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Properties: Comprehend/Apply The learner will be able to
comprehend and apply the distributive, associative, commutative, inverse, identity, and substitution property to evaluate algebraic expressions.
Expressions: Procedures/Apply The learner will be able to
apply procedures for operating on algebraic expressions, commutative, associative, identity, zero, inverse, distributive, substitution, multiplication over addition.
Functions: Linear/Equations/Inequalities The learner will be able to
create equations and/or inequalities that are based on linear functions, apply many different methods of solution, and/or study the solutions in the context of the situation.
Figures: Two-/Three-Dimensional Objects The learner will be able to
precisely explain, classify, and comprehend relationships among types of two- and three-dimensional objects by applying their defining properties.
Math Concepts: Identify The learner will be able to
recognize concrete and/or symbolic illustrations of vertical, supplementary, complementary, and straight angles, parallel and perpendicular lines, transversals, and/or special quadrilaterals, and apply them to obtain solutions to problems.
Mathematical Reasoning: Explain The learner will be able to
apply many different methods to describe mathematical reasoning such as words, numbers, symbols, graphical forms, charts, tables, diagrams, and/or models.
Area/Volume/Length: Differences The learner will be able to
identify the differences and relationships between perimeter, area, and volume (capacity) measurement in the metric and U.S. Customary measurement systems.
Surface Area/Volume: Compute/Solve The learner will be able to
compute the surface area and volume of pyramids, cylinders, cones, and spheres and obtain solutions to problems involving volume and surface area.
Units: Choose/Metric/Customary The learner will be able to
choose suitable customary and metric measurement units for length (include perimeter and circumference), area, capacity, volume, weight, mass, time, and temperature.
Magnitude: Illustrate/Understanding The learner will be able to
illustrate an understanding of magnitudes and relative magnitudes of real numbers (integers, fractions, decimals) using scientific notation and exponential numbers.
Strategies: Daily life/Apply The learner will be able to
apply various methods, including common mathematical formulas, to obtain problem solutions of routine and non-routine problems drawn from everyday life. |
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
New Senior Mathematics for Years 11 & 12 is part of a new edition of the well-known mathematics series for New South Wales. We've completely updated the series for today's classrooms, continuing the much-loved approach to deliver mathematical rigour with challenging student questions. The first three chapters of this student book contain revision material, providing the necessary foundation for the development of senior mathematical concepts.
Table of contents
Arithmetic and surds
Algebra
Equations and inequalities
Plane geometry
Trigonometic ratios and applications
Coordinate geometry - straight lines
Functions and relations
Locus and regions
Quadratic functions and the parabola
Differential calculus
Plane and coordinate geometry
Geometrical applications of differentiation
Integral calculus
Exponential and logarithmic functions
Trigonometic functions
Series and applications
Applications of calculus to the physical world
Probability
Features & benefits
Improved grading of questions
Clearer worked examples
5 exam-style papers
Chapter reviews for each chapter
Technology tips and suggested GeoGebra use
Summary section
Series overview
A feature of NSW classrooms for almost 30 years, the New Senior Mathematics books make up the most respected and trusted senior Mathematics series in the market. |
Algebra And Trigonometry - Text Only - 2nd edition
This text presents the traditional content of the entire Precalculus series of courses in a manner that answers the age-old question of "When will I ever use this?" Highlighting truly relevant applications, this text presents the material in an easy to teach from/easy to learn from approach.
Helps students who will be going on to Calculus, and gives them an enhanced understanding of functions graphs and how those graphs are changing.
NEW--Reorganized content in Chapters P and 1--Moves complex numbers and the discussion of graphs and graphing utilities from Chapter P to Chapter 1.
Enables students to immediate apply their understanding of complex numbers to their work in solving quadratic equations, and sets the stage for using graphing to support the algebraic work in solving equations and inequalities developed in Chapter 1.
Presents business majors with important topics, and gives students additional practice in developing functions that model verbal conditions.
NEW--Applications and updated real-world data--Provides more interesting, real-world applications than found in any similar text.
Brings relevance to examples, discussions, and applications.
NEW--Rewritten, extensive, and well-organized exercise sets--At the end of each section exercises are organized by level within six category types: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Group Exercises.
NEW--Enrichment Essays and section openers--Includes the five all-time celebrity winners on Jeopardy!, and a comparison between the probability of dying and the probability of winning Floridas lottery.
Provides historical, interdisciplinary, and interesting connections throughout the text.
NEW--More Study Tip boxes--Appear in abundance throughout the book.
Offers students suggestions for problem solving, point out common student errors, and provide informal tips and suggestions.
NEW--Expanded number of optional technology boxes.
Illustrates the many capabilities of graphing utilities that go beyond just graphing.
Quadratic Functions. Polynomial Functions and Their Graphs. Dividing Polynomials: Remainder and Factor Theorems. Zeros of Polynomial Functions. More on Zeros of Polynomial Functions. Rational Functions and Their Graphs. Modeling Using Variation.
The Law of Sines. The Law of Cosines. Polar Coordinates. Graphs of Polar Equations. Complex Numbers in Polar Form; DeMoivre's Theorem. Vectors. The Dot Product.
8. Systems of Equations and Inequalities.
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Partial Fractions. Systems of Nonlinear Equations in Two Variables. Systems of Inequalities. Linear Programming.
9. Matrices and Determinants.
Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems and Their Applications. Matrix Operations and Their Applications. Multiplicative Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule.
10. Conic Sections and Analytic Geometry.
The Ellipse. The Hyperbola. The Parabola. Rotation of Axes. Parametric Equations. Conic Sections in Polar Coordinates |
Shell Centre for Mathematical Education Publications Ltd.
Publications, Downloads and Licensing
Main Menu
The Shell Centre is known around the
world for its innovative work on mathematics education. The Shell Centre
team has a wide range of ongoing activities including design,
development and research.
Shell Centre Publications Ltd. was set up to distribute and
license materials developed at the Centre, and offers a range of
innovative teaching materials for mathematics education, together with
research publications and tests from the Centre and its collaborators.
Announcement regarding sales of publications
The aim of Shell Centre Publications has always been to ensure
that a number of seminal works in the field of mathematical education
remained available.
We have now reached the point where our most popular items are
out of stock, and have come to the decision that it is time to stop
storing and selling physical books. Digital distribution is the
best way to keep these works available, so in the coming months, we will be
making many of the publications on our list available, for free, as PDF
downloads. Currently, we can offer:
...thanks to the work of the National STEM Centre who
now operate a wonderful archive of classic education materials from
Science and Maths. The Standards Unit Improving Learning in Mathematics materials, partly developed at the Shell Centre, can also be found there.
We are also investigating the possibility of keeping a few
popular titles - staring with The Language of Functions and Graphs -
available in print using a third party 'print-on-demand' service who
will accept orders, print and ship the books internationally. If you are
potentially interested in this, please let us know at
[email protected] as it will help us set priorities.
Shell Centre Publications remains active, licensing the work of
the Shell Centre for Mathematical Education and Mathematics Assessment
Resource Service around the world, as well as developing new materials
in conjunction with the Centre for Research in Mathematical Education at
the University of Nottingham. The work of our current flagship project,
developing formative and summative assessments for the new US Common
Core State Standards in Mathematics, can be found at map.mathshell.org.
Note: The Chelsea Diagnostic Tests are no longer available from us, but we understand that the authors are planning to make them available from their own website shortly. We will post a link here when they are available.
Page updated 28 November 2012 - Contact [email protected]. This
page is published and maintained by Shell Centre for Mathematical
Publications Ltd. |
This module helps the introductory Calculus student visually see how they can use the
Chain Rule to differentiate functions with an animation featuring Bob the Blob, followed
by a couple specific examples. |
Precalculus : Schaum's Outline - 2nd edition
Summary: If you want top grades and thorough understanding of precalculus, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you more than 600 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers provided to show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dre...show moreary minutiae, Schaum's Outlines have sold more than 30 million copies worldwideand this guide will show you why |
Singapore is number one in Mathematics and number two in Science worldwide in the Third International Mathematics And Science Study (TIMSS) 1999. 93% and 80% of our students are in the international top half for Mathematics and Science respectively.
The mathematics and science curriculum in Singapore has been found to be more comprehensive than that of many countries. Singapore's rigorous curriculum is continually reviewed to ensure that it remains relevant for our students.
Editor's picks. C. H."
This is a comprehensive curriculum that will give your child a solid foundation in mathematics, build up their confidence and give them a head start on their peers.
"Dear Friends ! Great thanks! We received our order yesterday, 24 of June. Great thanks for good service. We have two books (Secondary 2) which we received two years ago from you. That are excellent books! And we recommend these books to all our friends to use in teaching children. Good luck. Sincerely yours Vladimir and Rita Kononenko"
This is a comprehensive curriculum that will give your child a solid foundation in mathematics, build up their confidence and give them a head start on their peers.
"Dear SGBox The books arrived last Friday. The parcel arrived in perfect condition and we are very satisfied with the contents. My daughter has started work in the maths books and finds that they are very well laid out with clear examples and instruction. We have had a quick look through the science books and they promise to be as good as the maths! So far we find that these are excellent products and look forward to ordering from you in the future. Best wishes Sandie McDonnell"
Your child will learn new concepts in a straight-forward and interesting way. He will develop creative and critical thinking and master problem-solving strategies through the worked examples in this section.
These Singapore Mathematics textbooks and workbooks uses the concrete-pictorial-abstract approach to get your child involved in the learning of mathematics.
"Good Morning, We have now received this shipment. Thank you very much for the fantastic course books, good packaging and fast shipment. Your customer service has been exceptional and I apologise for "loosing" your e-mails in the spam filters. We will be ordering a lot more in the future. Best Regards Matthew MorrisThe questions in this Singapore Mathematics workbook are designed to develop and enhance your child's problem-solving skills, stimulate their creative thinking and build up their interest in Mathematics. |
Technology Enhanced Redesign of Mathematics (TERM)
What you can expect from your TERM course.
Computer-based Learning
Mathematical content instruction and homework is delivered via the web-based software MyLabsPlus, which includes an e-text (no need to purchase a textbook), video instruction, homework exercises, and tests.
Interactive Group Instruction
Each class meets one day a week in a classroom with an instructor.
The first part of the class time is devoted to interactive group
instruction designed to help students find success in learning
mathematics. The remaining class time is for individual work and
consultations with the instructor. Students also benefit from forming
study teams and working collaboratively.
Tutoring Support
Instead of meeting for two additional class periods each week,
students work in the Hub – a computer lab specifically serving TERM
students. Tutors and instructors provide personalized assistance as
students study and learn math.Tutoring assistance is
available to students beyond their required hub time, to assist students
to complete one module each week. Students learn better by discussing
mathematics with a tutor and/or instructor.
Computerized Testing
Students are provided with three attempts
to pass (at 70%) each module quiz and comprehensive test. Quizzes and
tests are taken in the Hub Testing Centers. A Wildcard ID is needed to
use the Hub Testing Center. Final exam week is reserved strictly for
final exam testing.
Fast Track
Currently available for Math 0950, students have the option of
testing out of a module prior to doing any homework for the module. This
is a great benefit for students who need a quick refresher of the
Pre-Algebra content.
Free Math Credit
To pass the course, students must demonstrate mastery of the 10 modules by passing the module quizzes, comprehensive tests, and final exam. Each course is completed in one semester. However, the individualized structure of TERM allows students to work ahead of schedule. A student can complete two (or three) courses in one semester and does not have to pay tuition for the second (or third) courses completed within one semester. |
Join the thousands of students that have used our Calculus Video Tutorials since 2004 to master the subject!
There is no easier way to learn Calculus than to have a calm teacher show you each and every step. We don't focus on shortcuts - we focus on you truly understanding the subject so that every step makes sense!
Detailed Description of this Course Calculus can be an intimidating subject. For many students, even the name sounds intimidating. The truth is that Calculus is based on a few very powerful principles and once you fully understand those principles all of the additional topics naturally follow.
Most Calculus textbooks begin the subject with a nauseating discussion of limits and then proceed to the introduction of a derivative which is one of the core topics in Calculus. This DVD series begins the discussion immediately with the concept of the derivative without any math at all and spends some time ensuring that this concept is solidified.
Limits are used to explain the derivative via example problems beause that is how they are defined, but you will not be presented with endless lectures on abstract math topics that are not directly related to the core topics of Calculus.
All of the other topics are taught in the very same manner, relying on the power of learning by working fully narrated example problems in a step-by-step fashion. |
Overview
Main description
An ideal course text or supplement for the many underprepared students enrolled in the required freshman college math course, this revision of the highly successful outline (more than 348,000 copies sold to date) has been updated to reflect the many recent changes in the curriculum. Based on Schaum's critically acclaimed pedagogy of concise theory illustrated by solved problems, Schaum's Outline of College Mathematics features:
Mathematical modeling throughout
Modernized graphs
Graphing and scientific calculator coverage
More than 1,500 fully solved problems
Another 1,500 supplementary problems
And much more
Table of contents
Elements of AlgebraFunctionsGraphs of FunctionsLinear Equations Simultaneous Linear EquationsQuadratic Functions and EquationsInequalitiesLocus of an Equation The Straight LineFamilies of Straight Lines The CircleArithmetic and Geometric Progressions Infinite Geometric Series Mathematical Induction The Binomial Theorem Permutations Combinations Probability Determinants of Order Two and ThreeDeterminants of Order nSystems of Linear EquationsIntroduction to Transformational GeometryAngles and Arc LengthTrigonometric Functions of a General AngleTrigonometric Functions of an Acute AngleReduction to Functions of Positive Acute AnglesGraphs of the Trigonometric FunctionsFundamental Trigonometric Relations and IdentitiesTrigonometric Functions of Two AnglesSum, Difference, and Product Trigonometric FormulasOblique TrianglesInverse Trigonometric FunctionsTrigonometric EquationsComplex NumbersThe Conic Sections Transformations of CoordinatePoints in SpaceSimultaneous Quadratic EquationsLogarithmsPower, Exponential, and Logarithmic CurvesPolynomial Equations, Rational RootsIrrational Roots of Polynomial Equations Graphs of PolynomialsParametric EquationsThe Derivative Differentiation of Algebraic Expressions Applications of DerivativesIntegration Infinite SequencesInfinite SeriesPower SeriesPolar CoordinatesIntroduction to the Graphing CalculatorThe Number System of AlgebraMathematical Modeling
Author comments
Philip Schmidt, Ph.D. was the associate provost of Berea College, with the academic rank of professor of mathematics. He is the author of several Schaum's Outline titles.
Back cover copy
Perfect for high-school seniors and college freshman
Covers the fundamentals of basic college mathematics
Reflects the newest curriculum
Over 1500 solved problems
Use with these courses:
College Algebra
Trigonometry
Discrete Mathematics
Pre-Calculus
Calculus
Introduction to Mathematic Modeling
SCHAUM'S OUTLINES
OVER 30 MILLION SOLD
Master the fundamentals of College Mathematics with Schaum's--the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams and projects!Inside, you will find:
Complete coverage of the basics in Algebra, Trigonometry, Discrete Mathematics, and Calculus |
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them. This book introduces the basic concepts to... More > help you prepare for higher levels of Algebra.
-JwL< Less |
Mathematics
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Did you know...
Multiple mathematics professors have been awarded an Endowed Teaching Chair.
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Seminole State Advance is a new program to strengthen the math abilities of students seeking careers in science, engineering or mathematics.
Whatever your math level, from basic arithmetic to differential equations, Seminole State College offers math courses that can help you learn new ways to approach problem-solving.
Seminole State's math students enjoy easy access to computers in classrooms and the fully staffed Academic Success Center. Statistical Methods I (STA2023) is taught entirely in computer labs, so students can work closely with their professors.
Whether you have math anxiety, find math challenging or desire a quality foundation in math, Seminole State's diverse array of math courses ensure that every student will learn in classes that meet their skill level and pacing.
Many courses are taught with a choice of traditional, distance learning or computer-based instruction to best suit your preferred learning style.
Math Department Facts
Math professor Martha Goshaw was awarded a national Teaching Excellence Award in 2003 and 2012.
The Math Department hosts the Seminole County High School Math Contest in cooperation with the Seminole County Teachers of Mathematics, where high school students compete in calculus, pre-calculus, algebra, geometry and statistics. Also, there is a scholarship competition to win a 60 credit-hour scholarship to Seminole State.
Calculator workshops for graphing calculators are offered at the beginning of each fall and spring term.
Near the end of most terms, the Math Department offers review sessions for classes with departmental finals. |
This isn t just a regular calculator; it is a scientific and algebraic 15-digit calculator. ACalc has built-in functions and constants. Just input the problem using the keys on the screen, and poof, your answer appears without a hassle. |
Normal 0 false false false The Rockswold/Krieger algebra series fosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question "When will I ever use this?" Rockswold teaches students the math in cont... |
Statistical Mechanics
The theory of knots and models of simple magnets have suddenly become
interwowen over the last two decades. Both fields have benefitted from
this interaction - with ideas in one helping solve problems in the other.
This course shows how progress in pure mathematics
can help understand problems in apparently totally unrelated branches of
science - this
interaction is typical of modern mathematical physics which has blurred the
distinction between
pure and applied mathematics on many fronts. No pre requisites from
applied mathematics or statisics courses are necessary for this module. |
Derivatives Derivatives is spent with a lot of effort throughout the book explaining what lies behind the formal mathematics of pricing and hedging. Questions ranging from 'how are forward prices determined?' to 'why does the Black-Scholes formula have the form it does?' are answered throughout the text. The authors of this first edition use verbal and pictorial expositions, and sometimes simple mathematical models, to explain the underlying principles before proceeding to a formal analysis. Extensive uses of numerical examples for ill... MOREustrative purposes are used throughout to supplement the intuitive and formal presentations.
It has been the authors' experience that the overwhelming majority of students in MBA derivatives courses go on to careers where a deep conceptual, rather than solely mathematical, understanding of products and models is required. The first edition of Derivatives looks to create precisely such a blended approach, one that is formal and rigorous, yet intuitive and accessible. |
1990
Florida Department of Education
CURRICULUM FRAMEWORK - GRADES 9-12, ADULT
Subject Area: Mathematics
Course Number: 1202800
Course Title: Calculus - International Baccalaureate
Credit: 1.0
Will meet graduation requirement for Mathematics
A. Major concepts/content. The purpose of this course is to
provide a foundation for the study of advanced mathematics.
The content should include, but not be limited to, the
following:
- elementary functions
- limits and continuity
- derivatives
- differentiation
- application of the derivative
- antiderivatives
- definite integral
- applications of the integral
B. Special note. This course will include periodic
comprehensive reviews of the International Baccalaureate
mathematics courses in preparation for the International
Baccalaureate examination.
Students in this course may be preparing for the subsidiary-
level International Baccalaureate examination.
C. Intended outcomes. After successfully completing this
course, the student will:
1. Identify and apply properties of algebraic,
trigonometric, exponential, and logarithmic functions.
2. Understand sequences and series.
3. Apply the concept of limits to functions.
4. Find derivatives of algebraic, trigonometric,
exponential, and logarithmic functions.
5. Find derivatives of the inverse of a function.
6. Define relations between differentiability and
continuity.
7. Apply the idea of derivatives to find the slope of a
curve and tangent and normal lines to a curve.
8. Identify increasing and decreasing functions, relative
and absolute maximum and minimum points, concavity, and
points of inflection.
9. Find antiderivatives.
10. Apply antiderivatives to solve problems related to
motion of bodies.
11 Use techniques of integration.
12. Find approximation to the definite integrals using
rectangles.
13. Apply knowledge of integral calculus to find areas
between curves and volumes of solids of revolution.
14. Understand sequences of real numbers and of convergence.
15. Solve elementary differential equations. |
This collection of more than 55 activities compiled specifically for Algebra 1 including updated activities from Exploring Algebra with The Geometer's Sketchpad and many new ones cover topics such as fundamental operations; ratios and exponents; algebraic expressions; solving equations and inequalities; coordinates, slope, and distance; variation and linear equations; and quadratic equations. This curriculum module includes teacher's notes; activity prerequisites; time requirements; detailed answers; demonstration sketches enabling teachers to present the activities to the entire class; Explore More sections; Project Ideas; and a CD containing activity, demonstration, and supplemental sketches and other resources. Click here to download free sample activities from the book!
