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Tucson ACTNow the student must learn to see it from the perspective of functions: polynomial, rational, radical, exponential and trigonometric functions. Calculus, as Algebra, is an art; the artist needs a palate. In this case the palate is the coordinate plane and the student must learn to draw the faces (graphs) of all the functions and recognize them from their faces |
Math 110 (Elementary Mathematical Models) is
an algebra-based elementary modeling course intended for students who need a
mathematics course but who do not need calculus. Linear, polynomial, exponential,
and logarithmic functions are studied. The emphasis is on real-world problems
and models, and rates of change. Algebra is reviewed as needed. Upon completing
the course, the student will be able to
work with functions and data represented graphically, numerically, analytically,
and verbally;
use technology appropriately in mathematical problem solving, and recognize
its limitations;
Math 150 (Precalculus) is a traditional precalculus
course intended solely for students who need extra preparation before attempting
Math 160, the first course in the regular calculus sequence. The mathematical
concepts that are a prerequisite to the study of calculus (functions, domains,
ranges, graphs, equations, and inequalities) are covered. Upon completing the
course, the student will be able to
manipulate algebraic expressions easily;
work with polynomial and rational functions, including finding their values,
graphing them, understanding their basic properties, and solving equations
and inequalities;
work with trigonometric functions, including finding their values, graphing
them, using trigonometric identities, understanding their basic properties,
solving equations, and solving problems in triangle trigonometry;
work with exponential and logarithmic functions, including finding their
values, graphing them, understanding their basic properties, and solving equations;
communicate mathematical information in written form.
The courses Math 157/158 (Calculus I and II for Social/Life Sciences) form
a two-semester terminal calculus sequence that gives primarily a conceptual
treatment of calculus and is less theoretical than the regular calculus sequence.
The intended audience is economics, biology, and environmental science students.
Math 157 (Calculus I for Social/Life Sciences) is an introduction to
the differential calculus of algebraic, logarithmic, and exponential functions.
The emphasis is on the concept of the derivative and its applications of calculus
to the life and social sciences. Precalculus topics are covered as needed.
Upon completing the course, the student will be able to
work with functions and data represented graphically, numerically, analytically,
and verbally;
demonstrate an understanding of the concept of the limit of a function and
the rules for showing the existence of and finding limits;
demonstrate an understanding of the concept of the derivative of a function:
the definition, as well its connection to the slope of tangent lines and
instantaneous rates;
Math 158 (Calculus II for Social/Life Sciences) is a continuation of
the differential calculus begun in Math 157, and an introduction to integral
calculus of one variable and the differential calculus of multivariable functions
involving algebraic, logarithmic, and exponential expressions. Applications
of these topics in the life and social sciences are considered. Upon completing
the course, the student will be able to
demonstrate how the derivative can be used to determine monotonicity, concavity,
points of inflection, and maximums and minimums of functions;
demonstrate an understanding of the definite integral
as representing area and accumulated change, antiderivatives, and the Fundamental
Theorem of Calculus;
demonstrate familiarity with functions of several variables, partial differentiation
and the information partial derivatives reveal about functions;
accurately perform the algebraic and calculus computations with functions
of several variables that involve algebraic, logarithmic, and exponential
expressions; |
Tag: rapidli acco... ...Learni...'s text-based input is a simply faster way to input math.
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Student Resources
Student study group in the Rat Room.
Math Student Resource Room
The Math Student Resouce Room is located in Olin 203. This is a walk-in help center for students. The room, nicknamed the Ratiocination or "Rat" Room, is staffed by experienced mathematics students that are available to help you understand the material covered in class and provide guidance with your homework. The tutors are available in the afternoons and evenings. This service provides a convenient option for those who encounter difficulties with their mathematics work and would benefit from immediate help. The tutors provide this assistance free of charge.
This is a good location to meet and work with friends and others who are taking the same course. It's also a great meeting place for small study groups even if you do not need the tutor resources.
In addition to offering generalized mathematics tutoring, the room is also staffed (hours may differ) during winter and spring terms for MATH 203 & 204 (Mathematics for Elementary Teacher I and II) students. See the schedule below for details. |
View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library)
A View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library)
(Paperback) by Alex Iosevich48
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Book Summary of A View From The Top: Analysis, Combinatorics And Number Theory (Student Mathematical Library)
This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another. In teaching his readers a variety of problem solving techniques as well, the author succeeds in enhancing the readers' hands-on knowledge of mathematics and provides glimpses into the world of research and discovery. The connections between different techniques and areas of mathematics are emphasized throughout and constitute one of the most important lessons this book attempts to impart. This book is interesting and accessible to anyone with a basic knowledge of high school mathematics and a curiosity about research mathematics. The author is a professor at the University of Missouri and has maintained a keen interest in teaching at different levels since his undergraduate days at the University of Chicago. He has run numerous summer programs in mathematics for local high school students and undergraduate students at his university. The author gets much of his research inspiration from his teaching activities and looks forward to exploring this wonderful and rewarding symbiosis for years to come.
Books Similar to : A View From The Top: Analysis, Combinatorics And N |
I for Dummies
One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, ...Show synopsisOne of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you "power"" - the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on. Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, "Algebra I For Dummies" can provide the help you need. This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works. In "Algebra I For Dummies," you'll discover the following topics and more: All about numbers - rational and irrational, variables, and positive and negativeFiguring out fractions and decimalsExplaining exponents and radicalsSolving linear and quadratic equationsUnderstanding formulas and solving story problemsHaving fun with graphsTop Ten lists on common algebraic errors, factoring tips, and divisibility rules. No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, "Algebra I For Dummies" can give you the tools you need to succeed.Hide synopsis
Reviews of Algebra I for Dummies
Simple explanations to problems. I needed a book that would explain formulas in simple terms without insulting my intellegence or I wouldn't bother to continue to read it. Excellent choice for first time learners at any age |
Bell Schedule
School Hours
After School
Block Schedule
Office Hours
Mon - Fri: 7:30am - 4:30pm
Mathematics
MATHEMATICS 7
36 weeks (year)
Grade: 7
Students examine algebra- and geometry-preparatory concepts and skills; strategies for collecting, analyzing, and interpreting data; and number concepts and skills especially
proportional reasoning. Reasoning, problem solving, communication, concept representation, and connections among mathematical ideas are emphasized in a hands-on learning
environment. Graphing calculators and computers are integrated with instruction. This course provides students the opportun ity to acquire the concepts and skills necessary for
success in Algebra I or Algebra I Honors.
Students are required to take the Standards of Learning End of Course Test.
MATHEMATICS 7 HN
36 weeks (year)
Grade: 7
The depth and level of understanding in Mathematics 7 Honors is beyond the scope of Mathematics 7. This course is based on Mathematics 8 curriculum and includes extensions and
enrichment. Emphasis is placed on mathematical reasoning, non-routine problem solving, and algebraic connections among mathematical ideas. This course provides students the
opportunity to acquire the concepts and skills necessary for success in Algebra I or Algebra I Honors.
Students are required to take the Standards of Learning End of Course Test.
MATHEMATICS 8
36 weeks (year)
Grade: 8
Prerequisite: Mathematics 7
Students extend their study of algebra- and geometry-preparatory concepts and skills; strategies for collecting, analyzing, and interpreting data; and number concepts and skills
especially proportional reasoning. Reasoning, problem solving, communication, concept representation, and connections among mathematical ideas are emphasized in a hands -on
learning environment. Graphing calculators and computers are integrated with instruction. This course provides students the opportunity to acquire the concepts and skills necessary
for success in Algebra I or Algebra I Honors.
Students are required to take the Standards of Learning End of Course Test.
ALGEBRA 1
36 weeks (year)
Grade: 8
Credit: one
Prerequisite: Middle School Mathematics
This course extends students' knowledge and understanding of the real number system and its properties through the study of v ariables, expressions, equations, inequalities, and
analysis of data derived from real-world phenomena. Emphasis is placed on making connections in algebra to geometry and statistics. Calculator and computer technologies will be
used as tools wherever appropriate. Use of a graphing calculator is considered essential to provide a graphical and numerica l approach to topics in addition to a symbolic approach.
