorithms, an introduction into fantastic fractals such as the Mandelbrot set and the Julia sets, together with a detailed discussion of algorithms and fractal modeling of real world objects. 142 illustrations in 277 parts. 39 color plates.
Math & Science Curiosity. Skepticism. Persistence. Precision. Such qualities of mind have empowered every human step up from the depths of superstition and ignorance. Mathematics and science have produced walks on the moon, cures to dreaded diseases, a growing appreciation of our planet's delicate balance of life, and methods to help achieve more and more of what seems to be our limitless potential as a species. ASFA mathematics and science students realize their own personal potential through hands-on learning in labs, in research projects, on academic teams and in lecture demonstrations in other school and community settings. Honors level courses and Advanced Placement rigor, coupled with a high-level individual research project, build a foundation for important contributions to the math and science of tomorrow. This website describes the present courses, requirements, programs and services of the Alabama School of Fine Arts, which are subject to change at any time according to state requirements and the policies and procedures of the school.
Buy Used Textbook Buy New Textbook eTextbook 360 day subscription $93.59 More New and Used from Private Sellers Starting at $31.09Worksheets for Classroom or Lab Practice for Elementary and Intermediate Algebra Summary KEY BENEFIT:Elementary and Intermediate Algebra, Third Edition, by Tom Carson, addresses two fundamental issuesindividual learning styles and student comprehension of key mathematical conceptsto meet the needs of todayrs"s students and instructors.Carsonrs"s Study System, presented in the "To the Student" section at the front of the text, adapts to the way each student learns to ensure their success in this and future courses. The consistent emphasis on thebig picture of algebra, with pedagogy and support that helps students put each new concept into proper context, encourages conceptual understanding. KEY TOPICS: Foundations of Algebra; Solving Linear Equations and Inequalities; Problem Solving; Graphing Linear Equations and Inequalities; Systems of Linear Equations and Inequalities; Polynomials; Factoring; Rational Expressions and Equations; Roots and Radicals; Quadratic Equations MARKET: For all readers interested in algebra. Author Biography Tom Carson's first teaching experience was teaching guitar while an undergraduate student studying electrical engineering. That experience helped him to realize that his true gift and passion are for teaching. He earned his MAT. in mathematics at the University of South Carolina. In addition to teaching at Midlands Technical College, Columbia State Community College, and Franklin Classical School, Tom has served on the faculty council and has been a board member of the South Carolina Association of Developmental Educators (SCADE). Ever the teacher, Tom teaches outside the classroom by presenting at conferences such as NADE, AMATYC, and ICTCM on topics such as Combating Innumeracy, Writing in Mathematics, and Implementing a Study System. Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Jordan has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In addition to his work on the Carson series, Jordan is also the lead author of _Integrated Algebra and Arithmetic, 2/e, also published by Pearson. In his spare time, he enjoys fishing, traveling, and hiking. Table of Contents 1. Foundations of Algebra 1.1 Number Sets and the Structure of Algebra 1.2 Fractions 1.3 Adding and Subtracting Real Numbers; Properties of Real Numbers 1.4 Multiplying and Dividing Real Numbers; Properties of Real Numbers 1.5 Exponents, Roots, and Order of Operations 1.6 Translating Word Phrases to Expressions 1.7 Evaluating and Rewriting Expressions 2. Solving Linear Equations and Inequalities 2.1 Equations, Formulas, and the Problem-Solving Process 2.2 The Addition Principle of Equality 2.3 The Multiplication Principle of Equality 2.4 Applying the Principles to Formulas 2.5 Translating Word Sentences to Equations 2.6 Solving Linear Inequalities 3. Problem Solving 3.1 Ratios and Proportions 3.2 Percents 3.3 Problems with Two or More Unknowns 3.4 Rates 3.5 Investment and Mixture 4. Graphing Linear Equations and Inequalities 4.1 The Rectangular Coordinate System 4.2 Graphing Linear Equations 4.3 Graphing Using Intercepts 4.4 Slope-Intercept Form 4.5 Point-Slope Form 4.6 Graphing Linear Inequalities 4.7 Introduction to Functions and Function Notation 5. Polynomials 5.1 Exponents and Scientific Notation 5.2 Introduction to Polynomials 5.3 Adding and Subtracting Polynomials 5.4 Exponent Rules and Multiplying Monomials 5.5 Multiplying Polynomials; Special Products 5.6 Exponent Rules and Dividing Polynomials 6. Factoring 6.1 Greatest Common Factor and Factoring by Grouping 6.2 Factoring Trinomials of the Form x2 + bx + c 6.3 Factoring Trinomials of the Form ax2 + bx + c, where a ≠ 1 6.4 Factoring Special Products 6.5 Strategies for Factoring 6.6 Solving Quadratic Equations by Factoring 6.7 Graphs of Quadratic Equations and Functions 7. Rational Expressions and Equations 7.1 Simplifying Rational Expressions 7.2 Multiplying and Dividing Rational Expressions 7.3 Adding and Subtracting Rational Expressions with the Same Denominator 7.4 Adding and Subtracting Rational Expressions with Different Denominators
... read more Customers who bought this book also bought: Our Editors also recommend:A Vector Space Approach to Geometry by Melvin Hausner This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965Lectures on Analytic and Projective Geometry by Dirk J. Struik This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition. Projective Geometry by T. Ewan Faulkner Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960Non-Euclidean Geometry by Stefan Kulczycki This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition. 1961Vector Geometry by Gilbert de B. Robinson Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition. Product Description: explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals. Reprint of the McGraw-Hill Book Company, Inc., New York, 1970 edition. Bonus Editorial Feature: Clarence Raymond Wylie, Jr., had a long career as a writer of mathematics and engineering textbooks. His Advanced Engineering Mathematics was the standard text in that field starting in the 1950s and for many decades thereafter. He also wrote widely used textbooks on geometry directed at students preparing to become secondary school teachers, which also serve as very useful reviews for college undergraduates even today. Dover reprinted two of these books in recent years, Introduction to Projective Geometry in 2008 and Foundations ofGeometry in 2009. The author is important to our program for another reason, as well. In 1957, when Dover was publishing very few original books of any kind, we published Wylie's original manuscript 101 Puzzles in Thought and Logic. The book is still going strong after 55 years, and the gap between its first appearance in 1957 and Introduction to Projective Geometry in 2008 may be the longest period of time between the publication of two books by the same author in the history of the Dover mathematics program. Wylie's 1957 book launched the Dover category of intriguing logic puzzles, which has seen the appearance of many books by some of the most popular authors in the field including Martin Gardner and, more recently, Raymond Smullyan. Here's a quick one from 101 Puzzles in Thought and Logic: If it takes twice as long for a passenger train to pass a freight train after it first overtakes it as it takes the two trains to pass when going in opposite directions, how many times faster than the freight train is the passenger train? Answer: The passenger train is three times as fast as the freight train
Allergic to Algebra? Use these resources One of the complaints I've heard about Math for Grownupsis that it only covers basic math. And I'm not apologetic about that. The whole point of the book is to make basic math a little less mysterious and a little more practical. But there may be times when you need an Algebra II refresher or review of basic calculus facts. If we don't use this stuff we lose it. Throughout the years, I've discovered a few really wonderful websites that offer just this kind of assistance. From explaining basic math in theoretic terms (which may be necessary to help our kids with their middle school math homework) to reviewing more complex math topics, these sites are really wonderful. When you need a little more than the basics, I recommend taking a look. This site offers a wide variety of resources for parents, teachers and students. But the part I love the most is Ask Dr Math. Hundreds of college professors answer math-related questions from students, teachers and parents around the world. These responses are archived in a searchable database. Plus there are broad categories to browse, like Formulas and Middle School. This site is devoted to algebra–from absolute value to solving systems of linear equations. Students (and parents) can skim lessons for quick answers or read them carefully for more in-depth review of the topics. You can also post a question in the forums and receive a thoughtful response that invites you to think critically or refers you back to the lessons themselves. (There are no quick answers here!) Have you forgotten what a Cartesian plane is? Are you wracking your brain trying to remember why the y-intercept is a big deal? Mathwords offers definitions for thousands of math terms. There are no examples or explanations here, but sometimes knowing a definition is enough to jog the old synapses. Right? Do you have any favorite math resources? Share them in the comments section! No Comments I don't know why people complained about the basic math. To me the title implied it would everyday math. I for one I'm glad you started there. Plus this is only your first book. There are many avenues you can take with future books if you like.
Introduction. Types of Optimization Problems. Engineering Applications. Optimization Methods from Differential Calculus. Linear-Programming Problem. Simplex Method. Search Methods for Nonlinear Optimization. Optimization of a Function of a Single Variable. Unconstrained Minimization of a Function of Several Variables. Constrained Minimization of a Function of Several Variables. Choice of Method. Use of Software Packages. Computer Programs. 13. Finite-Element Method. Introduction. Engineering Applications. Discretization of the Domain. Interpolation Functions. Derivation of Element Characteristic Matrices and Vectors. Assemblage of Element Characteristics Matrices and Vectors. Solution of System Equations. Choice of Method. Use of Software Packages. Computer Programs. Appendix A: Basics of Fortran 90. Appendix B: Basics of C Language. Appendix C: Basics of MAPLE. Appendix D: Basics of MATLAB. Appendix E: Basics of MathCAD. Appendix F: Review of Matrix Algebra. Appendix G: Statistical Tables. Index. Features & benefits A variety of engineering applications at the beginning of each chapter—Illustrate the practicality of the methods considered in that chapter. Software and programming methods are discussed in every chapter. Illustrative examples in MATLAB, MathCAD, MAPLE, Fortran, and C are given. A section in every chapter discusses the trade-offs of each of these tools and how to choose the most effective tool for a problem type. Over 800 problems including open ended, project type and design problems at the end of chapters—With guidelines for their solution in Instructor's Manual. Review question sections in each chapter which are separate from end-of-chapter problems—Includes multiple choice questions, questions with brief answers, true-false questions, questions involving matching of related description, and fill-in-the-blank type questions. Answers are provided to students on the book's website. Helps students in reviewing and testing their understanding of the text material.
This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a "most readable book." An ideal introduction to groups and Galois theory, it provides students with an appreciation of abstraction and arbitrary postulational syste... read more Customers who bought this book also bought: Our Editors also recommend:Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems.Numerical Methods by Germund Dahlquist, Åke Björck Practical text strikes balance between students' requirements for theoretical treatment and the needs of practitioners, with best methods for both large- and small-scale computing. Many worked examples and problems. 1974 edition. Product Description: This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a "most readable book." An ideal introduction to groups and Galois theory, it provides students with an appreciation of abstraction and arbitrary postulational systems, ideas that are central to automation. The authors take the algebraic equation and the discovery of the insolubility of the quintic as their theme. Starting with treatments of groups, rings, fields, and polynomials, they advance to Galois theory, radicals and roots of unity, and solution by radicals. Thirteen appendixes supplement this volume, along with numerous examples, illustrations, commentaries, and exercises. Students who have completed a first-year college course in algebra or calculus will find it an accessible and well-written treatment
.... Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole....
Sunday, October 01, 2006 Up next, students will learn to evaluate composite functions. First, they will do a worksheet with function notation practice problems. I set the problems up in groups of 4 as follows: f(2), f(-4), f(a), f(2x - 5). I think that sneaking up this way on the idea of plugging in an expression for x will help students better understand how to evaluate f(g(x)) as an expression. I remember having a lot of difficulty when I first learned this concept, and this method helps make it clearer for me anyway... Then, we'll use this dual lens model. I hope it will help them visualize what "the output of f is the input of g" means. After the model, we'll go through the concept of composing functions, and do some example problems together. In an upcoming class, I will give students a chance to do function composition when given graphs or tables instead of equations. 5 comments: Anonymous said... Not only do kids have trouble with function composition, the young adults in introductory abstract algebra classes seem to have the worst time with it. Luckily you are working on maps from R to R, so the lens approach will probably serve you well. One thing that's worth doing is asking them to figure out whether or not map composition is associative, and then commutative. Thanks for your response. For commutativity, they can switch the order of the lenses and see if the final projection is the same or not. This should help them understand why they get different results when switching the order of the functions. But I'm not clear on what you mean by associativity. In the mapping model, you have to start at the initial input and follow the order of the lenses. If you try to start somewhere else, there will be no data to use. Could you give an example of what you mean, because it sounds interesting and I don't think I'm getting it.. I use the lens just for the first day as a way to introduce the concept. We also look at composition in other ways. I'm not sure yet if it is helpful or not, but I think different students will remember different methaphors for the same concept. On the first quiz, I ask them to use the lens model, but I don't assess them on it by the time we get to the unit test or final exam. At that point, I just care if they have mastered the skill of composition
Explorations in College Algebra, 5th Edition Explorations in College Algebra, 5/e and its accompanying ancillaries are designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates students to grasp abstract ideas by solving real-world problems. The problems lie on a continuum from basic algebraic drills to open-ended, non-routine questions. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in the social, physical, and life sciences. The goal of Explorations in College Algebra, 5/e is to prepare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us. Explorations in College Algebra was developed by the College Algebra Consortium based at the University of Massachusetts, Boston and funded by a grant from the National Science Foundation. The materials were developed in the spirit of the reform movement and reflect the guidelines issued by the various professional mathematics societies (including AMATYC, MAA, and NCTM). for Explorations in College Algebra, 5th Edition. Learn more at WileyPLUS.com Explore & Extend: are a new feature in this edition. These "mini exploration" problems provide students with ideas for going deeper into topics or previewing new concepts. They can be found in every section. Accumulation of tools: The authors added a transformation to each chapter that covers functions. The intention of these changes is to progressively accumulate (about one per chapter) the tools for transforming functions. This is a way to discuss properties of functions using function notation and to use the transformations as new functions are introduced. Chapter 8 reconfigured: Ch. 8 has been split into two chapters: New Ch 8 covers quadratics and polynomials, while Ch. 9 is titled "Creating New Functions from Old." Data: Data are updated throughout. Extended Explorations: The two Extended Explorations have been integrated into the text as sections in relevant chapters. Algebra developed from real-world applications: These materials are based on problems using actual data drawn from a wide variety of sources including: the U.S. Census, medical texts, the Educational Testing Services, the U.S. Olympic Committee, and the Center for Disease Control. Flexibility of use: The materials are designed for flexibility of use and offer multiple options for adapting them to a wide range of skill levels and departmental needs. The text is currently used in both small and large classes, two and four-year institutions, and taught with technology (graphing calculators and/or computers) or without. Many optional special features are described in following points. Many opportunities for students to practice: Each section includes Algebra Aerobics, which are intended to help the student practice the skills they just learned. At the end of each chapter the Check Your Understanding and Review Summary sections can help students review the major ideas of the chapter. Actively involved students: The text advocates the active engagement of students in class discussions and teamwork. The Something To Think About questions, open-ended exercises, and the Explorations are tools for stimulating student thought. The Explorations are an opportunity for students to work collaboratively or on their own to synthesize information from class lectures, the text, and the readings, and most importantly from their own discoveries. Emphasis on verbal and written communication: This text encourages students to verbalize their ideas in small group and class discussions. Suggestions for writing "60-second summaries" are included in the first chapter, and many of the assignments require students to describe their observations in writing. Throughout the text there references to wide a variety of essays, articles, and reports included either in the Anthology of Readings (in the appendix of the text) or on the book companion website at: Many of the Explorations conclude with group presentations to the class. Technology integrated throughout: While the materials promote the use of technology and include many explorations and exercises using graphing calculators and computers, there are no specific technology requirements. Some schools use graphing calculators only, others use just computers, and some use a combination of both. This flexible approach allows Explorations in College Algebra, 4/e to meet the needs of many varying courses. Student Solutions: Step-by-step solutions to selected problems are provided at the end of the book.
The TI-89 Home Screen The home screen is the screen you see when the calculator is first turned on. (Note: On the TI-89 Titanium, you can get to the home screen by selecting "Home" from the Apps menu, or by pressing the <Home> key.) You can reach it at any other time by pressing the <HOME> key. Here is a brief explanation of the various areas on the home screen. The Menus allow you to select various functions, options, and tools. You access a function by pressing one of the blue keys <F1> through <F5>. Menus F6 through F8 are accessed by pressing <2nd><F1> through <2nd><F3>. The History Area is where your previous entries and results are temporarily stored. You can scroll through the history area using the blue arrow keys. You can erase the history area by selecting "8: Clear Home" from the "F1 - Tools" menu. The Entry Line is where the current function, equation, expression, or command is displayed before it is executed. To execute the instruction on the entry line, press the blue <ENTER> key. The Status Line displays important information about the calculator's current mode. The items on this line can be edited by pressing the <MODE> button: The Current Folder is the folder in which any saved items will be placed. The MAIN folder is the default. Angle mode (RADians or DEGrees) tells you how angles will be interpreted. In AP Calculus, you will use RADian mode almost exclusively. If you also use your calculator in DEGree mode, in science class for instance, be sure that you return to RADian mode for AP Calculus. Evaluation Mode (AUTOmatic, EXACT, or APPROXimate) determines how the calculator will evaluate expressions: EXACT mode means that the calculator will try to evaluate expressions exactly. For instance, will evaluate to . APPROXimate mode means that the calculator will return an approximate value for expressions - like a "normal" calculator would. For instance, will evaluate to 0.707107. AUTOmatic mode means that the calculator will return an exact result whenever possible, and an approximate result otherwise. This is the mode that we will normally use in class. If you definitely want an approximate result, press <Diamond><ENTER> instead of just <ENTER>. The Graph Mode tells you what type of graph will be displayed. In our class, we will use FUNCtion mode almost exclusively. History Memory Status tells you how many expressions the history area is currently holding followed by the number of expressions that it can hold.
If you are not using algebra on a daily basis, you should probably kill yourself. It's a pretty basic skill
Math Course 4 - Basic Measurement v2.0 Math Course 4, Basic Measurement: Step by Step addresses the major ideas of measurement by identifying measurable properties – length, area, volume, time, and temperature. Students explore the standard units of measurement for both the customary and metric measurement systems, the conversion between units, and estimation techniques for regular and irregular shapes. The Basic Measurement: Step by Step Course has 38 Lessons organized in 8 Units. Math Course 4 - Basic Measurement Textbook Covers 38 learning objectives over 8 units of the Basic Measurement: Step by Step Course. Use this textbook in conjunction with our course workbook containing Excercises and Activities to help increase the students understanding of Basic Measurement. Topics include Length, Area, Volume, Time and Temperature. Covers both Customary and Metric Systems. Product #: BMTX-4346Price:$9.95 Math Course 4 - Basic Measurement Workbook This Workbook contains numerous excercises and activities to help master Basic Measurement: Step by Step. Our workbook covers 38 learning objectives over the 8 units of the Basic Measurement Course. Topics include Length, Area, Volume, Time and Temperature. Covers both Customary and Metric Systems. Product #: BMWB-4347Price:$9.95 Math Course 4 - Basic Measurement Help Guide The Help Guide provides guidance on achieving the 38 learning outcomes contained in the 8 Units of the Basic Measurement: Step by Step Course. The Help Guide supports and augments the course textbook and workbook. Intended as an instructional aid for use by parent, tutor or teacher.