Available only in UK and Europe. Not available to US or other international customers
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£36.00 inc Vat
All required fields are marked with a star (*). Click the 'Add To Cart' or 'Add To Wish List' button at the bottom of this form to proceed. |
engineering resource, produced by Mathematics in Education and Industry (MEI) for the Royal Academy of Engineering, asks the question: how can production outcome data from a manufacturing process be analysed to optimise the process?
Students consider the outputs of resistors to see the outcomes form a normal distribution.…
This engineering resource, produced by Mathematic in Education and Industry (MEI) for the Royal Academy of Engineering, asks the question: how can you predict future power requirements?
Students are required to complete a table by substituting values into a formula and plot a graph. The interactive file can be used to demonstrate…
This engineering resource, produced by Mathematics in Education and Industry (MEI) for the Royal Academy of Engineering, asks the question: how can you calculate the energy used, or made available, when the volume of a gas is changed?
A bicycle pump, a refrigerator and the internal combustion engine change the volume of a gas…
This engineering resource, produced by Mathematics in Education and Industry (MEI) for the Royal Academy of Engineering, asks the question: how can a camera, mounted on a helicopter, be used to track the location of a ground-based object?
A number of discussion ideas are considered before using 2D and 3D coordinates to represent 2011.
Advancing the digital arts
Mathematicians help to produce computer animations for cinema and television screens.
An energy evolution
Maximising the yield of oil and gas from availableProduced by the Learning Skills Improvement Service, these materials help to demonstrate effective practice. By Cambridge Regional College, this case study looks at the themes of functional skills, equality, engineering and mathematics.
The aim of the project was to work with staff to raise awareness of the requirements of functional…
This Mathematics Matters case study looks at how Formula One teams use mathematical methods such as fluid mechanics and Navier-Stokes equations to improve performance. Every second counts in the fast-paced world of Formula One, so race teams use advanced mathematics to squeeze the best performance out of their cars. Computational research report written by Kevin Golden for More Maths Grads which aimed to develop a market research led strategy for identifying opportunities for continuing professional development programmes involving mathematics and statistics within the workplace.
As a case study, this particular report uses the aerospace sector in theFrom the LSIS, these materials cover two sessions designed to take students through the basic principles of manipulating and solving equations. The learners work through building an equation, checking the equation and solving the equation. They are then asked to create their own equation and swap it with a partner to be 'undone'… |
Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places read more
$16.95
How Dangerous Is Lightning? by Christian Bouquegneau
Vladimir Rakov This highly readable survey explores the history of lightning, from ancient myth to modern times. Topics include sources of lightning, physical effects, protection of structures and power lines, and current research. 2006 edition. read more
The Electromagnetic Field by Albert Shadowitz Comprehensive undergraduate text covers basics of electric and magnetic fields, building up to electromagnetic theory. Related topics include relativity theory. Over 900 problems, some with solutions. 1975 edition. read more read more read more
Problem Book in the Theory of Functions by Konrad Knopp Single-volume edition of renowned collection of problems. Part 1 contains more than 300 problems dealing with fundamental concepts; part 2 has over 230 problems in advanced theory. Includes hints and full solutions to all problems. read more
Theory of Functions, Parts I and II by Konrad Knopp Handy one-volume edition. Part I considers general foundations of theory of functions; Part II stresses special and characteristic functions. Proofs given in detail. Introduction. BibliographiesFourier Series and Orthogonal Functions by Harry F. Davis An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes. read more |
The first edition of this book (1965; Zbl 0193.34701) consisted of three parts: basic concepts, field theory and linear algebra, and as a modern down-to-earth approach with a personal touch it attained great popularity. The second edition (1984; Zbl 0712.00001) added some topics, mainly on commutative algebra and homological algebra.\par The current third edition has grown again, the additions dealing with topics close to the author's heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields: Bernoulli numbers, Fermat's last theorem for polynomials, the Gelfond-Schneider theorem and (as an exercise, with a hint) the Iss'sa-Hironaka theorem. This makes it a fascinating book to read, but despite its length it leaves large parts of algebra untouched. Semisimple algebras get a very cursory treatment (no mention of crossed products or the Brauer group) and there is only the merest trace of Morita theory; there are no Ore domains, Goldie theory or PI-theory. Graphs, linear programming and codes, constructions like ultraproducts and Boolean algebras are also absent, and lattices are only of the number-theoretic sort (reseaux, not treillis).\par Bearing these limitations in mind, the reader will nevertheless find a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items.\par Editorial comment: Note that there is also a 3rd ed. published by Addison-Wesley 1993 reviewed in Zbl 0848.13001. [Paul M.Cohn (London)] |
Linear Algebra
Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which will be suitable for all students coming to the subject for the first time.
The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including dimension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader's grasp of the material and to elaborate on ideas from the text. As a result, this book presents a well-rounded and mathematically sound first course in linear algebra.
show more show less
Vector Spaces
Linear Mappings
Structure of Vector Spaces
Matrices
Inner Product Spaces
Determinants (2 x 2. and 3. x 3)
Determinants (n x n)
Similarity (Act I)
Euclidean Spaces (Spectral Theorem)
Equivalence of Matrices Over a Principal Ideal Ring
Similarity (Act II)
Unitary Spaces
Tensor Products
Table of Contents provided by Publisher. All Rights Reserved.
List price:
$39.95
Edition:
1992
Publisher:
Oxford University Press, Incorporated
Binding:
Trade Cloth
Pages:
376
Size:
7.69" wide x 9.56" long x 1.04 |
Advanced Algebra (M Level only)
Aims
The aim of the module is to develop the theory of finite groups up to the Sylow Theorems and to study factorisation in commutative integral domains.
Learning objectives
At the end of the module you should be able to...
Work with group actions;
Use Sylow's Theorems;
Recognise examples of various types of integral domain;
Use Euclid's algorithm in Euclidean domains.
Syllabus
Revision of basic group theory, finite abelian groups. Group actions: orbits, stabilisers. Conjugation and the class equation; conjugacy in Sn and the simplicity of An. p-groups. Orbit counting theorem and examples. Finite direct products. Sylow Theorems with proofs and applications. Non-simplicity tests and techniques for showing that certain numbers cannot be the orders of simple groups. |
Saxon Mathematics
Saxon Math is a basal math curriculum that distributes instruction, practice, and assessment of related topics over a year rather than grouping concepts into chapters or units. This distributed approach is designed to increase student understanding of mathematics concepts and promote long-term retention of skills. Teachers introduce a new concept and work examples with the class. Next, students solve problems that cover the new concept and then concentrate on problems that cover previously introduced material as well as the new concept.In this way, the Saxon math program provides for a continual flow of learning through the incremental daily introduction of new math concepts and ideas, which are then mastered through guided and individual practice.Students also benefit through the daily review of the concepts they have learned in the past, and at the same time add a new piece of knowledge to their growing storehouse of information. |
M4Maths.com
Tricks, discussion groups, short puzzles, and answers. Subscribe to receive the daily puzzle; solve it fastest for a chance to win prizes.
...more>>
Mad Maths - Philippe Chevanne
Word problems, with short solutions and "details" that reveal steps in solving number theory, logic, geometry, and more. Scripts include original JavaScript about continued fractions, Apollonius circles, Pythagorean triples, decompositions of sums of
...more>>
Mamikon - Mamikon Mnatsakanian
Thought-provoking Shockwave Flash animations of geometric constructions, graphs, games, and much more. Mnatsakanian's site links to dozens of the articles he has co-authored with Tom Apostol in journals such as American Mathematicalhematica in Higher Education - Wolfram Research
Lessons, resources, books, and classroom packs for making Mathematica software an integral part of math education in university and college classrooms. Also features Mathematica versions geared and priced for students, as well as flexible academic purchase
...more>>
Mathematical Publications - ZIB/Math-Net
A page on electronic publishing in mathematics, with sections on mathematical journals and bibliographies, separated into references to E-journals, General Journals and Bibliographies, and Subject Specific Journals and Bibliographies. Also Preprint Archives,
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Mathematica: Tour of Features - Wolfram Research, Inc.
Pages that guide you through an interactive demonstration of some of Mathematica's capabilities. New features; using the program as a calculator; power computing; accessing algorithms; building up computations; handling data; visualization; MathematicaSource - Wolfram Research
An extensive electronic library of Mathematica material and notebooks, with over 100,000 pages of immediately accessible Mathematica programs, documents, examples, and more. You may browse the archive or search by author, title, keyword, or item number.
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Math Tools Discrete Math - Math Forum
A community library of software tools for discrete math students and their teachers. Discrete Math is one section in the Math Forum's Math Tools digital library of software for computers, calculators, PDAs, and other handheld devices, with related lesson
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Matrices Help Relationships - William A. McWorter Jr.
This page uses examples to illustrate the use of matrices in solving problems of relations between variables, and continues with an "airline" problem involving networks, also solvable with matrices. The page is hosted by Alexander Bogomolny's Interactive
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Monopoly Dollars and Sense - Ivars Peterson (MathLand)
The same rules underlie all of the varied editions of Monopoly, which feature themes ranging from golf to your favorite city. It's possible to describe the game in terms of a mathematical construction called a Markov chain, named for the Russian mathematician |
Does the instruction in Mathematics
Plus provide an opportunity for students to learn the benchmark ideas and skills?
Numerous
sightings were analyzed to determine the instructional criteria ratings for Mathematics
Plus. The following chart provides a typical example of the sightings that were
analyzed to determine each criterion rating. Looking at these sightings will provide a
picture of the overall instructional guidance provided in the textbook.
The graph below depicts major strengths and weaknesses in the overall instructional
guidance provided by Mathematics Plus.It does so by showing the average
score Mathematics Plus received on each of the 24 instructional criteria, across
all six of the benchmarks used for the evaluation.
Overall, analysts rated Mathematics Plus as unsatisfactory in helping students achieve the number, geometry, and algebra benchmarks used for the evaluation. The
following describes the seven instructional categories and their criteria and summarizes
the analysts' justification for their ratings for Mathematics Plus.
Instructional Category I
Identifying a Sense of Purpose Part of planning a coherent curriculum involves deciding on its purposes
and on what learning experiences will likely contribute to achieving those purposes. Three
criteria are used to determine whether the material conveys a unit purpose and a lesson
purpose and justifies the sequence of activities.
Mathematics Plus provides a purpose at the beginning of the chapters and lessons
in the teacher's edition, implying that the teacher is to relate the purpose to the
students. The purpose of the chapters and lessons is not made explicit to the students.
The material seems to have a rationale, although it is unstated, for the overall sequence
of the lessons; the sequence reflects the stated purpose of the chapter. The format is
consistent throughout each textbook.
Instructional Category II
Building on Student Ideas about Mathematics Fostering better understanding in students requires taking time to attend
to the ideas they already have, both ideas that are incorrect and ideas that can serve as
a foundation for subsequent learning. Four criteria are used to determine whether the
material specifies prerequisite knowledge, alerts teachers to student ideas, assists
teachers in identifying student ideas, and addresses misconceptions.
There are only infrequent attempts to make the teacher aware of prerequisite knowledge
or skills. For the number and geometry skills, the prerequisite knowledge is more
apparent. Through Error Alerts, minimal support is given to help the teacher identify
students' commonly held ideas or misconceptions, but these often don't provide
sufficient explanation of the difficulty students have with understanding ideas.
Suggestions and assistance for addressing student misconceptions are in the teacher notes
section accompanying each lesson.
Instructional Category III
Engaging Students in Mathematics For students to appreciate the power of mathematics, they need to have a
sense of the range and complexity of ideas and applications that mathematics can explain
or model. Two criteria are used to determine whether the material provides a variety of
contexts and an appropriate number of firsthand experiences.
Mathematics Plus provides numerous activities that address benchmark ideas about
number and geometry and provides a variety of contexts and firsthand experiences.
Manipulative activities include drawing activities using graphing paper in the
algebra-related exercises; protractors, rulers, compasses, geoboards, and pattern blocks
are used in the geometry lessons. Some activities call for the use of a calculator or
computer for extended practice. Other than activities using graph paper, few hands-on
experiences are provided in addressing algebra graphing and equations concepts.
Instructional Category IV
Developing Mathematical Ideas Mathematics literacy requires that students see the link between concepts
and skills, see mathematics itself as logical and useful, and become skillful at using
mathematics. Six criteria are used to determine whether the material justifies the
importance of benchmark ideas, introduces terms and procedures only as needed, represents
ideas accurately, connects benchmark ideas, demonstrates/models procedures, and provides
practice.
With the exception of the criterion "justifying the importance of benchmark
ideas," the text adequately develops the mathematical ideas in the sampled
benchmarks. Mathematics Plus only implicitly communicates the importance or
validity of the mathematical concepts or skills. Terms and procedures are introduced
appropriately and with accuracy and without undue use of extraneous mathematics
vocabulary. Representation of ideas and demonstration of the use of skills and knowledge
are accurate and comprehensible. Connections are made between ideas through the use of
numerous examples and activities. Practice is present throughout the lessons including
word problems that require detailed responses that go beyond a numerical or one-word
answer.
Instructional Category V
Promoting Student Thinking about Mathematics No matter how clearly materials may present ideas, students (like all
people) will devise their own meaning, which may or may not correspond to targeted
learning goals. Students need to make their ideas and reasoning explicit and to hold them
up to scrutiny and recast them as needed. Three criteria are used to determine whether the
material encourages students to explain their reasoning, guides students in their
interpretation and reasoning, and encourages them to think about what they've
learned.
Mathematics Plus rarely encourages students to explain their reasoning. The
"What Did I Learn?" section provides questions about the lessons within the
chapter, but the students are not given the opportunity to develop their own ideas or
reflect on their understanding. They are only asked direct and mostly routine questions
about the lesson. When students are asked to express ideas, there are few opportunities
for students to receive explicit feedback on clarifications and justifications.
Instructional Category VI
Assessing Student Progress in Mathematics Assessments must address the range of skills, applications, and contexts
that reflect what students are expected to learn. This is possible only if assessment
takes place throughout instruction, not only at the end of a chapter or unit. Three
criteria are used to determine whether the material aligns assessments with the
benchmarks, assesses students through the application of benchmark ideas, and uses
embedded assessments.
The text contains numerous assessment items and tasks that are aligned and on target
with the benchmark ideas; however, assessment items that require application of benchmark
concepts and skills are not as numerous, and embedded assessment is not widely used in the
lessons.
Instructional Category VII
Enhancing the Mathematics Learning Environment Providing features that enhance the use and implementation of the textbook
for all students is important. Three criteria are used to determine whether the material
provides teacher content support, establishes a challenging classroom, and supports all
students.
A section at the end of the textbook called Alternate Teaching Strategies does not
focus on teacher content understanding that might help improve instruction or on teaching
specific benchmark ideas. The few activities that do prompt student creativity are not
consistent enough to promote a sense of exploration and individual development. The
material avoids stereotypes and contains relevant illustrations of the contributions of
women and minorities in mathematics. |
Maths Tuition
TUITION INFORMATION
Tutors 4 GCSE Mathematics Tuition
Adult Numeracy programmes are available at a number of different levels starting right at the basics running through to Level 2 (equivalent to Grade C at GCSE) so whatever your skill level, there is an Adult Numeracy programme which is right for you.
The Primary years are fundamental in the development of building blocks for all subjects, but particularly Maths and English. Children often find the regular repetition of times tables tedious and carry feelings of insecurity regarding their Maths education, well into adulthood.
Functional maths develops those practical, real life skills required in everyday situations. Problem solving skills, whilst closely related to logical mathematics skills, are different in the way they are developed.
There have been a number of changes to the GCSE Maths specifications and assessment practices over recent years, but the content and topics studied have remained fairly static.
Whether you are studying a Linear or Modular course at school at either Foundation or Higher tier, you will study: Number, Algebra, Geometry and Measure and Statistics both with and without a calculator. |
All incoming freshman: See Mrs. Sorochynskyj's site for the Algebra I summer assignment.
Algebra I
This class is the first in the sequence of college prep math courses. Algebra I is the most useful course for a college bound student as it teaches the student various approaches to problem solving. Topics include simplifying algebraic expressions by combining like terms and doing distributives, solving linear equations in 1 and 2 variables, graphing linear and non linear equations, solving systems of linear equations, solving linear and non linear inequalities, simplifying exponents using scientific notation and laws of exponents, performing operations on polynomials, factoring polynomials of degree 2 and 3, solving quadratic equations using the quadratic formula.
Prerequisite for Geometry Honors. This class is the first course in the honors curriculum. It is designed to give students a solid foundation in mathematics. Topics include operations with real numbers, simplifying algebraic expressions by combining like terms and doing distributives, solving linear equations in 1 and 2 variables, graphing linear and non linear equations and inequalities, solving systems of linear and non linear equations, simplifying exponents using scientific notation and laws of exponents, performing operations on polynomials, factoring all polynomials, solving higher order polynomial equations by factoring, solving quadratic equations using the quadratic formula. Additionally, students will be introduced to SAT questions. Methods of finding solutions will be done in conjunction with the class to improve student scores on standardized tests.
Prerequisite for the students who will take Advanced Placement Calculus in their senior year. This is a rigorous course dealing with polynomial equations, functions, domain, range, logarithms, trigonometry, continuity, limits, and derivatives. |
MATLAB and SCILAB for Economists, Scientists and Engineers
Discover the full flexibility of these powerful platforms for mathematical computation. Explore the wonderfully concise and expressive use of MATLAB's advanced language features for data mining, financial forecasting, investment management, Monte Carlo simulation, statistical testing, pixel classifiers, predator-prey, fluid flow, and various other applications. This course covers dataset structures, optimization tips, manipulations of complex datasets, and high performance benefits of distributed computing (using an example based on SCILAB's Parallel Virtual Machine). You gain a deep understanding and problem-solving experience with these powerful platforms.
Future-Term Courses and Enrollments
Courses are offered three terms per year: spring, summer, fall. Information about upcoming courses is available when enrollment opens each term. |
JUNIOR HIGH MATHEMATICS DEPARTMENT 7 MATH (STANDARD)
Contact Information
Philip Stameris
Building Department Leader, Mathematics
R.J. Grey Junior High School
16 Charter Road
Acton, MA 01720
Telephone: (978) 264-4700, x3384
E-mail: [email protected]
The Department's Educational Philosophy
The study of mathematics will enhance the ability of all students to problem solve and to reason. Through a strong standardized
departmental program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using
representations, students will develop organizational skills, self-confidence and a positive attitude toward mathematics. Our
curriculum matches that of the Massachusetts Mathematics Curriculum Framework, and we are philosophically aligned with the
National Council of Teachers of Mathematics Standards.
Guiding Principles
• All students can learn mathematics.
• Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of
understanding.
• Effective mathematics programs focus on problem solving and require teachers who have a deep knowledge of the discipline.
• Technology is an essential tool in a mathematics education, and all students should gain facility in using it where advantageous.
• All students should have a high-quality mathematics program.
• Assessment of student learning in mathematics should take many forms to inform instruction and learning.
• All students should recognize that the techniques of mathematics are reflections of its theory and structure.
• All students should gain facility in applying mathematical skills and concepts.
• All students should understand the role of inductive and deductive reasoning in mathematics and real life situations.
7 MATH (STANDARD)
Course Frequency: Full year course, five times per week
Credits Offered: None
Prerequisites: None
Background to the Curriculum
This course is now using the 2008 edition of the Glencoe Pre-Algebra text: An Integrated Transition to Algebra & Geometry by Price,
Rath, Leschensky, Malloy, and Alban. The text is supplemented with designated materials from the "Pre-Algebra with Pizzazz"
resource binder. Selected lessons in Chapters 1 through Chapter 12 are covered and address the Massachusetts State Frameworks, as
well as the 2000 edition of the National Council of Teachers of Mathematics. The course is well aligned with national and state
standards. Teachers utilize other materials to enhance and deepen the curriculum content where appropriate and make minor changes
after consultation with the BDL. Core topics that were begun in sixth grade will be expanded in order to prepare students for the
eighth-grade math courses, which begin the study of Algebra.