Topics include linear equations and inequalities, systems of linear equations, relations, functions, polynomials, and statistics.
Students are required to take the Standards of Learning End of Course Test.
When Algebra 1 is taken in middle school, it becomes part of the high school transcript record and is included in the determin ation of the high s chool grade point
average (GPA) and counts as one of the required mathematics credits for high school graduation. Parents may request that the Algebra 1 grade be omitted from the
student's transcript and not earn high school credit for the course.
Note: Admission to the Thomas Jefferson High School of Science and Technology requires the compl etion of Algebra 1 prior to grade 9.
Rising 7
th
grade students will be placed in Algebra I Honors by meeting the following division-wide requirements:
1. Participation in sixth grade Compacted Mathematics or a full year' s advanced mathematics program in grade 6.
2. A score at the 92nd
percentile or better on the Iowa Algebra Aptitude Test (IATT) in grade 6. 3. A score of 500 or better (pass advanced) on the Virginia Standards of Learning Grade 7 mathematics test at the end of grade 6.
ALGEBRA 1 HONORS
36 weeks (year)
Grade: 7, 8
Credit: one/weighted +.5
Prerequisite: Mathematics 7 and/or Mathematics 8
The depth and level of understanding expected in Algebra I Honors is beyond the scope of Algebra I. Students are expected to master algebraic mechanics and understand the
underlying theory, as well as apply the concepts to real -world situations in a meaningful way. Students extend knowledge and understanding of the real number system and its
properties through the study of variables, expressions, equations, inequ alities, and the analysis of data fro m real world phenomena. Emphasis is placed on algebraic connections to
arithmetic, geometry, and statistics. Calculators and computer technologies are integral tools. Graphing calculators are an essential tool for every student to explore graphical,
numerical, and symbolic relationships.
Students are required to take the Standards of Learning End of Course Test.
GEOMETRY HONORS
36 weeks (year)
Grade: 8
Credit: one/weighted +.5
Prerequisite: Algebra 1
The depth and level of understanding expected in Geometry Honors is beyond the scope of Geometry. This course emphasizes two - and three-dimensional reasoning skills, coordinate
and transformational geometry, and the use o f geometric models to solve problems. A variety of applications and some general problem-solving techniques, including algebraic skills,
will be used to explore geometric relationships. Conjectures about properties and relationships are developed inductively an d then verified deductively. Students investigate non-
Euclidean geometries, formal logic, and use deductive proofs to verify theorems. Calculators, computers, graphing utilities, dynamic geometry software, and other appropriate
technology tools will be used to assist in teaching and learning.
Students are required to take the Standards of Learning End of Course Test.
Mathematics Department Chair: Dana Scabis
This web page contains links to one or more web pages that are outside the FCPS network. FCPS does not control the content or relevancy of these pages. |
Certificate in Senior Secondary Mathematics - Arithmetic and Algebra is a well organized, accessible and in-depth course book designed to teach the fundamental aspects of elementary mathematics that are indispensable in building interest, confidence and competence in mathematical reasoning and problem solving. This reader-friendly course book is presented in a format that encourages the average student and challenges the more able student, starting with the basic aspects and progressing to the more advanced aspects of secondary level mathematics.
With well over 1000 worked-through examples, more than 840 exercises (answers provided), 20 chapters and 4 appendices; numerous graphs, diagrams and tables, this comprehensive course book is a necessary text for students who desire to do well in secondary or high school mathematics.
Emphasis has been laid on detailed presentation and communication through out the course book with the intention of engaging to a greater extent, the attention of the reader. From fractions, logarithms, number system to graphs, equations (literal, simultaneous, quadratic), inequalities, sets and probability, this comprehensive course book furnishes detailed theories, practice and formulae that will ultimately benefit the reader.
Certificate in Senior Secondary Mathematics is a valuable course book created to tutor students studying privately to earn good grades in mathematics in certificate and matriculation examinations. Teachers and students in normal classroom studies will also find this book quite helpful.
Preview coming soon.
Dili Okay Nwabueze at various times taught mathematics at both Ordinary and Advanced (Pure and Applied) Levels. He was formally a Polytechnic/University lecturer in mechanical engineering.
He has written publishable books and papers in diverse areas including but not limited to Mathematics, Mechanical Engineering, Petroleum Engineering, Petroleum Refining, and Materials Management.
Dili Okay Nwabueze is a registered Engineer.
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MATH 110: College AlgebraTEXTBOOK
College Algebra, byBeecher, Penna, Bittinger, Second Edition, 2005.
CORE SKILL OBJECTIVES
1. Thinking Skills:
A. Using reasoned standards in solving problems and presenting arguments.
2. Communication Skills:
A. Reading with comprehension and the ability to analyze and evaluate.
A. Demonstrating knowledge of the signs and symbols of another culture.
B. Participating in activity that broadens the student's customary way of thinking.
5. Aesthetic Skills:
A. Developing an aesthetic sensitivity.
COURSE OBJECTIVES
1. Thinking Skills:
A. Studying briefly the basic ideas of a first algebra course.
B. Learning to solve quadratic equations by factoring, completing the square, and by use of the quadratic formula.
C. Improving one's ability to read and solve application problems by means of constructing appropriate algebraic models and then applying algebraic techniques to find a solution.
D. Exploring exponential and logarithmic functions, including application problems, and the efficient and appropriate use of logarithms and their properties.
E. Learning the techniques of solving systems of equations and appropriately applying these processes to word problems.
2. Communication Skills:
A. Producing both written and oral communication throughout the course; particular attention is paid to the accurate and appropriate use of the language of algebra.
B. Using technology - calculators, in some cases graphing calculators - to solve problems and to be able to communication solutions and explore options.
3. Life Value Skills:
A. Developing an appreciation for the intellectual honesty of deductive reasoning; a mathematician's work must Aesthetic Skills:
A. Developing an appreciation for the austere intellectual beauty of deductive reasoning.
B. Developing an appreciation for mathematical elegance.
ADDITIONAL COMMENTS
This course is designed to give students the algebraic tools required in subsequent courses, specifically MATH 180 (Elementary Functions), MATH 230 (Elements of Statistics), or MATH 270 (Managerial Mathematics). "Tools" here means web sites)Mr. Maresh, math department chair believes This idea will be stressed repeatedly during the course.
You
Homework:
There will be a daily homework assignment. While most of the assignments
People have various learning styles; some of us learn best by working alone in silence, others learn best by talking about the material with peers. Therefore, there will be some group work in class, not because it is the best way for all of you to learn but because some of you learn best by talking about ideas with others. You are strongly encouraged to find at least one other person to work with on the assignments if that is a good way for you to learn the ideas in this course.
Use of Technology:
It is important to make use of technology, specifically computers and calculators, in doing mathematics. While it is not require the purchase of a specific calculator, you will find it very helpful to acquire and learn to use a graphing calculator of some sort, such as a TI-83, TI-83 Plus, TI 84 Plus or a TI 85. This is especially important for those of you who will be taking additional math courses. While some class time will be used to talk about the use of a calculator you will need to spend out of class time to become proficient in the use of a calculator to solve problems.
Grading Procedure:
In general the following minimum levels are required for the grades indicated: 90% for an "A", 85% for an AB, 80% for a "B", 75% for a BC, 70% for a "C", 65% for a CD and 60% for a "D". Quizzes, tests, attendance, homework collected, extra credit and class participation will be factors in determining points earned in this course. There should be adequate opportunities |
She Does Math!
edited by Marla Parker
The range of applications is broad. The examples are easy to understand and are generally supported by interesting problems. The book is carefully edited and the graphic and text style are consistent from chapter to chapter—the hallmark of attention to detail in a book with numerous authors. — Mathematical Reviews
Finally—a practical, innovative, well-written book that will also inspire its readers. The wonder is...it is a mathematics text and a biography! The idea of women telling their own career stories, emphasizing the mathematics they use in their jobs is extremely creative. This book makes me wish that I could go through school all over again! — Anne Bryant, Executive Director, American Association of University Women
She Does Math! presents the career histories of 38 professional women and math problems written by them. Each history describes how much math the author took in high school and college; how she chose her field of study; and how she ended up in her current job. Each of the women present several problems typical of those she had to solve on the job using mathematics.