A Level Mathematics By the end of your course, you will be able to work with complex functions and understand how to calculate forces in mechanics. You will cover topics such as geometry, calculus, trigonometry and algebra and gain the ability to manipulate figures, and use abstract reasoning and logic in problem solving. The first three modules constitute AS Level and the later three modules are A2 Level. Each module is presented separately. The content of the modules have references to Edexcel Modular Mathematics textbooks, which will need to be purchased in conjunction with the course. The course builds up understanding of key mathematical concepts gradually and sequentially. Topics such as differentiation and integration are covered in all the Core modules and form part of the essential mathematical toolkit needed for higher study. For each module there are two or three formal tutor-marked assessments which, when completed, should be sent to your tutor, via e-mail or conventional post. All of the information within the units is written in line with the requirements of the Edexcel examination board specification and the demands of the examination. All units are broken down into clear subject topics, and students should spend the amount of time studying for each topic as advised by their course tutor. Each topic module has been written for ease of understanding and topic coverage may be of different length and difficulty depending on the level of detail and information required. You will need to study the modules in the sequence provided.Further DetailsAlgebra and functions The sine and cosine rules Exponentials and logarithms Coordinate geometry in the (x, y) plane The binomial expansion Radian measure and its application Geometric sequences and series Graphs of trigonometric functions Trigonometrical identities and simple equations Intergration Module 3 - Mechanics 1 Topics included: Mathematical models in mechanics Kinematics of particles Dynamics of particles Statics of a particle Moments Vectors A Level Module 4 - Core 3 Topics included: Algebraic fractions Functions The exponential and log functions Numerical methods Transforming graphs of functions Trigonometry: looking at the secant, cosecant and cotangent Differentiation: using the various rules for complex functions
Previewing and saving your file. Mathematical concepts that are reviewed and reinforced: 1) the use of ratios to describe proportional relationships involving numbers, geometry, measurement, probability, and adding and subtracting decimals and fractions; 2) the purpose of algorithms and propert... ...My passion includes physics, chemistry, biology, astronomy, and weather. My masters degree is in Electrical and Computer Engineering. I learned how to build a computer, hardware and software, from the ground up.
Algebra 1/2 represents a culmination of pre-algebra mathematics, covering all topics normally taught ... more » in pre-algebra, as well as additional topics from geometry and discrete mathematics (used in engineering and computer sciences). This program is recommended for seventh-graders who plan to take first-year algebra in the eighth grade or for eighth-graders who plan to take first-year algebra in the ninth grade. With Algebra 1/2, children can deepen their understanding of pre-algebra topics such as fractions, decimals, percents, mixed numbers, signed numbers, order of operations, evaluation of algebraic expressions, and solutions for linear equations in one unknown. « less Ships within 1 to 2 business days. We guarantee all of our items, your satisfaction is our main priority! " -- goodwill southern california @ California, United States "Usually ships in 1 2 business days. Book is complete and intact, but does not meet the criteria for Good or higher. Book may contain stickers, markings or highlighting. A reading copy. " -- goodwill of silicon valley @ California, United States "Ships same or next business day! Multiple available! Book exterior is worn but text is still usable. isbn|1565771494. Algebra 1/2: An Incremental Development (Saxon Algebra) (c. )2004 (pj) WQ " -- all american textbooks @ Michigan, United States "Usually ships in 1 2 business days. Book shows wear from use and shelf. used textbook! We pack all items in a protected and padded bubble mailer! Your item deserves more than just some plastic bag! writing inside. " -- brooks4books @ Florida, United States Locations, United States "Usually ships in 1 2 business days. Ships from Texas! Shelf wear on the front/back cover that includes wear/creasing/smudges. Pages appear clean and have folded/creased edges/corners. There are smudges visible on the edges of the pages. Thank you for choosing us! " -- vintage books by lane @ Texas, United States "Used book in good condition. May be ex library copy. May contain some marks such as highlightings, writings and cover wear. Good enough to read. May not include accessories such as CD, dvd, access code etc. Satisfaction guaranteed. Fast Shipping. Prompt Customer Service. " -- amazingbookdeals @ Illinois, United States "Ships same or next business day! Multiple available! Very minor wear. Algebra 1/2: An Incremental Development (Saxon Algebra). isbn|1565771494. (c. )2004. (plf) WQ " -- all american textbooks @ Michigan, United States "Usually ships in 1 2 business days. 2004 copyright (N 220)Some of the books have a number on the end. Return Policy: You pay shipping both ways plus a 20% restocking fee. " -- wildcat65 @ Oklahoma, United States
Prerequisites: MATH20132 Calculus of Several Variables; MATH20222 Introduction to Geometry (optional); MATH31051 Introduction to Topology (optional) Future topics requiring this course unit: differentiable manifolds are used in almost all areas of mathematics and its applications, including physics and engineering. Details of prerequisites: standard calculus and linear algebra; familiarity with the statements of the implicit function theorem the existence and uniqueness theorem for ODEs (students may consult any good textbooks in multivariate calculus and differential equations); some familiarity with algebraic concepts such as groups and rings is desirable, but no knowledge of group theory or ring theory is assumed (students may refresh basic definitions using, e.g., J. Fraleigh, A First Course in Abstract Algebra); some familiarity with basic topological notions (topological spaces, continuous maps, Hausdorff property, connectedness and compactness) may be beneficial, but is not assumed (a good source is M. A. Armstrong, Basic Topology). Last modified: Monday 8 (21) May 2012. (Refresh the browser to get the updated page.) Differentiable manifolds are among the most fundamental notions of modern mathematics. Roughly, they are geometrical objects that can be endowed with coordinates; using these coordinates one can apply differential and integral calculus, but the results are coordinate-independent. Examples of manifolds start with open domains in Euclidean space Rn, and include "multi-dimensional surfaces" such as the n-sphere Sn and n-torus Tn, the projective spaces RPn and CPn, and their generalizations, matrix groups such as the rotation group SO(n), etc. Differentiable manifolds naturally appear in various applications, e.g., as configuration spaces in mechanics. They are arguably the most general objects on which calculus can be developed. On the other hand, differentiable manifolds provide for calculus a powerful invariant geometric language, which is used in almost all areas of mathematics and its applications. In this course we give an introduction to the theory of manifolds, including their definition and examples; vector fields and differential forms; integration on manifolds and de Rham cohomology. Textbooks: No particular textbook is followed. Students are advised to keep their own lecture notes and use my notes posted on the web. There are many good sources available treating various aspects of differentiable manifolds on various levels and from different viewpoints. Below is a list of texts that may be useful. More can be found by searching library shelves. Exam structure The exam paper will consist of 4 questions (for 10 credit version) or 5 questions (for 15 credit version). You will have to answer any 3 questions out of Questions 1 to 4 (everybody). Those taking 15 credit version will also have to answer Question 5 (compulsory). Therefore, those taking 10 credit version will altogether answer 3 questions and those taking 15 credit version, 4 questions. Questions 1 to 4 Each of them will consist of parts (a), (b), and (c): (a) A definition or a group of related definitions and a question concerning a simple statement or example directly related with the definition. (b) An important statement from the course (a theorem, or a lemma, or a part of a theorem). Possibly requiring some definition(s). You will be asked either to give the full statement and prove it; or quote a general statement and then prove some part of it; or you will be given a statement and you will have to give a proof; and/or you may be asked to deduce something from a general statement. (c) A problem where you will have to calculate something or to show something about a concrete example. Compulsory question 5 (15 credit version only) (a) A definition and an important statement. You will have to quote some statements and give a proof. (b) and (c) An advanced problem, subdivided into two parts. Main exam topics Questions 1 and 2. Charts, atlases, smoothness. Smooth manifolds and smooth maps. Diffeomorphism. Algebra of smooth functions. Specifying manifolds by equations. Submanifolds. Products. Tangent vectors and tangent spaces. Velocity of a parameterized curve. The natural basis of tangent vectors associated with a coordinate system. Tangent bundle. Partitions of unity. Questions 3 and 4. Derivations of an algebra and derivations over an algebra homomorphism. Vectors and vector fields as derivations. Commutator of vector fields. Exterior differential: axiomatic definition and properties. Integration of forms and Stokes theorem. Closed and exact forms. De Rham cohomology: definition and examples. Pull-back and homotopy invariance of de Rham cohomology. Application to distinguishing manifolds. Question 5. Embedding manifolds into RN. Existence of an embedding. Corollary from Sard's Lemma. Reducing the dimension of the ambient space (Whitney's Theorem). See § 4.3 of the online notes. Nota bene: This question will also include a more advanced problem concerning differential forms, Stokes theorem and de Rham cohomology.
The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math 9780691134932 ISBN: 0691134936 Pub Date: 2009 Publisher: Princeton University Press Summary: Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. His books include the best-selling Sync: The Emerging Science of Spontaneous Order (Hyperion). Rating:(0) Ships From:Scarborough, ONShipping:Standard, Expedited, Second Day, Next DayComments:166 Pages. New book as received from the publisher. Synopsis from the jacket: "The Calculus of Fr... [more]166 Pages. New book as received from the publisher. Synopsis from the jacket: "The Calculus of Friendship" is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus-until a day comes when calculus is no longer enough. Like calculus itself, "The Calculus of Friendship" is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, "The Calculus of Friendship" is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, "The Calculus of Friendship" will be an unforgettable journey. [less]
Solving numerical problems is a critical aspect of scientific work. Your calculations must be neat and carefully done, and must be accompanied by explanations of the computations. Here's how to do well on solving numerical problems: * Start with lots of clean scratch paper. * Write down information given; write what you need to find. * Solve the problem in a logical sequence of steps that take you from what you know to what you want to know. * Convert units as necessary. For more on units, see p. 19-20 in Fetter's Applied Hydrogeology textbook. * At each step, write in words what process that step involves. * Check to be sure your answer is reasonable, that you included units of measurement, and that the answer is in a convenient unit and order of magnitude. * Check the number of significant figures (digits) in the answer. For more on significant figures, see p. 18-19 in the textbook. * Then, copy your work onto a clean sheet of paper. * Leave lots of blank space. * Write no unexplained numbers or words on the paper. * Put a box around the final answer. * Start each problem on a new sheet of paper. * On every graph, label each axis, including units of measurement; give title and date; and write chapter and problem number. * Some answers are best given in tables. If your answer includes a table, make it neat. Each column needs a heading; the heading must include units of measurement. If applicable, show a sample calculation after the table. * Write your name on every page. * Staple or clip pages together. * Trim ragged edges. * Write the units of measurement at every step in the solution. This really is important!
The Mathematics Department of Lake Forest High School will prepare students for life in a increasingly technological world in the following core areas: problem solving, logical reasoning, communicating mathematical ideas, applying mathematics to real-world situations and using technology as a mathematical tool to solve mathematical problems. We will maintain learning environments and classroom situations in which students can develop confidence in the above endeavors.
In this course, we will collaboratively explore the fundamental ideas of calculus, including limits, derivatives, antiderivatives, and integrals, through the use of dynamic geometry software. While the course will cover a variety of calculus content, it is not a calculus course. This course is designed to enrich students' understanding of calculus ideas, to collaboratively explore these ideas with colleagues, and to engage in professional conversations about the implications of these developing experiences and technologies on the learning and teaching of calculus. Each module of the course will involve a short overview, a set of problems (including relevant GSP sketches and technology resources), and a set of discussion questions. The primary mode of instruction will be collaborative problem solving, including developing initial thoughts/responses to particular technology-enhanced mathematical tasks, discussing them with colleagues, and revising your work based on your conversations and collaboration. The course will emphasize active participation in the learning and teaching process and will not involve significant amounts of passive learning through lectures or demonstrations. One of the interesting aspects of this course is that we will have a mix that includes graduate students from the Mathematics Learning and Teaching master's program (who are taking MTED 775 - Special Topics in Mathematics Education for graduate credit) and teachers from the wider Math Forum community (who are taking it for continuing education credits only). This should provide a nice sized group for interaction, along with useful variety in mathematical approaches and teaching experience. This moderated course will be led by Annie Fetter, Problem of the Week Administrator. It will take place online using Blackboard. The only technical requirements are a web browser, Internet access, and Sketchpad 5* Who: Open to all teachers and tutors interested in exploring calculus topics. Historically, we have had middle school teachers through AP calculus teachers taking the course together. When: New dates will be posted here soon for the next scheduled session. There will be approximately 30 hours of seat-work involved in this course. Credit: All individuals who successfully complete this pass/fail course will receive a certificate indicating that they have completed 30 hours of professional development. This is equivalent to 3 Continuing Education Units (CEUs). Note that CEUs can never be converted to graduate credits for this course. Cost: $149 * While there are no books to buy for the course, participants are required to have a copy of The Geometer's Sketchpad 5, which is available directly from Key Curriculum Press. (All purchasing options of the program are the same in terms of the product you get. The differences are in the licensing terms, so you can choose the one that makes the most sense for you.)
1990 | Series: Penguin Science A demontration of how the true mathematician learns to draw unexpected analogies, tackly problems from unusual angles and extract a little more onformaiton from the data; a collection of truly practical lessons. A demontration of how the true mathematician learns to draw unexpected analogies, tackly problems from unusual angles and extract a little more onformaiton from the data; a collection of truly practical lessons. {"itemData":[{"priceBreaksMAP":null,"buyingPrice":7.58,"ASIN":"0140124993","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":22.92,"ASIN":"0273728911","isPreorder":0}],"shippingId":"0140124993::SjHSRCMQfmxH8b1HjgDVz3XSAobdltbsgGBQ2b6%2BAuUU60ivsonciPhK025f%2FDZDELoo2uWI8BpfBTuUSYYkUxBjUN1OzAF4,0273728911::QjmjNvDiz26O0FzX%2FdPaJLH%2FqiXQb%2B9xaONfK83DtPdhsSSt%2Ff2melE3B8kdm5foUxNA83sJN7P%2Bj63nQAmV5Vua9Kmshen prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' (E. T. Bell Mathematical Monthly ) [This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected. (Herman Weyl Mathematical Review ) I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it. (Scientific Monthly ) Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art. (A. C. Schaeffer American Journal of Psychology ) Every mathematics student should experience and live this book (Mathematics Magazine ) --This text refers to an out of print or unavailable edition of this title. About the Author George Polya (1887-1985) was a Professor of Mathematics at Stanford University. I have had a love affair with Mathematics for over forty-five years. This little book was one of the first books to awaken that interest - my edition on my bookshelf is dated 1957! George Polya had the reputation of a very great teacher and inspirer of students of mathematics as well as making original contributions of his own. I recommend it to any young person (or anyone)as an excellent introduction to mathematical thinking. I thought I would buy this book after seeing it reviewed on a Japanese mathmatics program on TV . I found the contents difficult to read not being a higher maths candidate myself. How ever after trying to digest the words of wisdom in the theory of solving problems I had to admit it is only suitable for those amongst us who have a higher maths certificae than myself.very much higher ! The authur G.Polya was an aclaimed world wide mathematician, so if you are in his league then the book is worth reading ..TR
Mathematics (GCSE) Introduction: Getting a C in Maths is very important for many degree courses and jobs. We offer the chance to join a foundation maths class for a year. There is also one higher Level class for those who have a C already but wish to improve their grade.
Combinatorics Topics, Techniques, Algorithms 9780521457613 ISBN: 0521457610 Pub Date: 1995 Publisher: Cambridge University Press Summary: A textbook in combinatorics for second-year undergraduate to beginning graduate students. The author stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter. The book is divided into two parts, the second at a higher level and with a wider range than the first. More advanced topics are given as projects, and there are a number of exercise...s, some with solutions given
Classical algebraic geometry has been virtually ignored in computer-aided geometric design. However, because it deals strictly with algorithms, it is really more suited to this field than is modern algebraic geometry, which introduces abstractions far removed from the algorithmic nature of computer-aided design. This tutorial examines resultants, curve implicitization, curve inversion, and curve intersection. Discussion follows a series of examples simple enough for those with only a modest algebra background to follow. (c) 1986
The teaching and learning of mathematics are increasingly dependent on technology. Computer programs have become an integral part of mathematics education at all levels but most especially at the tertiary and pretertiary levels. Graphing packages are widely used at the secondary level, as are those that investigate the foundations of calculus, such as A Graphic Approach to the Calculus (Tall, Blokland, and Kok 1985). At the tertiary level, computer algebra systems such as Mathematica and Maple have become essential tools for university mathematics, and statistics packages such as Minitab and SPSS are a sine qua non for data analysis and display. The Internet and e-mail are widely used for finding information and for communicating with fellow students and teachers. Mathematics education is very different technologically from what it was even 10 years ago.
MyMathSpace NEW! These Wolfram|Alpha widgets can be very useful. Change the entries in the box, and try them out! You can even embed them to your own web site. Type in an equation to solve, or a function to graph in the dialog box for Wolfram Alpha! Use it to explore concepts and check homework problems. For example, type solve x^2-9=0 or plot x^2-9, x=-2 to 4 Free videos from Brightstorm These videos are very well done and address all the main topics of algebra and precalculus. Free registration is required. Study Guide for Precalculus - This notebook organizer will help you develop a section-by-section summary of the key concepts in Precalculus. It is a set of templates to help you take notes, review section highlights, draw graphs, and keep track of homework assignments. From the Cengage companion web site to Larson's Precalculus, 4th ed. (but you can use it with any textbook - the page numbers and section numbers may differ, but the content will be very similar .) Modeling with Excel. A self contained Excel workbook showing how to graph functions, build tables and perform curve fitting with polynomials. The file contains macros to use for graphing. Download and open with Excel for maximal functionality. Student success organizer - This notebook organizer will help you develop a section-by-section summary of the key concepts in College Algebra. It is a set of templates to help you take notes, review section highlights, draw graphs, and keep track of homework assignments. From the Cengage companion web site to Larson's College Algebra, 6th ed..
Differential equations This unit extends the ideas introduced in the unit on first-order differential... This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers. After studying this unit you should: be able to solve homogeneous second-order equations; know a general method for constructing solutions to inhomogeneous linear constant-coefficient second-order equations; know about initial and boundary conditions to obtain particular values of constants in the general solution of second-order differential equations. Contents Differential equations Introduction This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers
This resource looks at three detailed case studies in the form of student projects which clearly illustrate how mathematics and geography can be effectively linked. This booklet serves as good preparation material for CPD work between departments. Food and settlement This case study looks at Nomads and talks about the areas booklet is primarily aimed at the mathematics teacher, but should also be of interest to teachers of science. It sets out a number of case studies suitable for mathematical modelling. The book starts with an explanation of the mathematical modelling process then suggests specific areas of study which include: Forecasting: booklet is primarily aimed at the mathematics teacher, but should also be of interest to teachers of science. It sets out a number of case studies suitable for mathematical modelling with calculus. The book starts with an explanation of the mathematical modelling process then suggests specific areas of study which include: King… This resource looks at three areas of the physics curriculum where functions are used, creating an opportunity for cooperation between physics and mathematics teachers. This booklet serves as good preparation material for CPD work between departments. Hooke's Law and the idea of a function Part one explores the data produced… This booklet is unusual in this series as it develops one theme, genetic inheritance , to show the use of mathematical ideas and terminology in science and serves as good preparation material for CPD work between departments. The areas covered are: the inheritance of a single character, the inheritance of two characters, the genetics… This resource looks at areas of the chemistry curriculum where mathematics is used, creating an opportunity for co-operation between chemistry and mathematics teachers. This booklet serves as good preparation material for CPD work between departments. Section One considers how proportion is used in chemical equations, the need… This Nuffield Foundation publication was prepared to help students master the calculations involved in GCSE Science courses. The book is divided up into a series individual topics. Each topic is presented in three parts. • A summary of the ideas students need to know, including any important formulas. • Worked examples,…
Mathematics Mathematics at MGHS is continually evolving in response to student needs and the social and environmental demands of our rapidly changing world. Students are provided with the opportunity to select and engage in one of the numerous courses on offer, all designed to meet the current needs and future goals of each individual. The Mathematics faculty is dynamic in its approach to student learning and places a large emphasis on incorporating technology into all of its courses. Students have ready access to equipment such as: Interactive Whiteboards, Graphic Calculators, ClassPad 300's, Digital Theodolites, Speed/Radar Guns, Data Loggers and associated probes, a specialised computer room featuring 28 computers - all loaded with mathematical software, including graphing packages and interactive geometry software. Such technology is supplemented with a huge selection of hands on resources and teacher reference books.