Core Topics/Questions/Concepts/Skills
Improve Study Skills and Organization
Tools for Algebra and Geometry
Exploring Integers
Exploring Factors and Fractions
Rationals: Patterns in Addition and Subtraction
Rationals: Patterns in Multiplication and Division
Solving Equations and Inequalities
Functions and Graphing
Ratio, Proportion, and Percent
Statistics and Probability
Applying Algebra to Geometry
Measuring Area and Volume
RJGrey (Standard Math: Grade 7) revised 2007-2008 page 2
Course-End Learning Objectives
Learning objectives Corresponding state standards, where applicable
1] Gather and record data in a frequency table 8.D.01
2] Construct and interpret bar graphs, stem and leaf plots, line plots, scatter 8.D.02
plots, and box and whisker plots
3] Use measures of central tendency to analyze data 8.D.03
4] Use tree diagrams, tables, organized lists, and the fundamental counting 8.D.04
principle to find the probability of compound independent events
5] Find missing angle measures of triangles and quadrilaterals 8.G.01
6] Identify corresponding and congruent parts of plane and solid geometric 8.G.02
figures
7] Identify points, lines, planes, rays, segments, angles, and parallel, 8.G.02
perpendicular, and skew lines
8] Classify angles, triangles, and quadrilaterals 8.G.02
9] Demonstrate an understanding of the relationships of angles formed by 8.G.03
intersecting lines, including parallel lines cut by transversal
10] Construct congruent line segments and angles with a compass and 8.G.05
straightedge
11] Investigate tessellations and identify reflections, translations, rotations, 8.G.06
and symmetric figures
12] Convert measurements within the metric system 8.M.01
13] Use ratio, proportion and percent to solve problems 8.M.03
14] Find surface areas of triangular and rectangular prisms and cylinders 8.M.03
15] Find volumes of triangular and rectangular prisms and cylinders 8.M.03
16] Find the area, perimeter, and circumference of geometric figures 8.M.03
17] Compare, order, and graph integers, fractions, and mixed numbers on a 8.N.01
number line
18] Represent numbers in scientific notation and use them in calculations and 8.N.04
problem-solving situations
19] Apply number theory concepts, including prime factorization and 8.N.05
relatively prime numbers
20] Use order of operations to evaluate numerical and algebraic expressions 8.N.07
with whole numbers, integers and rational numbers
21] Use positive powers and exponents in expressions 8.N.07
RJGrey (Standard Math: Grade 7) revised 2007-2008 page 3
22] Use commutative, associative and distributive properties to simplify 8.N.08
expressions and equations
23] Estimate sums differences, products, and quotients of rational numbers 8.N.10
24] Calculate sums, differences, products, and quotients of rational numbers 8.N.10
without a calculator
25] Identify, compare, rename, and compute using rational numbers 8.N.12
26] Identify and extend the terms of arithmetic and geometric sequences 8.P.01
27] Introduce functions and relations 8.P.01
28] Graph points and line on a coordinate plane using a table of values and 8.P.05
slope
29] Introduce slope and be able to identify positive, negative, zero, and no 8.P.05
(undefined) slope
30] Determine the slope of a line using a graph or using two points 8.P.05
31] Graph linear equations using a table of x and y values 8.P.06
32] Translate verbal phrases and sentences into algebraic expressions and 8.P.07
equations
33] Solve one- and two-step equations and inequalities using rational
numbers
34] Solve verbal problems by writing and solving equations
35] Use a variety of problem-solving techniques to solve problems
Assessment
Students are generally assessed by in-class tests and quizzes, which are administered regularly throughout a marking period.
Generally, two quizzes are equivalent to a test. Organization of a math notebook is an emphasis in this grade and is typically assessed
as a quiz grade. The students' attitude, effort, and quality of homework preparations will also impact their term grade to a small
degree. Teachers informally assess students every day by asking pivotal questions, as well as questions involving mechanics or
concepts. A standardized midyear examination and final examination are administered to all students in this course in order to assess
their long-term retention of the course material.
RJGrey (Standard Math: Grade 7) revised 2007-2008 page 4
Technology Learning Objectives Addressed in This Course
(This section is for faculty and administrative reference; students and parents may disregard.)
Course activity: skills &/or topics taught Standard(s) addressed through this activity
1] Appropriate use of a calculator in solving problems
2] Some exposure to use of computers in programs such as
Graph Action, Stock Market, Tesselmania
Materials and Resources
Teachers use other texts for supplementary ideas and more challenging examples, in addition to "Pre-Algebra with Pizzazz" puzzle
sheets. Worksheets that coordinate to each lesson are used.
RJGrey (Standard Math: Grade 7) revised 2007-2008 page 5 |
An Online Algebra Class that Guarantees Your Success In Algebra 1
An affordable online Algebra Class for students who are struggling with Algebra 1
Is this a picture of you as you sit down to complete your Algebra work? Do you feel your blood pressure start to rise even before you turn to the correct page in your book? Do you end up crumpling your paper and feel like you're about to throw your Algebra book out of the window?
If you answered "YES" to all of these questions, then join the club!
That's right - you are NOT the only one feeling this way! The number one subject in school that causes anxiety in students is Math!
It doesn't matter whether you are home schooled, attend public or private school, or whether you are attending college - the answer is always the same..... Math!
Check It Out
Who Should Take This Online Algebra Class?
This online algebra class was created with "Any" Algebra student in mind. It's perfect for the home school student who is looking for an easy to understand curriculum that allows for independent study.
It's also perfect for a middle or high school student who needs extra help with their Algebra class.
Many teachers and tutors use it for students who are falling behind in class and I also have many adults purchase the curriculum so that they can brush up on their skills before taking an introductory Algebra class in college.
How Does The Online Algebra Class Work?
You will log in to the E-course from any computer that you choose.
You will start by watching a video lesson. Each video explains the concept in "bite size pieces". Through several examples, you are guided step by step through the process.
You are also given a pre-designed "notes worksheet" to take notes on as you watch the video. In this way, you'll have notes to refer back to when completing your practice problems.
You will then have ample practice problems to complete in order to fully master each skill.
The BEST part is that you will have step-by-step solutions to every single problem! You will never have to spend time trying to figure out where you made your mistake. This allows you to learn from your mistakes and to fully understand the concept.
If you are using this online algebra class as your only curriculum (for home schooling or teaching purposes), I've also included chapter quizzes, tests, and a mid-term and final exam. (Yes - with step-by-step solutions!)
It Really Does Work...
Take a look at this email that I received from a struggling 38 year old mother of five.
Dear Karin,
I am a 38 year old mother of five who has never done mathematics in high school. I am considering a career change so I need mathematics desperately. In my attempts to learn high school maths, I had tried several programs from the internet. I had bought at least three maths programs locally.
Then I Googled something on equations and came across your web page. As I have stated earlier in the previous email, it is the best! I have not seen anything that comes close to your material. You have taken away my frustration and made learning maths very easy and fun for me.
For me, your course explains even better than one of the high school teachers whose services I had acquired to help with my studies. I literally came from one of his classes crying, thinking that I had become so dumb that I could not comprehend a thing in what he was trying to explain.
Until I used your material, I felt that mathematics was not for "dummies" like me. Since I started using your program less than 4 weeks ago, I already feel like one of the Professors in Mathematics. I am learning from home now without any maths tutor. I love maths. You are a great teacher. Thank you very much.
Regards,
Ntombifuthi
So... What Units Will You Study?
The Algebra 1 course consists of the following ten units:
Unit 1: Solving Equations
Unit 2: Graphing Equations
Unit 3: Writing Equations
Unit 4: Systems of Equations
Unit 5: Inequalities
Unit 6: Functions
Unit 7: Exponents and Monomials
Unit 8: Polynomials
Unit 9: Factoring Polynomials
Unit 10: Quadratic Equations
You'll have instant access to all ten units of the Algebra Class curriculum, plus a mid-term and final exam! Click here for more detailed information on the curriculum.
Sign up Now for only $8.99 per month OR Save 40% and Subscribe for a Whole Year for just $64.99
That's right, all you have to do is choose a username and password and you will have instant access to the entire Algebra Class curriculum! There is absolutely nothing that you have to download! It can't get much easier!
Please Note: You will not receive an actual book in the mail. This is an online course, and all materials can be saved or printed from your computer. You will access all worksheets and videos once you login to the secure online course.
A home school mom says...
Dear Karin,
I am a home school mom of five who struggled with finding a solid Algebra program for my older boys until I came upon your online algebra class. Your tutorials are straight forward and detailed.
Your assignments are designed in such a way that we can spend extra time on what my children need to and move on when they understand something more easily. I am a math-lover myself and am excited that you have finished Part 2 of this course.
My boys are understanding Algebra in a way that they never were able to with other courses due to the detail and care that are in each of your lessons. I also appreciate that you are available to answer questions.
Thank You!
Jacqui Coleman
Another Home school Parent Says...
My daughter is a ninth grade student attending a local high school in Toronto, Ontario. I am using the online Algebra Class to help her. She was not well prepared in Pre-Algebra, hence most of the subjects in Algebra 1 are new to her.
Algebra 1 is not a well taught subject. Her high school Math teacher does not use the method that you use, consequently, she is not grasping the subject matter thoroughly. Your step-by-step problem solving technique is helping her to understand the subject matter and individual topics.
My daughter comments that she likes your video presentations and wishes she could see a picture of you.
This e-course has helped my daughter to better understand Algebra in the following ways:
The topic (e.g.. Solving Equations) is explained and every detail of one step, two step, etc... is explained in such a clear manner that sometimes she stops the video to work out the problem, and then continue.
She can now distinguish between solving equations, writing equations, graphing equations, systems of equations, and word problems because of your video presentations.
In subtracting polynomials, she could not grasp it until she began to follow your Keep-Change-Change procedure.
We have used other Algebra products, but this differs because Karin is the only teacher who makes my daughter feel as if she is sitting beside the teacher.
Thank You!
Reggie Clark
Is this How You Want to Feel?
When you sign up, you'll have instant access to Algebra Class. No waiting for books to arrive in the mail.
You can sign on from anywhere that you have internet access. Use this online Algebra Class at school, work, and at home! You never have to download anything on to your computer.
Watch step-by-step videos that guide you every step of the way. You will feel confident in completing your work after truly understanding how to complete each problem.
If you have trouble staying organized or taking notes, use the notes worksheets that are pre-designed for each lesson. You'll create your own little Algebra text book that you can refer back to as you complete the program.
Use the many graphic organizers provided to help you build a solid understanding of each concept. These graphic organizers are unique to Algebra Class. You cannot find these in any text book!
Complete your practice problems with confidence knowing that you can check your work with the step by step answer key! You will never spend 20 minutes trying to figure out where you went wrong! Once you learn from your mistake, you'll never make it again!
Assess your skills throughout with the quizzes, chapter tests and exams. You will know instantly if you are on track and ready to continue making progress.
Watch your stress melt away as you go into class with confidence. No more dreading Math!!!
Have instant access to all 10 units of an Algebra 1 curriculum. Upon completion of this course, you will be ready for Algebra 2.
Every package is backed by my 60 day guarantee. I am so confident that you will find success with Algebra Class, that I will give you 60 full days to use the workbook and video tutorials. If for any reason, you are not satisfied, just contact me and I will promptly refund your money!
If you have questions regarding your Algebra Class purchase, you may contact me at: 410-937-8468 or you can contact me via email and I will respond in less than 24 hours.
Frequently Asked Questions
What if I order and for some reason it doesn't work for me? We know that everyone has different learning styles. If you feel that you are not mastering Algebra 1, simply contact me (within 60 days of signing up) and I will refund your money promptly. (I've only had one return and that was because the customer thought this curriculum covered Algebra 2.)
Will I receive the books in the mail that are shown on website? No, the books are simply a graphic. This is an E-course and all of the materials can be printed. You will login and have access to all materials. Nothing will arrive in the mail.
Can I try it out before I purchase? Yes, I have one unit that you can access for free. It's a pre-algebra refresher and it will give you an idea of how the E-course is set up. You can sign up here.
Does this program work with Mac computers? Yes, you can use a Mac computer, a PC computer, or a tablet. All videos are formatted to be viewed on all computers.
What if I'm a teacher and need multiple logins for my students?Contact me and I will give you my group rates for schools or teachers.
What if I have trouble logging on or need technical support? Simply contact me through the website and I will respond within 24 hours, usually must sooner. I can also be reached by phone at 410-937-8468.
Do I have to use Pay Pal? No, you may use pay pal or you can use your credit card. The box below the Pay Pal payment information is the link for using your credit card.
Is your payment processor secure? Yes! I use Pay Pal and it's very secure. You can verify this by checking your address bar on the payment page. It will start with https if the payment page is secure.
Can I pay by check or money order?Yes! If you are not comfortable with using your credit card or pay pal, simply contact me and I will give you an address to send the payment.
Get rid of that frustration and math anxiety today!
Create your user name and password and get started instantly!
Get Instant Access for only $8.99 per month OR Save 40% and Subscribe for a Whole Year for just $64.99 |
Course Objectives: To learn differential and the integral calculus
skills which are needed for the successful study of upper-level science,
mathematics, and engineering courses, including the ability to communicate
using the language of mathematicsCourse Format:We will have approximately, each week,three hours of lecture, one and half hours of
exercises, and one and half hours of lab (Maple).We will learn and use Maple during the lab
hours as we advance in the course.You
will be asked to continue the apprenticeship of Maple outside class hours in
order to be able to do your Maple homework.Tutoring worksheets are available with the Maple Software on all
computers in room 213 and 223, and other rooms.
Teamwork for the Maple Homework: The class will be divided into
two-person teams. In extenuating circumstances, other size teams are possible.
Generally all team members get the same homework grade, but it is possible that
a team member get an inferior grade if his participation is proven to be
inferior. Teams may be broken up and reformed at my discretion..No plagiarizing, please!
Homework: The assignments will consist of computer problems through
Maple worksheets and pencil and paper problems at the end of each section from
the textbook.. During the semester there will be six or seven computer homework
assigned which will be due about a week later.
Late homework will not ordinarily be accepted.
Speak to the instructor right away if you have some problem.Turn in your assignment through the Shared
area of the LAN under the Fadimba
directory in the subdirectory Amth141w, as explained by the instructor. Keep a
copy of your work in your ftp area in case it is lost. The format for your work
isMaple (.mws)Each notebook should begin with the names of
the team members.
Quizzes: There will be given
approximately one quiz per week.There
will be no make up for quizzes, for what ever reason.Two quizzes will be dropped at the end of the
semester before computing your final grade.
.TestsThere will be three literacy tests given
throughout the semester.Normally, there
will be no make up for tests, except under special documented
circumstances.In any case, no student
will be allowed more than one make up test. The approximate dates of the tests
are as follow:
Test 1
Week of February 11
Test 2
Week of March 17
Test 3
Week of April 14
.
Final Exam: A pencil and paper comprehensive final examination is on
Friday May 2 at 8:00 AM. The Maple part of the final exam will be given in
class prior to the end of classes. The final will be graded upon your ability
to apply the principles covered in this course.
WEIGHTS:
GRADE SCALE
1. Three exams (100 each)
90-100
A
70-74
C
2. Quizzes and Computer AlgebraNOTES: No use of cell-phones
will be allowed during an exam.Please
make sure you have turned off the cell-phones during class time.
Attendance: Class attendance is mandatory. You should consult with your
professor if you must miss a class. As many as five absences may preclude your
receiving credit for the course. In addition to scheduled class hours you will
need to spend many extra hours in the lab completing your homework assignments.
How many extra hours will vary depending upon the individuals doing the work.
Disabilities: If you have a physical, psychological, and/or learning
disability which might affect your performance in this class, please contact
the Officecopying a computer file done by others and
submitting it as your own, but also for leaving computer files on a USCA
computer's hard disk where someone else could copy it. If two very similar
computer files are submitted, both files may receive a grade of zero. Your
instructor will show you how to keep work on private LAN disk space instead of
on a desktop computer hard disk. |
Institute of Mathematics and Statistics - Software Products number of equations at their fingertips. The program is also indispensable for students and teachers. Understandable and convenient interface: A flexible work area lets you type in your equations directly. It is as simple as a regular text editor. Annotate, edit and repeat your graphings in the work area. into a text or graphic file. Comprehensive online help is easily accessed within the program. Features: -------- *Scientific graphings *Unlimited expression length *Parenthesis compatible *Scientific notation *More than 35 functions *More than 40 constants *User-friendly error messages *Simple mode (medium size on desktop) *Paste expressions into EqPlot *Online documentation *All the benefits that Windows bestows, such as multi-tasking and print formatting are available. education mathematics shareware listed in education mathematics section.
SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator. In addition to arithmetic operation, more than hundred built-in constants and functions can also be used in your expression. SimplexCalc also has the unlimited ability to extend itself by using custom (user-defined) variables. You can add your own variables for SimplexCalc in order to tackle complex problems with ease and fun. and students, financiers and other professionals. Features include: * Ease of use * Scientific calculations and unlimited expression length * Unlimited customizable variables * Parenthesis compatible and unlimited nesting for expression * Upper case and lower case can be freely used in expression * An impressive number of built-in formulas * High precision calculaton -up to 24 decimals for scientific calculations * Comprehensive help * Calculation range: - maximal positive number: 1.797E+308 - minimal positive number: 2.225E-308 * Your can do standard manipulation with "Expression" edit box such as cut, copy and paste operations. This is a shareware listed under education mathematics category.
CompactCalc is an enhanced scientific calculator for Windows with an expression editor. It embodies generic floating-point routines, hyperbolic and transcendental routines. Its underling implementation encompasses high precision, sturdiness and multi-functionality. With the brilliant designs and powerful features of CompactCalc, you can bring spectacular results to your calculating routines. CompactCalc features include the following: * You can build linear, polynomial and nonlinear equation set. You are not limited by the size or the complexity of your mathematical expressions. * Scientific calculations and unlimited expression length. * Parenthesis compatible and unlimited nesting for expression. * Accurate result display - features up to 24 digits after the decimal point for scientific calculations. * Calculation range (1.79E-308, 2.22E308). * Comprehensive help. * CompactCalc has almost hundred of physical and mathematical constants built in, which can be easily accessed and used in calculations. No longer do you have to search the physic textbook for that common physical constant data. * Possibility to enter mathematical formulas as with a keyboard as with calculator-buttons. * The interface is straightforward and very easy to navigate through. This is a shareware listed under education mathematics category and engineers the power to find the ideal model for even the most complex data, including equations that might never have been considered. You can build equation set which can include a wide array of linear and nonlinear models for any application. Its state-of-the-art data fitting includes the following capabilities: *Any user-defined equations of up to nine parameters and eight variables. *Linear equations. *Nonlinear exponential, logarithmic and power equations. *A 38-digit precision math emulator for properly fitting high order polynomials and rationals. Graphically Review Curve Fit Results: Once your data have been fit, Curvefitter automatically sorts and plots the fitted equations by the statistical criteria of Standard Error. A residual graph as well as parameter output is generated for the selected fitted equation within the Review Curve Fit window. With All This Power, it is Still Easy to Use: Curvefitter takes full advantage of the Windows user interface to simplify every aspect of operation -- from data import to output of results. Import data from many popular file formats including Excel, Lotus and ASCII. Once your data are in the editor, create a custom equation set and start the automatic fitting process with a single mouse click. Curvefitter is highly intuitive, easy-to-use and remarkably simple to learn. Regression analysis - CurveFitter license is shareware and it is listed in education mathematics software Multiple MultiplexCalc is an indispensable calculator designed for math teachers, scientists, engineers, university and college faculty and students, financiers and other professionals. Multiple help * Calculation range: (1.797E-308, 2.225E308) * High precision calculation - features up to 38 digits after the decimal point * Accurate result display - features up to 24 digits after the decimal point * Your can do standard manipulation with "Expression" edit box such as cut, copy and paste operations. This education software is listed under education mathematics.