There are many good reasons to buy this book:
It contains real-life problems. Any student who asks the question, "Why do I have to learn algebra (or trigonometry or geometery)?" will find many answers in its pages. Students will welcome seeing solutions from real-world jobs where the math skills they are learning in class are actually used.
It provides strong female role models.
It supplies practical information about the job market. Students learn that they can only compete for these interesting, well-paying jobs by taking mathematics throughout theur high school and college years.
It demonstrates the surprising variety of fields in which mathematics is used.
Who should have this book? Your daughter or granddaughter, your sister, your former math teacher, your students — and young men, too. They want to know how the math they study is applied — and this book will show them. |
Mathematical Methods in the Physical Sciences, 3rd Edition
This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications. |
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COMPARATIVE STATICS AND THECONCEPT OF DERIVATIVEChapter 6Alpha Chiang, Fundamental Methodsof Mathematical Economics3rd editionNature of Comparative Staticsconcerned with the comparison of different equilibriumstates that are associated with differ
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Econ 509, Introduction to Mathematical Economics IProfessor Ariell ReshefUniversity of VirginiaLecture notes based on Chiang and Wainwright, Fundamental Methods of Mathematical Economics.1Mathematical economicsWhy describe the world with mathematica "competition"Lecture 11: Rock deformation The movements of Earth's tectonic plates creates stressesrocks subject to stress will deform (change in volume or shape of a body of rock) ways in which rocks deform are varied; which style a particular rock mass adoptsdep
GENERAL A RTICLEAlfred Wegener From Continental Drift toPlate TectonicsA J Saigeetha and Ravinder Kumar BanyalWhat is the nature of the force or mechanism that movesmassive continents thousands of miles across? What causesviolent earthquakes to dis
Mathematics 17Fifth Long ExamGENERAL DIRECTION: Write the exam code of the test paper at the upper right corner of yourbluebook (front). Write your student number below the code. Show all necessary solutions and box the nalanswers. Refrain from using
Math 17 TWHFW-71st Sem AY 2010-11Exercise 1 Part I Answer KeySolutions to Exercise Set I. Please remember that there may be (and probably are) multiple ways to go about a given problem. As long as the techniquesare valid and the computations are caref
Math 17 TWHFW-7Ex 1 (HW 4) Part IIPlease do the exercises as indicated. Write down all nal answers on aseparate piece of paper.I. Simplify the following expressions: Consider simplest assumptions on radicandsand variables and that all divisors are no
Exercise Set 2 - Part 1 (HW 8)July 18, 2011Math 17 TWHFW-71st Sem AY 2011-12Use a separate piece of paper as your answer sheet. Show as complete a solution as youare able to. Remember to box all nal answers. Submission is on Thursday, July 21.Good l
Exercise Set 2 - Part 2 (HW 12)August 23, 2011Math 17 TWHFW-71st Sem AY 2011-12Use a separate piece of paper as your answer sheet. Show as complete a solution as youare able to. Remember to box all nal answers. Submission is on Friday, August 26.I.
Math 17 TWHFW-71st Sem AY 2011-12Exercise Set 5 (HW 14)October 4, 2011Use a separate piece of paper as your answer sheet. Show ascomplete a solution as you are able to, unless otherwise specied.Remember to box all nal answers when solutions are nece |
This course together with the course Numerical Methods II provides
complete explanation of numerical mathematics as the separate
scientific discipline.
The emphasis is given to the algorithmization and computer implementation.
Some examples with graphical outputs help to explain even some
difficult parts.
At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines e.g. in statistical methods. |
College Algebra
Whether you're looking to study mathematics, social sciences, or a hard science at a college level, a solid foundation of algebra is essential. The material covered in this course mirrors that of the CLEP exam on College Algebra, making this a great resource for studying. The material contained herein will prepare you well for a colelge level course in algebra.
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What Are The Characteristics of a Good Group Problem?
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Good Group Problems What Are The Characteristics of a Good Group Problem? Group problems should be more difficult to solve than easy problems typically given on an individual test. But the increased difficulty should be primarily conceptual, not mathematical. Difficult mathematics is best accomplished by individuals, not by groups. So problems that involve long, tedious mathematics but little physics, or problems that require the use of a shortcut or "trick" that only experts would be likely to know do not make good group problems. In fact, the best group problems involve the straight-forward application of the fundamental principles (e.g., the definition of velocity and acceleration, the independence of motion in the vertical and horizontal directions) rather than the repeated use of derived formulas (e.g., v 2 2 f - vo = 2ad).
There are twenty-one characteristics of a problem that can make it more difficult to solve than a standard textbook exercise:
Approach 1 Cues Lacking A. No explicit target variable. The unknown variable of the problem is not explicitly stated. B. Unfamiliar context. The context of the problem is very unfamiliar to the students (e.g., cosmology, molecules). 2 Agility with Principles A. Choice of useful principles. The problem has more than one possible set of useful concepts that could be applied for a correct solution. B. Two general principles. The correct solution requires students to use two major principles (e.g., torque and linear kinematics). C. Very abstract principles. The central concept in the problem is an abstraction of another abstract concept. (e.g., potential, magnetic flux). 3 Non-standard Application A. Atypical situation. The setting, constraints, or complexity is unusual compared with textbook problems. Page 48
Unusual target variable. The problem involves an atypical target variable when compared with homework problems. Analysis of Problem 4 Excess or Missing Information A. Excess numerical data. The problem statement includes more data than is needed to solve the problem. B. Numbers must be supplied. The problem requires students to either remember or estimate a number for an unknown variable. C. Simplifying assumptions. The problem requires students to generate a simplifying assumption to eliminate an unknown variable. 5 Seemingly Missing Information A. Vague statement. The problem statement introduces a vague, new mathematical statement. B. Special conditions or constraints. The problem requires students to generate information from their analysis of the conditions or constraints. C. Diagrams. The problem requires students to extract information from a spatial diagram. 6 Additional Complexity A. More than two subparts. The problem solution requires students decompose the problem into more than two subparts. B. Five or more terms per equation. The problem involves five or more terms in a principle equation (e.g., three or more forces acting along one axes on a single object). C. Two directions (vector components). The problem requires students to treat principles (e.g., forces, momentum) as vectors. Mathematical Solution 7 Algebra Required A. No numbers. The problem statement does not use any numbers. B. Unknown(s) cancel. Problems in which an unknown variable, such as a mass, ultimately factors out of the final solution. C. Simultaneous equations. A problem that requires simultaneous equations for a solution. 8 Targets Math Difficulties A. Calculus or vector algebra. The solution requires the students to sophisticated vector algebra, such as cross products, or calculus. B. Lengthy or Detailed Algebra. A successful solution to the problem is not possible without working through lengthy or detailed algebra (e.g., a messy quadratic equation). Page 49 Good Group Problems BEWARE! Good group problems are difficult to construct because they can easily be made too complex and difficult to solve. A good group problem does not have all of the above difficulty characteristics, but usually only 2- 5 of these characteristics. Page 50 How to Create Context-rich Group Problems
One way to invent group problems is to start with a textbook exercise or problem, then modify the problem. You may find the following steps helpful: 1. If necessary, determine a context (real objects with real motions or interactions) for the textbook exercise or problem. You may want to use an unfamiliar context for a very difficult group problem. 2. Decide on a motivation -- Why would anyone want to calculate something in this context? 3. Determine if you need to change the target variable to (a) make the problem more than a one-step exercise, or (b) make the target variable fit your motivation. 5. Determine if you need to change the given information (or target variable) to make the problem an application of fundamental principles (e.g., the definition of velocity or acceleration) rather than a problem needing the application of many derived formulas. 4. Write the problem like a short story. 5. Decide how many "difficulty" characteristics (characteristics that make the problem more difficult) you want to include, then do some of the following: (a) think of an unfamiliar context; or use an atypical setting or target variable; (b) think of different information that could be given, so two approaches (e.g., kinematics and forces) would be needed to solve the problem instead of one approach (e.g., forces), or so that more than one approach could be taken (c) write the problem so the target variable is not explicitly stated; (d) determine extra information that someone in the situation would be likely to have; or leave out common-knowledge information (e.g., the boiling temperature of water); (e) depending on the context, leave out the explicit statement of some of the problem idealizations (e.g., change "massless rope" to "very light rope"); or remove some information that students could extract from an analysis of the situation; (f) take the numbers out of the problem and use variable names only; (g) think of different information that could be given, so the problem solution requires the use of vector components, geometry/trigonometry to eliminate an unknown, or calculus. Page 51 Creating Context-rich Problems 6. Check the problem to make sure it is solvable, the physics is straight-forward, and the mathematics is reasonable. Some common contexts include: ¢" physical work (pushing, pulling, lifting objects vertically, horizontally, or up ramps) • suspending objects, falling objects • sports situations (falling, jumping, running, throwing, etc. while diving, bowling, playing golf, tennis, football, baseball, etc.) • situations involving the motion of bicycles, cars, boats, trucks, planes, etc. • astronomical situations (motion of satellites, planets) • heating and cooling of objects (cooking, freezing, burning, etc.)