In this section Mathematics New National Qualifications Mathematics sits within the mathematics curriculum area. Finalised documents have now been published for all the new Curriculum for Excellence Advanced Highers. This means that, along with the documents that were published last April, finalised Course and Unit documents are now available for all the new qualifications, from National 2 to Advanced Higher. These documents contain both mandatory information (in the Specifications) and advice and guidance (in the Support Notes). You can download all of these documents for this subject from our download page, using the button below, or use our check-box facility to download a selection of documents. Assessment support materials are also now available for all the new National 2, National 3, National 4 and National 5 qualifications. Information on Course assessment support material (such as Specimen Question Papers and coursework information) is available on the National 5 subject page and, for all National 2 to National 5 qualifications, information on how to access Unit assessment support materials can be found on each subject page. Following the development of these support materials, some documents with mandatory information (in particular the Course Assessment Specifications) will be updated with further information and clarifications by mid-June. In line with our standard practice, these documents will contain version information and a note of changes, if necessary. This will ensure that you can recognise the most up-to-date documents. Development process The final documents have been published following a lengthy engagement process. Find out how we got here. Considerable work has been carried out by the Curriculum Area Review Groups (CARGs), the Qualifications Design Teams (QDTs) and Subject Working Groups (SWGs) to develop the final documents. At each stage of the qualification development process, we publish draft documents outlining our proposals and plans. Visit our timeline to find out when the next documents for each qualification will be published. Key points motivates and challenges learners by enabling them to select and apply mathematical techniques in a variety of mathematical and real-life situations equips learners with the skills needed to interpret and analyse information, simplify and solve problems, and make informed decisions has a skills-based Unit structure, with reasoning skills developed within all Units provides opportunities for combined assessment in the Units has an embedded Numeracy Unit at National 4 has a hierarchical Unit structure that provides progression from National 4 to Higher* has a test as the added value assessment at National 4, and question papers at National 5 and Higher * There is no direct hierarchy (of Course and Unit titles) between National 3 Lifeskills Mathematics and National 4 Mathematics. However, learners can use the Units of the National 4 Mathematics Course to achieve the National 3 Lifeskills Mathematics Course. There is no direct hierarchy (of Unit titles) between National 4 Mathematics and National 5 Mathematics. However, learners can use the Units of the National 5 Mathematics to achieve the National 4 Mathematics Course, as long as they also pass the National 4 Added Value Unit and Numeracy Unit (or alternatively learners could use the freestanding Numeracy Unit at SCQF 5). Unit Outcomes, Assessment Standards and Evidence Requirement statements (including the National 4 Added Value Unit) have all been revised to increase flexibility, and additional information has been provided in the Evidence Requirements for all Units.
The grades 8-10 Patterns, Functions and Algebra Benchmark C: Translate information from one representation (words, table, graph or equation) to another representation of a relation or function is one of the benchmarks most frequently tested on the 8th grade Ohio Achievement Assessment (OAA). The lesson materials and assessment items in this mini-collection support instruction related to this benchmark. This lesson provides students with the description of an authentic situation (buying DVDs) and data points that fit that situation. Students graph the line that contains those points; determine its y-intercept, slope, and equation; and interpret the slope and y-intercept in the context of the problem. Finally, students extrapolate to determine a functional value that is outside the domain they have graphed. Questions for students, suggestions for assessment, extensions of the lesson, and questions for teacher reflection are included. (author/sw) This lesson uses an airline ticket counter as a context for teaching students about queueing theory and average waiting time. Activity sheets take students step by step through the basic problem. A 38-page background manual for the teacher explains in clear and comprehensive detail the mathematical ideas behind queueing theory and the numerous real-life applications people encounter every day. Blackline masters and Internet extensions are included. (sw) Students investigate the pattern determined by the areas of squares inscribed in squares formed by joining the midpoints of the sides of the previous square. The sequence generated is a simple geometric sequence. One special feature of this lesson is the use of the TI-92, which is used to generate the data. Students find both the explicit and recursive forms for the sequence. At the algebra I level, students do not necessarily need the formal notation, but are very capable of exploring the pattern, plotting the model, and describing how to generate the sequence. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Squares Inside Squares lesson and then access the appropriate video clips at the PBS TeacherSource website. The video player necessary to view the video clips can be downloaded for free from the site. (author/pk) This lesson focuses on connections between the factors of quadratic polynomials of the form x2 + bx + c, algebra tile representations of the factorization, and roots of the quadratic function. Students use algebra tiles to identify binomial factors and then use the graphing calculator to verify the result. In addition, students identify the x-intercepts and y-intercepts of each quadratic function and explore relationships between the graph of x2 + bx + c and its factored form (x + m)(x + n). An activity sheet and related assessment items are included. Though the suggested time period for the lesson is one class period, ORC reviewers thought the ideas were rich enough to require more than a single day. (author/sw) Students use graphs, tables, number lines, verbal descriptions, and symbolic representations to analyze the domains of various functions. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included. (author/sw) Students will investigate the input/output model for building function tables. Then they will connect tables, graphs, function rules, and equations in one variable. Finally, they will work backwards to determine function rules for given data sets or graphs. Four multi-page activity sheets, discussion questions, a lesson extension, and suggestions for assessment are included. (author/sw)
Rules/Expectations Algebra II Rules: 1. Have respect for yourself and others. 2. Bring all needed materials to class. 3. Be in your assigned seat and ready to work when the bell rings. 4. If you are absent, make up all missed quizzes, tests, and homework within 4 days of returning. 5. Do your best work and never give up! Homework: Homework will be assigned almost every night and will be checked the next day. These grades will be averaged together and count as a quiz or test depending on what grades we have gotten in that quarter. Your homework assignments will be given in class and also posted online on my web page. You can get to my web page by going to and clicking on GNA High School. Once you are at that page clock on teacher/support staff and then on my name. Cell Phones/I pods: In accordance with school policy you are not permitted to use cell phones or I pods in class. I do not want to see them under any circumstances. I am especially unforgiving about seeing your cell phones during a test (even if you are finished with the test. If this occurs I will give your cell phone to Mr. Tripler and you may retrieve it from him at the end of the day. NO WARNINGS WILL BE GIVEN. Grades: Your grades for this class will be calculated using the following: Test scores: NO drop grade Quiz average: Counts as one test Homework/Class Participation: Counts as one test/quiz Notebook Test: Counts as one test I reserve the right to give pop quizzes at any time. If you want to know a past test or quiz grade, or your grade prior to the end of the quarter, you must come during seventh period. No exceptions. At the end of each quarter we will calculate your final average together. It is your responsibility to keep track of your quiz and test grades in order to ensure the grade you are receiving for the quarter is correct. Absences: If you are absent on the day of a test review and return the day of the test, you have the option to take the test or make it up. If you choose to make up the test, you must make it up the next day you are in school. There will be three folders of work containing extra sheets for absent students. If you are absent extra worksheets will be placed in your class�s folder. It is your responsibility to check the folder BEFORE I begin class. If you are late to class without a pass, you will be given one warning and then subsequently written up. If you are coming to class late, you must have a pass. You will not be allowed to leave class to go and get a pass no matter whom you were with (even if it is the principal). You must come with a written pass. NO EXCEPTIONS. PSSA Problems: When you come into class there will be a problem on the side board. Work on this problem quietly. Problems will be gone over before the start of a new lesson and kept in your PSSA notebook (to be discussed later). Everyone will be required to explain one PSSA problem to the class every quarter (to be counted as a quiz grade). You will have quizzes on these problems every Friday. If you have questions on these problems, please ask them during class to be sure you are prepared for the quiz. PSSA problems must be copied exactly the way they appear on the side board to receive full credit. Testing: You will be assigned a testing seat before the day of the first test. I may choose to move you from that seat at any time (even during a test). Tests must be taken on the day they are given, unless you were absent on the day of the review. You will NOT be exempt from any test if you missed material, but have since returned to school. If you were absent on Monday and the test is Thursday, you will be taking it. There will be no extra time given on tests. You must finish during class time. The only exception to this is if we have made other arrangements before the day of the test. This must be cleared by me first. Make Up Test Policy: Any missed tests must be made up the day you come back to school. The only exception is for an extended absence. That work must be made up within one week of returning to school. On test days I become �dumb.� I will not answer any questions regarding homework or the review sheet on the day of the test. ABSOLUTELY, no retaking any test or quiz. Period. Don�t ask. Remember: No saying, �I can�t do this.� All tests are to be completed in pencil. Be on time. Always ask for help when you need it. ABSOLUTELY NO TOLERANCE FOR: Food or drinks in the classroom. Keep them in your locker. Friends coming to the door. You will not be able to leave to speak with them. Language Absence of a written pass when late. Cell Phones/ I pods
Basic elements offinite-dimension vector spaces as such as bases and generator systems, linear maps and dual vector space. Study of alternate multilinear forms and concept of determinant. Basic properties of determinants and their calculation. Matrix diagonallization. Basic concepts of affine spaces with special mention to dimensions 2 and 3. Definition of projective space and projectivization of an affine space. Professor: María Luz PUERTAS GONZÁLEZ. Teaching Method: Theoretical and practical lectures. Solution of problems by the student in the lecture hall. An introductory subject which briefly tackles an introduction to Descriptive Statistics, followed by some basic elements of probability from the Kolgomorov Axiomacy. Following, the concept of random variable is treated, basically the study of the Distribution Function, types of variables, changes of variable and their characteristics. The subject ends with an overview of the different types of distribution models. Professor: Francisco HERRERA CUADRA. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Numerical Method I Part One; Second term subject; 4 hours per week. 4.5 Cred. E.C.T.S. In many scientific disciplines the presence of mathematical problems requiring the solution of large linear equation systems, mostly difficult to be explicitally solved, is frequently found. This subject develops direct and indirect solution methods for linear equation systems, analyzing the method´s convergence order. A basic study of MatrixAlgebra for its use in some practical problems like population matrixes, constant coefficients differential equation systems a.o. are also introduced. Professor: Manuel GÁMEZ CÁMARA; Antonio ANDÚJAR RODRÍGUEZ. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Task works. Second Year First term subjects Matrix Algebra: Canonic Forms. Part One; First term subject; 6 hours per week. 6 Cred. E.C.T.S. Rings and Modules: Factorization in a domain of principal ideals.Basic concepts of the theory of modules. Special classes of modules. Theorem of structures. Submodules of free modules. Theorems of descomposition. Applications of the Structure Theoreme: Finitelly generated abelian groups. Canonic forms of matrixes. Effective calculus of canonic forms. Multilinear Algebra: Tensor product of modules and algebras: tensor algebra of one module. External algebra of one module: determinants. Professor: María Jesús ASENSIO DEL ÁGUILA. Teaching Method: Theoretical and practical lectures. Assessment Method: Written/oral examination. Real Analysis II Part One; First term subject; 7 hours per week. 7 Cred.E.C.T.S. Analysis of some real variables: Lebesque´s Integral. Vector functions and sets: continuity, differentiability. Extremi. Inverse functions and Implicits. Conditioned extremi. Professor: Antonio JIMÉNEZ VARGAS. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Calculus of Probabilities and Mathematical Statistics. Part One; First term subject; 7 hours per week. 7 Cred.E.C.T.S. This subject is a continuation of the subject "Introduction to the Calculus of Probabilities". It starts with some basic elements of the Measurement Theory in order to harshen the approach to Probability. Following, the study of bidimensional random variables is tackled, specifying the importance in the obtention of the relationship among unidimensional variables. This is generalized to n-dimensional variables. The subject ends with the study of Succesions of random variables and their boundary theorems. An introduction to Sampling Statistics and their distributions is given. Professor: Francisco HERRERA CUADRA. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Geometry II Part One; First term subject; 5 hours per week. 5 Cred. E.C.T.S. General vision of vector spaces, particularly euclidean spaces. Study of projectivities among projective spaces and classification ofP1, P2, P3 ´s. Study of the double ratio and armonic quaternin the projective line and of the dual projective space, the principle of duality and dual projectivities. Study of projective hyperquadrics, classified for conics and quadrics, tackling polarity, tangency, cone of tangents and tangential hyperquadric. Study of the hyperquadrics sheafs and classification of the conic and quadric sheafs, and their reduced equations. At last, the study of euclidean hyperquadrics, metric elements and unvariants for conics and quadratics. Professor: Rosendo RUIZ SÁNCHEZ. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Requirement: Theoretical/practical written examination. Numerical Methods II Part One; First term subject;5 hours per week. 5 Cred. E.C.T.S. The approximation to functions of one real variable is one of the pillars of numerical methods. The first chapter considers Hermite´s interpolation, together with the convergence and minimization of the interpolation error. Splines interpolation is also studied. The second chapter consists of an approximation in euclidean spaces and in the uniform norm (theorems of existence and unicity, characterization of the best approximation, constructive methods, ortogonal polynomials). Rational approximation is briefly introduced.These topics support others like: numerical derivation methods (based upon Taylor expansion, the interpolation polynomial, together with the convergence acceleration by means of the Richardson´s extrapolation) and numerical integration (simple and compound Newton-Cotes quadratures, Romberg method and Gaussian quadratures). Professor: Juan José MORENO BALCÁZAR; Andrei MARTÍNEZ FINKELSHTEIN. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Task works. Second term subjects Advanced Mathematical Statistics. Part One; Second term subject; 5 hours per week: 5 Cred. E.C.T.S. The major techniques and methods of the Statistical inference are developed, specially in parametrical models, studying in depth the sufficiency, completion, invariance, unbiasness, efficiency and asintotic properties of statistics. The Theory of Point Estimation, the Hypothesis Test and the Regions of Confidence are studied in depth. The basic techniques of non-parametrical Inference and linear models are presented, together with an introduction to the Theory of Decision. Three differentiated parts. The first one completes some of the topological concepts not studied in previous subjects (separation axiomes and numberability, included in the Tietze´s extension theorem and the Urysolin´s theorem. The second part studies the differential curves in plane and space by means of the Frenet-Serre equations (thus, locally). It also uses topology introduced in the first part to demonstrate the Jordan´s curve theorem (by means of the Brouwer´s fixed pointtheorem) and the Isopermetric theorem (the most important global theorem for plane curves). In the third part, the followig concepts are introduced: smoothing of maps among them, Gauss mapping, fundamental quadratic forms, the various types of curvature and methods for their calculation, and the Gauss´s Egrgium Theorem. This forms the starting point of the most classical topics of the Intrinsec Geometry. In many scientific disciplines the presence of mathematical problems that require the solution of equations, in most of the cases difficult or impossible to be explicitally solved, is frequently found. This subject introduces numerical methods developed to obtain approximate solutions for non-linear equations. The search of the approximate solution does not pose any ambiguity because error bounding is also studied. An approximate solution with a pre-determined margin of error can be equally found. Re-activation of the language knowledge by means of grammar exercises and syntax structurization. Reading and comprehension of scientific texts. Study of the retorical functions of the scientific speech pursuying cohesion, organization and coherence of the information to be transmited. Specific lexicon and word formation. Arithmetical operations in spoken english. Mathematical definitions. The use of mathematical simbols taking notes in English-spoken Congresses. Listening exercises. The linear finite differences equation with constant coefficients. The space of possible strings. The obtaining of the Riemann integrals. The factorial function (Gamma) as a solution for a equation in linear difference, of first degree and variable coefficients. Linear SDO and complete linears. Improper integrals. Convergence criteria in improper integral of first and second specie. The Cauchy Criteria. Circular elemental functions. Solutions of the EDO. The Flee´s transform. Transform of EDO and linear EDP of constant coefficients. Series of Fourier integrals. The theorem of convolution. Fourier inverse transform. The objective of this optional subject is to complete the geometry background of the student in aspects not tackled in the core subjects of the programme. The name of the subject comes from the study of the vector metric Geometry, that is to say quadratic forms (symmetrical or not) and the type of Geometry they determine. The student is also introduced in the study of convex bodies in Rn, the simplest objects after vector spaces. Other classical topics of elementary geometry like tessellates, simplicees and polyhedrons are also treated. This subject tackles the classification and solution of problems. Different classifications of mathematical problems are analyzed, classroom problems, classification of arithmetical problems. Phases in the problem-solving process. Teaching models of the problem-solving process. Heuristic techniques and strategies. Factors and requirements of the problem-solving process. Obstacles and blockings in the problem-solving process. Elaboration and analysis of protocols. Practicals about the theoretical contents by means ofindividual and small-groups problem-solving. Holomorphic functions: Basic Theory: the concept of derivative, Cauchy-Riemann´s equations. Holomorphic functions. Series of powers. Analytical functions. Exponential function, trigonometric functions, multiform functions. The Local Cauchy´s theory: curvilinear integral. Cauchy´s theorem for star-shaped domains. Cauchy´s integral formula. Taylor´s expansion in serie. Equivalence between analyzicity and holomorphy: Riemann´s theory of avoidable singularities. The Principle of identity. The principle of maximal module. Theorems of the open map and the inverse function. Singularities: Laurent´s expansion in serie. Classification of singularities. The Theory of residues. Mappings. The Principle of the argument. The Theorems of Rouché and Hurwitz. Requirement: Every 1st and 2nd year Mathematic subjects should have been passed. Basics in Physics Part Two; First term subject; 4 hours per week. 4.5 Cred. E.C.T.S. In this subject some of the most fundamental Nature processes are studied. The subject has been structured in three blocks tackling different aspects of the Physical sciences: Mechanics, Thermodynamics and Electricity and Magnetism. The first block tackles Classical mechanics (Kinematics and Dynamics of the particle; the gravitational Field; Dynamics of the Rigid Solid; Elasticity) with an introduction to the Quantum Mechanics. The second block tackles concepts like Heat and his propagation, ideal and real gases, and the Principles of Thermodynamics. The last block shows and studies the electric and magnetic fields in the vacuum. Professor: Francisco LUZÓN MARTÍNEZ. Teaching Method: Theoretical and practical lectures. Mét. Exámen: Written examination. Second Term Functional Analysis I Part Two; Second term subject; 5 hours per week. 5.5 Cred. E.C.T.S. Basic theory of normed spaces: linear and continuous mappings among normed spaces, finite dimension normed spaces, topological dual. Hilbert´s spaces: The theorems of the optimal approximation, of the orthogonal projection and Riesz-Fréchet´s. Orthonormal bases. Operators in Hilbert´s spaces, spectral theorem for a compact normal operator. Fundamental Principles of the Functional Analysis and Duality in Banach´s Spaces: the Hahn-Banach´s Theorems (the extension and separation theorems). Banach´s reflexive spaces, weak topologies, the Helly´s, Goldstine and Milman-Pettis Theorems. The Banach-Alaoglú Theoreme. Consequences of the Baire Theoreme: Theorems of the open map, of the Banach´s isomorphisms and of the closed graphic. The Steinhaus-Banach Theoreme. Professor: Juan Carlos NAVARRO PASCUAL. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Practical reports. Numerical Calculus I Part Two; Second term subject; 6 hours per week. 6.5 Cred. E.C.T.S. The mathematical modelization of the real phenomena around us requires the solution of ordinary differential equations or equations in partial derivatives. In most of the cases these equations do not show analytically explicit solutions, so the use of numeric methods is necessary in order to obtain a solution. The mathematical fundaments of numeric methods for the solution ofproblems of initial values are studied: 1-step methods (special attention paid to the Runge-Kutta methods), multi-step methods (the Adams methods), and methods for special problems (stiff problems, and so on). Numeric methods to solve contour problems are also studied: shots, resolution in differences, variational methods, and so on. Finally solving methods for Fredholm and Volterra´s integral equations are introduced. This subject consists of two parts: 1st.- Advanced Geometry of regular surfaces. Intrinsic Geometry of surfaces. Global Theorems of the Theory of surfaces. Need of abstraction and generalization of the surface concept. 2 nd .- Theory of the differentable varieties. Assessment Method: Written/oral examination. Work presentation. Work in groups. Presentations. Mathematic Didactics in Baccalaureate Second Part; First term subject; 4 hours per week. 4.5 Cred. E.C.T.S. Curriculum of Mathematics. Teaching. Learning. Elements of curriculum design. The process in class. Mathematics programmes in second-grade education. Design and development of the curriculum. The community of mathematic lecturers. Comparative vision of the Mathematics Curriculum. The objective of this subject is to introduce and analyze the major models of design of statistical experiments. After tackling the Analysis of Variance technique we develope the completely randomized, randomized, factorial, nestedand mixed models. The analysis of models is carried out by using statistical packages such as Statgraphics. The methodology of response surfaces is also introduced. Second Part; First term subjects; 4 hours per week. 4.5 Cred. E.C.T.S. First order partial derivative equations. The general Cauchy´s problem. The Cauchy-Kowalewsky Theorem. The Unicity Theorem. Quadratic equations. Classification. The Divergence Theorem. The potential equation. The waves equation. An introduction to the Theory of Partial Derivative Equations modern expansion. Professor: Bernardo LAFUERZA GUILLÉN. Teaching Method: Assessment Method: Statistical Inference II Part Two; First term subject;3 hours per week. 3.5 Cred. E.C.T.S. The purpose of this subject is to tackle statistics from different points of view: Bayes model and theory of decision. The subject is divided in three different parts: 1,. Interpretation of probability: Classical method, frequentist model and subjective model. 2.- Approach to statistical problems under the bayes perspective. 3.- Introduction and study of statistical problems by means of Theory of Decission´s tools. The objective of this subject is to instruct the students in the analysis of efficient algorithms, the different techniques in the conception of algorithms, and let them know the basic tools for the development of their own algorithms applied to mathematics. The following topics will be developed: 1- Analysis of the algorithm´s efficiency. 2.- Algorithms "divide and rule". 4.- Voracious algorithms. 4.- Dynamic programmation. 5.- Graph exploration. 6.- Elements ofcalculation complexity. Definition of the first group of homotopy in a topological space. Calculation of the first group of homotopy of the unit circunference.The Seifert-van Kampen theorem and his application to the calculation of the first homotopy group in different vector spaces. Definition of the singular homotopy groups of a topological space. Contruction of the Mayer-Vietoris string of a topological pair. The Scission theorem and construction of the Mayer-Vietoris string and its use for the calculation of the sphere´s singular homology groups. Singular homology techniques used for the demonstration of classical theorems in Topology: the theorem of dimension invariance. The Brouwer´s theorem of the fixed point and the Jordan-Brouwer´sseparation theoreme. Global description of the Universe; a description surging from interpretation of observational aspects through fundamental physical theories: the theory of radiation, classical and relativity dynamics and nuclear physics. The two-bodies problem. Motion of the Solar System bodies. Earth motion. Double-stars. Brief introduction to spheric trigonometry. Introduction to co-ordinates systems and co-ordinate change systems. Problems associated to the daily movement (rising and setting of stars, maximal disgressions and first vertical). Correction in the astronomic co-ordinates: refraction and light aberration, equinox precession, parallax. The problem of time: Sidereal, true, mean, civil, and official. The solar system: the sun, the moon, the planets. Eclipses. Professor: David LLENA CARRASCO. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Numerical Calculus II Part Two; Second term subject; 4 hours per week. 4.5 Cred. E.C.T.S. The theoretical fundaments and mostly used algorithms in interpolation and approximation of functions of some real variables are studied. The general analysis of the problems of existence and unisolvency, is followed by the interpolation in regular grids. The interpolation of scattered data is discussed: unisolvency, error, algorithms, together with different approximation methods (uniform, square minimums, a.o.) The local methods are analyzed; a central place occupied by multivariated splines and their use for approximation and interpolation. In this sense, triangulation and surface partitioning methods are studied. As a Bezier´s application, the Coon patches and the method of finite elements. This subject tackles the bonds between Statistics and Computer Science. We start studying the generation of randomized numbers and variables (in general), followed by the Monte Carlo´s simulation and its use for integrals estimation. The use of statistical techniques in the construction of expert systems is also studied. Different statistical packages are used during practicals. The objective of Computational Geometry is to tackle geometry problems with computational methods. The focus of the subject lies on the discovery of effective algorithms (necessary to introduce first the concepts of algorithm and efficiency) for rather simple problems (due to the impossibility for the student to solve complex problems which are in some cases still object of research).An example of the treated topics would be: Voronoi´s diagrams, "guarded vigilance" (the Chevall´s art gallery theoreme), uses in visibility and robotics. Professor: Mª Luz PUERTAS GONZÁLEZ y M. A. SÁNCHEZ GRANERO. Teaching Method: Theoretical and practical lectures. Assessment Method: Written examination. Differential Geometry Part Two; Second term subject; 4 hours per week. 4.5 Cred. E.C.T.S. In the solving-process of many mathematical problems lies the idea of reasonably disturbing the given hypothesis in order to simplify the situation; this is the idea of "general position" in Geometry, or "non-degenerated case" in Analysis. The most fruitful expression of this argument is the transversality notion, which, created by René Thorn, introduced the Differential Topology.In order to tackle this notion, it was necessary to introduce the fundaments of the study of varieties with boundary (fibrated, inmersions and summersions, orientations) and from there, reach the Sand-Brown theorem and the Whitney´s theorem. On the other hand the construction of tubular environments in the normal fibrate gives us some approximation theorems that, if combined with transversality, constitute a powerful tool to classify curves, demonstrate the Brouwer´s fixed point theorem and introduce the concept of degree. Teaching Method: Theoretical and practical lectures. Practicals. Seminars. Discussion on specific topics which in relation with the subject, have been collected in recent journals. Literature retrieval. Assessment Method: Written examination about basic theoretics and problems. Presentation of complementary exercises. Work in groups (max. two students). Presentation of complementary advanced topics. Requirement: In order to follow this subject it is necessary to be proficient in Mathematics Didactics. Numerical Solution of Partial Derivative Equations Part Two; Second term subject; 4 hours per week. 4.5 Cred. E.C.T.S. The subject starts introducing physical situations modelled with P.D.E. The classical equations of Mathematical Physics are studied, together with the maximum-minimum concepts for armoric and parabolic functions. By means of the variable separation method mixed problems like the heat and waves equations are solved, together with problems of the Dirichlet type in rectangle and disc. The core part of the programme is dedicated to the study of explicit and implicit methods in finite differences, together with the finite elements method and the Galerkin semi-discrete methods. Mathematica and Ansys will be used as software packages. Automata Theory and Formal Languages Part Two; Second term subject; 4 hours per week. 4.5 Cred. E.C.T.S. Finite automata. Regular expressions. Context free grammar. Battery automata. Turing´s machines. Computability. Chomsky´s hierarchy. This subject deals with some of the principles or fundaments of Computer Science supporting the global theoretical and practical frame of this science, for example, the automata theory, the computation theory and the formal languages theory. Professor: Manuel CANTÓN GARBÍN. Teaching Method: Theoretical/practical (problem-solving) lectures. Assessment Method: Two examinations during this term. Requirement: Basic knowledge of Mathematics. [1] Subjects that been of a different degree, the student can choose between the ones that have been offered by the University in order to complete the number of credits needed. [2] All subjects in this term are Optional or FreeConfiguration subjects. * Every subject of this term period are Optionals or Free Configuration.
Saxon Teacher provides comprehensive lesson instructions that feature complete solutions to every practice problem, problem set, and test problem, with step-by-step explanations and helpful hints. These Algebra 1 CD-ROMs contain hundreds of hours of instruction, allowing students to see and hear actual textbook problems being worked on a digital whiteboard. A slider button allows students to skip problems they don't need help on, or rewind, pause, or fast-forward to get to the sections they'd like to access. Problem set questions can be watched individually after the being worked by the student; the practice set is one continuous video that allows for easy solution review. For use with Algebra 1 3rd Edition. Five Lesson CDs and 1 Test Solutions CD included. Do you need a solutions manual or anything in addition to these cd's to do the curriculum? Besides the student book, of course. asked 1 year, 10 months ago by Shelley on Saxon Teacher for Algebra 1, Third Edition on CD-ROM 0points 0out of0found this question helpful. 5 answers Answers answer 1 I recommend getting the solutions manual.Would be a lot faster when correcting problems. answered 6 months ago by Home school mom Ohio 0points 0out of0found this answer helpful. answer 2 You don't need a solutions manual. I purchased everything Saxon has for Algebra 1, Third Edition. The CDs have all the lessons, problems, and solutions. It's great. answered 1 year, 7 months ago by domjoer3 0points 0out of0found this answer helpful. answer 3 Yes, you need the solutions manual and the tests. answered 1 year, 8 months ago by momof6boys 0points 0out of0found this answer helpful. answer 4 A solution manual would make grading the student's work faster, however, the cds go over each problem individually. It shows how to work each practice problem along with each problem from the lessons. answered 1 year, 9 months ago by Lissa Mississippi 0points 0out of0found this answer helpful. answer 5 Saxon Teacher is a supplement to the Saxon Math Homeschool Kit, not a replacement for the Textbook, Solutions Manual or Tests & Worksheets books. You would want to purchase the full kit for use with the Saxon Teacher CD-ROMs.
Beginner's Guide to Discrete Mathematics 9780817642693 ISBN: 0817642692 Publisher: Springer Verlag Summary: This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Included are discussions of scientific notation and the representation of numbers in computers. Lists are presented as an example of data structures. A...n introduction to counting includes the Binomial Theorem and mathematical induction, which serves as a starting point for a brief study of recursion. The basics of probability theory are then covered.Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined. The book concludes with an introduction to cryptography, including the RSA cryptosystem, together with the necessary elementary number theory, e.g., Euclidean algorithm, Fermat's Little Theorem.Good examples occur throughout. At the end of every section there are two problem sets of equal difficulty. However, solutions are only given to the first set. References and index conclude the work.A math course at the college level is required to handle this text. College algebra would be the most helpful
Project Description The main thrust of the grant program is to improve student mathematics scores on standardized tests. The grant project will enrich the academic program of students by enhancing the mathematics curriculum with the exploration of mathematical modeling, data analysis, statistics, forming conjectures, establishing justifications, and other problem-solving topics by integrating hand-held technology, specifically, graphing calculators with computer connectivity. Students will discover mathematics with the TI-73 graphing calculator as they work through a series of investigations that are designed to spark their curiosity and make them want to discover the mystery of why, and to motivate them to want to probe into some important mathematical concepts. All of the math concepts that will be addressed are indicated across the strands in the Core Curriculum Content Standards. The interesting problems and investigations that students will explore will enable them to gain a deeper understanding of mathematical concepts that will help them better approach the more routine problems that are on the standardized tests.
RESOURCES Absorb Mathematics Absorb Mathematics is an interactive course written by Kadie Armstrong, a mathematician and an expert in developing interactive online content. It offers a huge amount of interactivity - ranging from simple animations that show hidden concepts, to powerful models that allow flexible experimentation. Absorb Mathematics is divided into units – roughly corresponding to a lesson – so you can follow the structure of the course all the way through or use the units individually when covering a particular topic or concept. Each unit provides an engaging narrative supported by interactive animations, our unique simulations and exercises to ensure concepts have been understood. Try the free sample units in your class. Throughout the years as an engineer, I have needed to research topics on engineering, physics, chemistry, mechanics, mathematics, etc. The Internet has made the job infinitely simpler, with the caveat that you have to be careful of your sources. Anyone can post anything on the Internet without peer review, and errors are rampant. The topics listed below are primarily ones that I have researched and generated custom pages for the content. I welcome visitor review and comments on my material to help ensure accuracy. Click here for an incredible resource from the the U.S.
Math-Quadratic Equation-PSS-4 This is a numerical based class that will cover the fundamental concepts of Quadratic Equation. In this class we will cover different question of the quadratic equation. This class has been designed for Engineering Aspirant. This class covers curriculum of 11th-grade Mathematics, CBSE, ISC and various state board examinations. This session will gradually take you to various pattern of question with different level of difficulty. The session has been specially designed to cover problems of different pattern of IITJEE-Math, AIEEE-Math, BITSAT-Math, VIT-Math and other entrance examinations. The session will cover various concepts with their application in different problems. About Learners Planet . (Teacher) Learner's Planet is a rich source of online content, video lectures, mock tests, educational games and much more in kindergarten to Grade-12 segment. A subscription for Learner's Planet would bring tons of learning material at your mouse click. Print thousands of worksheets, try online quizzes and see instant results. Brush up your concepts with the help of recorded lectures by experienced teachers. Learn anytime anywhere at your own pace !
Explore the language of numbers in small class settings. Mathematics is the doorway to science and technology. Computer Science is the study of algorithmic processes to ultimately solve the complex computational challenges of our time. read more...
MAT 206 - Math for Elementary Education II This is the second course of a two-semester sequence which explores the mathematics content in grades K-6 from an advanced standpoint. Topics include: descriptive statistics; probability; algebra; geometry and measurement. This course is open to elementary education and early childhood students only.
The Learn Math Fast System is a math program designed to be read by older students from the beginning to the end in about one year. A younger student will quickly advance and have a solid foundation in math at a young age, but it will take longer than one year. All lessons, worksheets, tests, and answers are included in each book with the option of printing duplicate worksheets yourself. Watch the demo video in the drop down menu and read the explanation of what is in each volume. Then read through the testimonials and reviews on the "Testimonials" page. If you still have questions about the books, send us and email or call us during business hours (Pacific time).
Rent Textbook Buy Used Textbook Buy New Textbook Usually Ships in 3-5 Business Days $185.59 eTextbook We're Sorry Not Available More New and Used from Private Sellers Starting at $0Introductory Algebra prepares students for Intermediate Algebra by covering fundamental algebra concepts and key concepts needed for further study. Students of all backgrounds will be delighted to find a refreshing book that appeals to every learning style and reaches out to diverse demographics. Through down-to-earth explanations, patient skill-building, and exceptionally interesting and realistic applications, this worktext will empower students to learn and master algebra in the real world. Table of Contents Introductory Algebra Chapter R Prealgebra Review R.1 Fractions Building and Reducing R.2 Operations with Fractions and Mixed Numbers R.3 Decimals and Percents
These are some of my Matlab assignments which I've used when teaching EAS 105 and EAS 205. Towers of Hanoi: In the tradiational computer science exercise, students are asked to explore the path between perfect states of this puzzle. That is, they are asked to get the tower from one post to another post, moving one disc at a time, without placing a larger disc on top of a smaller disc. However, in this project, students find the optimal path between any two valid states of this puzzle. This involves graph theory, binomial expansion of integers, random numbers, Sierpinski triangles, user interface, and GUI writing. In some courses, I assign only the non-graphical version of this problem. I give the GUI version of this assignment in two parts. The GUI version includes a hint feature which makes an intelligent next-move for the user. The heart of this assignment is the puzzle-state conversion process. There are four different representations of a given state of a puzzle which are used in this assignment. The student must understand the four representations and write functions/methods which convert between these four representations. One of these representations makes it quite easy to calculate distances between states. Steganography: This lab is about steganography, the hiding of messages in plain sight! This is not "encryption" but students often view it this way. Students really love to manipulate sounds and photos in the computer, and this gives them a chance to do that. (It's easier to use photos than sounds, only because many of their favorite sound clips are copyrighted songs.) This assignment starts by asking the students to go online and grab some freely distributed Matlab files which implement the common "LSB" (Least Significant Bits) Steganography algorithm. This allows them to immediately begin hiding and finding messages, while also acquainting them with freely available resources. The second part of the assignment asks them to implement a steganography algorithm I wrote. In class, I emphasize that they can create their own algorithms for doing these things, and the fun part is not to try to make their system completely uncrackable, but rather to hide messages where nobody will be looking for them. Flashcards: In this project, students are provided with several text files of words which are all identical except for the language they are in! (This works in theory, but most of the word lists were generated from Google translator, so this project is more for amusement than for actual serious study of a language. However, I did use it to help me prepare for my trip abroad one summer!) When the project is run, the user is asked to choose two different languages, one for the question set, and another one for the answer set. So, for example, a user may choose to find the correct French word which corresponds to a given German word (or Italian, English, Spanish, or Piglatin). Once the languages are chosen, the GUI is launched, and the user begins answering questions by clicking the appropriate radio buttons. User feedback is given. When the user is bored, the user may save the session and choose later to reopen an old session rather than start fresh. The program starts with a randomly generated itinerary which includes each question word once. If a question is answered incorrectly, the same question is inserted into the itinerary several more times to ensure the user learns that question. If the itinerary is finally completed successfully, the user is congratulated. Some of the additional concepts in this lab include the generation of and use of random numbers. The student has to find a way to "seed" the random number generator in matlab so the user is not given the exact same question set each time the program is opened! Students have quite a bit of fun personalizing the GUI with photos, colors, and various methods of rewarding and punishing the users. Cubic Spirals: I reserve this project for my more advanced course. The students create a small Computer-Aided Design GUI without using the Matlab GUI IDE (GUIDE), but they are given a small sample GUI which contains all the necessary commands and concepts they will need to use. This GUI allows the user to move two control points around on the screen, thereby creating a parametric cubic using standard CAD formulas such as found in Gerald Farin's book and elsewhere. Matlab calculates the curvature of this function as well as the derivative. If the derivative has no zeros, the resulting parametric cubic is a spiral. Additionally, Matlab produces a diagram of this curve as it appears if used as the basis shape for a repeated structure as shown below. This is done to aid the human eye in its appreciation of the spiral shape, as this process will emphasize "corners" which may be present in the original cubic. When Matlab detects that the user has found a spiral, colors of various plots change, giving the user immediate feedback about the curve. This can be a mesmerizing solitaire game of "see if you can find a new cubic spiral" for awhile.