ScienCalc is a convenient and powerful scientific calculator. ScienCalc calculates mathematical expression. It supports the common arithmetic operations (+, -, *, /) and parentheses. The program contains high-performance arithmetic, trigonometric, hyperbolic and transcendental calculation routines. All the function routines therein map directly to Intel 80387 FPU floating-point machine instructions. Find values for your equations in seconds: Scientific constants Understandable and convenient interface: A flexible work area lets you type in your equations directly. It is as simple as a regular text editor. Annotate, edit and repeat your calculations in the work area. done during a session can be viewed. Print your work for later use. Comprehensive online help is easily accessed within the program. Features: -------- *Scientific calculations *Unlimited expression length *Parenthesis compatible *Scientific notation *More than 35 functions *More than 40 constants *User-friendly error messages *Simple mode (medium size on desktop) *Paste expressions into ScienCalc *Online documentation *All the benefits that Windows bestows, such as multi-tasking and print formatting are available. This is a shareware listed under education mathematics category. |
7-8 Courses/CLE's
7-8 Courses/CLE's
ALGEGRA I (8, 9)
Algebra I is the sequential development of problem solving using our real number system. The language and symbolism of algebra becomes understandable and useful as everyday jargon for algebraic problem solving. Students will learn to solve equations as well as inequalities. Functions and relations will be discussed in relationship to ordered pairs on the Cartesian Coordinate plane. Equations of two variables, as well as polynomials and their factoring will be discussed with enough repetition for the fundamental background to encounter Algebra II. There is also a reinforcement of basic math skills, although mastery of operations with negative numbers, decimals, and fractions are necessary before beginning this course. Students will be required to bring a basic calculator. Although a scientific calculator (with sin, cos, and tan keys) is recommended. This course is the basic of all advanced math. This course is required for admissions to most colleges, and is suggested for most tech schools.
Students study the American History from the time period of the American Indians through the Reconstruction after the Civil War. Students study the Revolutionary War, the opening of the West, the Mexican War and land obtained and problems faced by our country during this time period.
Textbook: The Americans, McDougal Littell, 2005.
BAND (7, 8)
During their two years in Junior High Band, third year and level three objectives are taught as listed in instrumental curriculum guide. Competition, creativity, and self-discipline begin to become more important at this level. Enjoyment and pride are instilled from performing good music well and being able to take a few trips. Three to four concerts are performed and trips are taken when possible during Junior High Band.
EARTH SCIENCE (8) Earth Science exposes students to a variety of topics dealing with the earth and its surroundings such as astronomy, meteorology, geology, and oceanography. Earth structures are discussed including rocks, minerals, and the internal workings of our planet. The care and preservation of our planet is stressed. All students are required to develop a scientific experiment dealing with earth science related topics in which they practice using the scientific method. Textbook: Prentice Hall, 2009
ENGLISH (7) In the Seventh grade, the curriculum focuses on vocabulary and writing skills, applied grammar and literature. Literature consists of poetry, plays, short stories, and novels. The vocabulary study is taken from the literature read in class, novels, Wordskills and Mastering Spelling, which utilize weekly lessons and quizzes.
ENGLISH (8) The curriculum focuses on vocabulary, writing skills, applied grammar, and literature. Literature consists of poetry, plays, short stories, non-fiction and fiction. Emphasis is placed on reading comprehension, elements of literature, and figurative language. Vocabulary development is done weekly with word usage and weekly quizzes. Much of the curriculum is state standards assessment driven with special attention given to descriptive writing in preparation for the statewide writing assessments. Other course work involves note taking, listening, oral presentation and writing conventions.
The students study basic weather, climate, and biomes of the world. Later students are to study the landforms, agriculture, climate, resources, and minerals of the European, Asian, and African continents. Map work is incorporated into the study along with class projects.
The students have a brief review of the keyboard, the students will use the Microsoft Word program on a computer, build speed and accuracy, learn how to type letters, memos, tables, and reports (unbound).
LIFE SCIENCE (7) The main topics covered in Life Science are the human body—its systems and cell functions--and the characteristics and grouping of living things. In the study of cells, students will examine the structures and processes in the cell and relate them to everyday activities. All students will be required to develop a scientific experiment dealing with living things in which they practice using the scientific method. Textbook: Prentice Hall, 2009
PHYSICAL EDUCATION (7, 8)
Students will be involved Sports practices and in between seasons will play games of agility, possible weight training, and health topics. Sports involved are Football, Volleyball, Basketball, and Track.
PRE ALGEBRA (8, 9)
Materials needed: Scientific calculator all important Pre-Algebra concepts and skills are presented to prepare students for success in Algebra I. This rigorous course introduces variables, expressions, equations, and graphing, as well as a five-step problem-solving strategy to help students apply mathematical concepts. |
hard algebra problems and answers
I'm not understanding hard algebra problems and answers |
COURSE DESCRIPTION
Finally make sense of two fundamental branches of mathematics with this accessible and thorough two-course set delivered by ideal experts and professors.
First, imContinue learning with Algebra I, which is designed to meet the concerns of both students and their parents. These 36 accessible lectures make the concepts of first-year algebra—including variables, order of operations, and functions—easy to understand
1
of
2:
Algebra I Professor
Professor James A. Sellers,
The Pennsylvania State University Ph.D., The Pennsylvania State University Algebra I is an entirely new course designed to meet the concerns of both students and their parents. These 36 accessible lectures make the concepts of first-year algebra—including variables, order of operations, and functions—easy to grasp Lecture Titles
36
Lectures
30
minutes/lecture
1.
An Introduction to the Course
Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and operations.
19.
Factoring Trinomials
Begin to find solutions for quadratic equations, starting with the FOIL technique in reverse to find the binomial factors of a quadratic trinomial (a binomial expression consists of two terms, a trinomial of three). Professor Sellers explains the tricks of factoring such expressions, which is a process almost like solving a mystery.
2.
Order of Operations
The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply when you need to simplify algebraic expressions, making it critical to master them now.
20.
Quadratic Equations—Factoring
In some circumstances, quadratic expressions are given in a special form that allows them to be factored quickly. Focus on two such forms: perfect square trinomials and differences of two squares. Learning to recognize these cases makes factoring easy.
3.
Percents, Decimals, and Fractions
Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.
21.
Quadratic Equations—The Quadratic Formula
For those cases that defy simple factoring, the quadratic formula provides a powerful technique for solving quadratic equations. Discover that this formidable-looking expression is not as difficult as it appears and is well worth committing to memory. Also learn how to determine if a quadratic equation has no solutions.
4.
Variables and Algebraic Expressions
Advance to the next level of problem solving by using variables as the building blocks to create algebraic expressions, which are combinations of mathematical symbols that might include numbers, variables, and operation symbols. Also learn some tricks for translating the language of problems (phrases in English) into the language of math (algebraic expressions).
22.
Quadratic Equations—Completing the Square
After learning the definition of a function, investigate an additional approach to solving quadratic equations: completing the square. This technique is very useful when rewriting the equation of a quadratic function in such a way that the graph of the function is easily sketched.
5.
Operations and Expressions
Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression, making combining them relatively easy.
23.
Representations of Quadratic Functions
Drawing on your experience solving quadratic functions, analyze the parabolic shapes produced by such functions when represented on a graph. Use your algebraic skills to determine the parabola's vertex, its x and y intercepts, and whether it opens in an upward "cup" or downward in a "cap."
6.
Principles of Graphing in 2 Dimensions
Using graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane, how to choose a scale for labeling the x and y axes, and how to graph a linear equation.
24.
Quadratic Equations in the Real World
Quadratic functions often arise in real-world settings. Explore a number of problems, including calculating the maximum height of a rocket and determining how long an object dropped from a tree takes to reach the ground. Learn that in finding a solution, graphing can often help.
7.
Solving Linear Equations, Part 1
In this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step equation and gives tips for how to solve it.
25.
The Pythagorean Theorem
Because it involves terms raised to the second power, the famous Pythagorean theorem, a2 + b2 = c2, is actually a quadratic equation. Discover how techniques you have previously learned for analyzing quadratic functions can be used for solving problems involving right triangles.
8.
Solving Linear Equations, Part 2
Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every number is a solution.
26.
Polynomials of Higher Degree
Most of the expressions you've studied in the course so far have been polynomials. Learn what characterizes a polynomial and how to recognize polynomials in both algebraic functions and in graphical form. Professor Sellers defines several terms, including the degree of an equation, the leading coefficient, and the domain.
9.
Slope of a Line
Explore the concept of slope, which for a given straight line is its rate of change, defined as the rise over run. Learn the formula for calculating slope with coordinates only, and what it means to have a positive, negative, and undefined slope.
27.
Operations and Polynomials
Much of what you've learned about linear and quadratic expressions applies to adding, subtracting, multiplying, and dividing polynomials. Discover how the FOIL operation can be extended to multiplying large polynomials, and a version of long division works for dividing one polynomial by another.
10.
Graphing Linear Equations, Part 1
Use what you've learned about slope to graph linear equations in the slope-intercept form, y = mx + b, where m is the slope, and b is the y intercept. Experiment with examples in which you calculate the equation from a graph and from a table of pairs of points.
28.
Rational Expressions, Part 1
When one polynomial is divided by another, the result is called a rational function because it is the ratio of two polynomials. These functions play an important role in algebra. Learn how to add and subtract rational functions by first finding their common divisor.
11.
Graphing Linear Equations, Part 2
A more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis. Work through several examples and become comfortable determining the equation using the line and the line using the equation
29.
Rational Expressions, Part 2
Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicated-looking equations is to proceed one step at a time. Close the lesson with a problem that brings together all you've learned about rational functions.
12.
Parallel and Perpendicular Lines
Apply what you've discovered about equations of lines to two very special types of lines: parallel and perpendicular. Learn how to tell if lines are parallel or perpendicular from their equations alone, without having to see the lines themselves. Also try your hand at word problems that feature both types of lines.
30.
Graphing Rational Functions, Part 1
Examine the distinctive graphs formed by rational functions, which may form vertical or horizontal curves that aren't even connected on a graph. Learn to identify the intercepts and the vertical and horizontal asymptotes of these fascinating curves.
13.
Solving Word Problems with Linear Equations
Linear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at a linear rate?
31.
Graphing Rational Functions, Part 2
Sketch the graphs of several rational functions by first calculating the vertical and horizontal asymptotes, the x and y intercepts, and then plotting several points in the function. In the final exercise, you must simplify the expression in order to extract the needed information.
14.
Linear Equations for Real-World Data
Investigating more real-world applications of linear equations, derive the formula for converting degrees Celsius to Fahrenheit; determine the boiling point of water in Denver, Colorado; and calculate the speed of a rising balloon and the time for an elevator to descend to the ground floor.
32.
Radical Expressions
Anytime you see a root symbol—for example, the symbol for a square root—then you're dealing with what mathematicians call a radical. Learn how to simplify radical expressions and perform operations on them, such as multiplication, division, addition, and subtraction, as well as combinations of these operations.
15.
Systems of Linear Equations, Part 1
When two lines intersect, they form a system of linear equations. Discover two methods for finding a solution to such a system: by graphing and by substitution. Then try out a real-world example, involving a farmer who wants to plant different crops in different proportions.
33.
Solving Radical Equations
Discover how to solve equations that contain radical expressions. A key step is isolating the radical term and then squaring both sides. As always, it's important to check the solution by plugging it into the equation to see if it makes sense. This is especially true with radical equations, which can sometimes yield extraneous, or invalid, solutions.
16.
Systems of Linear Equations, Part 2
Expand your tools for solving systems of linear equations by exploring the method of solving by elimination. This technique allows you to eliminate one variable by performing addition, subtraction, or multiplication on both sides of an equation, allowing a straightforward solution for the remaining variable.
34.
Graphing Radical Functions
In previous lessons, you moved from linear, quadratic, and rational functions to the graphs that display them. Now do the same with radical functions. For these, it's important to pay attention to the domain of the functions to ensure that negative values are not introduced beneath the root symbol.
17.
Linear Inequalities
Shift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up frequently in business applications.
35.
Sequences and Pattern Recognition, Part 1
Pattern recognition is an important and fascinating mathematical skill. Investigate two types of number patterns: geometric sequences and arithmetic sequences. Learn how to analyze such patterns and work out a formula that predicts any term in the sequence
18.
An Introduction to Quadratic Polynomials
Transition to a more complex type of algebraic expression, which incorporates squared terms and is therefore known as quadratic. Learn how to use the FOIL method (first, outer, inner, last) to multiply linear terms to get a quadratic expression.
36.
Sequences and Pattern Recognition, Part 2
Conclude the course by examining more types of number sequences, discovering how rich and enjoyable the mathematics of pattern recognition can be. As in previous lessons, employ your reasoning skills and growing command of algebra to find order—and beauty—where once all was a confusion of numbers.
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. |
Project maths is bloody great, it's so much easier than having to learn off methods of doing stuff, you actually understand all the probability stuff. The problem here is that everyone resists any sort of change.
My biggest problem is that anyone who does project Maths now, and wants to do Maths in college hasn't a hope. Any other problem is fairly irrelevant in comparison.
What I do like is the whole idea of understanding, and the fact that, because it's so much easier than before (from what I can see so far), I actually have a chance of getting a C or D in Maths now.
Each and every one of the twenty-five extra points are also quite beautiful.
In terms of getting points it's fantastic, but if you want to be able to do Maths after school it's absolutely hopeless, but I think the old course was the same because students were rarely thought to understand the topics.
Pretty sure project maths has the exact same calculus in it as the old maths course..
Then the course has been taught wrong for the past few years. It's just worse now because project Maths seems to be easier. Either way Maths lecturers haven't too much praise for the Leaving Cert, to say the least.Not a fan of project maths at all. I'm liking the idea of 25 extra points but starting in fifth year is just a joke! Imo its not proper maths now with all the explaining and stuff. I personally don't think this was properly thought through, the book we are using wasn't even out until the middle of October! My teacher hardly understands it and is convinced that we will be moving back to the old course very soon. Anyone else confused by the little boxes we have to write in?I have always found that the best engineers, programmers and scientists are generally not the ones who got A1's in exams but the ones who can interface between the non-techies, understand what they want, and implement it.
In the real world, you will need to be able to talk to people who waffle on forever about what they want but can't describe it in any meaningful technical sense. So Project Maths sounds to me more like the real world than the fantasy academic world.
I did a Maths degree with pass Maths for the LC, as did a few of my college buddies - and outperformed a lot of my honours Maths classmates. So there must be something wrong with the old LC.
Edit: On second thoughts the major problem with LC Maths - at least in my day - were:
1. Bad teachers
2. Bad textbooks with examples for the easiest 1 or 2 problems and then 40 much harder problems with new concepts thrown in and not explained. |
Precalculus Essentials, CourseSmart eTextbook Essentials' table of contents is based on learning objectives and condensed to cover only the essential topics needed to be successful in calculus. Using the text with MyMathLab, students now have access to even more tools to help them be successful including "just-in-time" review of prerequisite topics right when they need it.
This text offers a fast pace and includes more rigorous topics ideal for students heading into calculus.
Table of Contents
P. Basic Concepts of Algebra
P.1 The Real Numbers; Integer Exponents
P.2 Radicals and Rational Exponents
P.3 Solving Equations
P.4 Inequalities
P.5 Complex Numbers
1. Graphs and Functions
1.1 Graphs of Equations
1.2 Lines
1.3 Functions
1.4 A Library of Functions
1.5 Transformations of Functions
1.6 Combining Functions; Composite Functions
1.7 Inverse Functions
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Exercises for Calculus
Chapter 1 Practice Test A
Chapter 1 Practice Test B
2. Polynomial and Rational Functions
2.1 Quadratic Functions
2.2 Polynomial Functions
2.3 Dividing Polynomials and the Rational Zeros Test
2.4 Zeros of a Polynomial Function
2.5 Rational Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Exercises for Calculus
Chapter 2 Practice Test A
Chapter 2 Practice Test B
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Rules of Logarithms
3.4 Exponential and Logarithmic Equations and Inequalities
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Exercises for Calculus
Chapter 3 Practice Test A
Chapter 3 Practice Test B
4. Trigonometric Functions
4.1 Angles and Their Measure
4.2 The Unit Circle; Trigonometric Functions
4.3 Graphs of the Sine and Cosine Functions
4.4 Graphs of the Other Trigonometric Functions
4.5 Inverse Trigonometric Functions
4.6 Right-Triangle Trigonometry
4.7 Trigonometric Identities
4.8 Sum and Difference Formulas
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Exercises for Calculus
Chapter 4 Practice Test A
Chapter 4 Practice Test B
5. Applications of Trigonometric Functions
5.1 The Law of Sines and the Law of Cosines
5.2 Areas of Polygons Using Trigonometry
5.3 Polar Coordinates
5.4 Parametric Equations
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Exercises for Calculus
Chapter 5 Practice Test A
Chapter 5 Practice Test B
6. Further Topics in Algebra
6.1 Sequences and Series
6.2 Arithmetic Sequences; Partial Sums
6.3 Geometric Sequences and Series
6.4 Systems of Equations in Two Variables
6.5 Partial-Fraction Decomposition
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Exercises for Calculus
Chapter 6 Practice Test A
Chapter 6 Practice Test B
Appendix: Answers to Practice |
This whole series of books is very popular among homeschoolers. It works especially well for the student who is coming out of a school situation and needs work on foundational math. It also works well for the student who is intimidated by Saxon or other texts.
Sets include answer keys. You can also order the books without answer keys if you already have the answer keys. |
(8-10) D. Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.
Patterns, Functions and Algebra Standard
(8-10) D. Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. |
Query by Black Dash: Why do we have to have to understand sophisticated mathematics?
It truly is so pointless and it have nothing at all to do with potential, these kinds of as employment and carrer, why would we have to understand innovative math, like Calculus? If you want to turn out to be engineer, I recognize, but most people won't… Why do we have to discover superior math? -_-
I do. I currently take Pre-Calculus and I will not see why we are required to discover those things.
Had you ever resolve calculus troubles in your positions? I don't assume so.
If no a single can solution my question, then my question having been answered. Advanced math is virtually pointless…
Concern by Bth: What would I discover in a rules of arithmetic class?
Is it math concept? Do you actually find out math? I'm baffled.
Here's the training course description:
"Supposed to satisfy common transfer or degree requirements in fields other than mathematics, physical science, and engineering conceptual treatment of quantity concept, contemporary algebra, geometry, fundamentals of logic and sets, and other matters." |
This course provides a review
of fundamental concepts of geometry and an investigation of their significance
in teaching of secondary school mathematics. Concepts to be analyzed include: logic, proof, and axiomatic
systems; physical and geometric models; sets, relations, and transformations;
non-metric and metric concepts; and coordination of spaces. Attention is given to: historical
considerations bearing on the teaching of geometry; integration of geometry
with algebra and science; and significant literature on the subject. This course requires evidence that the
student can make effective use of these concepts in the classroom.
Course Goals
Students
will:
·
Use
basic concepts of geometry to solve a variety of geometry problems.
·
Examine
the significance of fundamental concepts of geometry in the teaching of secondary
school mathematics.
·
Develop
geometric proofs within the context of a specific axiomatic system.
· Examine the
role of axiomatics in secondary school geometry.
·
Identify
geometrical and algebraic relationships.
·
Examine
the interaction of algebra and geometry in the curricula for secondary school
geometry.
·
Create
and present a geometry lesson or lesson plan that effectively uses concepts
learned in the course.
Course Requirements
Your grade will be based on:
3 quizzes
A midterm
A final exam
Weekly assignments (computer labs and special assignments)
A final project
consisting of the preparation and presentation (written and oral) of a lesson
plan or lesson in geometry
There will also be weekly
ungraded homework assignments. Tests and quizzes will be based on these
assignments, plus whatever is covered in class.
If you are absent on the date
of a test or quiz, you must contact the instructor
immediately to explain why you were absent and to request
permission to make up the test or quiz.
This permission is not automatic; you must present the instructor with a
valid excuse for your absence and, in some cases, appropriate
documentation. Do NOT wait until
the class meets again to contact the instructor—send an email or call and leave
a voice mail if necessary.
Late Work Policy
The instructor reserves the
right to refuse any work that is submitted late. If late work is accepted, points may be deducted for
lateness. |
Offers an approach to introductory analysis with a constructive approach as opposed to the classical approach. There is no comparable book on the market.
Constructivism proves a chain of results and shows, ultimately, that the quantity can be constructed. This approach is gaining appreciation as an increasingly large number of computer science and related fields are encouraging a real analysis course for students.