Sometimes it is difficult to think of a motivation. We have used the following motivations: • You are . . . . (in some everyday situation) and need to figure out . . . . • You are watching . . . . (an everyday situation) and wonder . . . . • You are on vacation and observe/notice . . . . and wonder . . . . • You are watching TV or reading an article about . . . . and wonder . . . • Because of your knowledge of physics, your friend asks you to help him/her . . . . • You are writing a science-fiction or adventure story for your English class about . . . . and need to figure out . . . . • Because of your interest in the environment and your knowledge of physics, you are a member of a Citizen's Committee (or Concern Group) investigating . . . . • You have a summer job with a company that . . . . Because of your knowledge of physics, your boss asks you to . . . . • You have been hired by a College research group that is investigating . . . . Your job is to determine . . . . • You have been hired as a technical advisor for a TV (or movie) production to make sure the science is correct. In the script . . . ., but is this correct? • When really desperate, you can use the motivation of an artist friend designing a kinetic sculpture!
Outlined below is a decision strategy to help you decide whether a context-rich problem is a good individual test problem, group practice problem, or group test problem.
1. Read the problem statement. Draw the diagrams and determine the equations needed to solve the problem (through plan-a-solution step).
2. Reject if: • the problem can be solved in one step, • the problem involves long, tedious mathematics, but little physics; or • the problem can only be solved easily using a "trick" or shortcut that only experts would be likely to know. (In other words, the problem should be a straight- forward application of fundamental concepts and principles.)
3. Check for the twenty-one characteristics that make a problem more difficult:
4. Decide if the problem would be a good group practice problem (20 - 25 minutes), a good group test problem (45 - 50 minutes), or a good (easy, medium, difficult) individual test problem, depending on three factors: (a) the complexity of mathematics, (b) the timing (when problem is to be given to students), and (c) the number of difficulty characteristics of the problem:
Page 53 Judging Problem Difficulty
Type of Problem Timing Diff. Ch. Group Practice Problems should be just introduced to concept(s) 2 - 3 shorter and mathematically easier than just finished study of concept(s) 3 - 4 group test problems. Group Test Problems can be more just introduced to concept(s) 3 - 4 complex mathematically. just finished study of concept(s) 4 - 5
There is considerable overlap in the criteria, so most problems can be judged to be both a good group practice or test problem and a good easy, medium-difficult, or difficult individual problem.
Page 54 Judging Problem Difficulty
Examples of how to judge context-rich problems
Example Problem #1: You are helping your friend prepare for her next skate board exhibition. For her program, she plans to take a running start and then jump onto her heavy duty 15-lb stationary skateboard. She and the skateboard will glide in a straight line along a short, level section of track, then up a sloped concrete wall. She wants to reach a height of at least 10 feet above where she started before she turns to come back down the slope. She has measured her maximum running speed to safely jump on the skateboard at 7 feet/second. She knows you have taken physics, so she wants you to determine if she can carry out her program as planned. She tells you that she weighs 100 lbs.
Assume that students have just started to study the conservation of energy and conservation of momentum.
The approach to solve this problem involves using conservation of energy and conservation of momentum.
Should we reject it? • The problem can be solved in one step. NO. • The problem involves long, tedious mathematics, but little physics. NO. 3, two of which are in the approach. The mathematics involved is easy. This would make a decent group practice problem or a medium- difficult individual test problem. It is too easy for a group test problem.
If teaching this as a group practice problem, you could expect students to spend more time on the setup of the problem, and less time on the math.
Example Problem #2:
Electric and Gravitational Force: You and a friend are reading a newspaper article about nuclear fusion energy generation in stars. The article describes the helium nucleus, made up of two protons and two neutrons, as very stable so it doesn't decay. You immediately realize that you don't understand why the helium nucleus is stable. You know that the proton has the same charge as the electron except that the proton charge is positive. Neutrons you know are neutral. Why, you ask your friend, don't the protons simply repel each other causing the helium nucleus to fly apart? Your friend says she knows why the helium nucleus does not just fly apart. The gravitational force keeps it together, she says. Her model is that the two neutrons sit in the center of the nucleus and gravitationally attract the two protons. Since the protons have the same charge, they are always as far apart as possible on opposite sides of the neutrons. What mass would the neutron have if this model of the helium nucleus works? Is that a reasonable mass? Looking in your physics book, you find that the mass of a neutron is about the same as the mass of a proton and that the diameter of a helium nucleus is 3.0 x 10-13 cm.
Assume that students have just finished studying electric forces.
The approach to solve this problem involves using the idea of electric force and gravitational force.
Should we reject it? • The problem can be solved in one step. NO. • The problem involves long, tedious mathematics, but little physics. NO. Page 56 Judging Problem Difficulty 5, four of which are in the approach. The mathematics involved is easy, but the difficulty is all in the setup. Students probably have not studied gravitational force lately, which makes the problem more difficult. This would be a difficult group test problem. If teaching this as a group test problem, you could expect groups to spend most of their time on the setup of the problem, so don't worry if they haven't gotten to the math by the middle of the hour. Page 57 |
Links to the Web sites on the History of Mathematics This site, hosted by the British Society for the
Historyof Mathematics, offers a large collection of
links to sites related to the history of mathematics.
The list of contents includes General Sites, Web
Resources, Biographies, Regional Mathematics, Museums
with Mathematics Exhibits, Special Exhibits, Books
On-Line, Student Presentations, Miscellaneous,
Bibliography, Societies, Journals, Philosophy of
Mathematics, History of Computing, Scholarly Articles
and Education. The collection is very good, and from
there one can probably eventually connect to a site
where information one seeks can be found.
The Mathematical Atlas: a Gateway to Modern
Mathematics
This site is organized according to the Mathematics
Subject Classification devised by the American
Mathematical Society and its German counterpart. A guide
to mathematics that explains the various divisions of
math and provides links to appropriate pages on the Web
site, providing information generally easy to understand
and a unique look at the entire field of mathematics.
S.O.S.
MATHematics
Offers straightforward technical assistance primarily to
high school and college students, although some of its
sections will be useful to both adult learners and
professionals. A healthy variety of subjects already
appear-from simple fractions and algebra to calculus,
different equations, and matrix algebra-with the promise
of more to come. The organization is by topic, with
numerous cross-links so that navigation is
straightforward.
Professor
Freedman's Math Help
Freedman provides materials to accompany a basic algebra
course. The site not only provides algebra problems and
instruction, but also offers encouragement and specific
suggestions for success to its audience, including
strategies for note taking and test preparation.
Although a few of the instructions are a bit cryptic, a
good number provide thorough, step-by-step guides
through algebra problems, in the students' own words,
which makes it a clear and easy-to-follow site.