MATHEMATICS 198 &C1: Mathematics Via Problem-Solving Call # 05056 10 M W F ??? Altgeld Hall 3 hours This course introduces students to mathematical ideas, improving their ability to understand and communicate careful arguments via practice in problem-solving and writing proofs. We develop techniques to solve interesting problems that may sound like "brain-teasers" (sample problems appear below). After understanding the structure of logical statements, many problems can be solved using elementary techniques involving functions, induction, counting models, and equivalence relations. Later techniques include the pigeonhole principle, recurrence relations, and limits. Mathematics is an active process of thought; one learns mathematics best by doing mathematics. Understanding of mathematical ideas is clarified by communicating them to others. For these reasons, this course will run in seminar format, with no lectures. Class time will be spent mostly on student presentations of solutions to problems, with comments by fellow students and by the instructor. For well-motivated students in a small group, this format provides a more enriching experience than a lecture course about proofs, and it encourages students to develop their talents more fully and quickly. Skills in written communication of logical arguments are also valuable. Students will write solutions for two problems per week in addition to the problems discussed in class. Most of the problems and the development of mathematical ideas useful for solving them come from the text Mathematical Thinking: Problem-Solving and Proofs, by John D'Angelo and Douglas West. This course has no college-level mathematics prequisite. Furthermore, since it introduces students to the discovery and communication of logical arguments, students should not have taken Math 247 or 300-level mathematics courses before or with this course. It will be good preparation for advanced courses (or occupations) where such skills are used. Here are examples of problems we may solve: Does every year have a Friday the 13th? Which positive integers are sums of consecutive smaller positive integers? How does one count the squares of all sizes in a square grid, or the triangles of all sizes in a triangular grid? At a party with five married couples, no person shakes hands with his or her spouse. No two people other than the host shake hands with the same number of people. With how many people does the hostess shake hands? If each resident of New York City has 100 coins in a jar, is it possible that no two residents have the same number of coins of each type (pennies, nickels, dimes, quarters, half-dollars)? How can we find the greatest common divisor of two large numbers without factoring them? Why are there infinitely many prime numbers? A dart board has regions worth a points and b points, where a and b are positive integers with no common factors. What is the largest point total that cannot be obtained by throwing darts at the board? A bear's cage has two jars of jelly beans, one with x beans and the other with y. Each jar has a button. When a jar has at least two beans, pressing its button gives one bean to the bear and moves one bean to the other jar. Under what conditions (on (x,y)) can the bear eat all the beans except one? 1500 soldiers arrive in training camp. A few soldiers desert. The sergeants divide the remaining soldiers into groups of 5 and discover that there is 1 left over. When they divide them into groups of 7 or 11, there are 3 left over. How many soldiers deserted? Are there more rational numbers than integers? Are there more real numbers than rational numbers? What does ``more'' mean for infinite sets? Airlines A and B serve the same airports. Can A have a better on-time performance than B at every airport but worse on-time performance than B over the full system? Candidates A and B in an election receive a and b votes, respectively. If the votes are counted in a random order, what is the probability that candidate A never trails? Can a 6 by 6 chessboard be covered with 1 by 2 rectangles so that the arrangement cannot be cut along any horizontal or vertical line? How many positive integers less than 1,000,000 have no common factors with 1,000,000? After n students take an exam, the papers are distributed randomly for peer grading. What is the probability that no student gets his or her own paper? There are n girls and n boys at a party, and some boy/girl pairings are compatible. Under what conditions is it possible to pair off the girls and boys using only compatible pairs? How many regions are created by drawing all chords joining n points on a circle, if no three chords have a common point? Why are there only five Platonic solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron)? n spaces are available for parking along a curb. Rabbits take one space, and Cadillacs take two spaces. In how many ways can we fill the spaces? In other words, how many lists of 1's and 2's sum to n? What numbers have more than one decimal expansion? For each point in a tennis game, the server has probability p of winning the point, independently of other points. What is the probability that the server wins the game? Two thieves steal a circular necklace with 2m gold beads and 2n silver beads arranged in some unknown order. Can they cut the necklace along some diameter so that each thief gets half the beads of each color? Does every circular wire always contains two diametrically opposite points having the same temperature? How are these questions related? INSTRUCTOR: Douglas West received his Ph.D. in mathematics from the Massachusetts Institute of Technology. He then taught one year at Stanford University and three years at Princeton University before joining the U. of I. faculty in 1982. He has published two textbooks and numerous research articles. His area of research is discrete mathematics, especially graph theory and partially ordered sets. He is currently Vice Chair of the Activity Group in Discrete Mathematics of the Society of Industrial and Applied Mathematics, and he is an Associate Editor of the American Mathematical Monthly. He also sings in the chorus of the Illinois Opera Theatre and is an avid squash player.
Course Lecture Titles 36 Lectures 30 minutes/lecture 1. An Introduction to Precalculus—Functions Precalculus is important preparation for calculus, but it's also a useful set of skills in its own right, drawing on algebra, trigonometry, and other topics. As an introduction, review the essential concept of the function, try your hand at simple problems, and hear Professor Edwards's recommendations for approaching the course. 19. Trigonometric Equations In calculus, the difficult part is often not the steps of a problem that use calculus but the equation that's left when you're finished, which takes precalculus to solve. Hone your skills for this challenge by identifying all the values of the variable that satisfy a given trigonometric equation. 2. Polynomial Functions and Zeros The most common type of algebraic function is a polynomial function. As examples, investigate linear and quadratic functions, probing different techniques for finding roots, or "zeros." A valuable tool in this search is the intermediate value theorem, which identifies real-number roots for polynomial functions. 20. Sum and Difference Formulas Study the important formulas for the sum and difference of sines, cosines, and tangents. Then use these tools to get a preview of calculus by finding the slope of a tangent line on the cosine graph. In the process, you discover the derivative of the cosine function. 3. Complex Numbers Step into the strange and fascinating world of complex numbers, also known as imaginary numbers, where i is defined as the square root of -1. Learn how to calculate and find roots of polynomials using complex numbers, and how certain complex expressions produce beautiful fractal patterns when graphed. 21. Law of Sines Return to the subject of triangles to investigate the law of sines, which allows the sides and angles of any triangle to be determined, given the value of two angles and one side, or two sides and one opposite angle. Also learn a sine-based formula for the area of a triangle. 4. Rational Functions Investigate rational functions, which are quotients of polynomials. First, find the domain of the function. Then, learn how to recognize the vertical and horizontal asymptotes, both by graphing and comparing the values of the numerator and denominator. Finally, look at some applications of rational functions. 22. Law of Cosines Given three sides of a triangle, can you find the three angles? Use a generalized form of the Pythagorean theorem called the law of cosines to succeed. This formula also allows the determination of all sides and angles of a triangle when you know any two sides and their included angle. 5. Inverse Functions Discover how functions can be combined in various ways, including addition, multiplication, and composition. A special case of composition is the inverse function, which has important applications. One way to recognize inverse functions is on a graph, where the function and its inverse form mirror images across the line y = x. 23. Introduction to Vectors Vectors symbolize quantities that have both magnitude and direction, such as force, velocity, and acceleration. They are depicted by a directed line segment on a graph. Experiment with finding equivalent vectors, adding vectors, and multiplying vectors by scalars. 6. Solving Inequalities You have already used inequalities to express the set of values in the domain of a function. Now study the notation for inequalities, how to represent inequalities on graphs, and techniques for solving inequalities, including those involving absolute value, which occur frequently in calculus. 24. Trigonometric Form of a Complex Number Apply your trigonometric skills to the abstract realm of complex numbers, seeing how to represent complex numbers in a trigonometric form that allows easy multiplication and division. Also investigate De Moivre's theorem, a shortcut for raising complex numbers to any power. 7. Exponential Functions Explore exponential functions—functions that have a base greater than 1 and a variable as the exponent. Survey the properties of exponents, the graphs of exponential functions, and the unique properties of the natural base e. Then sample a typical problem in compound interest. 25. Systems of Linear Equations and Matrices Embark on the first of four lectures on systems of linear equations and matrices. Begin by using the method of substitution to solve a simple system of two equations and two unknowns. Then practice the technique of Gaussian elimination, and get a taste of matrix representation of a linear system. 8. Logarithmic Functions A logarithmic function is the inverse of the exponential function, with all the characteristics of inverse functions covered in Lecture 5. Examine common logarithms (those with base 10) and natural logarithms (those with base e), and study such applications as the "rule of 70" in banking. 26. Operations with Matrices Deepen your understanding of matrices by learning how to do simple operations: addition, scalar multiplication, and matrix multiplication. After looking at several examples, apply matrix arithmetic to a commonly encountered problem by finding the parabola that passes through three given points. 9. Properties of Logarithms Learn the secret of converting logarithms to any base. Then review the three major properties of logarithms, which allow simplification or expansion of logarithmic expressions—methods widely used in calculus. Close by focusing on applications, including the pH system in chemistry and the Richter scale in geology. 27. Inverses and Determinants of Matrices Get ready for applications involving matrices by exploring two additional concepts: the inverse of a matrix and the determinant. The algorithm for calculating the inverse of a matrix relies on Gaussian elimination, while the determinant is a scalar value associated with every square matrix. 10. Exponential and Logarithmic Equations Practice solving a range of equations involving logarithms and exponents, seeing how logarithms are used to bring exponents "down to earth" for easier calculation. Then try your hand at a problem that models the heights of males and females, analyzing how the models are put together. 28. Applications of Linear Systems and Matrices Use linear systems and matrices to analyze such questions as these: How can the stopping distance of a car be estimated based on three data points? How does computer graphics perform transformations and rotations? How can traffic flow along a network of roads be modeled? 11. Exponential and Logarithmic Models Finish the algebra portion of the course by delving deeper into exponential and logarithmic equations, using them to model real-life phenomena, including population growth, radioactive decay, SAT math scores, the spread of a virus, and the cooling rate of a cup of coffee. 29. Circles and Parabolas In the first of two lectures on conic sections, examine the properties of circles and parabolas. Learn the formal definition and standard equation for each, and solve a real-life problem involving the reflector found in a typical car headlight. 12. Introduction to Trigonometry and Angles Trigonometry is a key topic in applied math and calculus with uses in a wide range of applications. Begin your investigation with the two techniques for measuring angles: degrees and radians. Typically used in calculus, the radian system makes calculations with angles easier. 30. Ellipses and Hyperbolas Continue your survey of conic sections by looking at ellipses and hyperbolas, studying their standard equations and probing a few of their many applications. For example, calculate the dimensions of the U.S. Capitol's "whispering gallery," an ellipse-shaped room with fascinating acoustical properties. 13. Trigonometric Functions—Right Triangle Definition The Pythagorean theorem, which deals with the relationship of the sides of a right triangle, is the starting point for the six trigonometric functions. Discover the close connection of sine, cosine, tangent, cosecant, secant, and cotangent, and focus on some simple formulas that are well worth memorizing. 31. Parametric Equations How do you model a situation involving three variables, such as a motion problem that introduces time as a third variable in addition to position and velocity? Discover that parametric equations are an efficient technique for solving such problems. In one application, you calculate whether a baseball hit at a certain angle and speed will be a home run. 14. Trigonometric Functions—Arbitrary Angle Definition Trigonometric functions need not be confined to acute angles in right triangles; they apply to virtually any angle. Using the coordinate plane, learn to calculate trigonometric values for arbitrary angles. Also see how a table of common angles and their trigonometric values has wide application. 32. Polar Coordinates Take a different mathematical approach to graphing: polar coordinates. With this system, a point's location is specified by its distance from the origin and the angle it makes with the positive x axis. Polar coordinates are surprisingly useful for many applications, including writing the formula for a valentine heart! 15. Graphs of Sine and Cosine Functions The graphs of sine and cosine functions form a distinctive wave-like pattern. Experiment with functions that have additional terms, and see how these change the period, amplitude, and phase of the waves. Such behavior occurs throughout nature and led to the discovery of rapidly rotating stars called pulsars in 1967. 33. Sequences and Series Get a taste of calculus by probing infinite sequences and series—topics that lead to the concept of limits, the summation notation using the Greek letter sigma, and the solution to such problems as Zeno's famous paradox. Also investigate Fibonacci numbers and an infinite series that produces the number e. 16. Graphs of Other Trigonometric Functions Continue your study of the graphs of trigonometric functions by looking at the curves made by tangent, cosecant, secant, and cotangent expressions. Then bring several precalculus skills together by using a decaying exponential term in a sine function to model damped harmonic motion. 34. Counting Principles Counting problems occur frequently in real life, from the possible batting lineups on a baseball team to the different ways of organizing a committee. Use concepts you've learned in the course to distinguish between permutations and combinations and provide precise counts for each. 17. Inverse Trigonometric Functions For a given trigonometric function, only a small part of its graph qualifies as an inverse function as defined in Lecture 5. However, these inverse trigonometric functions are very important in calculus. Test your skill at identifying and working with them, and try a problem involving a rocket launch. 35. Elementary Probability What are your chances of winning the lottery? Of rolling a seven with two dice? Of guessing your ATM PIN number when you've forgotten it? Delve into the rudiments of probability, learning basic vocabulary and formulas so that you know the odds. 18. Trigonometric Identities An equation that is true for every possible value of a variable is called an identity. Review several trigonometric identities, seeing how they can be proved by choosing one side of the equation and then simplifying it until a true statement remains. Such identities are crucial for solving complicated trigonometric equations. 36. GPS Devices and Looking Forward to Calculus In a final application, locate a position on the surface of the earth with a two-dimensional version of GPS technology. Then close by finding the tangent line to a parabola, thereby solving a problem in differential calculus and witnessing how precalculus paves the way for the next big mathematical adventure. Course Lecture Titles 36 Lectures 30 minutes/lecture 1. A Preview of Calculus Calculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the course. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits. 19. The Area Problem and the Definite Integral One of the classic problems of integral calculus is finding areas bounded by curves. This was solved for simple curves by the ancient Greeks. See how a more powerful method was later developed that produces a number called the definite integral, and learn the relevant notation. 2. Review—Graphs, Models, and Functions In the first of two review lectures on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics. 20. The Fundamental Theorem of Calculus, Part 1 The two essential ideas of this course—derivatives and integrals—are connected by the fundamental theorem of calculus, one of the most important theorems in mathematics. Get an intuitive grasp of this deep relationship by working several problems and surveying a proof. 3. Review—Functions and Trigonometry Continue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees. 21. The Fundamental Theorem of Calculus, Part 2 Try examples using the second fundamental theorem of calculus, which allows you to let the upper limit of integration be a variable. In the process, explore more relationships between differentiation and integration, and discover how they are almost inverses of each other. 4. Finding Limits Jump into real calculus by going deeper into the concept of limits introduced in Lecture 1. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit. 22. Integration by Substitution Investigate a straightforward technique for finding antiderivatives, called integration by substitution. Based on the chain rule, it enables you to convert a difficult problem into one that's easier to solve by using the variable u to represent a more complicated expression. 5. An Introduction to Continuity Broadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity—along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem. 23. Numerical Integration When calculating a definite integral, the first step of finding the antiderivative can be difficult or even impossible. Learn the trapezoid rule, one of several techniques that yield a close approximation to the definite integral. Then do a problem involving a plot of land bounded by a river. 6. Infinite Limits and Limits at Infinity Infinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology. 24. Natural Logarithmic Function—Differentiation Review the properties of logarithms in base 10. Then see how the so-called natural base for logarithms, e, has important uses in calculus and is one of the most significant numbers in mathematics. Learn how such natural logarithms help to simplify derivative calculations. 7. The Derivative and the Tangent Line Problem Building on what you have learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation. 25. Natural Logarithmic Function—Integration Continue your investigation of logarithms by looking at some of the consequences of the integral formula developed in the previous lecture. Next, change gears and review inverse functions at the precalculus level, preparing the way for a deeper exploration of the subject in coming lectures. 8. Basic Differentiation Rules Practice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion. 26. Exponential Function The inverse of the natural logarithmic function is the exponential function, perhaps the most important function in all of calculus. Discover that this function has an amazing property: It is its own derivative! Also see the connection between the exponential function and the bell-shaped curve in probability. 9. Product and Quotient Rules Learn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous lecture. Also investigate higher-order derivatives, differential equations, and horizontal tangents. 27. Bases other than e Extend the use of the logarithmic and exponential functions to bases other than e, exploiting this approach to solve a problem in radioactive decay. Also learn to find the derivatives of such functions, and see how e emerges in other mathematical contexts, including the formula for continuous compound interest. 10. The Chain Rule Discover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum. 28. Inverse Trigonometric Functions Turn to the last set of functions you will need in your study of calculus, inverse trigonometric functions. Practice using some of the formulas for differentiating these functions. Then do an entertaining problem involving how fast the rotating light on a police car sweeps across a wall and whether you can evade it. 11. Implicit Differentiation and Related Rates Conquer the final strategy for finding derivatives: implicit differentiation, used when it's difficult to solve a function for y. Apply this rule to problems in related rates—for example, the rate at which a camera must move to track the space shuttle at a specified time after launch. 29. Area of a Region between 2 Curves Revisit the area problem and discover how to find the area of a region bounded by two curves. First imagine that the region is divided into representative rectangles. Then add up an infinite number of these rectangles, which corresponds to a definite integral. 12. Extrema on an Interval Having covered the rules for finding derivatives, embark on the first of five lectures dealing with applications of these techniques. Derivatives can be used to find the absolute maximum and minimum values of functions, known as extrema, a vital tool for analyzing many real-life situations. 30. Volume—The Disk Method Learn how to calculate the volume of a solid of revolution—an object that is symmetrical around its axis of rotation. As in the area problem in the previous lecture, you imagine adding up an infinite number of slices—in this case, of disks rather than rectangles—which yields a definite integral. 13. Increasing and Decreasing Functions Use the first derivative to determine where graphs are increasing or decreasing. Next, investigate Rolle's theorem and the mean value theorem, one of whose consequences is that during a car trip, your actual speed must correspond to your average speed during at least one point of your journey. 31. Volume—The Shell Method Apply the shell method for measuring volumes, comparing it with the disk method on the same shape. Then find the volume of a doughnut-shaped object called a torus, along with the volume for a figure called Gabriel's Horn, which is infinitely long but has finite volume. 14. Concavity and Points of Inflection What does the second derivative reveal about a graph? It describes how the curve bends—whether it is concave upward or downward. You determine concavity much as you found the intervals where a graph was increasing or decreasing, except this time you use the second derivative. 32. Applications—Arc Length and Surface Area Investigate two applications of calculus that are at the heart of engineering: measuring arc length and surface area. One of your problems is to determine the length of a cable hung between two towers, a shape known as a catenary. Then examine a peculiar paradox of Gabriel's Horn. 15. Curve Sketching and Linear Approximations By using calculus, you can be certain that you have discovered all the properties of the graph of a function. After learning how this is done, focus on the tangent line to a graph, which is a convenient approximation for values of the function that lie close to the point of tangency. 33. Basic Integration Rules Review integration formulas studied so far, and see how to apply them in various examples. Then explore cases in which a calculator gives different answers from the ones obtained by hand calculation, learning why this occurs. Finally, Professor Edwards gives advice on how to succeed in introductory calculus. 16. Applications—Optimization Problems, Part 1 Attack real-life problems in optimization, which requires finding the relative extrema of different functions by differentiation. Calculate the optimum size for a box, and the largest area that can be enclosed by a circle and a square made from a given length of wire. 34. Other Techniques of Integration Closing your study of integration techniques, explore a powerful method for finding antiderivatives: integration by parts, which is based on the product rule for derivatives. Use this technique to calculate area and volume. Then focus on integrals involving products of trigonometric functions. 17. Applications—Optimization Problems, Part 2 Conclude your investigation of differential calculus with additional problems in optimization. For success with such word problems, Professor Edwards stresses the importance of first framing the problem with precalculus, reducing the equation to one independent variable, and then using calculus to find and verify the answer. 35. Differential Equations and Slope Fields Explore slope fields as a method for getting a picture of possible solutions to a differential equation without having to solve it, examining several problems of the type that appear on the Advanced Placement exam. Also look at a solution technique for differential equations called separation of variables. 18. Antiderivatives and Basic Integration Rules Up until now, you've calculated a derivative based on a given function. Discover how to reverse the procedure and determine the function based on the derivative. This approach is known as obtaining the antiderivative, or integration. Also learn the notation for integration. 36. Applications of Differential Equations Use your calculus skills in three applications of differential equations: first, calculate the radioactive decay of a quantity of plutonium; second, determine the initial population of a colony of fruit flies; and third, solve one of Professor Edwards's favorite problems by using Newton's law of cooling to predict the cooling time for a cup of coffee.