Provides a unique look at the construction of real numbers as "consistent and fine families of rational intervals"
Includes hundreds of examples throughout the book, in all ranges of difficulty and length
Supplemented by a related web site that contains summaries of results with linked commentaries and references. Also includes links to web sites containing supplementary material and historical background.
Authored with a friendly voice, the book encourages and helps readers to conquer difficult points. |
Galvin Physics mastering reading comprehension, we learn to identify the main elements of story, talk about the story problems and how they get resolved, and draw conclusions. Predicting outcomes, talking about cause and effect relationships, and writing our own stories is part of the fun. Learning to use
...I use the book Algebra and Trigonometry with Analytic Geometry, by Swokowski and Cole, 10th edition. This is a college level book and I am confident it will help with learning the concepts of the course. High school algebra 2 requires students to dig deeper than the basic principles introduced ... |
Materials
Text The text book will be Precalculus by Stitz and Zeager. This
is an excellent, free book avalaible via a
Creative Commons
license. You can download the entire book for free from the
Stitz-Zeager website and you can purchase the first half of the book from
Lulu for $16. Here are direct links to the PDF
and Lulu pages:
Technology A graphing calculator is nice to have, but not a necessity
for this class. Some quizzes and some exams will require a simple (or better)
calculator. We'll have a few quizzes where calculators are not permitted.
Advice
Learning mathematics I expect that you wouldn't be in calculus
if you didn't already know that
mathematical study is a challenging, yet worthwhile endeavor. Mathematics
is the most natural language with which we describe the world around us and,
I believe, this this helps us better comprehend and enjoy the world.
However, understanding this deep language has a price - it's hard and takes
loads of work! I suggest that you spend at least 1.5 hours between classes
and at least 3 hours over the weekend studying each math class. Remember
that college is a full time job!
The Typical Week Typically, Monday and Wednesday will be
devoted to lecture over new material. I will assign a bit of homework
both of these days and you should do it as soon as you can. Thursdays
will usually be devoted to problem sessions. After I briefly answer a
couple of questions, you will work on a problem sheet in groups. This
is a great opportunity for you to learn material and to get feedback.
Furthermore, quizzes, (typically on Friday) will take problems right
off of these sheets.
Exam Week The exams are all on Friday. Problems will
be taken from homework, in class sheets, and a small collection of
review problems. We will typically review on the day before the
exam.
Help You are not undertaking this challenging task alone. Here
are a few sources of assistance.
Me I like to talk to people about mathematics! That's why I
chose this profession. Please feel free to approach me any
time you have questions.
Your classmates Most people learn mathematics best by talking it
through with others. You will find that you can both learn from and help
your fellow classmates. In particular, if your classmate is explaining a fine
point to you, then you are helping them!
The Math Lab We all know the Math Lab rocks! It's open long hours
and is located right across the hall from my office. You will welcome there and
will definitely find people to talk to about mathematics.
Grading
Exams There will be three exams during the term worth about 100
points apiece. The tentative dates for those exams are Friday February 3,
Friday March 2, and Friday April 6. There will be a comprehensive final exam worth
around 150 points on Friday April 27 at 8:00 AM for the early section and at 11:30 AM
for the later section.
Quizzes There will be quizzes worth 10 to 20 points
apiece almost every Friday.
In class work We will work problem sheets together most Thursdays.
You will earn a class participation grade of up to 40 points for this work.
Homework Homework will be assigned daily but not generally
collected. You will not be able to do well in the class without
doing the homework.
Final Grades I will determine final grades using
a scale not more stringent than the standard 90-80-70-60 scale.
You will be apprised of your standing as the term
progresses.
Late Work In general, I do not accept late work. I
understand, of course, that emergencies do arise. If so, please
contact me as soon as possible.
Cheating I trust students implicitly. I give take home exams
(in proof based courses)
and frequently leave the room during in class quizzes and exams. I
won't watch you like a hawk. However, it is surprisingly evident to
most instructors when cheating has occurred. I take cheating very
seriously, as I believe it undermines the objectives of academia and
the casual atmosphere I attempt to instill. If I have reason to
believe that cheating has occurred, I will not hesitate to inform the
provost and assign the offender a failing grade for the class. In
blatant or repeat offenses, my recommendation to the provost will be
dismissal from the university. Note that in the vast majority of
incidents of academic dishonesty, the potential rewards are very small
and the potential penalties are very high. |
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Courses
Course Details
MATH 034A Basic Mathematics and Study Skills
4
hours lecture,
4
units
Letter Grade or Pass/No Pass Option
Description: This course is an introduction to fundamental concepts of arithmetic. Emphasis is placed on
addition, subtraction, multiplication, division and exponentiation on whole numbers, fractions, and decimals. Topics also include simple percents and ratios, systems of measurement, and applications of these topics. Students learn basic study skills necessary for success in mathematics courses. This course is intended for students preparing for Prealgebra. |
Are
you ready for Calculus? This is a short pre-test
to see if you have the algebra skills needed for calculus. Some of the
material will be reviewed in class.
Algebra & Trigonometry web site that accompanies a book
we use to teach Math 150 and Math 151 (which are the prerequisites for this course). Select the chapter for the
area you're having difficulty with and try some of the "warm
up" exercises and quizzes for practice.
To check your algebra
skills, you can attempt practice test and quizzes taken from
the text book used in MATH 150, College Algebra and MATH 151, Pre-calculus.
The first
6 chapters relate to college algebra, with trigonometry covered in the later chapters. You can jump to each chapter
by clicking on the link below. |
Introduction to Reasoning and Proof Prek - 2
9780325011158
ISBN:
032501115X
Pub Date: 2007 Publisher: Heinemann
Summary: "In Introduction to Reasoning and Proof, Karren Shultz-Ferrell, Brenda Hammond, and Josepha Robles familiarize you with ways to help students explore their reasoning and support their mathematical thinking. They offer an array of entry points for understanding, planning, and teaching, including strategies for encouraging children to describe their reasoning about mathematical activities and methods for questioning st...udents about their conclusions and their thought processes in ways that help support classroom-wide learning."--BOOK JACKET.[read more] |
Articles of Interest
Culver Students Discover Math by Nick Counts
"All truths are easy to understand once they are discovered; the point is to discover them." - Galileo Galilei
Although I have not been at Culver very long, I know that the mathematics department has been built upon greatness. The names of Al Donnely, Ray Jurgensen, and many other pioneers who came before us still echo through the Dicke Hall of Mathematics.
In the fall of 2004, Culver math instructors made a very positive move by instituting a progressive discovery-based curricula for all Algebra 1 and Algebra 2 courses. During the 2003-2004 school year, discovery-based textbooks were researched and selected. Jerald Murdock, an author of Discovering Algebra and Discovering Advanced Algebra, the books chosen for Algebra 1 and Algebra 2, was brought to campus to lead everyone through the transition that would soon be occurring. Although this was not an easy transition, it was one filled with excitement as teachers learned how to lead students through investigations by using use motion detectors, temperature probes, and other new devices. These investigations now allow our students to discover algebraic fundamentals while enhancing their critical thinking and problem solving skills.
Change is tough for the students. The new curricula was met with a fair amount of classroom grumbling. The students are now expected to understand and justify what they are doing in their guided investigations. Many of my students have stated- "This is a lot harder than the other math classes I've taken." Students are no longer passive learners, but now take center stage. In a typical class period, the students are split up into groups of two or three, and they are given an investigation that has a series of steps they need to research and answer cooperatively. The investigation usually begins with some sort of an introduction or a hook that gets the students interested and gives them a foundation for the investigation. The groups are then set free to explore the questions that are posed to them in the investigation, while the teacher circulates through the classroom making sure that students are discovering the points they need to. The lesson is then completed by having a classroom discussion (usually led by one of the groups) to summarize findings.
This process gets to the core of the issue of what math really is. Although it is important for our students to be able to solve a variety of algebraic problems and demonstrate the same skills that we have expected of our students in the past, math is so much more. It is a problem solving process, a way of thinking, and an approach to learning. Learning this process is something that will benefit our students in any field they pursue.
As we build new math programs, the Culver mathematics department endeavors to keep our feet planted firmly in our rich history while we look forward to curricular developments in the future. |
Enough math in my physics program?
Enough math in my physics program?
Greetings, everyone!Thanks!
My advice regarding extra mathematics as a physics major is only take it for its own sake, not for its application to physics. The mathematics courses outside those required for the physics major are likely very abstract by comparison, and I can almost guarantee you will find little to no use for them in your coursework. This isn't to say that it isn't useful, but just that its use is above that of the standard undergraduate physics curriculum, and even most graduate work. So if you go into it expecting to enhance your comprehension of physics, you'll likely be disappointed. |
Description of Algebra Basics BB Set by TREND enterprises, Inc.
Colorful examples and clear definitions make it easy to introduce key algebra concepts: Vocabulary, Properties, How to Solve An Equation, Order of Operations, Graphing, and Formulas. 7 pieces, up to 23" wide. |
Book Description: Matrix Algebra is a vital tool for mathematics in the social sciences, and yet many social scientists have only a rudimentary grasp of it. This volume serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. Namboodiri's presentation is smooth and readable: it begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors -- supplying illustrations through fully-worked examples.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it |
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Beginning Algebra With Applications - 7th edition
Summary: Intended for developmental math courses in beginning ...show moreproblem areas, and, overall, promoting student success.
New! Interactive Exercises appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles.
New! Think About It Exercises are conceptual in nature and appear near the end of an objective's exercise set. They ask the students to think about the objective's concepts, make generalizations, and apply them to more abstract problems. The focus is on mental mathematics, not calculation or computation, and help students synthesize concepts.
New! Important Points have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently.
New! A Concepts of Geometry section has been added to Chapter 1.
New! Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction
New! A Complex Numbers section has been added to Chapter 11, "Quadratic Equations."
New Media! Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool7.488.078.07 +$3.99 s/h
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Bringing a new vitality to college mathematics
In our Mathematical Literacy course, we are working through concepts from a numeric point of view with less emphasis on algebraic (symbolic) statements. This weeks' content dealt with ratios, scaling rates up or down, linear rate of change and exponential rate of change. Our work might indicate what our students are capable of, in a general way.
This course is 'at the same level' as beginning algebra, which means that we share prerequisite settings for math, reading, and writing; the students are similar, in many ways, to a typical beginning algebra class. The Math Lit class also has a few students who did not meet all three prerequisites (due to some system problems at the college).
It's true that students struggled at times in class. One of those struggles dealt with language processing; we are using nutrition labels as a context for working on rates and scaling. When students needed to read specific questions and then extract information from the label, most students did not see what they should do. This is not a matter of mathematical ability or skills; in fact, students who have passed our beginning algebra class often exhibit the same pattern when I see them in the applications course (Math – Applications for Living). A few students are having trouble with the scaling ideas, which is a non-standard approach; however, since they usually know an alternate method this is not a big issue.
Although I have not done an individual assessment yet, students did not seem to have any trouble with the concepts of linear and of exponential change. We did numeric examples in two settings, and I observed groups and individuals — no issues spotted. Most students are having difficulty connecting a situation to a symbolic model — both linear and exponential. In the case of linear, we did "the salary is increased by 5%" … all of them could calculate the result for a given salary, but few of them could make the transition to the symbolic model (new = 1.05S). The same kind of thing happened with exponential models. Since we are not emphasizing symbolic work (yet!), this gap is not a big problem (yet!).
I've dealt with exactly the same issue in the Applications course (symbolic models for linear and exponential change), and observed the same proportion of students having difficulty. The traditional beginning algebra course has an insignificant impact on students' abilities to write symbolic models for situations — except when the correct key words are used in the problem. If the problem is stated in a way that "normal" people talk every day, students can not make the connection to symbolic forms (in general).
In some ways, this was a discouraging week. The difficulty with language is very frustrating; my judgment is that students (and people in general) are far less skilled with the written word than in prior decades. Basic verbal skills like parsing and paraphrasing are not normally seen. The transition to symbolic forms seems like such a small step, so that difficulty is troubling to a mathematician. Our course is designed to build these skills over the course by visiting similar ideas from different points of view; I can hope it gets better! However, I find it encouraging that these students — even the ones who lack all the prerequisites — are having no more difficulty than students who passed our beginning algebra course.
This Math Lit course is a good class for a mathematician to teach; we deal with basic ideas in detail and work on transfer of knowledge, with an emphasis on problem solving (as opposed to exercises and repetition). In that work in-depth, we can see where students really do not get the idea and work on creating better mathematical knowledge.
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It does get better. These students often struggle with reading comprehension. I've had students who took trig and calculus in high school, yet place into this class and be challenged. And they are surprised! But there is a big difference in doing algebra and doing mathematics. What is exciting is that the students will grow over the semester and have insights that will surprise you. And they will be able to judge a linear situation over an exponential one, something I rarely see a student in any STEM course do easily. |
This book is based on an honors Calculus course given in the 1960s. The book contains more material than was normally covered in any one year. It can be used (with omissions) for a year's course in Advanced Calculus, or as a text for a 3-semester introduction to analysis. There are exercises spread throughout the book [via]
How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic. [via]
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
Whether you're brushing up on pre-Algebra concepts or on your way toward mastering algebraic fractions, factoring, and functions, CliffsQuickReview Algebra I can help. This guide introduces each topic, defines key terms, and carefully walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as
Equations, ratios, and proportions
Inequalities, graphing, and absolute value
Coordinate Geometry
Roots and radicals
Quadratic equations
CliffsQuickReview Algebra I acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review you decide what works best with your needs. Here are just a few ways you can search for topics:
Use the free Pocket Guide full of essential information
Get a glimpse of what you'll.
With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades. [via] main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle.
With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory.
Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences.
The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the secondA fast-reference source for advanced high school and college math students. Also useful to professionals who use math on the job. Approximately 700 math terms are defined. Includes illustrative diagramsChinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of schooling.
Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.
This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.
The studies described in this book suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students, continues to grow throughout their professional lives.
Teaching conditions in the United States, unlike those in China, militate against the development of elementary teachers' mathematical knowledge and its organization for teaching. The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics. [via]
More editions of Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States:Graduate school marks the first step toward a career in mathematics for young mathematicians. During this period, they make important decisions which will affect the rest of their careers. Here now is a detailed guide to help students navigate graduate school and the years that follow.
In his inimitable and forthright style, Steven Krantz addresses the major issues of graduate school, including choosing a program, passing the qualifying exams, finding an advisor, writing a thesis, and getting that first job. As with his earlier guide, How to Teach Mathematics, he avoids generalities, giving clear advice on how to handle real situations. The book also contains a description of the basic elements of a mathematical education, as well as a glossary and appendices on the structure of a typical department and university and the standard academic ranks.
Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published 130 research articles and 45 books. He has worked in many different types of mathematics departments, supervised both masters and doctoral students, and is currently the Chair of the Mathematics Department at Washington University in St. Louis. [via]
More editions of A Mathematician's Survival Guide: Graduate School and Early Career Development pressureInspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this expanded edition, the author takes a new generation of readers on a mathematical journey into the world of polyominoes, incorporating important recent developments. Deceptively simple, polyominoes are a collection of squares joined together along their edges. But how many different polyominoes can you make with 5 squares, 6 squares, n squares? Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop an understanding of their extraordinary properties. In this new edition, he addresses the properties of octominoes and enneominoes and the problem of how to cover a doughnut with polyominoes. An extensive bibliography has been included to guide the reader to other interesting mathematical conundrums and to more advanced mathematical theories of polyominoes. [via]
More editions of Polyominoes: Puzzles, Patterns, Problems, and Packings:
"The evolution of science, philosophy, and mathematics, all related, is far more important to the history of humanity than a parade of rulers and a procession of wars." Strong words, but Richard Mankiewicz comes mighty close to backing them up in his fascinating book, The Story of Mathematics.
Divided into brief chapters, the book traces the development of mathematics from a baboon's fibula with 29 clearly visible notches (from Swaziland, circa 35,000 B.C.) to the Babylonian sexagesimal--or base 60--number system, which survives to this day in our method of timekeeping, to Euclid's Elements, described as "the most important textbook of all time," to fractals and other Mandelbrot sets. Along the way, Mankiewicz pays tribute to the men and women at the forefront of mathematics, though he's not afraid to dispel some myths: the Pythagorean theorem was widely known in antiquity before Pythagoras was even born, and a 14th-century Chinese manuscript clearly depicts what is now known as "Pascal's Triangle," a good three centuries before Pascal was born. Most entertaining are the chapters on practical applications of mathematics: astronomy, codemaking and -breaking, military strategy, modern art, and navigation.
At times, it is difficult to follow the actual complex mathematics, but the vast majority of the book is readily accessible to the general reader. Filled with beautiful illustrations taken from ancient papyri, medieval manuscripts, scientific instruments, Renaissance painting, and computer-generated art, The Story of Mathematics is a singularly handsome volume and a pleasure to read. --Sunny Delaney[via]
This concise "Teach Yourself" text provides a thorough, practical grounding in the fundamental principles of trigonometry, which any reader can apply to his or her own field. The text explores the use of calculators and contains worked examples and exercises (with answers) within each chapter. [via]
"Remarkable...It will surely remain the unique reference in this area for many years to come." Roger Penrose , Nature "...an outstanding achievement in mathematical education." Bulletin of The London Mathematical Society "I am enormously impressed...Will be the definitive reference on tiling theory for many decades. Not only does the book bring together older results that have not been brought together before, but it contains a wealth of new material...I know of no comparable book." Martin Gardner [via]
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods. |
While we understand printed pages are helpful to our users, this limitation is necessary
to help protect our publishers' copyrighted material and prevent its unlawful distribution.
We are sorry for any inconvenience.
The Elements of a Theory and a Report on the Teaching
of General Mathematical Problem-Solving Skills1
Alan H. Schoenfeld
INTRODUCTION
Can students be taught general strategies that truly enhance their abilities to
solve mathematical problems? Or are the heuristics described by Polya and
others merely a description of the actions of accomplished problem solvers? Are
they essentially valueless as prescriptions for problem solving? While many
mathematicians are convinced that they employ heuristics, there is little evidence that general problem-solving skills can be taught.I offered a course based on the applications of heuristics to mathematics majors at the University of California, Berkeley. This article presents the rationale
for heuristics and notes some questions about their effectiveness in the teaching
of problem solving. I offer some suggestions regarding these questions, and
describe the course I used to implement these suggestions. I discuss what we can
and cannot expect students to assimilate--heuristics they can learn to use and
obstacles that prevent them from employing others effectively.
SECTION 1. Problem Solving in Perspective: Theory and Practice
George Polya How to Solve It was published in 1945. That and his subsequent work laid the foundations for the study of general strategies for problem
solving in mathematics, focusing on the broad strategies he called "heuristics."
Definitions vary, but the following is compatible with Polya's usage:
A heuristic is a general suggestion or strategy, independent of subject matter,
that helps problem solvers approach, understand, and/or efficiently marshal
their resources in solving problems.
Examples of heuristics are: "draw a diagram if possible," "try to establish
subgoals," and "exploit analogous problems"; a more complete list is given in Section 3. A rationale for the study and teaching of heuristics is the following:
1.
Through the course of his career, a problem solver develops an idiosyncratic
style and method of problem solving. A systematic use of these strategies
may take years to develop fully.
2.
In spite of these idiosyncracies, there is a surprising degree of homogeneity in
the approaches of expert problem solvers. |
2nd Millennium Invisible Calculator 3.1 description
2nd Millennium Invisible Calculator allows you to make calculations in any place where it is possible to enter expressions (e.g. text editor, lines of input, etc.).
After
The calculator is able to count arithmetic expressions with brackets, trigonometrical functions, logarithms, exhibitors, roots etc. |
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. It analyzes the idea of a generalized limit and explains sequences and functions to those for whom intuition cannot suffice. ... read more
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Calculus: A Short Course by Michael C. Gemignani Geared toward undergraduate business and social science students, this text focuses on sets, functions, and graphs; limits and continuity; special functions; the derivative; the definite integral; and functions of several variables. 1972 edition. Includes 142 figuresMathematical Fallacies and Paradoxes by Bryan Bunch Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition Red Book of Mathematical Problems by Kenneth S. Williams, Kenneth Hardy Handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition.
Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.
Challenging Problems in Geometry by Alfred S. Posamentier, Charles T. Salkind Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and more. Arranged in order of difficulty. Detailed solutionsProduct Description:
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. It analyzes the idea of a generalized limit and explains sequences and functions to those for whom intuition cannot suffice. Many exercises with solutions. 1966 |
0201699516
9780201699517 real world.The goal is to achieve the optimum balance between presenting a thorough development of mathematical content and presenting it in a way that is understandable by students. The material has been revised so that it powerfully embodies the new Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics. «Show less... Show more»
Rent Mathematics for Elementary School Teachers 2nd Edition today, or search our site for other O'Daffer |
Binghamton ACTOne of the great things about math is that there is minimal memorizing involved, just understanding. Once you understand a concept, you are golden! I give my students the support they need to reach that point.Algebra 1 generally includes introductory topics such as equations, graphing and order of operations. |
Mathematics in Non-Math Courses
In introductory courses such as chemistry, economics, political
science, and psychology, you will often see discussions of examples
and topics that require an understanding of concepts in mathematics
such as algebra. The examples below are taken directly from different
economics textbooks and they demonstrate the kinds of skills that
you will be required to use in many non-math introductory courses.
Example
Production costs are
divided into fixed costs and variable costs. All production costs
fall within these two categories, so total costs (TC)
equal total fixed costs (TFC) plus total variable costs
(TVC), or
The example above demonstrates the use of basic algebra skills
in economics. Without the ability to substitute values for the
variables, or the ability to evaluate this equation, there would
be no meaning to this paragraph or equation.
Below is a more complex linear equation that relates the yield
of lumber to maintenance of land. |
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic, by Bender
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
This text serves as an introduction to the programming language Java for scientists and engineers, as well as experienced programmers wishing to learn Java as an additional language. The authors have ... |
Instructions for Submitted Work
When
preparing solutions for marking please note the following points.
Not attempting a solution is generally unacceptable.
Set out your solution as a coherent narrative explaining any
principles used. The final solution should be underlined, or a
reasonable gap left in the text so the end of the question is obvious.
In general solve problems algebraically before inserting values.
In multiple part questions, identify all the answers being asked for
and present a solution that answers them all. Counting the things asked
for in a problem, and matching this to the number of underlined results
in your manuscript, can ensure this.
Do not use different notation from that used in the question. Define
any new variables you introduce.
Write legibly. If you struggle to do this in first draft then rewrite
your solutions when complete.
Solutions should be presented on 1 side of the paper and stapled at
the top left hand corner (or otherwise held together).
Obeying these rules is good practice and will pay off in exams.
Scripts that fail to respect these rules will be returned to be rewritten. |
The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrate...
For departments of computer science offering Sophomore through Junior-level courses in Algorithms or Design and Analysis of Algorithms. This is an introductory-level algorithm text. It includes worked-out examples and detailed proofs. Presents Algorithms by type rather than application.
Designed for use in a variety of courses including Information Visualization, Human—Computer Interaction, Graph Algorithms, Computational Geometry, and Graph Drawing. This book describes fundamental algorithmic techniques for constructing drawings of graphs. Suitable as either a textbook ... |
Constructing and Exploring Composition of Functions with Sketchpad (Intermediate/Advanced)
Composition is hard for students—but the multiple representations shown in this webinar will get them over the rough spots and help them to generalize and master the concept of composition. We'll compose functions both geometrically and symbolically, find the links between different representations, and put the behavior of the variables front and center. We'll show, and make available to attendees, composition activities that are accessible to early-algebra middle-school students and activities that will give high school algebra and pre-calc students new insights. The function dance activities from this webinar (in which the dependent variable dances with the independent variable) are likely to become a favorite for students at all levels.
Presenter
Scott Steketee taught secondary math and computer science in Philadelphia for 18 years and received the district's Teacher of Excellence award. Since 1992 he has worked on Sketchpad software, curriculum, and professional development for Key Curriculum and KCP Technologies. He also teaches Secondary Math Methods in the graduate teacher education program at the University of Pennsylvania. |
Mathematics
The vision of the mathematics standards is focused on achieving one crucial goal:
To enable ALL of New Jersey's children to acquire the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives.
Perhaps the most compelling reason for this vision is that all of our children, as well as our state and our nation, will be better served by higher expectations, by curricula that go far beyond basic skills and include a variety of mathematical models, and by programs which devote a greater percentage of instructional time to problem-solving and active learning.
The sequential nature of mathematics requires attention to proper placement. Decisions will be based on student aptitude and demonstrated performance. A detailed analysis of the department's procedures for placement is available from the department supervisor or the school counselor. All courses are closely aligned with the Common Core State Standards for Mathematics.
The Mathematics Department offers the opportunity for a student to learn different programming languages while at Livingston High School. The Computer Programming course introduces students to JAVA and Alice. The Programming for Problem Solving and Computer Science Seminar courses, offered in alternate years, use JAVA to solve technical application problems and to create programs and graphic displays. The AP Computer Science course further explores JAVA.
There are two statistics electives: Statistics CP and AP Statistics. Both courses are taught using the combined technology of the graphing calculator and FATHOM computer software. Interested students may double in a statistics elective along with Pre-Calculus or Calculus. |
Description
For freshman/sophomore, 1- or 2-semester/2—3 quarter courses covering finite mathematics for students in business, economics, social sciences, or life sciences departments.
This accessible text is designed to help students help themselves excel in the course. The content is organized into two parts: (1) A Library of Elementary Functions (Chapters 1—2) and (2) Finite Mathematics (Chapters 3—11). The book's overall approach, refined by the authors' experience with large sections of college freshmen, addresses the challenges of teaching and learning when students' prerequisite knowledge varies greatly. Student-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for today's students and instructors.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Part One: A Library of Elementary Functions
Chapter 1: Linear Equations and Graphs
1-1 Linear Equations and Inequalities
1-2 Graphs and Lines
1-3 Linear Regression
Chapter 1 Review
Review Exercise
Chapter 2: Functions and Graphs
2-1 Functions
2-2 Elementary Functions: Graphs and Transformations
2-3 Quadratic Functions
2-4 Polynomial and Rational Functions
2-5 Exponential Functions
2-6 Logarithmic Functions
Chapter 2 Review
Review Exercise
Part Two: Finite Mathematics
Chapter 3: Mathematics of Finance
3-1 Simple Interest
3-2 Compound and Continuous Compound Interest
3-3 Future Value of an Annuity; Sinking Funds
3-4 Present Value of an Annuity; Amortization
Chapter 3 Review
Review Exercise
Chapter 4: Systems of Linear Equations; Matrices
4-1 Review: Systems of Linear Equations in Two Variables
4-2 Systems of Linear Equations and Augmented Matrices
4-3 Gauss-Jordan Elimination
4-4 Matrices: Basic Operations
4-5 Inverse of a Square Matrix
4-6 Matrix Equations and Systems of Linear Equations
4-7 Leontief Input-Output Analysis
Chapter 4 Review
Review Exercise
Chapter 5: Linear Inequalities and Linear Programming
5-1 Inequalities in Two Variables
5-2 Systems of Linear Inequalities in Two Variables
5-3 Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Review
Review Exercise
Chapter 6: Linear Programming: Simplex Method
6-1 A Geometric Introduction to the Simplex Method
6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≥
6-3 The Dual; Minimization with Problem Constraints of the form ≥
6-4 Maximization and Minimization with Mixed Problem Constraints
Chapter 6 Review
Review Exercise
Chapter 7: Logic, Sets, and Counting
7-1 Logic
7-2 Sets
7-3 Basic Counting Principles
7-4 Permutations and Combinations
Chapter 7 Review
Review Exercise
Chapter 8: Probability
8-1 Sample Spaces, Events, and Probability
8-2 Union, Intersection, and Complement of Events; Odds
8-3 Conditional Probability, Intersection, and Independence
8-4 Bayes' Formula
8-5 Random Variables, Probability Distribution, and Expected Value
Chapter 8 Review
Review Exercise
Chapter 9: Markov Chains
9-1 Properties of Markov Chains
9-2 Regular Markov Chains
9-3 Absorbing Markov Chains
Chapter 9 Review
Review Exercise
Chapter 10: Games and Decisions
10-1 Strictly Determined Games
10-2 Mixed Strategy Games
10-3 Linear Programming and 2 x 2 Games--Geometric Approach
10-4 Linear Programming and m x n Games--Simplex Method and the Dual
Chapter 10 Review
Review Exercise
Chapter 11: Data Description and Probability Distributions
11-1 Graphing Data
11-2 Measures of Central Tendency
11-3 Measures of Dispersion
11-4 Bernoulli Trials and Binomial Distributions
11-5 Normal Distributions
Chapter 11 Review
Review Exercise
Appendixes
Appendix A: Basic Algebra Review
Self-Test on Basic Algebra
A-1 Algebra and Real Numbers
A-2 Operations on Polynomials
A-3 Factoring Polynomials
A-4 Operations on Rational Expressions
A-5 Integer Exponents and Scientific Notation
A-6 Rational Exponents and Radicals
A-7 Quadratic Equations
Appendix B: Special Topics
B-1 Sequences, Series, and Summation Notation
B-2 Arithmetic and Geometric Sequences
B-3 Binomial Theorem
Appendix C: Tables
Table I Area Under the Standard Normal Curve
Table II Basic Geometric Formulas
Answers
Index
Applications Index
A Library of Elementary Functions |
Search Course Communities:
Course Communities
Lesson 32: Properties of Logarithms
Course Topic(s):
Developmental Math | Logarithms
The properties of logarithms are presented after the corresponding laws for exponents are reviewed. Various exercises in simplifying logarithmic expressions are provided before solving logarithmic and exponential equations is introduced. The lesson ends with an application problem and a few exercises in solving formulas. |
Mathematics is a subject that entails counting, computing and calculating of numbers and at times even variables. Earlier, abacus was used by man for the purpose of mastering the skill of counting but with the passage of time more sophisticated calculators were developed. Thanks to technological advancement now there are various types of electronic calculators which are available for purchase, a percentage calculator being one of them. These calculators can be extremely handy in many situations. For instance, if you had to calculate some percentages then it is advisable to use a percent calculator.
Using the technology of a percentage calculator or any other kind of calculator for that matter has its own advantages and disadvantages. Calculators are considered as a normal tool these days, which can prove to be indispensable at times. There are two kinds of calculators: handheld calculators and online versions and an example of the latter would be the percent calculator. Online calculators are different from handheld calculators in the sense that they are far more superior because they provide a lot more functions. Some of these net calculators can even plot an equation into a graphical form.
Popular math calculators such as the percent calculator or other types of calculators are used by people from different walks of life such as technicians, students, engineers and teachers. Online calculators, including the percentage calculator, equip the user with a superior understanding of mathematical operations. These calculators assist them in the process of verifying their knowledge of mathematical formulae and theory. With the help of such a tool, they will be able to visualize a possible value of an unknown answer. Technicians and engineers rely on online calculators heavily because their line of work calls for the use of such devices.
A lot of people have prejudices against mathematics and they are just scared of what the subject entails. On the contrary, mathematics is a subject that is very logical and unless the individual understands the logic behind it, he/she would always find it hard to figure things out. Online calculators like percentage calculator can remove some of the prejudices against mathematics to a certain extent. If you are wondering how a percent calculator or any calculator can help one understand mathematics, then the answer lies in the tendency of such calculators to provide explanations to its workings.
In order to understand how such calculators can help you understand math, make use of a high quality and ultra efficient percentage calculator. This can easily be located online in various websites and you just have to ensure that the option which you have chosen provides explanation of how the answer or solution was obtained. Now use the percent calculator to solve a sum that you do not understand. Once you verify the accuracy of the answer, you can then access the explanation part and see the step-by-step instructions on how the answer was calculated.
If you combine online calculators with online self-tutor resources then you will get the ultimate "dream team" to help you combat all your math problems. Using an online percent calculator is not at all difficult – you just have to enter some information from the sum that you are looking to solve. After this, you just have to click on a mouse button and the percentage calculator would do all the hard work for you and display the answer on your computer screen. So the next time when you are having difficulty with your mathematics homework or anything related to mathematics then make use of free online calculators as these magnify the beauty of mathematics.
Given the rising popularity of the Internet it is but natural for people to shift to an online percentage calculator to assist them in their work. Amongst the many advantages of a percent calculator one of the foremost is its convenience which adds to the fun of solving |
Mathcad - a software tool to perform various mathematical and engineering calculations, which provides the user with tools for working with formulas, numbers, graphics and text. Also present in the assembly videokurs «MathCad 14." |
Griffin, GA CalRadicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals. Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials |
Click on the links below to access the extensive collection of educational materials in our library.
These materials are designed to aid your learning in Mathematics, English and Science. There are study guides, exam tips, common mistakes students make and more...
Please note that these are only supplementary materials. Students still need to study their textbooks and course notes. |
Polar to cartesian
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b
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Graph C correct
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In American mathematics
education, precalculus
(or Algebra 3 in some
areas), an advanced
form of secondary school
algebra, is a
foundational mathematical
discipline. It is also called
Introduction to Analysis.
In many schools,
precalculus is actually
two separate courses:
Algebra and
Trigonometry.
Precalculus prepares
students for calculus the
same way as pre-
algebra prepares
students for Algebra I.
While pre-algebra
teaches students many
different fundamental
algebra topics,
precalculus does not
involve calculus, but
explores topics that will
be applied in calculus. It
often involves covering
algebraic topics that
might not have been
given attention in earlier
algebra courses. Some
precalculus courses
might differ with others
in terms of content. For
example, an honors
level course might spend
more time on conic
sections, vectors, and
other topics needed for
calculus. A college
prepatory class might
focus on topics used in
business-related
careers, such as
matrices, or power
functions. |
COLLEGE ALGEBRA >CUSTOM<
Book Description: New Features
* Objective Based Learning: Introductory section objectives have been expanded to include the "what and why" of the objectives, followed by icons within the text identifying the specific areas of focus. A summary of chapter objectives will now be featured in the chapter summary material.
* Mathematical Modeling and Data Analysis: A focus on mathematical modeling and data analysis, specifically establishing a step by step process for understanding word problems and gathering the data from said problems.
* Graphical Interpretation:
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it |
The Fundamental Theorem of Algebra
The Fundamental Theorem of AlgebraI think that by asking these types of questions you will help yourself to understand complex concepts intuitively. So keep it up.
The quadratic formula gives us the real and complex roots of a 2nd degree polynomial. We can not use it to solve higher degree polynomials.
Sometimes the quadratic will just give us one answer for x. This is a case where we have found a root with multiplicity 2. This concept is a bit tough to explain. Here is a link to give an exact definition. See if you can understand it: Wikipedia.
Complex analysis will certainly help, but I think the real meat and potatoes is in a general field of mathematics that some people refer to as Abstract Algebra.
The Fundamental Theorem of Algebra
Quote by V0ODO0CH1LD
Thanks! Would you say I should learn complex analysis first or abstract algebra? Or are the two unrelated enough that it won't matter?
The two have small intersection at the introductory level. Neither are prerequisites for the other. But I have found that there are junior level complex analysis classes, while algebra does not come till senior level.
The two have small intersection at the introductory level. Neither are prerequisites for the other. But I have found that there are junior level complex analysis classes, while algebra does not come till senior levelRight, since complex analysis is not considered on the main track, some people take algebra without ever having taken complex analysis. There is some flexibility in paths through a math department.
For instance, a computer scientist might conceivably take algebra (maybe combinatorics is even more likely) but not complex analysis, while the the closely related field of electrical engineering might use more from complex analysis.There's a formula for 2nd degree equations -- quadratics. There's a formula for third-degree equations (cubics). There's a formula for fourth degree equations (quartics). But there is NO general formula for solving 5th degree equations or higher.
To learn about that, you'd study abstract algebra.
What you'd learn from complex analysis is a proof that every polynomial of degree n has n complex roots. But there are other proofs that don't explicitly use complex analysis. But from complex analysis you'd understand why the n roots of the polynomial zn = 1 are the vertices of a regular n-gon in the plane -- a very cool fact indeed.
So it sounds like you'd be more interested in abstract algebra if you want to learn about formulas for finding roots; and complex analysis if you're interested in the roots in general.
Here's a fascinating article about the beautiful images you get when you plot all the roots of various classes of polynomials. |
Precalculus is a preparatory course for calculus and covers the following topics: algebraic, exponential, logarithmic, trigonometric equations and inverse trigonometric identities. Prerequisite: Grade of b or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam. G.E.
Prerequisite(s) / Corequisite(s):
Grade of B or higher in MATH 150, or a score of 24 or above on the math portion of the ACT or 540 or above SAT score or a passing score on the Columbia College math placement exam.
Course Rotation for Day Program:
Offered Fall and Spring.
Text(s):
Most current editions of the following:
Most current editions of the following:
Trigonometry
By Stewart, Redlin, & Watson (Brooks-Cole) Recommended
Precalculus
By Blitzer, R. (Prentice Hall) Recommended
Course Objectives
To demonstrate fundamental technical skills and clear understanding of the basic concepts of algebraic and transcendental functions.
To solve real-world problems using algebraic and transcendental functions.
To identify connections between mathematics and other disciplines.
To use appropriate technology to enhance their mathematical understanding and to solve real-world problems.
Measurable Learning Outcomes:
• Determine if a relation is a function. • Identify the domain and range of a function. • Use the graph of a function to identify characteristics of the function such as symmetry and intervals of increasing, decreasing, and constant behavior. • Recognize graphs of common functions and graph transformations of these common functions. • Combine functions arithmetically and through composition and identify the domain of the resulting functions. • Describe and explain the fundamental concepts associated with inverse functions, including the definition of one-to-one functions and the graphical interpretation of inverses. • Define, evaluate and graph trigonometric functions • Define, evaluate and graph inverse trigonometric functions. • Solve rational and polynomial equations including those with complex numbers. *Solve simple problems using the Law of Sine and the Law of Cosines to compute angle measures and side lengths of triangles. *Know the basic trigonometric identities, addition formulas, double- angle formulas, and half-angle formulas for the sine and cosine functions. *Solve basic trigonometric equations. *Simplify exponential and logarithmic expressions and solve exponential and logarithmic equations. *Solve applied problems using exponential and logarithmic functions |
Specification
Aims
To introduce students to representations of groups over the
field of complex numbers.
Brief Description of the unit
In the second and third year course units on group theory we have
seen that abstract groups are quite complicated objects. One of the most fruitful
approaches to studying these objects is to embed them into groups of matrices (to
"represent" the elements of an abstract group by matrices). The advantage of
this approach lies in the fact that matrices are concrete objects, and explicit
calculations can easily be performed. Even more importantly, the powerful methods of
linear algebra can be applied to matrices. The course is devoted to representations of
finite groups by matrices with entries in the field of complex numbers.
Learning Outcomes
On successful completion of this course unit students will
know the basic properties of complex
representations of finite groups and be able to use them in examples;
understand the relationship between a representation and its character;
know the basic properties of characters and use them in examples;
know the basic properties of a character table and be able to calculate character tables for certain small
groups. |
Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning. |
Short Description for Advancing Maths for AQA: Statistics 2 (S2) Statistics 2 was written to provide thorough preparation for the revised 2004 specification. Based on the first editions, this series helps you to prepare for the new exams. Full description
Full description for Advancing Maths for AQA: Statistics 2 (S2)
Thorough revision for the AQA exams These brand new revision guides contain all the help, guidance and support students need in the run-up to the 2005 exams, ensuring they achieve the grades they deserve. The familiar format helps to trigger students' memories, making revision easier. Key point summaries at the start of each chapter focus students' minds on what they need to know for the exam. Worked examples with examiners' hints ensure students are following the best practice and approach for answering questions successfully. Practice questions, including a test-yourself section that references the main textbooks, encourage independent revision. Written by a Senior Examining Team to make sure students get the most beneficial advice on tackling their exams. Revision exercises and an exam-style paper give essential preparation for the AQA exams. |
The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol.
For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.
Readership
Mathematics graduate students and faculty.
Reviews
"Gives a highly readable introduction into class field theory ... clearly written and may be recommended to everybody interested in the subject."