Mathematical Functions
This site includes elementary and special functions that
are significant not only in mathematics but also in the
natural sciences, engineering, and other fields. This is
the largest compilation of mathematical functions on the
Web, and they are committed to maintaining and expanding
it over time. The developers have created a citation
format that will allow validity of a citation over time.
BioMed
Central
BioMed Central represents a new model for access to
published results of research projects. Encompassing
many medical subjects in about 50 journal titles, the
site invites researchers to publish results online and
have their full-text information linked to PubMed, the
National Library of Medicine's premiere database of
mechanical research. Registration is not required but
takes only a few moments.
Cancer Mortality Maps & Graph Link The Cancer Mortality Maps & Graph Web Site provides
interactive maps, graphs (which are accessible to the
blind and visually-impaired), text, tables and figures
showing geographic patterns and time trends of cancer
death rates for the time period 1950-1994 for more than
40 cancers.
Harvard World Health News
World Health News is an online news digest produced by
the Center for Health Communication at the Harvard
School of Public Health. Covering critical public health
issues, it is an excellent resource for readers who are
interested in public health and related issues. The site
uses a newspaper format with three columns with an
excellent selection of information.
HighWire Press
HighWire Press is the largest archive of free full-text
science on Earth and is a division of the Stanford
University Libraries. It hosts the largest repository of
high impact, peer-reviewed content, with 1067 journals and 4,439,098 full text
articles from over 130 scholarly publishers. HighWire-hosted
publishers have collectively made 1,791,613 articles
free. These articles cover areas in biological, medical,
physical and social sciences and humanities.
HIV InSite
HIV insite is the only source of information on the
Internet about HIV disease written and edited by
researchers from a leading health science institution.
This resource is a leading Web site, not only because of
its user-friendly design and the depth, scope, and
quality of content, but also because it effectively
links together existing HIV resources on the Web.
Recommended for all levels of the academic community.
Intute: Health & Life Sciences
This a Web site of a consortium led and hosted by the
University of Nottingham and other UK partners. It
offers free access to an extensive array of high-quality
Internet resources in life and health sciences. Intute
provides access to the very best web resources for
education and research, evaluated and selected by a
network of subject specialists. There are over 31,000
resource descriptions listed here that are freely
accessible for keyword searching or browsing. This site
was previously called BIOME.
Lumen: Structure of the Human Body
This Web site provides significant resources for human
anatomy students to review structural nomenclature and
relationships using multimedia visual aids. Effective
use of multimedia, frames, and links to supplementary
study aids makes this site a superior learning tool.
Upper-division undergraduates; graduate students in
medical and nursing curricula.
National
Women's Health Information Center This site is an outstanding resource for anyone
interested in women's health issues. Sponsored by the US
government, it targets many of the most popular health
concerns and issues facing women today and offers
up-to-date information. the home page highlights current
educational campaigns, providing links to the primary
Web sites representative of each topic. A particularly
valuable resource is the Women's Health Indicators
database. Overall, this well-designed, easy-to-navigate
site provides a plethora of information.
NewScientist.com: Special Reports on Key
Topics in Science and Technology This resource is a commercial Web site tied closely
to the well-established New Scientist magazine in
Britain. It has a long list of free science and
technology hot topic news and short articles from which
to learn. Many general areas are updated weekly and some
really hot topics are updated almost daily. Some of the
hot topics covered recently are: Clone Zone, GM Food,
Quantum World, Mobile Phones, Emerging Technologies, and
Climate Change. Overall, this resource definitely keeps
one posted on the latest important science and
technology news with briefs and articles that are a joy
to read.
Nutrition Source Nutrition Source Web site is maintained by the
Department of Nutrition at the Harvard School of Public
Health. The aim of the site is to provide timely
information on diet and nutrition for clinicians, allied
health professionals, and the public. The content covers
nutrition news and healthy eating advice with access to
the following topics: interpreting news about diet; fats
and cholesterol; carbohydrates; protein; fiber; fruit
and vegetables; calcium and milk; vitamins; healthy
weight; food pyramids; and other general sources of
reliable nutrition information from books, linkages to a
few Web sites, and nutrition-related projects. Much of
the nutrition information is related to relationships
between diet and chronic diseases such as cancer and
heart disease.
BioNetbook
BNB consists of some 4,500 databases cross-listed into
searchable combinations of categories in three headings:
database types, organisms, and domain of science-or by
specific words or country of origin. This is strictly a
high-level index, not a "Web-crawler". It is more
broadly based than sites linked to it and gathers
together access to a heterogeneous collection that should
prove convenient for scientists, researchers, teachers,
and students in all kinds of higher education
institutions.
DOEgenomes.org
This site is sponsored by the National Institutes of
Health and the US Department of Energy and is a
fantastic compilation of detailed information. The
attractive main page contains abundant white space and
simple graphics that load quickly. Organized under six
major sections- About Education, Research, Medicine,
Ethical, Legal and Social Issues and Media - the site
allows users to focus quickly on the type of material
wanted. Much research is written for those in the field,
while the Education page has links for both teachers and
students, in appropriate format and vocabulary.
Genetics
Education Center
Everything anyone ever wanted to know about genetics and
the Human Genome Project is included in this site. This
is a rich source for educators, students from the
secondary level to graduate programs, and the public
interested in seeking information on genetic conditions,
progress on the human genome project, and related
topics.
Kimball's
Biology Pages
Biology Pages is an online reference manual designed for
introductory biology students but for higher levels too.
It includes an alphabetical list of terms with brief
definitions or, in some cases, a link to a brief essay
on the subject. Most of the terms used are in the areas
of cellular and molecular biology. The definitions are
clearly written, and many provide simple graphics and
links to related topics. The Web site is easy to
navigate by clicking on the first letter of the term of
interest, then scrolling through the terms to find the
desired word. An excellent resource for biology
instructors and students.
Linus Pauling and the Race for DNA This site features a first-person history about
the race to solve the structure of DNA, primarily from
Pauling's perspective. The site is divided into three
sections: the first is a narrative about the work that
led to solving the structure of DNA; a second section
consists of digitized documents, along with audio, and
video clips relating to the DNA structure. The final
section provides a day-by-day summary of Pauling's
activities from 1952-1953. The site is easy to navigate,
with many links between pages. The documents and images
reproduced in the site are of very high quality and have
the look of the original. This very focused site will be
particularly useful to those wishing to know more about
the history of molecular biology. The ability to view
original documents opens the study of the history of
science to a much broader group of researches and
students.
Nature Online The Natural History Museum in London has built a
large virtual museum modeled after and supporting the
physical entity. The educational, entertainment, and
commercial aspects of a museum are represented
throughout the site. Each area has a short topic page
with a drop-down menu leading to more short pages and
videos. The Life page offers the most information,
including many streaming videos, with sets of links
about birds, reptiles, insects, other invertebrates,
dinosaurs, plants and fungi and human origins. Evolution
features page's about the work and time lines of Darwin,
Wallace, Owens, Huxley and Willberforce. The other
topics offer similar introductions. This site is well
worth exploring and using in this way.
Neurosciences
on the Internet
This Web site is clear, organized, informative, more
accessible and intelligent than most. An important
quality is that it is visually simple. The subject
matter is divided into such topics as neuroanatomy,
biochemistry, medicine, and cognitive neurosciences. The
site has been recently updated. Related sites of
interest are
Elsevier Science.
Online Mendelian Inheritance in Man
This is the authoritative reference for information on
the inheritance of human characteristics. Recommended
for Genetics students, professionals, biology teachers
and physicians.
The Tree of Life
One of the early Web projects on biodiversity and
phylogeny, The Tree of Life, has continued to
grow and change. It now includes over 4,000 Web pages
and 526 scientist contributors worldwide. Each page
within the tree presents information written by experts
on a group of organisms. Most also provide images and
extensive bibliographies. These pages are "linked one to
another hierarchically, in the form of the evolutionary
tree of life". Visitors may thus focus on a specific
group, or travel up or down the tree to follow "the
genetic connections between all living things".