DescriptionThe text is available with a robust MyMathLab® course–an online homework, tutorial, and study solution designed for today's students. In addition to interactive multimedia features like Java™ applets and animations, thousands of MathXL® exercises that reflect the richness of those in the text are available for students. Part 2 consists of chapters 9—15 of the main text. Table of Contents 9. Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 The Ratio and Root Tests 9.6 Alternating Series, Absolute and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 The Binomial Series and Applications of Taylor Series 10. Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing in Polar Coordinates 10.5 Areas and Lengths in Polar Coordinates 10.6 Conics in Polar Coordinates 11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces 12. Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates 13. Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multipliers 14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Moments and Centers of Mass 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals 15. Integration in Vector Fields 15.1 Line Integrals 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green's Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes' Theorem 15.8 The Divergence Theorem and a Unified Theory 16. First-Order Differential Equations (Online) 16.1 Solutions, Slope Fields, and Euler's Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes 17. Second-Order Differential Equations (Online) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power Series Solutions This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.
Math Mania 1999 Math Mania has two important applications. One application is the use of math lessons to teach formulas and other methods of solving various math problems. The other application is to predict the outcome of certain problems based on given data with the Math Mania Math Solver. Math Mania is full of useful information to help one learn the language of mathematics. This site incorporates the principles of math and presents them using a collection of math lessons. These math lessons are assisted by a mailing list, a message board, and chat. These tools provide an interactive line of communication between Math Mania and the online users. Math Mania also includes an online search and sitemap to allow users to quickly navigate the site and find desired information. With Math Mania, we hope users will develop a greater appreciation for math and a greater knowledge of math and its applications.
Winter Quarter 2003 The Many Hats of CHE 1205 In CHE 1205 Computation Lab, you will solve chemical engineering problems using mathematical tools and software applications in Excel, MatLab, and Maple. The following paragraphs describe the overall goals of this course, the relevance of this course to your role as a chemical engineer, and the specific concept goals of this course. Overall Goals of CHE 1205 The overall goal of this course is to to fortify the chemical engineering concepts you are learning in CHE 1201 to give you the mathematical tools for solving several types of problems encountered as engineers to apply Excel, MatLab, and Maple to simplify problem solving or to minimize repetitive calculations to develop problem solving strategies and good documentation skills Relevance of CHE 1205 to Your Role as a Chemical Engineer CHE 1205 will introduce you to the types of problems you will face as a chemical engineer. Say that you are a process engineer for the production of an important pharmaceutical. You have been given the responsibility of overseeing the production of this product. Below are some of problems associated with this process and the Lecture # where you will learn the concepts involved in addressing these problems. Lecture #1 and #2: Graphing and Least Squares Method You notice that the volumetric flow rate of the gas in the pipeline changes with the pressure. At a given pressure, the volumetric flow rate of the gas is measured. At a given temperature, what is the mathematical relationship between the pressure and the volumetric flow rate of the gas? Can you predict the volumetric flow rate of the gas under a new operating pressure? Lecture #3: Numerical Integration You want to operate a batch reactor at the temperature which optimizes the production of the desired compound while minimizing the undesired reactions. Working with the chemists in process development, the optimum operating temperature has been determined experimentally in the laboratory. Determine the total amount of heat that has to be supplied to the reactor to change the temperature of the vessel from room temperature to the initial optimum operating temperature. Lecture #4 and #5: Numerical Solution to Ordinary Differential Equations You start a process by filling an empty tank with two different reactants. Reactant A in Stream #1 is pumped into the tank at a constant rate while Reactant B in Stream #2 is being pumped into the tank at a rate which is increasing linearly. The concentration of the reactants and products in the tank are changing as the tank is being filled. Determine the concentration of Reactants A and B and the products with time. Lecture #6 and #7: Material Balances on Multiple Unit Processes with Reactions The chemists in the chemistry and drug discovery group have determined the optimum temperature and pressure for the reaction steps required to produce the drug. You are involved in designing the process by which the reactants are mixed, reacted, and separated from the products. You have been given the desired production rate. However, the reactions do not go to completion and moreover side reactions also decrease the amount of desired product generated. What percent of the reactants are converted to the product at the optimum conditions? What is the flow rate of product lost in the product purification step? What are the flow rates of the unreacted compounds? Can they be separated from the by-products and recycled back with the fresh feed to the reactor? Concept Goals: By the end of this course, you will understand the following chemical engineering concepts and be able to: write the material balances for a reactive system using the extent of reactions and determine the fractional conversion at a given temperature and pressure given the equilibrium constant (K) You will also learn to apply the following mathematical tools and be able to: recognize what a line, power, exponential function looks like on a rectangular, semi log, or log plot determine a mathematical equation which describes how y changes with x using the least squares method evaluate the integral of a function numerically using the trapezoidal rule solve an ordinary differential equation numerically using the Runge-Kutta method solve for the root of a nonlinear equation using Newton's rule solve a set of linear algebraic equations for the unknowns using matrices solve a set of nonlinear equations for the unknowns In the process you will be able to utilize the following functions in Excel, MatLab, and Maple: Apply the least squares method to determine the coefficients for the proposed equation and to determine the best fit equation by comparing the sum of the square of the errors and the r 2value using following built-in functions:Ê SLOPE, INTERCEPT, Trendline in Excel Calculate the integral of a function numerically using the trapezoidal rule in Excel and quad in MatLab Solve ordinary differential equations in Excel and MatLab using the Runge-Kutta method Find the roots of a nonlinear equation using the GoalSeek / Solver function in Excel Solve a set of nonlinear equations using Solve in Maple No matter what career you pursue, the ability to critically think and communicate effectively are just as important as your technical abilities. In CHE1205, you will also learn to communicate and document your solutions effectively and compile your projects into a well-organized notebook. This notebook will serve as your personal reference guide to the application of various mathematical tools and programs in (Excel, MatLab, Maple) for your later courses. Welcome to CHE1205 and I'm looking forward to a great quarter together!
Please Note: Pricing and availability are subject to change without notice. Math Pathways: Grades 6-8 from Sunburst Technology Guided by NCTM, a teacher-guided, self-paced, curriculum and standard-based math learning tool that creates a learning environment in which students can explore, visualize, and appreciate mathematics. Introduces and instructs students in major mathematic concepts utilizing a pathways methodology in which students are explained core mathematic concepts and then build on these concepts in their understanding of more complex mathematical problem solving. Guided by NCTM and designed as a teacher-guided, self-paced, curriculum and standard-based learning tool, Math Pathways creates a learning environment in which students can explore, visualize and appreciate mathematics. The unique combination of 3D animation and exercises will ensure all math students acquire necessary conceptual understanding and computational skills to achieve high school standards. With Math Pathways students will: Learn concepts and then build upon these concepts using various pathways that converge and build upon each other such that retention will be far greater than the traditional rote memorization method of teaching mathematics Access an online tool which allows them to self guide students through middle and high school major mathematical concepts Illustrate math concepts and their applicability to "real world" situations System Requirements Windows Platform Pentium Win 98/Win ME/Win 2000/Win NT/Win XP 32MB Macintosh Platform PowerMac Mac 8.6/Mac 9.1/Mac OSX 32MB
Textbook lessons are divided into three sections. The first section is "power-up practice," which covers basic fact and mental math exercises which improve speed, accuracy, the ability to do mental math, and the ability to solve complicated problems. The second part of the lesson is the "New Concept," which introduces a new math concept through examples, and provides a chance for students to solve similar problems. Thirdly, the "Written Practice" section reviews previously taught concepts. One "Investigation" per session is included; "Investigations" are variations of the daily lesson and often involve activities that take up an entire class. The included Power Up Workbook provides consumable pages for students to complete the Power Up exercises from the textbook, including the Facts Practice, Jump Start, Mental Math, and Problem Solving sections. The textbook may refer students to problems within this Power Up workbook, or the text may contain necessary problems and instructions (such as the mental math problems), which students will need to complete the exercises in this workbook. The Solutions Manual arranges answers by section and lesson, and includes complete step-by-step solutions to the Lesson Practice, Written Practice, and Early Finishers questions, as well as the questions and practice items in the Investigations. It does not contain the answers to the Power-Up Workbook, which are currently unavailable. The Homeschool Testing Book features reproducible cumulative tests which are available after every five lessons after lesson 10. Tests are designed to let students learn and practice concepts before being tested, helping them build confidence. Tests, a testing schedule, test answer forms, test analysis form, and test solutions are included. The three optional Test Solution Answer Forms provide the appropriate workspace for students to "show their work." The answer key shows the final solution only, not the steps taken to arrive at the answer. Big Fan of Saxon Math Date:March 20, 2013 ScottI like the Saxon Math concept of incremental development (the student revisits concepts already learned). It seems to keep the knowledge fresh. Occasionally, we will enhance the curriculum with a little deeper dive into the subject matter... but perhaps I do that to make myself feel useful! If I had a fault with the program it would be that each new year starts a little slow (I'm sure the authors assume the student has taken the summer off). Share this review: +1point 1of1voted this as helpful. Review 2 for Saxon Math Intermediate 3 Complete Homeschool Kit Overall Rating: 5out of5 Date:July 6, 2012 Judy R Location:Baytown TX Age:Over 65 Gender:female Quality: 4out of5 Value: 5out of5 Meets Expectations: 5out of5 I have been a long-term Saxon math user. My daughter who is now 30 years old used it, and now I am using the same series for my grandchildren, ages 7 and 10. I love the way the Saxon series has lots of repetition, and the way that material is presented in small bits and pieces. Both of my grandchildren love math and say it's so easy to do the "hard stuff" their friends have to do in public school. Share this review: +1point 1of1voted this as helpful. Review 3 for Saxon Math Intermediate 3 Complete Homeschool Kit Overall Rating: 5out of5 Perfect for those looking for a lot of repetition. Date:September 6, 2011 Xgraver Location:Lancaster have used Saxon K and 1st grade. I was looking for a curriculum that would just focus on the basics before moving on. I found that with Saxon Intermediate 3. The earlier versions were just too childish for my kids at this point. We did not require the use of manipulatives anymore and Inter. 3 provided that.
6th Grade Honors English Students will be challenged to develop literacy skills by exploration and application of English Language Arts concepts and practices. Reading, online discussion and activities, as well as practice, will form the structure within which students will learn literacy skills. Challenge and expectation will be enhanced consistent with abilities of students who have academic talents. 7th Grade Honors English This course is designed to challenge students with academic talents to explore and acquire advanced seventh grade literacy skills. Recognizing that some students are ready for analytic and critical thinking, lessons are designed to grow these important thinking skills, while developing advanced literacy skills and a love of literature. Course elements include advanced novel study, investigation of the short story, grammar skill development, and writing in multiple genres. 8th Grade Honors English Students will be challenged to master the standards of eighth grade English Language Arts when they study advanced grammar and diagramming, writing in multiple genres and writing as a social activity. Students will prepare and present a research project, and evaluate and critique media formats as they will be challenged to apply discernment in all aspects of literacy. Pre-Algebra Pre-Algebra helps students acquire problem-solving skills and facilitates a connection to more rigorous courses coming in later years. It centers on three themes: arithmetic, pre-algebra and pre-geometry. Students will discover the world around them in a variety of enrichment activities, group projects and explorations. The use of graphing calculators, online manipulatives and other computing experiences take learning mathematics beyond the physical classroom into a world far greater than textbook, pencil and paper. Access to a graphing calculator or familiarity with graphing calculator websites is required for this course. Algebra This accelerated Algebra course builds on algebraic concepts introduced in previous courses while preparing students for any standard geometry course. Students will use online manipulatives and graphing calculators to explore equations, expressions and functions in a variety of methods including using graphs, symbols and tables. Students will study linear equations and expressions through their studies of geometry and statistics and will use probability to reinforce concepts of fractions and algebraic functions. Access to a graphing calculator or familiarity with graphing calculator websites is required for this course. Geometry Geometry Online is a high school level math course, taught with middle school-aged students in mind. Students are introduced to geometry through the study of points, lines, angles and shapes. The students explore the world around them by studying reflections and symmetry and measurements like area and volume. Students use their talents for logic while being introduced to the concept of formal proofs, both indirect and coordinate. They will study order while also integrating discrete mathematics and algebra. This course employs the use of online math manipulatives, geometry-based computer drawing programs, graphing calculators, real data collection and group projects to make learning fun, relevant, and exploratory. Spanish I High school students who struggle with language acquisition should consider taking Spanish I online. Students who take this course will develop basic Spanish listening, speaking, reading and writing skills. Online instruction will use focus on development of vocabulary, as well as using newly developed vocabulary in discourse. Multimedia instruction will enhance the learning experience for those who benefit from alternate instructional methods. As teacher certified to teach Spanish and endorsed to teach students who have learning disabilities will teach the course. Ready to get started?
Algebra for College Students This book provides a comprehensive coverage of intermediate algebra to help students prepare for precalculus as well as other advanced math. The ...Show synopsisThis book provides a comprehensive coverage of intermediate algebra to help students prepare for precalculus as well as other advanced math. The material will also be useful in developing problem solving, critical thinking, and practical application skills. Real World Data and Visualization is integrated. Paying attention to how mathematics influences fine art and vice versa, the book features works from old masters as well as contemporary artists.Hide synopsis Description:BRAND NEW INSTRUCTOR'S 5TH EDITION WITH SEALED CD SAME AS THE...BRAND NEW INSTRUCTOR'S 5TH EDITION WITH SEALED CD SAME AS THE STUDENT'S EDITION PLUS MAY INCLUDE ANSWERS AND/OR TEACHERS NOTES. We ship DAILY with Free Tracking/Delivery Confirmation. Description:NEW AND NEVER READ. MINOR WEAR FROM SHELF AND TRANSPORTATION....NEW AND NEVER READ. MINOR WEAR FROM SHELF AND TRANSPORTATION. DOES HAVE SOME SHELF WEAR AND WEAR FROM STORAGE
MiraCosta College Math Instructor Hits Two Million Mark on YouTube It was just a year ago that MiraCosta College math instructor Julie Harland hit the one million mark on her YouTube channel, where she has posted more than 850 of her self-made math videos. And this week, she hit two million views. Harland's math videos have attracted attention from all corners of the earth, from an elderly man looking to augment his limited formal education, to a Bangladesh native who uses the videos to help his 10th grade son with algebra. Harland has also received emails, letters and postings from students around the world who have been helped by her math videos. "I thank you for helping me get through three algebra courses at my community college," writes a 55-year-old Florida resident. "I've been out of school for so long, it's been tough, especially math. I understand your explanation of the problems much better than what I was getting in class." Another viewer writes, "Your math videos are absolutely wonderful, and I shall be eternally grateful to you for explaining everything so clearly. Why couldn't my math teachers be like you?" "I like to share knowledge and make math lessons available to everyone—why limit it to my classroom," says Harland. "I enjoy the feeling that I'm helping people understand math—It's like turning on a light bulb." Harland graduated from Vista High School and taught there after getting her B.A. in mathematics at UC Santa Barbara. She went on to get her M.A. in applied mathematics at UC San Diego and joined the MiraCosta College faculty in 1987. She has since written her own math books, which are used at MiraCosta College. "I want students to know that math is everywhere. What they learn is how to problem solve. They can be good at math—all it takes is practice—I want them to know they can do it."