-- Zentralblatt MATH
"Provides a quick and self-contained introduction to the subject using only limited mathematical tools, hence it is accessible to a broader audience than most of the other texts on this topic." |
Foothill-De Anza Community College District
Community Education - Short Courses
Medical Math
Master medical calculations in an engaging environment! In these fun and practical lessons, you'll gain the medical math skills you need for anything from calculating dosages to using scientific formulas. Whatever medical field you're in, the hands-on activities in this course will help you perform day-to-day math tasks quickly and easily.
First, you'll brush up your basic math skills. You'll begin with a review of fractions, decimals, and percentages, and then dive into measurement systems and conversions used in the medical field.
Next, you'll do dosage calculations for oral, parenteral, and intravenous medications. You'll explore three different methods you can use for dosage calculations: proportions, dimensional analysis, and the formula method. You'll also learn an easy formula that you can apply to many dosage calculations.
Finally, you'll get an introduction to basic statistics and probability. You'll find out how to interpret the latest medical findings for your patients, and journal articles will no longer be a mystery!
Whether you're new to the field of medicine or want to enhance your skills, this is the course for you. By the time you finish these lessons, you'll have a solid grounding in basic medical math, and you'll be ready to tackle any calculation confidently |
Mathematical Mnemonics
Albert
Einstein, who fancied himself as a violinist, was rehearsing
a Haydn string quartet. When he failed for the fourth time to
get his entry in the second movement, the cellist looked up and
said, "The problem with you, Albert, is that you simply
can't count."
"Do
not worry about your problems with mathematics, I assure you
mine are far greater." A. Einstein
Calculus overview:
Calculus was developed
by both Leibnitz and Newton as a way of getting information from
graphs that stalled conventional mathematics. Calculus has two
forms: Integration and Differentiation. Basically, differentiation
reduces data to its essentials; integration enhances information
to create new products. Differentiation will reduce a 2-dimensional
plot to a 1-dimensional line whose length and slope reveal performance
data. Integration is used to estimate what data will arise when
a 2-dimensional graph is enhanced to 3-dimensions, or what volume
will result when rotated about its x-axis or y-axis.
For example, using a
graph plotting distance against time, differentiation will find
instantaneous velocity, point of maximum or minimum velocity.
Integration will find total distance covered.
Natural Logarithms and
trig functions and identities seem to give the most pain to students.
I think that is because while the basic trig functions can be
sketched on a graph paper, the concept of multiplying and dividing
trig functions seems ridiculous. Nevertheless, it is possible
and it is logical (well, from a mathematician's perspective anyway).
To visualize these functions, try downloading or buying graphing
software such as Equation
Grapher.
Trig Identities
tan = sin/cos (tanning at sun/coast)
sec = 1/cos (my secretary has one
over my cousin)
csc = 1/sin (my cousin's secretary
has won over sin)
cot = cos/sin (I find cotton is cozier
to wear over synthetics)
tan = sin/cos. A well-tanned-but-horny-and-cheap
man, pondering whether to pay for a hooker or save money, chooses
SIN OVER COST.
Trig Function in the
Unit Circle
The sign of a trig function
can easily be calculated by knowing that sin=y
and cos=x, and that all sine is positive in the
top half of the circle, all cosine is positive on the right half
of the circle, and that sin + cos combine to define
all trig functions. For example, the upper left quadrant has
sine + and cos -, so only sine and cosecant are positive. In
the lower left of the circle, both sine and cosine are negative
and -- because two negatives make a positive -- cos/sin (cot)
and sin/cos (tan) are positive.
Here are a few mnemonics
to help recall the trig values which are positive in the quadrants
of the unit circle. Starting from the upper right, we have All
Sinning Czechs are on Tan Cots with Costly Secrets, and All
Sing Christmas Carols wearing Tan Cottons with Cozy Secretaries.
I know the x-axis is related to cosine, and the y-axis is related
to sine by thinking of Cossacks in Sinai.(cos-x, sin-y)
Table of Trig Identities
This table shows trig
functions in the centre (center to Americans) column are
differentiated to the left, and integrated to the right. Notice
the integration process always adds the Constant. The
reason for the C is that when a function is differentiated,
the Constant is lost, and when the process is reversed, it must
come back somehow. So to compensate for any lost numbers, always
include the C, even if C = zero.
Differentiated
1
-sin x
cos x
sec2x
-csc2x
sec x tan x
-csc x cot x
Function
x
cos x
sin x
tan x
cot x
sec x
csc x
Integrated
Trig Derivatives in
a Secluded Cottage
How about a mnemonic
for the trig derivatives? Try: Scot's cozy sinner of a secretary
squarely and secretly co-seeks a cot. Sexy and tanned, cozy secluded
cottage, casual sexual contact twice. The functions are,
in order: derivative of sin = cos, cos =-sin, tan = sec squared,
sec = sec tan, csc = -csc cot, cot = -csc squared. Notice that
all of the co-functions have a negative value. Trying to get
a mnemonic phrase to help recall all of these is difficult; I
usually end up with confusing sentence fragments of secret tanning
spots and cosy secretaries. Personally, I remember tanning
on sun coast as the primary mnemonic, and memorize or know
how to calculate the rest of them.
Graphing Functions
in the Kingdom
The procedure for graphing
a function is long, but worthwhile. The steps should be done
in sequence, and this is where a lot of students get mixed up.
Briefly, the steps include: find the domain of the function,
the xy intercepts, the asymptotes, the symmetry, and the
first and second derivatives. To help remember the steps (which
can have different terms for the same step) I came up with a
story which applies memory pegs, and
a single sentence based on sex (mneumonic). I couldn't make an
acronym work for this one. First, the story:
In the DOMAIN
of Calculus the Difficult, the King (who leads a graphic lifestyle)
drives a Jensen INTERCEPTOR and greets people with "HA,
VA!". The citizenry are mostly inbred and regard people
having ASYMMETRICAL faces as odd. The King TOOK THE
PRIME Minister and taught him the CRITICALPOINTS
of running a government. It seems the economy was RISING and
FALLING relative to MAXwell House coffee and MINIMUM
wage. He took a SECOND PRIME Minister who had two CONCubines,
one of whom was born on the CUSP between Leo and Virgo.
Of course, "taking
the Prime" is another way of saying "finding the derivative",
and we find the critical points by examining the derivatives
of the function. HA and VA are the horizontal and vertical asymptotes.
The second prime tells us if the curve is concave up or concave
down, and the cusp. The first derivative indicates any maxima
or minima.
The single sentence
mnemonic: Does Intercourse in a Horizontal position Simply
Drive Critics of Up and Down to take a Second look at Concubines?
Easy to recall now??
Limits -- A Parable
Imagine an action movie
actor who must run down a path dodging bullets, bombs, and debris.
To make the action look real, the director has to have the projectiles
come as close to the actor as possible without touching him,
for as soon as the position of the bullet equals the position
of actor, he dies and the whole process halts. Similarly, in
calculus, the Limit x --> 0 expression means that the
value for the denominator can come as close to zero as possible
without actually being zero and killing the equation. Just as
the movie director overcomes this problem by manipulating the
images so the action appears real but the actor lives, the math
student manipulates the factors to remove the formula killer
and to see what happens at that point. Usually, this involves
finding the zero factor hiding in the denominator and removing
it so we can see what happens when x = 0. We can:
factor when we see
a perfect square or cube in the denominator
multiply by conjugate
when we have a root in the denominator
divide by highest exponent
when Limit --> infinity
My prof used to say
"This formula has a disease which makes it unable to
function. Mathematicians are surgeons who must find this disease
and remove it by cutting away misleading fat and tissue. The
disease is a zero virus which is always taking new shape and
hiding better." This is illustrated below, where you
can see a straight substitution of x=2 will result in
zero/zero. This zero virus is cured by a
dose of factoring medicine to make the function healthy.
Applications
of Calculus
Most problems in calculus
can be solved surprisingly easy -- if you follow the techniques.
I solve most calculus problems by taking 4 or 5 steps from this
list: find domain, find critical values, find formula, take the
derivative / anti-derivative, plug in the values, plot on a number
line, check your answer against the question, check your answer
against the domain, and factor the numerator and denominator.
In addition to these
nine, here are some sub-steps you may have to invoke to smooth
over bumps in the calculation process: simplify, use the quadratic
formula, factor top and bottom to remove common factors from
the numerator and denominator, know when to apply the Chain Rule,
U-substitution, look for horizontal or vertical asymptotes, find
where f'=0, find where f''=0, know the trig identities,
know how to factor the difference of squares/cubes, remember
to use absolute values, and did I mention Simplify?
Oil Spill Problem
Sometimes a story is
better way of remembering the procedure for solving a problem
in math. Here is the famous Oil Spill Rate problem paraphrased.
I saw a BSA motorcycle
parked outside of the Pies Are Square Bakery and Computer
Shoppe. As usual, there was a lot of oil leaking from the
motorcycle and I saw the puddle's radius was increasing at a
constant rate. Inside, the clerk greets me. "I'll take the
PRIME of your PIE selection, the RADIUS
monitor, and I want to see your RATES." I asked the man
with SQUAREFEET for the time. He replied in seconds.
At that moment, the oil spill stopped.
The steps: sketch, find
the two relevant formulae and merge them, simplify with respect
to the variable, differentiate and solve for radius.
Newton's Dirty Quotient
Finding the slope of
the tangent line gives us rise/run, a relationship used heavily
in physics. When used with Limit h--> 0 it gives us
instantaneous velocity. Here's a cute story to help remember
this formula:
I was working on MY
TAN when I saw this gorgeous woman jogging. Yes, I got a RISE
over her RUN and felt embarrassed, so I used NEWTON's Cream to
"relieve my sexual anxiety". Time was running out as
it APPROACHED THE ZERO hour, but I found the VELOCITY of my hand
was part of the solution.
Power Rule
The power rule is a
shortcut to finding the derivative of X. Instead of applying
Newton's Quotient, simply multiply the factor of X by the exponent,
then subtract 1 from that exponent.
Understanding Differentiation
Observe the animation
just above. See how the area of a square equals the square of
x? Now double the area, and the length of the side increases
by only the square root of two. Increase area to three times
the original size, and the length of a side increases by only
the square root of three, and so on. Differentiation (and its
reversed cousin, Integration) are based upon this phenomenon.
Thus, differentiation allows you to calculate the changing area
with respect to the changing sides of a square. This applies
not only to squares, but to rectangles, triangles, cones, spheres,
or just about all geometric figures.
Global Min/Max
Finding minima/maxima
of a curve is a technique with many practical applications, including
cost analysis, finding the most efficient way of building something,
or even streamlining a process.
One application of
the min/max problem is to calculate the maximum volume of a box
made from a sheet of paper from which the four corners are excised
and the sides folded. Let the dimensions of the paper be 5 by
3 feet, and the size of the corner we cut be x. Obviously,
if x=0, the volume is zero because we still have a flat
piece of paper. And if the 2 corners are just as big as the width
of the paper, then we're back to zero volume. Therefore, a graph
showing volume versus x will peak somewhere between 0
and 1.5 feet. The four steps to find where the graph peaks are:
FORMULA, DOMAIN, DERIVATIVE, MAXIMUM.
Formula: l x w x
h is not 3 x 5 x X, for the length is 5-2x;
width is 3-2x; and height is x. Volume is (5-2x)
(3-2x) x.
Find the domain by
finding the critical points of the volume formula, that is, when
3-2x=0, when 5-2x=0, and when x=0. The domain
is (1.5, 2.5, 0). Remove 2.5 from the list, as the domain ends
when we reach 1.5.
You must multiply out
the volume formula before taking the derivative. (5-2x)(3-2x)x
= 15x-16x2=4x3. The derivative is 15-32x+12x squared.
To find the critical
points, we usually factor the formula to make it easy. In this
case, there is no clear factor so we apply the quadratic formula.
Remember: a=12, b=32, c=15. The quadratic
gives two solutions: approximately 2.06 and 0.61. Which one falls
within the domain? The solution: maximum volume is achieved when
x = 0.61 feet.
Note: in math we are exact, but
in this case I rounded the solutions because exponents and roots
are awkward in html, and when we are dealing with scissors on
paper, we can only be accurate to a few thousandths of an inch
anyway. If you'd like to graph a related rate formula easily,
try the Markus Friberg Equation
Grapher. I used it to make the GIF image at the top of the
page. There may be some free math software available at Simtel.
I'm currently investigating more downloads from RocketDownload,
another good source of software evaluations.
The most basic steps
are: reduce all factors to variables of x, simplify
the expression as much as possible, find critical values
from the derivative, plug the critical values into the formula,
and decide if the solutions are maxima or minima.
Often, the quadratic formula will be used to find solutions.
These steps are intersperse in the following little story.
The Australian Director
Steve Miller, head of GLOBAL Productions, and an expert
in the DOMAIN of desert action films, REDUCES all
cinema plots to VARIATIONS ON SEX. His SIMPLEFORMULA
of lustful PRIME ministers DRIVEN by mathematics
have made him VALUED by CRITICS from the Daily
DERIVATIVE newspaper. These RECALCITRANT reviewers
either love him to the MAX, or MINIMIZE his accomplishments.
Sometimes, their reviews would QUADRUPLE ticket sales.
The Director established
a domain, reduced factors to x, simplified the formula,
derived a prime, found the critical values, recalculated the
simplified formula, and used the results to define the global
max or min. Sometimes the quadratic formula is used.
Integration
Integration is essentially
the reverse of differentiation. Whereas differentiation is useful
for reducing a curve to a tangent line, integration expands the
curve to the area under the line. To integrate x, simply
add 1 to the exponent, then divide by the new exponent. If you
are having difficulty solving integration problems, go to The Integrator, a web page
that will solve the problem for you.
Area between two lines
Calculating the area
between two curves on a graph is straightforward. The theory
is that if you can use integration to find the area under a curve,
then the area between two curves is found by subtracting the
smaller area from the larger. The steps:
Find the start and
finish points / upper and lower limits by finding where the two
curves intersect. Simply let (curve 1) = (curve 2), or (curve
1 - curve 2) = zero. If they don't cross, then use the start
/ end points. Write these points on the integration symbol as
shown below.
If working from the
x-axis [i.e., if your formulae are y=f(x)], find the upper
curve. If you are working from the y-axis, find the right-hand
curve. If you aren't sure which curve is what, simply replace
x by a number from the domain. The formula with the larger
answer is the upper or right hand curve.
Write the formula and
solve. Note that you solve by splitting the formula into four
parts: [(anti-derivative of upper curve evaluating b)
- (anti-derivative of upper curve evaluating a)] minus
[(anti-derivative of lower curve evaluating b) - (anti-derivative
of lower curve evaluating a)] = Area between the two curves
between endpoints.
NOTE: some curves cross the axes
in such as way as to lead the calculation to create a negative
area. In such a case, divide the problem into two: one part for
the upper side of the x-axis, and second part to calculate the
area below the x-axis.
Area of the surface
of a cone
We know it's easy to
find the area of the surface of a cylinder, well how about the
area of the surface of a truncated cone? Well, we find the surface
area of a standard cone by multiplying the circumference by height:
A = (pi)(diameter)(height). In calculus, we would see this as
the area between two curves. Looking at it another way, this
conic slice illustrated is what is left after a small cone is
subtracted from a larger cone. This is calculus-speak for finding
the difference between the upper and lower cones, and written
as: Area = Integral of 2(pi)(y)[square root (1+(dy/dx)2]
dx, where radius is dy, and height is not
necessarily dx so we used that larger factor instead to
represent the change in height. Solve as above, by plugging in
values for a,b (upper and lower limits) and radius for
dy.
Gravity and
Acceleration Problems
Upward motion of a
projectile
This is a classic. A
projectile is launched from a base in Jugoslavia 150 meters above
the Adriatic sea level with an initial velocity of 50 meters
per second. Find the maximum height, how long it will take to
reach max height, how long it will take to hit the ocean surface,
and at what speed will it be traveling at impact. (assume the
Patriot missiles are malfunctioning that day and all motions
are due to gravity)
Assume gravity is constant
and there is no wind resistance. Measurements are in meters and
seconds. The two formulae to use are shown here, where g
= 9.8 m/sec; v = velocity; s = position; t
= time; -4.9 is one half of the gravity constant (the negative
value indicates the direction of the gravity force. For this
argument, we say moving upward is positive acceleration, falling
to the earth is negative acceleration). Follow these four steps
in order, as the result of each step is used in the subsequent
calculation.
4 steps:
As the projectile rises,
its initial velocity is eroded by gravity at the rate of 9.8
meters/second2. When the cumulative effect of gravity
is equal to the initial velocity, we have reached the maximum
height and the velocity is zero. Calculate: (initial velocity)
= (gravity)(time), 50 = 9.8(t), t = 50/9.8, t = 5.1 seconds.
Now that we know it
takes 5.1 seconds to reach the apex, plug 5.1 into the next formula
to find height. Max height is reached when s(t) = 0, that is
the projectile's position is zero. In this case, s(t)
= -4.9(5.1)2 + (50)(5.1) + (150) = 277.55 meters.
Now that we know its
height above sea level, we can calculate its drop to the water.
Time to impact is determined by the gravity constant and the
distance the object falls. Solving -4.9(t)2 + 0(t)
+ 277.55, (t)2 = 277/4.9, t = 7.5 seconds to impact.
Now we can use this result to solve the other formula and find
impact velocity.
The only difficulty
I've had with this is getting the steps in the right order. I
overcame it by writing a paragraph on how each step is calculated
and why. Good luck!
Solving a Problem
of Varying Salt Concentration using
Saltwater dilution
problem
Problem:
A pipe is supplying 4 pounds of salt per gallon of water to a barrel at a rate of 2 gallons per minute.
The barrel originally held 25 pounds of salt dissolved in
50 gallons of water.
The barrel is losing 2 gallons of brine per minute through
a drain. Calculate how much salt will be in the barrel after
25 minutes.
This type of problem is suitable for integration
by calculus because the salt concentration changes with time
and volume. On a graph, we see the original salt concentration
(25/50, or 0.5) changes quickly at first, then levels off as
it nears the concentration of the inflow (4 pounds per gallon).
The curve is similar to a Michelson-Menton curve (resembling
a quarter ellipse) where the initial rate (slope) is very steep
but the curve flattens more and more slowly as the slope approaches
zero. Thus, the change in salt concentration is not linear and
so requires integration techniques to solve the area under the
curve. The general formula we use is derived from (rate
= inflow - outflow) and written as [dy/dt + p(x)y = q(x)], where:
dy/dt = change in salt concentration over
time
p(x) = outflow of salt solution, or p(x)
= (pounds of salt/gallons of water in the barrel)•(gallons
per minute drained from barrel)
y = pounds of salt
y(t) = pounds of salt at some point in
time
t = time
The key an easy solution is use something
called integration factor (IF). The integration factor
we use is designated IF in the general formula and is
used to remove a lot of ugly terms. The IF is the number e
with an exponent equal to the integral of p(x):
Create an integrating factor: integrate
1/25and make it an exponent of e. et/25 is added to the formula to enable us
to solve it by integration. This factor emerges unchanged by
integration process.
Divide both sides by et/25. This removes the integration factor
but adds e-t/25
to the Constant. Note: when you divide C by et/25, the result is Ce with a
negative exponent.
Solve for t = 0, y = 25. These are the
initial conditions of the water in the barrel and will solve
for C. In other words, 25 = 200 - C because when t = 0, et/25 becomes e0/25 which equals one. C = 25 - 200, C =
-175.
Rewrite the original formula using the
value for C. y = 200 - 175e-t/25.
Note the negative exponent.
To find the amount of salt (y) after 25minutes
(t), plug in the values and use a calculator to solve. You should
have 25 = 200 - 175e-25/25,
or y = 200 - 175e-1,
which is approximately 136 pounds. Would you like to see The Graph?
Radioactive
Decay
Radioactive decay occurs when an atom of
an unstable isotope emits particles. The time it takes for half
of the atoms to decay is called the "half-life" of
that element. The half life of carbon-14 is 5750 years, which
makes it an excellent clue to the age of organic materials between
1,000 and 10,000 years old. The radioactive carbon is formed
in the upper atmosphere from nitrogen, and combined with oxygen
to make carbon dioxide. This radioactive carbon dioxide is absorbed
by plants, which are eaten by herbivores, which in turn are devoured
by carnivores. That is how the carbon-14 enters our bodies.