AMG
allmusic
Now in its 10th year, this site has a new interface and
added content and features. The designer's commitment to
accuracy, currency and comprehensiveness continues
compensating for the site's unrelenting advertisements.
Contributors provide biographies, review, and essays on
popular music and with the latest revision, classical
music. Those wishing to access all features (e.g.
advanced searching, music samples) must register. A
basic search by name, album, song or classical work
appears on all pages, a clunky advanced search allows
specialized searches, including full text. Coverage is
impressive: 786, 000 albums (263,000 reviews), 6 million
samples, 265,000 classical compositions and 76,000
biographies. The site's strengths continue to be the
biographies, recording credits, and internal links to
performers and reviews. Samples are often available for
all of a recording's songs at 30 second per song and for
specific recordings or performers with three 10-second
samples of limited usefulness. Discographies are updated
quickly, sometimes just days after release.
Music, Theatre & Dance
This remarkable Web site consists of several databases
that enable users not only to access different kinds of
music, photographs, manuscripts, letters and other
documents, but to come as close as possible to
experiencing materials of the Library of Congress's
collections by exploring various kinds of digital media.
Special Presentations exemplifies a fascinating
coordination of texts, sound recordings, pictures,
catalogs, supporting documentation, and searching and
zooming capabilities. The Library of Congress plans to
include new presentations and to add or incorporate more
materials to some of the presentations already
available.
Mutopia
Collection of several hundred classical music scores
available in various text formats, some with MIDI audio
files. Browse by composer, instrument, or musical style,
or search by keywords.
Performing Arts in America, 1875-1923 Created and maintained by The New York Public
Library for Performing Arts , this site makes available
a sample of the library's extensive holdings in the
history of performing arts. Wishing to "offer a glimpse
inside" a society in which "entertainment for the masses
became a thriving industry", the library selected for
viewing and listening 16,000 primary documents and
original resources - a unique and valuable collection of
newspaper clippings, promotional and production
photographs, sheet music, publicity posters and lobby
cards, moving images, programs, and recorded sound. From
the straightforward home page, one can go to About the
Collection for a brief general overview and links to
overviews of dance, music and theater. The database is
rich with images, many with zoom and enlargement
capabilities.
Passion for Jazz Music and all art is an essential part of the
"human experience." Today, Jazz music is played, studied
and taught at private and public institutions around the
globe. Whether you are a musician, or just someone who
happens to like Jazz you may visit this site to see the
wealth of material it contains. Read about the history
of Jazz, its philosophy, interact with the virtual piano
chords, learn about improvisation, or visit the photo
gallery to see portraits of many great Jazz musicians.
Classical Composer Database
Offers basic biographical information about composers,
both well known and obscure, and links to information
about them on the Web. Includes chronologies and a
composer's calendar.
Classical Music Navigator Provides information on over 400 composers, with
works listed by musical genre, a geographical roster, an
index of forms and styles, and a glossary of musical
terms. |
Teaching Differential Equations with Modeling and Visualization
Abstract: In this article, I explain the history of using Interdisciplinary Lively Applications Projects (ILAPs) in an ordinary differential equations course. Students want to learn methods to "solve real world problems," and incorporating ILAPs into the syllabus has been an effective way to apply solution methods to situations that students may encounter in other disciplines. Feedback has been positive and will be shared. Examples of ILAPs currently used will be referenced. For more information about how to develop ILAPs, see Huber and Myers (in "Innovative Approaches to Undergraduate Mathematics Courses Beyond Calculus," 2005).
Included with this document are three Interdisciplinary Lively Applications Projects (ILAPs).
Antaeus.pdf This ILAP uses the Laplace
transform to model the struggle between Hercules and Antaeus, a tale
from Greek mythology.
It is appropriate for use in an introductory course on differential
equations.
MechanicalResonance.pdf This ILAP discusses mechanical
resonance in the context of a vibrating propeller on an airplane wing.
It is suitable for use in an introductory course in differential equations.
Fever.pdf This ILAP uses Newton's Law of Cooling
to explore the question: How long should a thermometer be held in the
mouth in order to get an accurate reading? The project is based on an
article by Elmo Moore and Charles Biles in the UMAP journal, and is
suitable for use in an introductory course in differential equations.
In the project, students relate actual temperature measurements to
derive the differential equations model, then use the model to answer
the question. |
This course will make math come alive with its many intriguing examples of algebra in the world around you, from bicycle racing to amusement park rides. You'll develop your problem solving skills as you learn new math concepts. Need a little extra help? Interested in an application? Click on the chapter links below to get lesson help or explore application and career links. |
This module introduces you to the mathematical notation and techniques relevant to studying engineering at undergraduate level. The emphasis is on developing the skills that will enable you to analyse and solve engineering problems. You cover algebraic manipulation and equations, the solution of triangles, an introduction to vectors and an introduction to probability and descriptive statistics. |
Top 100 records that match your search results Displaying the top 100 results that match your query.
Schaums outline of theory and problems of essential computer mathematics
by Lipschutz, Seymour.
The mathematical knowledge needed for computer and information sciences including, particularly, the binary number system, logic circuits, graph theory, lineary systems, probability and scatistics get clear and concise coverage in this invaluable study guide. Basic high school math is all thats needed to follow the explanations and learn from hundreds of practical problems solved step-by-step. Hundreds of review questions with answers help reinforce learning and increase skills. |
Mathematics
Math Review Tips
Buy the textbook. Too many people think that they can just borrow their book from other students, use the one in the Learning Center, or just do the class without it. There is no review tool which equals the textbook.
Ask specific questions. While doing homework, identify specific areas in which you're having difficulties. This can be crucial when trying to figure out what to study. It also can be extremely helpful when getting help from a tutor or professor.
Utilize the Learning Center. The Learning Center can be a great way to review or get help on the problems that you're having. With tutors and staff that are available to help you, you have many people that are willing to help you accomplish your goal.
Attend all classes. If you're not spending time in classes, you're most likely not learning very much. Math textbooks are hard to just sit down and study from scratch, and class periods can give you a great feel for the material as well as possibly answer questions you had.
Read the appropriate section before class. With a bit of preparation, class time can make much more sense with a bit of background in the topic before the professor talks about it.
Online Math Review Websites
Khan Academy - Thousands of lessons on topics ranging from arithmetic to calculus and beyond. |
Honor's Math - Dublin
Honor's Math Programs
The goal of regular math classes is to provide appropriate levels to each student. All students are required to take an ACEprep placement test before joining the class. ACEprep materials will be used and be coordinated to what a student is learning in school if necessary. When the teacher finds an area where the student is not proficient, additional homework will be assigned to assist the student.
2013 SPRING SESSION
Dublin: Spring 2013 (April 01 to June 15, 11 weeks)
Arithmetic D
Wed 2:00 - 3:30
Arithmetic C
Thu 6:00 - 8:00
Arithmetic B
Tue 4:00 - 6:00
Arithmetic A
Tue 4:00 - 6:00
Pre-algebra
Thu 4:00 - 6:00
Algebra B
Wed 4:00 - 6:00
Algebra A
Wed 6:00 - 8:00
Geometry
Thu 6:00 - 8:00
Algebra 2/Trig
Tue 6:00 - 8:00
Pre-calculus
Sat 1:30 - 3:30
Calculus
Wed 8:30 - 10:30
Computer Competition (NCSC C)
Sat 1:30 - 3:30
AP Computer Science
Sat 11:00 - 1:00
Computer Competition (NCSC A)
Sat 9:00 - 11:00 (FULL)
2013 SUMMER SESSION
Dublin: Summer 2013 (June 17 to August 17, 9 weeks)
Arithmetic C
Thu 3:30 - 5:30
Arithmetic B
Tue & Thu 1:30 - 3:30
Arithmetic A
Mon & Wed 9:00 - 11:00
Pre-algebra
Tue & Thu 11:00 - 1:00
Algebra B
Mon & Wed 3:30 - 5:30
Algebra A
Mon & Wed 11:00 - 1:00
Geometry
Tue & Thu 9:00 - 11:00
Algebra 2/Trig
Tue & Thu 11:00 - 1:00
Pre-calculus
Tue & Thu 6:00 - 8:00
Calculus
call
Computer Competition (NCSC C)
Sat 11:00 - 1:00
Computer Competition (NCSC B)
Sat 1:30 - 3:30
Computer Competition (NCSC A)
Sat 9:00 - 11:00
All lessons are synchronized with what a student is learning at school. ACEprep materials are used in the classes. Math contest problems cab be used in parallel for the advanced students. When a student is not proficient in a certain topic, special care will be taken with a good amount of separate homework. When two or more classes are open for the math lessons, both regular and advanced classes will be managed. One time registration fee per family of $30.00 is separate. |
My Advice to a New Math 175 Student:
Like all classes, you'll find that if you actually do all
of the homework when it is assigned, it will help you beyond belief. However,
for some of us, this isn't enough to guarantee a great grade in the class. I
found that doing all of the chapter reviews the few days before each test helped
me immensely. I thought this was the best way to study for a test because
you find yourself going back through your notes, the book, and your previous
homework assignments to finish them.