MAT 129 Introduction to the Mathematics of Playing Games Short Term 2001 Syllabus Please feel free to drop by other times-- I am in my office a great deal and always happy to help! INTRODUCTION TO THE MATHEMATICS OF PLAYING GAMES. Ancient game boards and game pieces have been found in nearly every area of the world, indicating that games may have been popular pastimes since the beginning of civilization. Today the abundance of game shows, board games, and lotteries demonstrates the endurance and evolution of various games. People often devise strategies for playing certain games based upon their instinct and/or intuition, but these strategies may or may not be "the best" possible strategies. In this course we will develop mathematical techniques for analyzing games of chance and other types of games, so that we can develop optimum strategies for some simple games. We will discuss topics such as "the law of averages" and what it means for a game to be "fair." Students are encouraged to bring games to class for discussion. Prerequisite: MAT 012 or waiver. This course may be used to fulfill the Quantitative Reasoning requirement. Please see the instructor if you have not yet completed or waived MAT 012. The Course Goals To apply ideas from probability theory to the analysis of selected games. To apply ideas from game theory to the analysis of selected games. To develop skills in formulating, solving, and interpreting mathematical problems. To discuss and apply the modeling cycle and to gain experience with real world applications of probability concepts. To develop the ability to work in a team. The Attendance Policy Class lectures, discussions, and in-class work are considered to be a vital key to success in this course. It is the hope of the instructor that class sessions are both informative and useful, therefore attendance is expected at each class session unless a specific exception is made. Quizzes may be announced or occasionally "popped," and because the lowest quiz grade will be dropped, under nearly all circumstances, make-up quizzes will not be given. Likewise, make-up tests will under almost no circumstances be given, since the lowest of the test and/or quiz total will be dropped. Absences from class are noted, and repeated absences will adversely affect the student's grade. The final grade may be lowered by one third of a letter grade for each absence after the third. Thus, it is the responsibility of the student to speak to the instructor about each absence from class. This should be done as soon as possible, and if at all possible before the absence occurs. Students who miss class are held responsible for all of the material covered, assigned, and collected during their absence. The Text The main text Probability: An Introduction is by Samuel Goldberg. We will cover selected topics from chapters 1-5: Chapter 1, Sets A set is just a collection of well-defined distinct objects. One example of a set is the collection of all red playing cards from a single full deck. Sets are useful for thinking about games and strategies in precise ways. Chapter 2, Probability in a Finite Sample Space The probability of an event happening is a mathematical way of defining the likelihood of the event happening. For example, when drawing a single card from a standard full deck of cards, the probability of drawing a red card is 1/2 because 1/2 of the cards are red. The sample space is simply a set of all the possible things that can happen. For example, suppose a coin is tossed twice. Then there are four possible things that can happen: Both can be heads, both can be tails, the first could be a head and the second a tail, or the first could be a tail and the second a head. The sample space for this example is S = {HH, TT, HT, TH}. Chapter 3, Sophisticated Counting This chapter is dedicated to finding probabilities of given events when the number of possibilities is large. This technique is needed as games become more complicated. Chapter 4, Random Variables A random variable is a formal way to consider all possible outcomes of a game event. For example, suppose again a coin is tossed twice. Then as discussed above, there are four possible things that can happen: Both can be heads, both can be tails, the first could be a head and the second a tail, or the first could be a tail and the second a head. An example of a random variable is one whose value is the number of heads obtained in these two tosses for a given item in the sample space. Chapter 5, Binomial Distribution and Some Applications This section is dedicated to certain types of experiments which occur again and again. The word binomial refers to the numbers that occur as coefficients in these experiments. The System of Evaluation Evaluated Items Points Grading Percentages Test 1 Test 2 Test 3 Quiz Total Homework Final Project 100 100 100 100 100 100 16.7 % 16.7 % 16.7 % 16.7 % 16.7 % 16.7 % Maximum 90-100 % 80-89 % 70-79 % 60-69 % 0-59 % Scale A's B's C's D's F The lowest of the three tests and the quiz total will be dropped before calculating the final grade. Please refer to the GRADING section of the current Berea College Catalog for the College-wide interpretations of these letter grades. The Grading Policies For the benefit of the students in the class, all course grade computations are continually updated by the instructor, so students may check frequently on their in-progress course grade during the term. The Tests and Quizzes Tests and frequent short quizzes will be given in this course. In general, the announced quizzes will consist of questions on the assigned text readings or homework-like problems. The most likely dates of the three tests will be: Test 1: Wednesday, January 10. Test 2: Wednesday, January 17. Test 3: Wednesday, January 21. Problems that appear on the tests will be more varied in nature, ranging from homework-like problems to problems that require a deeper synthesis of ideas and from true or false questions to short-answer questions. The Homework Bonus Homework will be assigned on a near-daily basis, since doing homework thoughtfully and conscientiously is one of the keys to success in this course. Through homework, students get the needed practice of application of the concepts. Because the instructor desires to strongly encourage a diligent effort on homework, students who turn in each of their homework assignments with no more than three assignments submitted late, will be awarded an additional 10% on the homework grade! On Homework Collection All written work should be neat, organized, and should show sufficiently many steps to demonstrate a clear understanding of the techniques used. Homework is due at the beginning of class on the announced date due. If a student must miss class due to either a sickness or a planned absence, homework is still expected to be submitted on time. Assignments may be requested in advance. Late assignments will be accepted for reduced credit up until the homework is returned, and late work must be labeled as late. Written or printed homework assignments may be turned in before class or at the instructor's office, but should NOT be sent through the CPO, attached in ccMail, or given to a student assistant. A selection of the assigned homework problems will be graded for credit, and assignments not meeting the above standards may receive reduced credit. The teaching assistant for this course will be assigned later. She or he and most of the other Math Lab Consultants will also be able to answer questions about the mathematical content in the course during consultations in the Math Lab whose hour will be announced later. Best results are obtained trying to solve problems alone or in a group before asking for help, so in either place, students should be prepared to show what they have already tried. Topics in this course build throughout the course, so students should be sure to do their best to keep up with the class, so as to not get behind and possibly forever lost. Remember, no question to which one does not know the answer is ever "dumb" unless it goes unanswered because it remained unasked. On Teamwork Learning to work in teams effectively is strongly encouraged. Some homework assignments may be specifically designed for teamwork, others for individual work, but on most homework you can choose to work alone or in a team. All homework assignments must clearly include all of the authors' names at the top of each page. On any assignment in which half or more of the work was completed in a team, a single copy of the assignment should be handed in with all of the team's participants listed as authors. Teams can generally consist of one, two, or three members due to the nature of the work in this course. Unless otherwise stated, teams shall not consist of more than three members for most work. On any assignment where less than half of the work was completed in a team, individual assignments should be handed in with the author acknowledging all of the help received for each problem. This includes significant help received from the instructor or in the Math Lab Consultants. Note that the instructor or a Math Lab Consultant may help with homework, and while this help should not be acknowledged as co-authorship, it should still be mentioned. This is meant to be a sharing process; do not "give credit" to other students who have not attempted to contribute to the work or to the team's work, because it is ultimately not a help for the student who did not contribute to the work. Thoughtful practice, not (even mindful) copying, is ultimately the best way to learn. Note that on all team-completed assignments, students must describe the roles played by each author on the assignment. Warning: Please be careful to conform to these standards for teamwork, since they are designed to encourage good learning practices. (Furthermore, copying another's work or otherwise failing to adhere to these standards may even result in a charge of academic dishonesty.) The Class Atmosphere The members of this class constitute a learning community. Learning in such a community best takes place in an atmosphere in which instructor and the students treat everyone with mutual respect. Students need not always raise their hands in order to ask questions or to make comments, but they should not interrupt the instructor or fellow students in doing so. Students typically find the atmosphere set by the instructor to be a sometimes playful and nearly always relaxed one, but students will still need to work hard and consistently both in and out of class in order to do well. If at anytime you have thoughts, comments, or suggestions about how the class atmosphere could be improved or made into one which is more supportive of your learning, please come by or drop me a note about it. I welcome such suggestions. The Final Project The final project in this course will be to find the solution to a complex and involved probability problem based upon a game. Students may work in a team of up to three students on this project. Some suggestions for problems are listed below, but teams are invited to propose their own problems. In any case the deadline for final projects proposals is Monday, January 15. Because easier problems are easier to explain, minor errors will be looked upon more leniently in a challenging problem. Monopoly Problem A player in Monopoly rolls two dice to see how many spaces the player's piece must be moved on the board. If the player gets doubles, then the player moves and rolls again. If the player rolls doubles a second time, the player moves and rolls again. If the player gets doubles a third time, the player goes to jail. The player's piece can be moved from 2 to 35 spaces, or it can go to jail. Find the probability of the player being able to move each of these number of spaces and the probability of the player going to jail. Price is Right Problem In the game show, "The Price is Right," three contestants face each other to decide who plays for the largest prize. A wheel is marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, and 100. Each player spins the wheel once to get a score. If desired, the player may then spin the wheel a second time and add the result to the result from the first spin. If the player gets a score over 100, then she is out of the game. After the first person spins to get a score, the remaining players attempt to beat that initial score. After all three players have gone, the person with the highest score goes on to compete for big prizes. The second and third players know exactly what score they must beat to stay in the game, but this is not so clear for the first player. Calculate at what point the first person should stop in order to maximize her or his chances to win. Poker Problem Compute the probability of getting each of the possible hands in a game of poker. Rank these hands according to the relative probabilities of getting each hand where the less likely a hand is, the higher the ranking. Next calculate these probabilities and ranking given that a single joker wild card (which can stand for any hand and any suit) is added to the deck. (Do not allow for 5 of a kind of any suit.) Explain whether or not adding a wild card changes the relative rankings of the hands. Risk Problem Risk is a board game of world conquest. When two players do battle in risk, the attacker rolls three dice and the defender rolls two dice. If the highest number that appeared on one of the attacker's dice is greater than the highest number on the defender's dice then the defender loses one army. If the attacker's highest roll is equal to or less than the defender's highest roll, then the attacker loses one army. In the same way, the attacker's second highest roll and the defender's second highest roll are compared and either the attacker or defender lose an army. So ultimately the attacker can lose two armies, the attacker can lose one army, or the attacker can lose no armies. Find the probability of each, and the average number of armies that the attacker will lose each time the dice are rolled.
Linear Algebra encompasses the various methodologies for using multiple equations to solve for multiple unknowns. Below
About America's Math Teacher Rick Fisher is a math instructor for the Oak Grove School District in San Jose, California. Since graduating from San Jose State University in 1971 with a B.A. in mathematics, Rick has devoted his time to teaching fifth and sixth grade math students. Each year approximately one-half of his students bypass the seventh grade math program and move directly to a high-powered eighth grade algebra program. Course 1 Basic Math Skills This course is for 4th and 5th graders. Topics include whole numbers, fractions, decimals, percents, integers, geometry, and much more. Course 2 Advanced Math Skills This course is for middle grades students. Students will master the critical skills necessary for success in pre-algebra. Topics include whole numbers, fractions, decimals, percents, integers, geometry, and much more. Course 3 Pre-Algebra This course is a must for students prior to taking Algebra I. Integers, exponents, order of operations, ratios & proportions number theory, linear equations, probability & statistics are just a few of the topics that students will learn and master. Course 4 Algebra I This course will guide students to master the "gateway" subject, algebra. Algebra opens the doors to more advanced classes in math, science, and technology. Students will learn and master all of the essential algebra skills. The lessons are carefully explained in clear, simple terms, so that all students will understand, learn, and master each and every topic. Rick has developed a highly functional, successful mathematics teaching system that produces amazing results. Results that he shares on this website in both elementary and middle grades versions. This is a tested teaching strategy that will produce dramatic results for students. This easy to follow, step-by step program provides all the video tutorials and exercises you will need to super-charge any math program. There is plenty of free video's and exercise material available for you to see how valuable this system will be to your students. Rick designed this system for elementary, middle grades and even high school students who were not prepared for algebra, to help bring them to algebra-readiness in less than one school year. Through this program, many of Rick's students have improved several grade levels in their math abilities in just one school year. Rick has also used the program successfully with students who are struggling with math and have limited English skills. This award winning program compliments all basic math textbooks, so it is a perfect partner program for schools.
Basic MathsBytes brings an affordable ICT element into the Maths curriculum without conflicting with proven teaching methods. It uses an effective methodology that ensures weaker pupils are fully supported, but enables students capable of more demanding exercises to move seamlessly to Intermediate Tier work. Working with an advisory team of practising teachers, Sue Chandler and Ewart Smith have developed a highly motivational route through the learning process. Basic MathsBytes gives full coverage of subject specifications for GCSE Foundation Tier. In addition, the course meets all the current requirements for the National Qualifications Standard Grade Arrangements for Scotland.
orations in College Algebra, 5th Edition is designed to make algebra interesting and relevant to the student. The text adopts a problem-solving approach that motivates readers to grasp abstract ideas by solving real-world problems. The problems lie on a continuum from basic algebraic drills to open-ended, non-routine questions. The focus is shifted from learning a set of discrete mathematical rules to exploring how algebra is used in the social, physical, and life sciences. The goal of Explorations in College Algebra, 5th Edition is to prep... MOREare students for future advanced mathematics or other quantitatively based courses, while encouraging them to appreciate and use the power of algebra in answering questions about the world around us.
Area Formulas - MAT-955 your students develop area formulas for parallelograms, triangles, and trapezoids. Using hands-on activities, video demonstrations, animations, and comics, your students will build a strong understanding of area formulas and how to use them in problem solving. This course is built around core propositions from the National Board for Professional Teaching Standards as well as national content standards. 2K 2K Testimonial "I enjoyed thinking how I can make my classes better by adding the use of online resources to help those students that fall through the cracks. But the best thing was I could work on this class whenever I wanted and could move on at my own pace. That right there is worth the price for my busy schedule."
Business Mathematics, CourseSmart eTextbook, 9th Edition Description For complete courses in business mathematics, personal finance, or small business management that are typically taught in either the first two years of college or the last two years of high school. This text brings together all the math tools students need to successfully handle everyday business transactions, manage their personal finances, and start or operate a small business. Throughout, students learn math in familiar contexts they already care about. Conversational, easy to read, and exceptionally accessible, this text combines depth and breadth with practical examples and clear step-by-step instructions — all delivered flexibly to support multiple modes of teaching and learning. This edition contains extensive new coverage of wealth building through investment; the latest insurance and credit trends, new tax rules and tables, and more. It is also accompanied by an expanded collection of interactive online learning and teaching resources unparalleled in its market, including Pearson's newly-revamped MyMathLab. Table of Contents 1. Review of Whole Numbers and Integers 2. Review of Fractions 3. Decimals 4. Bank Records 5. Equations 6. Percents 7. Business Statistics 8. Trade and Cash Discounts 9. Markup and Markdown 10. Payroll 11. Simple Interest and Simple Discount 12. Consumer Credit 13. Compound Interest, Future Value, and Present Value 14. Annuities and Sinking Funds 15. Building Wealth through Investments 16. Mortgages 17. Depreciation 18. Inventory 19. Insurance 20. Taxes 21. Financial Statements
AP Calculus BC: Logistic Growth Model Example Video sponsor: Secondary Math. Brendan Murphy teaches Math at John Baptist High School in Bangor, Maine. This series of videos provide direct instruction to students. Brendan asks his students what specific concepts they would like clarification on and then creates these short videos. This video is an example of the logistic growth model.
Course 18C Mathematics with Computer Science Mathematics and computer science are closely related fields. Problems in computer science are often formalized and solved with mathematical methods. It is likely that many important problems currently facing computer scientists will be solved by researchers skilled in algebra, analysis, combinatorics, logic and/or probability theory, as well as computer science. The purpose of this program is to allow students to study a combination of these mathematical areas and potential application areas in computer science. Required subjects include linear algebra (18.06, 18.700 or 18.701) because it is so broadly used; discrete mathematics (18.062J or 18.310) to give experience with proofs and the necessary tools for analyzing algorithms; and software construction (6.005 or 6.033 or 6.170) where mathematical issues may arise. The required subjects covering complexity (18.404J or 18.400J) and algorithms (18.410J) provide an introduction to the most theoretical aspects of computer science. Some flexibility is allowed in this program. In particular, students may substitute the more advanced subject 18.701 Algebra I for 18.06, and if they already have strong theorem-proving skills, may substitute 18.314 for 18.062 or 18.310. Students who have taken 6.001 before the course 6 curriculum change may use it instead of 6.01, and similarly students who have taken 6.170 may use it instead of 6.005 or 6.033. Students who have taken 18.410J before the curriculum change should not take 6.006, but must replace it with another Course 6 subject of at least 12 units. One Subject from Each of the Following Pairs 18.400J (Automata, Computability, and Complexity) or 18.404J (Theory of Computation) 6.005 (Principles of Software Development) or 6.033 (Computer System Engineering) Restricted Electives Four additional 12-unit subjects from Course 18 and one additional subject of at least 12 units from Course 6. The Course 6 subject may be 6.02, 6.041, 6.17x, a Foundation or Header subject, or, with permission of the Mathematics Department, an advanced Course 6 subject. The overall program must consist of subjects of essentially different content and must include at least five Course 18 subjects with first decimal digit one or higher.
Buy now Short description With an emphasis on the history of mathematics, this book offers a well-written introduction to number theory and calculus and presents numerous applications throughout to illustrate the accessibility and practicality of the topic. It features numerous figures and diagrams and hundreds of worked examples and exercises--and includes six chapters that allow for a flexible format for a one-semester course or complete coverage for a two-semester course.
Subject: Mathematics (9 - 12) Title: Focusing on Graphs Description: In this lesson, students will solve systems of linear equations by graphing. Systems of linear equations are two or more linear equations together. Subject: Mathematics (8 - 12) Title: Why so Cross? Description: This lesson will help students develop a deep understanding of what the solution to a system of linear equations means. They will investigate the graphs of systems as well as experiment with an online graphing calculator. Subject: Mathematics (9 - 12) Title: When Will Mr. "X" Meet Miss "Y"? Description: During this lesson, students will solve systems of equations graphically. Students will graph various equations individually using graphing paper. They will work with a partner to solve several system of equation problems and then graph them on chart paper to be displayed throughout the classroom. Subject: Mathematics (9 - 12) Title: Wild Water Adventure Description: Students will learn how a system of equations can be used to find the best use of information to make decisions in real-world situations.Students will work in groups of 3s or 4s to develop a system for the best buy on tickets at a water park. The lesson is also designed to help students develop a budget or a plan when their spending money is limited. Students will find that sometimes group prices or working as a team will help them save money. Subject: Mathematics (9 - 12) Title: Battleships Description: This lesson is designed to review and reinforce three methods (graphing, substitution and elimination) of solving systems of linear equations. The students will work together and independently to find the solutions to systems of equations that simulate the linear path of the battleship and the path of the battleships' torpedo. If the solution exists then we will be able to determine if one battleship might be able to sink another. (Shared with permission of Twyla Fryer.)This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project. Subject: Mathematics (9 - 12) Title: Systems of Linear Inequalities Project Description: The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation. Subject: Character Education (K - 12), or Mathematics (9 - 12) Title: Systems on a Mission Description: Students will solve systems of equations using 4 different methods. These methods include substitution, elimination by multiplication, elimination by addition or subtraction and graphing. Students will gain knowledge on how to use one method to solve a system of equations and another method to check their solution. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation. Subject: Mathematics (8 - 12) Title: Quadrilaterals Description: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation. Thinkfinity Lesson Plans Subject: Mathematics Title: There Has to Be a System for This Sweet ProblemAdd Bookmark Description: In this Illuminations lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics Title: Pick's Theorem as a System of EquationsAdd Bookmark Description: In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics,Social Studies Title: Supply and DemandAdd Bookmark Description: Students write and solve a number of systems of linear equations in the context economics as supply and demand. Students should be familiar with finding linear equations from two points or slope and y-intercept. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics Title: Escape from the Tomb Activity Add Bookmark Description: This reproducible activity sheet, from an Illuminations lesson, includes instructions and questions for a mathematical adventure game. In the game, students are given a problem in which two bowls are suspended from the ceiling by springs, and one bowl is lower than the other. Students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics Title: Escape from the TombAdd Bookmark Description: In this Illuminations lesson, students solve a system of equations when presented with a problem: two bowls are suspended from the ceiling by springs and one bowl is lower than the other. Placing only marbles in one bowl and bingo chips in the other, students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. There are also links to online activity sheets. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
2 products found As for economics student one of those is a must. Not sure if there is a point elaborating its functions, it's designated for people who deal with financial calculations such as interests, depreciation... read full review
Title: Patterns and Functions Description: Introduces various types of numeric and geometric patterns. Also includes lessons on function tables with one and two operations. Source: Teacher's Helper: Intermediate. April/May 2010. p.15-25
Pure Math Submitted by admin on Fri, 05/06/2011 - 5:08pm. The creation, development, and exploration of the form and knowledge of Mathematics itself, with elegance, aesthetic balance, and connections with other areas of Mathematics as the sought after, delineating features. Pure Mathematics (PMAT) is concerned with the development and exploration of structures and techniques that have proven invaluable in illuminating questions that arise in a wide range of problems in mathematics and sciences. The focus is on general methods, powerful ideas that are widely applicable, and theories that capture an elegance of design revealing a deeper richness and unity within mathematics. At the undergraduate level, the student begins with the basics of algebra, calculus and discrete math, then progresses towards a selection of courses in the theory of numbers, cryptography, topology and geometry, differential equations, analysis, set theory and logic. Number theory includes both deep results about our familiar numbers 1,2,3,4,... and their atomic constituents the primes 2,3,5,7,11,..., as well as results about richer collections of numbers obtained by extending the natural numbers through algebraic means. Number theory is intimately connected with cryptography, the science of passing secrets through encoded messages. The Department offers a concentration in cryptography as part of its undergraduate program in pure math. Topology and geometry involve the basic shapes of mathematics: from rigid objects such as lines, planes, circles and spheres, to bendable creations like loops, knots, and surfaces in space. Patterns, relations, transformations, and invariants for these objects are all of mathematical interest. Tools from algebra and analysis are both developed through topological and geometrical methods, as well as applied to study these creations. Differential equations model the physical world, from the propagation of seismic waves through the earth under our feet, to the transmission of heat through the expanding universe. Mathematicians are concerned with the general properties of differential equations, the nature of their solutions, their use in making accurate models of the real world, and efficient methods to compute answers from these equations. Analysis encompasses a wide range of techniques to study the properties of functions on a space. It is calculus taken to a higher level. Real and complex analysis examine functions on the real line and on the complex plane, while differential geometry examines functions on smooth spaces called manifolds. Analysis gives us a way to organize the infinite dimensions which arise in so many aspects of mathematical theories. Set theory and logic form the foundations of modern mathematics, assuring the truth of deep results based only on clear, precise axioms and the methods of deductive reasoning for their creation. Set theory concerns itself with collections of elements, and rules for decomposing and recombining sets in well-defined ways. It goes hand-in-hand with logic, the basis of our lemma-theorem-proof approach to establishing mathematical truths. Career options A degree in Pure Mathematics is excellent preparation for graduate work in mathematics, and in technical disciplines that make heavy use of mathematics, such as engineering, physics, and computer science.