Problem
A bone is tested and discovered to have
a ratio of carbon-14 to carbon-12 that is 60% that of a modern
bone. Using calculus, estimate the age of the bone, assuming
carbon-14 levels have remained steady for the past 10,000 years.
Solution
Use two formula to solve this problem:
the first formula generates the decay constant, k; the second
formula gives us the age and mass of carbon-14.
k = (-1/t) ln2, where t = half-life of
element and the natural log of 2 is about 0.69. In the case of
carbon-14, k = (-1/5750)(0.69) = -0.0002.
Age of the sample is related to the initial
mass and ekt, or (remaining mass) = (initial mass)(ekt).
Mass is 0.6; k = -0.0002; so 0.6 = (1.0)e-0.0002(t).
ln 0.6 = (0.0002)t, t = 3000 years.
Pi Numbers
Poetic Pi
Word-length pi
mnemonics have been around a long time. An old chestnut,
but still a favorite, is:
How I need a drink,
alcoholic in nature, after the heavy lectures involving quantum
mechanics.
A much less well-known
example is this nice poem by Joseph Shipley (1960):
But a time I spent wandering
in bloomy night;
Yon tower, tinkling chimewise, loftily opportune.
Out, up, and together came sudden to Sunday rite,
The one solemnly off to correct plenilune.
Calculus of Variations, how to solve Newton's aerodynamic
problem and more. Be patient as this server is in Russia.
Famous Unsolved
Problems in Mathematics, from a lecture delivered to the
International Congress of Mathematicians at Paris in 1900 by
Professor David Hilbert. Great reading for budding mathematicians
who want a shot at the Nobel Prize.
The Calculus Page offers many charts and Java
animations to illustrate principles of analysis.
Calculus animations from Douglas N. Arnold. "These
are excerpts from a collection of graphical demonstrations I
developed for first year calculus. I use many such demonstrations
to illustrate and enrich my classes in the McAllister Technology
Classroom. Those interested in higher math may also want to visit
my page of graphics for complex analysis."
Entertainment
MathTRIVIA
Each king in a deck
of playing cards represents a great king from history. Spades
= King David, Clubs = Alexander the Great, Hearts = Charlemagne,
and Diamonds = Julius Caesar.
111,111,111 x 111,111,111
= 12,345,678,987,654,321
One day while playing
with my new calculator, I wanted to see what would happen when
I multiplied 666 (the Number of the Beast, Scriptures?) by itself.
Surprise! 6.66 to the 4th power yields 1967.4192. To me, that
suggested a particular day in 1967, so I multiplied 0.4192 x
365 = 153.008. The 153rd day of that year (153-31-28-31-30-31=)
is June 02. Checking the history book, I discover that was the
day Israeli air force attacked Egypt. Even more coincidental
is the time. If you multiply 0.4192 by 365.25 instead of 365
(as the real year is almost a quarter of a day longer than the
calendar year) you get 153.1128 days into 1967. To find the exact
hour, multiply 0.1128 by 24 hours = 2.7072, or 02:43 a.m., which
is about the local time of the air attack on Egypt, 02 June 1967.
So ... did the Bible predict this? Did the Israeli military commander
read Scriptures with a calculator nearby? Or is it a coincidence?
Two trains 200 miles apart are moving toward
each other; each one is going at a speed of 50 miles per hour.
A fly starting on the front of one of them flies back and forth
between them at a rate of 75 miles per hour. It does this until
the trains collide and crush the fly to death. What is the total
distance the fly has flown?
The fly actually
hits each train an infinite number of times before it gets crushed,
and one could solve the problem the hard way with pencil and
paper by summing an infinite series of distances. The easy way
is as follows: Since the trains are 200 miles apart and each
train is going 50 miles an hour, it takes 2 hours for the trains
to collide. Therefore the fly was flying for two hours. Since
the fly was flying at a rate of 75 miles per hour, the fly must
have flown 150 miles. That's all there is to it. |
A score of 68% or higher in both MATH 321 (Real Variables II) and MATH
322 (Introduction to Aglebra).
Course Outline:
Topology is one of the
most active and advanced fields of mathematics, and it is
indespensible for many other fieds, such as Analysis, Geometry or
Algebra. This course is a standard introduction to Topology.
We will follow the textbook fairly closely, and attempt to cover most
topics included in the book.
The first part of the course will cover the basics of point set
topology: definitions and first examples of topologyical spaces and
continuous maps; basic constructions: products, subspaces, quotient
spaces; basic properties: connectedness, compactness, separation
axioms. A first peak will be Urysohn's lemma and some of its
consequences. Then we study metric spaces and function spaces.
The latter part of the course discusses the fundamental group of a
topological space, one the most interesting and important invariants
in all of topology. We will study the Jordan curve theorem, the
Seifert-Van Kampen theorem, and classify surfaces up to homeomorphism. |
Students build geometric models of polynomials exploring firsthand concepts related to them
Includes enough sets for 30 studentsEach classroom set also includes an overhead set (LER 7541) and a 40-page book enabling students can be actively involved in teacher-directed lessonsAges 11-17Small parts. Not for children under 3 years.
Product Information
Subject :
Algebra
Age(s) :
11-17
Usage Ideas :
Students can be actively involved in teacher-directed lessons. Ages 11 to 17 |
Math Place Online: Algebra
is a free online course for teachers and parents who feel that they never understood algebra. In this course participants will learn to solve and graph algebraic equations and use algebra for problem solving. Each week participants learn by watching videos, completing assignments, and communicating online and in live sessions with math learners and teacher experts. Through this experience participants will gain deep understanding of the fundamentals of algebra and gain experience that will enable them to help others learn algebra.
Instructor: Barbara Dubitsky is a faculty member in the Mathematics Leadership Department at Bank Street College. Recently, she co-presented The math place online: A model for synchronous teaching spaces to foster math learning for K-8 teachers and parents at the International Conference on Online Learning. The Sloan Consortium, Orlando, FL. (2012). Read more...
Contact Us
Student Experience
Students attending The Math Place Online: Algebra are asked to complete asynchronous work (done at one's own pace) and synchronous work (done together as a class and live online) to foster student comprehension of algebra.
Each week students spend two hours doing asynchronous work: watching videos, completing assignments, using Web-based math tools and games, and participating in online discussions with fellow students, and an hour and a half (Thursdays, 5:00 to 6:30 pm) doing synchronous work: collaborating online with fellow students under the guidance of Bank Street math experts. These sessions begin February 28 and end April 25. There's no meeting March 28.
If you are taking this course for continuing education credits (CEU) you will need to complete all asynchronous work and attend no less than seven synchronous sessions. You will also need to demonstrate your knowledge of the material through a culminating exercise. |
The strength of Engineering Computation is its combination of the two most important computational programs in the engineering marketplace today, MATLAB® and Excel®. Engineering students will need to know how to use both programs to solve problems.
The focus of this text is on the fundamentals of engineering computing: algorithm development, selection of appropriate tools, documentation of solutions, and verification and interpretation of results.
To enhance instruction, the companion website includes a detailed set of PowerPoint slides that illustrate important points reinforcing them for students and making class preparation easier.
PART 1: COMPUTATIONAL TOOLS
Chapter 1: Computing Tools
Chapter 2: Excel Fundamentals
Chapter 3: MATLAB Fundamentals
Chapter 4: MATLAB Programming
Chapter 5: Plotting Data
PART 2: ENGINEERING APPLICATIONS
Chapter 6: Finding the Roots of Equations
Chapter 7: Matrix Mathematics
Chapter 8: Solving Simultaneous Equations
Chapter 9: Numerical Integration
Chapter 10: Optimization |
College Algebra and Trigonometry that include highlights, exercise hints, art annotations, critical thinking exercises, and pop quizzes, as well as procedures, strategies, and summaries. This text is designed for a variety of students with different m... MOREathematical needs. for those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. for those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom. This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. for departments requiring both options, this text provides the advantage of flexibility. |
Math Class--Have You Seen the Preview?
H. Louise Amick, Washington College
I've always suggested to students that they read ahead in the text to have
some idea of what is to be discussed in class, but that suggestion hasn't
always been successful. Some students have ignored my advice knowing they
will survive by coming to class, while others have struggled to comply, but
found that the text really wasn't readable. My wish for previews that
students could really read and work through came true for one class when we
revised our Precalculus course.
When our department decided to require graphing calculators for
Precalculus, we were concerned about the financial burden that this
(together with the purchase of a text) would place on our students. We
decided that we could generate our own handouts for the course so that we
wouldn't need a text. A colleague and I agreed to collaborate on this
project. As we outlined and discussed the format of our handouts, our
summer project expanded into a summer spent writing a text.
Each chapter of the text is composed of three parts: a preview, a lesson,
and a problem set. The preview discussion and problems are to be done by
study groups prior to the presentation of the chapter in class. These
previews act as levelers---everyone comes to class with some knowledge to
contribute to the development of the chapter. The lesson section of the
chapter is very concise. Examples are included only when essential,
avoiding templates from which students can model their solutions to
problems. The problem sets contain a variety of problems, including
applications whenever possible.
We are not suggesting that it is necessary to write one's own text to
initiate class discussion and collaboration. While we are pleased with the
entire text and the changes it has produced in our classes, we believe the
previews are the key to our success. Consequently, we are advocating that
carefully developed previews can be used in any math class to foster
collaborative learning.
The nature of the previews we've developed for Precalculus varies over a
wide spectrum from reviews of prerequisite material to guided development of
formulas and identities. As we began to write each preview, we first asked
ourselves what prerequisite knowledge we would assume for the chapter and
how we could guide students to recall and review it. Then we focused on
how much of the chapter's content could be discovered by students through
experimentation with the graphing calculator, by applying geometry and
algebra, or through guided step-by-step examples that could be generalized.
One of the most successful previews has been the one shown below, which
introduced the chapter on composite and inverse functions. In developing
this lesson in class, I only had to provide the definition of a composite
function and the notation for an inverse function. Everything else sprang
from the students' discussion of their work on the preview.
Plot manually the three pairs of points and the line
y=x on the same coordinate system.
Describe as explicitly as possible the relationship of the
paired points to the line y=x.
If the coordinate system is folded using y=x as
a fold line, what relationship can be observed between the
paired points?
Show that the line segments
and are
perpendicular to the line y=x.
Show that y=x is the perpendicular bisector of
the line segments , and .
Show that , and in the
above problem satisfy the equation .
Show that , , and
in the above problem satisfy the equation .
Show that is
equivalent to .
Use your graphing calculator to sketch the graphs of , , and
y=x on the same viewing window without erasing.
These previews have allowed us to change our classes from lecture classes
into classes focusing on problem-solving and discussion. They have allowed
us to ``flesh out'' the lessons in class and develop our own examples.
Having done this, both the development of the lesson and the solving of the
problems in the problem sets become collaborative ventures. In addition to
the change in the atmosphere of our classes, we have seen measurable
success in another sense. Prior to the use of this approach, each year we
had approximately 25% of our Precalculus students either withdraw from
the course at midterm or fail at the end. Now only 14% do so. |
MAA Review
[Reviewed by Peter Olszewski, on 12/11/2012]
William Briggs, Lyle Cochran, and Bernard Gillett have written, in my opinion, a successful Calculus text. The true success of this text is that it reflects how today's college Calculus students learn: beginning with the exercises and referencing back to the worked out examples within the text.
The book has well thought out examples that will be clear to the student. Many pictures are given through out the text to aid students' understanding of the concepts. While reading the text, it was as though I was sitting in a Calculus class and my instructor was talking to me. In addition, there was a lot of handholding, but not overbearing handholding. The text is to the point! I fully enjoyed the pure mathematical examples with the well thought out pictures; they show the years of teaching experience of each author.
One of the first things I noticed in Chapter 1 was the way domain and range were treated from a graphical perspective, by taking any point on the curves and mapping it back to the x and y axes. The use of color is also helpful. In addition, I liked how the authors introduced the concept of secant lines early. In most other texts, they aren't introduced until the following chapter, which is typically about limits.
What I also really enjoyed about Chapter 1 was the review of trigonometry in Section 1.3. Many of my calculus students have forgotten the basic concepts of trigonometry, so it is a wonderful idea to have a review available, to be used at the instructors' choice.
As the title states, this text is for Scientists and Engineers, so it is fitting for secant lines to be quickly connected to velocity. The motivation for considering the slope of secant lines is very well done and the diagrams on page 41 are excellent. This is what the students need to see.
Jumping to the middle of the book, I strongly believe students are overwhelmed when it comes down to sequences and series. In most other texts I've read, sequences and series and all related topics are contained in one big chapter. Having these concepts broken into two chapters is more digestible for the students.
Of course, there are places where the book can be improved. I only mention a few.
In Chapter 1, the authors discuss domains and ranges of functions but not for compositions of functions. I would like to see examples of these, with graphics to support the solutions. In addition, having examples of finding domains and ranges of piecewise defined functions and domains and ranges of transformations of functions would further enhance this section. It has been my experience that students need extra guidance in finding domains and ranges.
After Theorem 2.2, I would recommend stating another theorem about using direct substitution of a polynomial and rational function followed by examples. In addition, I would like to see more examples following Example 6 on "other techniques" for finding limits analytically.
Many times, students forget simple algebraic concepts needed for Calculus. In the exercise set for Section 2.3, I believe the authors should limit the amount of problems where the limits of functions are tending towards a number a. I believe it would be more useful for students to see the direct numerical results as this is what they are more likely to see in their careers.
For Section 2.4, as an aid to help students understand the logic of when functions tend to zero and to infinity, it's useful to have an informal statement that 1/large tends to 0 and 1/small tends to infinity. This will help students quickly recall these two critical facts.
In Section 2.6, I feel as though there should be an example using the Intermediate Value Theorem involving a function before proceeding to the financial application.
The section on higher order derivatives in Section 3.2 is out of place. I strongly believe higher order derivatives need a section all their own, as there are many examples students need to see.
My suggestion for Sections 3.5 and 3.6 is that they be flipped. If the Chain Rule is learned first, many Chain Rule applications problems can be woven into the section on derivatives as rates of change.
I believe the statement of the Second Derivative Test in Section 4.2 will confuse students. Instead of saying, "If f′′(c) = 0, the test is inconclusive; f may have a local maximum, local minimum, or neither at c" I would suggest, "In such a case, the First Derivative Test can be used to determine if f is a local maximum, minimum, or neither."
While Example 3 is excellent in Section 4.3, I believe another example is needed before Example 3 involving a rational function that contains both vertical and horizontal asymptotes and a hole in the graph. In addition, Section 2.5 should be inserted in Chapter 4 before this section since the important connection to limits at infinity can now be made with the summary of curve sketching.
I was hoping to see more examples in Sections 4.5–4.7. I also feel as though Section 4.7, L'Hôpital's Rule, is out of place with the rest of the text. I believe this section should be either contained in Section 7.6 or be a new section before Section 7.6.
Reading further into the text, I believe there could be many more applications presented. For example, in Chapter 13, there are too many proofs in the homework set for dot products and the section on cross products ends very quickly with not enough applications. Section 13.7 is much better as the authors give many more applications. I especially enjoyed reading through Examples 5 and 6 in this section. So many times, students are told to ignore friction and air resistance. Here is a problem were the angle must be found to adjust the flight of a ball.
Moving to Section 13.9, once again, I believe there are too many proofs and not enough applied problems. After all, part of the title of the book is "for Scientists and Engineers"!
In the past, when I have taught engineering students, they wish to see how the mathematics they learn, whether it be calculus or matrices, will be used. Perhaps having student projects at the end of each chapter or section, specifically for the Sciences and Engineers could further enhance the text. The teaching and writing style of this text is excellent but I believe more applications would further student's motivation, creativity, and problem solving skills.
Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at [email protected]. Webpage: Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes. |
Product Description
About the Author
Trevor Johnson and Hugh Neill are both very well established authors, A Level examiners and maths consultants. Trevor is the Chief Examiner for Edexcel's International GCSE and was joint editor and author of the recently published Edexcel GCSE Mathematics series.
Customer Reviews
This book fits it's description and I'm satisfied with that. However, I would have liked to see it in a text book format because the binding doesn't look like it will last that long. But then again, it was only $15.00 so you get what you pay for.
3.0 out of 5 starsA lot of information but not quite enough.Mar 24 2013
By ReaderOne - Published on Amazon.com
Amazon Verified Purchase
This book is a basic primer for mathematics. Unfortunately, the examples and "quizes" are less than inclusive. A few examples are less than complete and left me wanting more. However, as a primer, this book serves as a good basic math book that will help students to get the feel for the math they are studying in school. This book serves as a good book for me to use in my tutoring capacity. Adding about another one-hundred pages to this publication in a future edition to include a bit more detail on certain subjects like the bacis geometry section might be due to be considered.
4.0 out of 5 starsthe best mathe book if it was not for its sizeMay 6 2012
By W. Douh - Published on Amazon.com
Amazon Verified Purchase
the book is very detailed and informative even for beginners.but its size is VERY small,it might give you headaches while reading it(seriously).other than that,a great buy!! |
Exponential
models help solve problems involving change in many areas, including
population, pollution, temperature,and investments. Students should
be able to create exponential models, match equations with graphs,
be able to answer questions about exponential change, and describe
major similarities and differences between exponential and linear
patterns of change. |
Grade 10 Introduction to Applied and Pre-Calculus Mathematics (20S)
Measurement
General Outcome: Develop spatial sense and proportional reasoning.
Relations and Functions
General Outcome: Develop algebraic and graphical reasoning through the study of relations.
Algebra and Number
General Outcome: Develop algebraic reasoning and number sense.
This "course" contains quick links to SMA library electronic resources such as eBooks, EBSCOHost, the Winnipeg Free Press materials and similar, as well as the login information needed to access them. (Guests do not have access to this section.) |
Description: In this presentation, the author will briefly introduce the subject of Descriptive Set Theory and the motivation for its study. The author will discuss the idea of a projective set and also define the mathematical notion of a "tree" as an example of a projective set. The author will conclude with a brief mention of a significant result that can be proved using the notion of a tree.
Description: This presentation discusses a research study on the effect of technology on achievement in mathematics in middle school. This presentation discusses the research, which analyzes how these concepts, ideas, and problems have been discussed in the past in order to form a solid platform that will support technology in schools in the future.
Description: This presentation discusses research on mathematics anxiety. The author describes the current state of research and understanding of math anxiety, expounds upon this information with independent research conducted at UNT, evaluates this research, and suggests a plan for improved results in mathematics education. |
interactive mathematics program, Im taking the last year,
and they sometimes give you POWs (problem of the week) pretty challenging sometimes, especially if you wait till the night before its due,...dear god haha |
The Mathematics of Money: Math for Business and Personal Finance Decisions
The Mathematics of Money: Math because Business and Personal Finance covers the whole of the traditional topics of the avocation math course, but with a again algebraic focus than many of the texts popularly on the market. The text develops a important understanding of percent and interest seasonable, then applies that foundation to other applications in calling and personal finance. While it is appropriate on the side of students of all levels, the volume takes the approach that even whether students are coming into the class with only high school math, nor one nor the other they nor the instructor need to subsist afraid of algebra; it takes care to clearly donation and reinforce the formulas given and to consistently go to them and apply the important to contexts that are relevant to the students. |
Secondary Mathematics II [2011]
Analyze functions using different representations. For F.IF.7b, compare and contrast absolute value, step and piecewisedefined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range and usefulness when examining piecewise-defined functions. Note that this unit, and in particular in F.IF.8b, extends the work begun in Mathematics I on exponential functions with integer exponents. For F.IF.9, focus on expanding the types of functions considered to include, linear, exponential, and quadratic.
Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factoredForming Quadratics
This lesson unit is intended to help educators assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representationGeoGebra
GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards Completing the Square Factoring |
Also,aGooglesearchmainlyturnsupsoftwareforsolvingfreshmanalgebraproblemsappreciated.]
Also, a Google search mainly turns up software for solving freshman algebra problems] |
Book Description: This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.
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