Along with doing homework when its assigned, I found its best
to do the web activities and quizzes before the weekend begins (especially if
you don't have class on Fridays). By not putting it off, the material covered
in the activity/quiz is still fresh in your mind, so it takes you about a quarter
of the time to complete it instead of strugging through it on Sunday night at
11pm.
Also, you will find the web activites actually helpful if
you pay attention to them while you are doing them. Like most people, when
you first start an activity online, you will usually brush it off and not pay
attention to what you are doing, but I urge you to actually analyze and pay attention
to what the site is trying to teach you. The activites that deal with the
first and second derivatives will prove a lot more helpful if you actually focus
on learning instead of trying to complete them in record time. |
Mathematics
MATHEMATICS DEPARTMENT
Integrated Math II (418)
Integrated math provides students with a spiral curriculum that encompasses algebra, geometry, probability,statisticsand data analysis each and every year over the course of three years. The program is meeting our goal of getting everyone to algebra 2 before they graduate.
MAT418 1.0 credit Prerequisite: See chart on pages 42-44
Geometry 404
This course is designed to incorporate basic Algebra skills into a geometric setting. Students will be required to use problem solving skills, oral and written communications, projects and structured activities to develop their reasoning and logic skills. Emphasis in this course will focus on transitioning from abstract thinking to specific applications through inductive and deductive reasoning. Students will extend their knowledge through a fundamental geometric theory system. Topics include triangles, parallel lines, coordinate geometry, quadrilaterals, right triangles, similar figures, volume and area.
MAT404 1.0 credit Prerequisite:See chart on pages 42-44
Honors Algebra II 406
Algebra II 407
This course will extend and develop concepts learned in Algebra I and Geometry as well as prepare students for the fundamentals needed in Pre-Calculus and Calculus. Students will develop their problem-solving skills and drawing connections to real-life situations to give Algebra greater meaning. Graphing calculators will be used extensively to aid in data analysis and investigating mathematical concepts. Topics include systems of linear equations and inequalities, quadratic functions, matrices and determinants, functions and relations, radicals, complex numbers, exponentials, polynomial and rational functions, trigonometric ratios, sigma notation, logarithms, probability and statistics.Honors Algebra II 406will receive honors credit.
MAT406 1.0 credit Prerequisite:See chart on pages 42-44
MAT407 1.0 credit
Pre-Calculus/Trigonometry Functions 415
This course is designed for students planning to go to college. The course will cover the topics of trigonometry and elementary functions, circular trigonometric functions and their graphs, sum and difference formulas and related reduction identities, trigonometric equations, inverses of trigonometric functions, trigonometric solutions of triangles and the Law of Sines and Cosines. The course will also explore functions and their graphs, logarithmic and exponential functions and their graphs. This course is designed to give a solid foundation in topics mentioned and will prepare the student for entry into Freshman College Calculus.
MAT415 1.0 creditPrerequisite:See chart on pages 42-44
Honors Pre-Calculus/Trigonometry Functions 409
This course is designed for accelerated college preparatory students planning to takeAP Calculus. It is intended to give a foundation in fundamental topics from trigonometry and elementary functions, circular trigonometric functions and their graphs, sums and differences formulas and related reduction identities, trigonometric equations, inverses of trigonometric functions, trigonometric solutions of triangles, complex numbers, and introductions to limits.This course will receive honors credit.
MAT409 1.0 credit Prerequisite:See chart on pages 42-44
Statistics and Trigonometry 410
This year-long course covers two distinct topics. One semester serves as an introduction to statistics. Topics covered include summarizing and presentation of numerical data, probability and their distributions, the normal distribution and linear regression. The other semester spotlights trigonometry. Some topics include a study of the six trigonometric functions and their graphs, Law of Sines, Law of Cosines, trigonometric identities and inverse trig functions.
MAT410 1.0 credit Prerequisite:See chart on pages 42-44
SATPrep Course 412
TheSATPrep Course, open to sophomores, juniors and seniors, is designed to help students improve theirSATscores by familiarizing students with various test taking strategies and test content. Ideally, students should register for this course prior to taking theSATfor the final time. Students will be able to identify their weaknesses by pre-testing and take a series of actualSATpractice tests. Students will also learn time-saving techniques and short-cuts to apply to theSATproblems. Students will complete a nine week session of Mathematics and a nine week session of Reading Comprehension/Essay writing to prepare them for the newSATexamination. This course is graded on a pass or fail basis.
MAT412 0.5 credit Prerequisite:Completed Grade 9
Statistics II 413
This semester course is designed as extensions of Statistics I. Topics include probability, distribution, Central Limit theorem, and inferential statistics.
MAT413 0.5 credit Prerequisite:See chart on pages 42-44
Pre-Calculus/Calculus 414
This course will explore functions and their graphs and exponential functions, logarithmic functions and their graphs. This course is for the college-bound student who has already taken Statistics and Trigonometry. Topics include analysis of graphs, limits of a function, and derivatives. A graphing calculator will be used consistently in this course.
MAT414 1.0 credit Prerequisite:See chart on pages 42-44
Calculus 416
This year-long course is designed for college-bound students and is intended to be rigorous and challenging. Topics include analysis of graphs, limits of functions, understanding the derivative graphically, numerically, analytically and verbally as a rate of change, the definite integral as a limit of Riemann sums, integrals, differential equations, and representations of differential equations with slope fields, and applications to modeling. A TI-89 graphing calculator will be used consistently.
MAT416 1.0 credit Prerequisite:See chart on pages 42-44
Financial Math 427
This practical mathematics course is designed to provide an understanding of typical mathematics calculations in the business world. Emphasis will be placed on the calculation process as well as the analysis of the calculation. In addition to the computation, students will utilize spreadsheet technology applicable to the various topics covered throughout the course.
MAT427 1.0 credit Prerequisite: See chart on pages 42-44
Building Mathematical Foundations I 285
A one semester mathematical foundations class will be required for all freshmen who scored Basic or Below Basic on the 8thgrade PSSA Assessment in math. The class will help to provide students with strong mathematical foundations. This course will include a semester of mathematical strategies and concepts presented through mini lessons and through a computerized mathematical program. The course will focus on strengthening students' skills needed to become more competent mathematicians.
MAT285 0.25credit Prerequisite: Score of Basic or Below Basic on the 8thgrade PSSA in math
Building Mathematical Foundations II 286
The Building Mathematical Foundations II course is a nine-week course that is required for all seniors who scored basic or below basic on the 11thgrade PSSA Assessment in math. The class will utilize both technology and teacher led instruction focusing on the Pennsylvania Academic Standards for Mathematics. Student progress will be tracked using a series of formative and summative assessments.
MAT286.25 creditPrerequisite:Score of Basic or Below Basic on 11thgrade PSSA in math
AP Statistics/Basic Applied Statistics (CHS) 905
This is an introductory college-level course in statistics and probability. The use of statistical methods in the modern world makes it imperative that students understand the fundamental ideas that underlie decisions that are reached by these methods. Probability will help students understand the kinds of regularity that occur amid mathematical models in the real world. Mathematical problems with computer solutions will be emphasized. This course is aimed at students who plan to enter such fields as economics, business, education, psychology, biology, medicine, mathematics, and engineering which now require statistics for their effective pursuit.(Fourcredits from the University of Pittsburgh can be earned when taken as a College in High School course).AP credit will be given.