Technology Requirements Network Requirements Special Technology Requirements Note: These are course-specific requirements that go above and beyond the Provider Baseline Technical Requirements. The school or student is responsible for providing: The student may be asked to complete several exercises using a graphing calculator. The student can purchase a graphing calculator, such as the Texas Instruments TI-83™, or download the DreamCalc™ graphing calculator, which is provided by Connections Academy. The DreamCalc graphing calculator is similar to most hand-held graphing calculators. Materials to be ordered via the DLD The DLD Registrar may order the following materials via the DLD upon registering the student: No additional materials required for this course. Description This is the first of two courses that comprise Algebra 2. In this course, the student will continue to study higher level mathematics. The student will begin by reviewing basic real number operations and properties as well as linear equations, linear inequalities, and functions. Next, the student will study linear systems, graphing, and matrices. Finally, the student will build upon previous knowledge of quadratic equations and functions, as well as begin to explore polynomials and their functions. Throughout the course the student will be introduced to many problem-solving strategies, exposed to various technologies, and taught test-taking strategies.
Foreword Volume 1B, Mathematics Curriculum Notes Four principles offer an inductive philosophy for the explanation and comprehension of math and reasoning skills. Three of the principles were met in a course on how to teach Nordic, that is cross-country skiing. The course was taught one weekend early in 1981, by an instructor-trainer from CANSKI, the CANadian association for Nordic SKIing in Flin Flon, Manitoba. Nordic ski instruction may begin with a lesson on how to put on the boots and attach them to the ski and also how to hold the ski poles – to be precise one holds not the poles, but their straps in way that will guide the poles. Mathematics Curriculum Notes understanding and explaining reason and math Volume 1 by Alan M. Selby Ph. D. Printed in Canada ISBN 0-9697564-6-1 There is a technique here, one that is not obvious. The course gave minute attention to the details which novice and even experienced skiers might not know. In this course on ski instruction, the more complicated movements or skills were deliberately preceded by simpler motions. Each of which was easy to describe, master and/or review separately. This course turned Nordic ski instruction into an art. The four principles follow. Each discipline needs to be presented, so that students understand what they are learning and why. Without a knowledge or an opinion of why, students may lose interest and not go further. The why could be approximate, a little uncertainty leaves room for thought. Pathways through easily described and repeated ideas may extend knowledge of any discipline, area of thought or belief. One or more paths through easily described and easily repeated topics may allow those who travel further to tell others willing to listen, what to expect and again possibly why. Of course, differences of opinion exist on which disciplines should be taught or what pathways in them should be followed. Awkwardness with an idea or skill often signals difficulty with previous ones. It may indicate at least one earlier skill has been missed or forgotten. When an awkwardness is felt or seen, learners should go or be taken back to practice the missing skills, more precisely the ones just before them. This retreat aims to restore confidence and build skills, so that the learner can go further. This requires a diagnostic skill, a knowledge of or opinion on how the topics in question can be organized and taught. Here again opinions may differ. Each collection of mental and physical skills should be organized into a ladder-like sequences of steps with the basic ones first and the more advanced ones second. Learning in any subject stumbles when a first or succeeding step is not easily reachable from those before them. [1] To climb a ladder, the initial steps must be reachable, and each further step must be reachable from the one or ones before it, else failure occurs. Explanations should follow chains of reasons or persuasion which begin at the level of the student. In mathematics education there are two barriers to comprehension to be lowered or removed. First, the algebraic or symbolic way of writing and thinking is better seen and read silently than read aloud or spoken. This has been an obstacle to the comprehension and communication of mathematical thought. Second, the deductive nature of formal mathematics exposition with its long chains of reason and preparation implies that concepts appearing at the end of a course are not comprehensible to students in the middle of the course nor at its beginning. Mathematics beyond the last concept mastered may seem impenetrable and mysterious. To lower both barriers, students may be given lessons, easily described and repeated, which require a minimal formal comprehension of mathematics and logic while presenting ideas essential to deductive and to algebraic or symbolic thought. Recognizing, collecting and offering first such lessons may extend the common knowledge of mathematics beyond the mastery of arithmetic, counting and simple formulas that should be obtained in elementary school. This work identifies such lessons and indicates ideas for math and logic instruction from primary school to the start of college. Some of the ideas may be worth reading, repeating or refining, the three Rs that this author hopes for. Alan Selby Montreal 1996 Selby A, Volume 1B, Mathematics Curriculum Notes, 1996. Postscript - February 2011 In two years of UK grammar school 1965-7, mathematics lessons consisted of given rules and patterns in algebra, trig and geometry, all given in what I presume was a mathematically correct manner. I was too young to know otherwise. In then next three years of English Quebec secondary schooling, rules and patterns were also given but in axiomatic structure. That is, rule and pattern mastery started from axioms - assumed patterns algebraically or geometrically put. The fine print in my Quebec high school textbooks emphasized or valued starting from a minimal set of axioms. The development was essentially logical. But there were four flaws in the Quebec portion of my secondary school and junior college education - nuances small and large. The arithmetic mastery of decimals and fractions met in my UK primary and secondary school days was required, but not explicitly sanctioned. That departed from the ideal in textbook fine print of building mathematical knowledge on explicitly given axioms The algebraic way of writing and reason was required to understand the shorthand role of letters and symbols in the axioms and in the further development of algebra, geometry and science in my UK and Quebec studies. But no course and the fine print in all of my textbooks did not provide any sanction for this shorthand role. While I found my own rationalization, self-constructed, I saw the instruction of myself and fellow students slowed by the silent assumption use of algebraic skill. Course design and delivery assumed it without clearly or explicitly discussing it. Talking about three skills for algebra, a lesson given in fall 1983, represented my second effort to address this flaw. The first was in a 1975 handout at a McGill University open house. The use of order pairs as coordinates in the plane ias in the analytic approach to geometry was mixed with synthetic Euclidean Geometry, the line, circle and triangle drawing approach. Having two approaches unreconciled departed from the fine-print promise in algebra of a minimal set of axioms. The use of drawings and diagrams, disowned in the algebraic course view of mathematics, was present in both high school level trigonometry and in later college level calculus. And geometric drawings were employed along side mathematically and algebraically deep utilization of epsilons and delta views of continuity and convergence, with the underlying theory avoiding decimals, while examples and illustrations employed or required decimals. My strength and weakness as a student and a human being was and may still be a reflex to take everything literally. So I was disappointed with my high school and college education because the algebraic way of writing and reasoning was not introduced in a clear step by step manner. In all the courses I took and in all the textbooks I saw, this shorthand way of writing and reasoning was required while the effort to explain it was absent or, when present, insufficient. I was also disappointed by the espousal of an ideal, the consistent and full logical development of mathematics from axioms - assumed patterns. Course design and delivery failed to deliver. In retrospect, following graduate studies and doctoral degree in mathematics, and further thought, the ideals espoused represented the hopes and motivation of modern mathematics. But mathematicians if not mathematics educators since Godel in the 1930s were aware that the hopes were not feasible. None the less, the modern mathematics curricula echoed those hopes and emphasized a rigour in ways that many tried to take literally. In retrospect, mathematics is an empirical subject. Its development is a mix of practice and theory. Given that, I first recommend K3-9 observable skills and practices with take home values be learnt and taught in manner that emphasizes their value, with explanations to aid mastery without overwhelming it, with the end of making students aware of the domino effect of errors in calculations and reasoning, and with the end of showing students how to do and record steps in manner they and others can do or check. With skills that have take home value, students may expect instructors to teach correct methods - methods that can be learnt by rote if the student wishes, methods for which explanations why are available for reading by students when or if they want. For skills that have high take home value for life in the street or work, rigourous mastery is more important than comprehension. But in the preparation of students for college programs, those that may employ one variable calculus, or more. skill development needs to show students how to use and combine rules and patterns in applications, and in the development of further rules and patterns. The ability to apply and the ability to reproduce in all or part what has been shown is in itself an observable skill. Skills that can be seen can be described, confirmed or corrected. But the thought-based development of skills and concepts does not require a minimal set of axioms. Minimality here represent a value of higher mathematics education. The development requires a convenient and consistent set. This set may provides the opportunity for students to see how rules and patterns may be applied to obtain results and combined to obtain further rules and patterns. The set develops and sanctions decimal, algebraic, geometric and logic skills and practices, so that the flaws indicated above are avoided while the stage is set for further studies in college programs. That represents the current or last objective of site material. The initial objective when writing began was not so large. Writing began with the inductive criteria for course design and delivery, with the question of how to motivate skill development, and with the hope of making the modern mathematics curricula of the years 1965-90 more accessible - less challenging to learn and teach. The initial aim was to report the inductive principles and a few appetizers and starter lessons to educational authorities, and then leave further work in this matter to others. However, I was not formally qualified to present ideas to educational authorities, or academic committees, more ideas followed, More over, in 1989, before I started writing, education had shifted from valuing skill development in reading, writing and arithmetic, mathematics included, to saying true knowledge is a personal affair, located in the mind, apart from observation and correction of teachers, and not associated with perfomance, that is, observable rule and pattern mastery. That subjective movement in education, led in US and Canadian mathematic education by the NCTM rtoday is the reverse of that espoused by the NCTM in the 1950s. Site material provides a rational alternative. A K1-9 emphasize of skills and practices with current or potential take home value for work or life in the street represent student-centered skill development. The K7-12 parallel or subsequent emphasis on skills for one-variable calculus and college programs in technical fields represents college oriented skill development for careers - not guaranteed - that may benefit the student or society. Such instruction has intellectual and/or take-home value for some, not all. That is not ideal. But recognizing this situation represent a step forward from the situation in which secondary mathematics instruction is clouded in mystery, with the question why learn or teach this has the bureaucratic answer: preparation for final examinations. Moreover, this college oriented instruction can be offered, does not have to be taken nor required, once most skills with take-home value have been covered. The latter needs to be done first. It will be useful to all, including those students aiming for college studies who might other wise miss it. As a high school teacher, I once had to give a mathematics course required for graduation to a group of students who have benefited from a review and consolidation of skills with take-home value. Instead, their time was wasted because of government standards for education that forced the learning and teaching of topics with no academic nor take home value for the students in question. That situation needs to be addressed
All Available Copies None(1 Copy): Fair Some shelf wear, may contain highlighting/notes, may not include cdrom or access codes, customer service is our top priority! HPB-059 TX, USA $17.44 FREE New: BRAND NEW 0547517653. indoo.com NJ, USA $19.64 FREE Used Very Good(2 Copies): Very Good 0547517653About the Book In 2010, award-winning professor Steven Strogatz wrote a series for the "New York Times" online called "The Elements of Math." It was a huge success. Each piece climbed the most emailed list and elicited hundreds of comments. Readers begged for more, and Strogatz has now delivered. In this fun, fast-paced book, he offers us all a second chance at math. Each short chapter of "The Joy of X" provides an "Aha " moment, starting with why numbers are helpful, and moving on to such topics as shapes, calculus, fat tails, and infinity. Strogatz explains the ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Assuming no knowledge, only curiosity, he shows how math connects to literature, philosophy, law, medicine, art, business, even pop culture and current events. For example, did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Strogatz is the math teacher you wish you'd had, and The Joy of X is the book you'll want to give to all your smart and curious friends.
About Concrete Mathematics: A Foundation for Computer Science The primary aim of this book's well-known authors is to provide a solid and relevant base of mathematical skills -- the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. About Concrete Mathematics: A Foundation for Computer Science
The Geometer's Sketchpad 5.04 description The Geometer's Sketchpad 5.04 is considered as the world's leading software which is capable of teaching mathematics. Sketchpad® gives students at all levels—from third grade through college—a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. Make math more meaningful and memorable using Sketchpad. Elementary students can manipulate dynamic models of fractions, number lines, and geometric patterns. Middle school students can build their readiness for algebra by exploring ratio and proportion, rate of change, and functional relationships through numeric, tabular, and graphical representations. And high school students can use Sketchpad to construct and transform geometric shapes and functions—from linear to trigonometric—promoting deep understanding. Sketchpad is the optimal tool for interactive whiteboards. Teachers can use it daily to illustrate and illuminate mathematical ideas. Classroom-tested activities are accompanied by presentation sketches and detailed teacher notes, which provide suggestions for use by teachers as a demonstration tool or for use by students in a computer lab or on laptops. Enhancements: Rounding errors no longer occur when measuring right angles in degrees. The Geometer\s Sketchpad Updater brings you an advanced and convenient to use tool which spans the mathematics curriculum from middle school to college, The Geometer\s Sketchpad brings a powerful dimension to the study of mathematics. Free Download Soccer Sketchpad is released as a high quality and smart sketch program that could produce and print a professional looking drawing in 4 minutes. It is designed for soccer coaches who teach the game. Free Download
Understanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with alge... read more Customers who bought this book also bought: Our Editors also recommend: Calculus: Problems and Solutions by A. Ginzburg Ideal for self-instruction as well as for classroom use, this text improves understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. Over 1,200 problems, with hints and complete solutions. 1963 editionAn Introduction to the Calculus of Variations by Charles Fox Highly regarded text for advanced undergraduate and graduate students explores first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963Calculus: A Modern Approach by Karl Menger An outstanding mathematician and educator presents pure and applied calculus in a clarified conceptual frame, offering a thorough understanding of theory as well as applications. 1955 edition. Calculus and Statistics by Michael C. Gemignani Topics include applications of the derivative, sequences and series, the integral and continuous variates, discrete distributions, hypothesis testing, functions of several variables, and regression and correlation. 1970 edition. Includes 201 figures and 36 tablesHarmonic Analysis and the Theory of Probability by Salomon Bochner Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955Understanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. In addition to three helpful appendixes, the text features answers to some of the exercises. Appropriate for advanced undergraduates and graduate students, it is also a practical reference for professionals. 1985 edition. 310 figures. 18 tables. Bonus Editorial Feature: Richard W. Hamming (1915–1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004. In the Author's Own Words: "The purpose of computing is insight, not numbers." "There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think." "Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way." "If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming
Description Math Basics for the Healthcare Professional, Third Edition draws on comments from the field to include more applications: thus, the expanded units on metric system conversions, pre-algebra, reading drug labels, medicine cups, and syringes, parenteral dosages, intravenous administration formulas, and basic dosages by weight have been included in the text. The appendix includes an additional practice tests for each unit. A student CD offers an additional two practice tests for student use. Table of Contents Table of Contents Preface Health Occupations Matrix of Math Skills and Self-Assessment Health Occupations Math Skills Self-Assessment Score Sheet Math for Healthcare Professionals Pre-test Unit 1 Whole Number Review Addition Subtraction Multiplication Division Number Statements Rounding Estimation Basics of statistical Analysis Mean/Average Median Mode Range Roman Numerals Concept 1 Concept 2 Concept 3 Whole Number Self-Test Unit 2 Fractions Part-to-Whole Relationships Equivalent Fractions Reducing to Lowest or Simplest Terms Multiplication Method Division Method Improper Fractions Adding Fractions with Like Denominators Finding the Common Denominator Ordering Fractions Subtraction of Fractions Borrowing in Subtraction of Fractions Multiplication of Fractions Multiplying a Fraction by a Whole Number Reducing before you Multiply as a Timesaver Multiplication of Mixed Numbers Division of Fractions Fraction Formula Complex Fractions Fraction Self-Test Unit 3 Decimals Rounding Decimals Comparing Decimals Addition of Decimals Subtraction of Decimals Multiplication of Decimals Division of Decimals Zeros as Placeholders in Decimal Division Simplified Multiplication and Division of Decimals Simplified Multiplication Simplified Division Changing Decimals to Fractions Changing Fractions to Decimals Temperature Conversions with Decimals Decimal Conversion Formula Solving Mixed Fraction and Decimal Problems Decimal Self-Test Unit 4 Ratio and Proportion Ratio Proportion Solving for x Word Problems Using Proportions Solving for x in More Complex Problems Using Proportion Nutritional Application of Proportions Ratio and Proportion Self-Test Unit 5 Percents Percent-to-Decimal Conversion Decimal-to-Percent Conversion Using Proportion to Solve Percent Problems Percent Strength of Solutions Single Trade Discount Percent Self-Test Unit 6 Combined Applications Conversion among Fractions, Decimals, Ratios, and Percent Suggested Order of Operations Using Combined Applications in Measurement Conversion Standard Units of Measure More Combined Applications Combined Applications Self-Test Unit 7 PreAlgebra Basics Integers Absolute Value Integer Operations Adding Integers with the Same Sign Adding Integers with Different Signs Subtracting Integers Multiplication of Integers Division of Integers Exponential Notation Scientific Notation Square Roots Order of Operations Algebraic Expressions Expressions Writing Expressions from Word Problems Solving Equations Writing Equations from Word Problems Literal Equations Pre-Algebra Basics Self-Test Unit 8 The Metric System Using the Metric Symbols Changing Unit Measures Metric System Self-Test Unit 9 Reading Drug Labels, Medicine Cups, Syringes, and Intravenous Fluid Administration Bags Reading Drug Labels Reading medicine Cups Reading Syringes Reading IV Adminstration Bags Reading Drug Labels, Medicine Cups, Syringes, and Intravenous Fluid Administration Bags Self-Test Unit 10 Apothecary Measurement and Conversions Apothecary Measurement and Conversions Apothecary System Self-Test Unit 11 Dosage Calculations Rounding in Dosage Calculations Dosage Calculations Formula Practice Practice Using Drug Labels Dosage Calculations Self-Test Unit 12 Parenteral Dosage Parenteral Dosage Parenteral Dosage Self-Test Unit 13 The Basics of Intravenous Fluid Administration IV Fluid Adminstration The Basics of Intravenous Fluid Administration Self-test Unit 14 Basic Dosage by Weight Basic Dosage by Weight Basic Dosage by Weight Self-Test Practice Post-Test Appenix Appendix of Practice Unit Exams 1-14 and Answers Answer Key
Learning Support Mathematics The Learning Support Mathematics program assists students in developing the ability to perform mathematical computations, use measurements, make estimates and approximations, judge reasonableness of results, formulate and solve mathematical problems, select appropriate approaches and problem-solving tools and use elementary concepts of probability and statistics. Learning Support mathematics courses are intended for students who need additional preparation in mathematics prior to enrolling in college-level courses. Learning Support Mathematics Course Descriptions Courses below constitute the TBR required sequence based on college placement.