MAT905 1.0 credit Prerequisite:See chart on pages 42-44
AP Calculus/Calculus with Analytic Geometry (CHS)906
This course is designed for accelerated students who plan to take the AP exam. It is intended to be rigorous and challenging. Topics included are analysis of graphs, limits of a function, understanding the derivative graphically, numerically, analytically, and verbally and as a rate of change, the definite integral as a limit of Riemann sums, integrals, differential equations, and representations of differentiated equations with slope fields, and applications and modeling. ATI-89graphing calculator will be consistently used in class.AP credit will be given.(Fourcredits from Seton Hill University can be earned when taken as a College in High School course).
MAT906 1.0 credit Prerequisite:See chart on pages 42-44
Calculus II/Calculus 2 with Analytic Geometry (CHS) 916
This course is designed for the serious Math student who has completed AP Calculus 906. It is taught as a second year college-level course focusing on all the topics of AP Calculus AB and beyond. Topics include: Logarithmic, Exponential and other Transcendental Functions; Differential Equations; Applications of Integration; Integration Techniques, L'Hopital's Rule, Improper Integrals; and Infinite Series. This course is an excellent option for students who plan to focus on mathematics and/or Engineering in college. Graphing calculator applications are included.AP credit given.(Fourcredits fromSetonHillUniversitycan be earned when taken as a College in High School course).
MAT916 1.0 credit Prerequisite:See chart on pages 42-44
CalculusIII/Calculus 3 with Analytic Geometry (CHS) 917
This course is designed for the serious math student who has completed AP Statistics 905, AP Calculus 906 and Honors Calculus II 916. It is taught as a third semester college-level course focusing on all the topics of AP Calculus AB and beyond. Topics include: Conics, Parametric Equations and Polar Coordinates, Vectors and the Geometry of Space, Vector-Valued Functions, Functions of Several Variables, Multiple Integration and Vector Analysis. This course is an excellent option for students who plan to focus on mathematics and/or engineering in college. Graphing calculator applications are included.AP credit given.(Fourcredits from Seton Hill University can be earned when taken as a College in High School course).This course is only offered online.
MAT917 1.0 credit Prerequisite: See chart on pages 42-44
Functional Math 9 (421), 10 (422), 11 (423), 12 (424)
These courses focus on providing students with a modified math curriculum to address the student's specific Individual Education Plan goals. These courses are designed to accommodate students who are working significantly below grade level who would not be successful meeting the course requirements of the general curriculum without extensive supports. The courses will address individual student needs to enhance math computations, problem solving, measurement, telling time and money concepts and will address math skills to build a solid foundation through extensive skills practice, real-life connections and functional daily living math skills. These courses are aligned to state standards. |
This is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
The book is an alphabetical dictionary and handbook that gives parents of elementary, middle school, and high school students what they need to know to help their children understand the math they're learning. |
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Related TERC Resources
EMPower
Topics:
General Math Grades:
High School, Adult/Post-Secondary
The EMPower curriculum, developed by TERC and published by McGraw-Hill, fills the tremendous need for a math and numeracy program for adult basic education. EMPower helps adults develop mathematical proficiency by combining the best teaching practices of the past two decades with insights culled from educational research and classroom practice.
EMPower focuses on mathematical reasoning, communication, and problem solving with strategies and approaches designed to appeal to a broad spectrum of learning styles. Each unit includes activities with clear mathematical goals and contexts that are engaging and useful for adult learners. |
Loviscach, as both a researcher and a professor, is interested in applying digital media to education -- he has published 1,800 video lectures on mathematics and computer science on his YouTube channel, and he is known as the Salman Khan of Germany.
When asked why he wanted to teach a course at Udacity, Joern answered, "Given that German students love my style of diagramatical, common-sense reasoning, rather than strict proofs, I'd love to hear what international students think about it." He also hopes to share with the world what it means to learn in context: "Hopefully, I can convince many people plagued by math anxiety that math tends to be presented in a far more complex way than it needs to be. Also, that math makes sense after all, and isn't just a collection of funny notations and hard-to-memorize facts.
Teaching his students to apply mathematics in order to solve real world problems means a lot to Laviscach. As he mentions, there is a difference between being taught math and really learning math, "In this class I want students to get a gut feeling for mathematical models. I want to demonstrate that there is a kind of mathematics that can actually be applied in engineering -- believe it or not! Regrettably, this is not necessarily the math you learn, or should I say, the math you are taught but do not learn in a regular university course."
In this class, you can expect to think outside the box. You'll develop an intuition for the use of differential equations in the applied sciences, as well as how to build mathematical models for systems of differential equations. Along the way, you'll also learn to translate mathematical expressions into Python code in order to solve some tough problems. As such, it is a good idea to come in with a basic understanding of a typical programming language and it will be good to know how to solve quadratic equations. If you are unfamiliar with these topics, Loviscach suggests taking Udacity's Intro to Physics class first. He also notes, "You can get astonishingly far with just basic arithmetic -- if you have a good understanding of what you are doing. In this course we're not solving a single integral and we only compute one derivative the way it's done in school."
Learn from Joern Loviscach and Assistant Instructor Miriam Swords Kalk this September in Making Math Matter! Enroll today |
Save and review work – create, edit and save problem solving in documents and pages similar to the word processing and file storage features of a computer.
Connectivity – easily link with another TI-Nspire family handheld or a PC for easy file transfer
Features a dedicated programming environment as well as programming libraries for global access to user-defined functions & programs
TI-Nspire Applications
CALCULATOR – Enter and view expressions, equations and formulas exactly as they appear in math textbooks. Quickly and easily select the proper syntax, symbols and variables from a template that supports standard mathematical notation. Scroll through previous entries to explore outcomes and patterns.
GRAPHS – Graph and explore functions, animate points on objects or graphs and explain their behavior, and much more.
GEOMETRY – Create and explore geometric shapes.
LISTS & SPREADSHEET – Capture and track the values of a graph and collected data, and observe number patterns. Organize the results of statistical analysis. Capabilities similar to using computer spreadsheets: label columns, insert formulas into cells, select individual cells and change their size.
NOTES – Put the math in writing. Include the word problem with its solutions and explain problem-solving approaches – right in the handheld or computer software. Question-and-answer templates allow educators to prompt students to show solutions.
Students learn mathematical concepts more readily with deeper understanding when they learn across different forms of representation
Students using TI-Nspire handhelds have demonstrated deeper understanding and greater abilities in drawing inferences
Appropriate use of TI-Nspire technology can facilitate use of shared resources for collaborative learning, high student engagement, and a novel, integrated format for instructional units. Beliefs that the calculator is an aid to learning mathematics (not just an efficiency device)
*SAT and AP are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Praxis is a trademark of Education Testing Service. Policies subject to change. Visit and |
Calculus (CA Textbook)
This Internet resource provides introductory information, concept or skill development in Mathematics for grade 9, 10, 11, and 12 students who are at grade level in a single student situation. This text was initially written by David Guichard. The single variable material (not including infinite series) was originally a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.
This digital textbook was reviewed for its alignment with California content standards.Mathematics and Statistics2009-08-14T12:18:26Course Related MaterialsWhitman Calculus
This calculus book covers a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus. There is no chapter on differential equations.David GuichardMathematics and Statistics2008-07-18T19:07:18Course Related Materials |
Find a Marana CalculusLearning math is more than just learning formulas or repeating a procedure. To be successful at math students must understand what they are doing. This will enable them to think creatively, reason effectively, approach challenges with confidence and solve problems with persistence |
Inverse, Exponential and Logarithmic Functions
Inverse, Exponential and Logarithmic Functions teaches students about three of the more commonly used functions, and uses problems to help students practice how to interpret and use them algebraically and graphically. Students can learn the properties and rules of these functions and how to use them in real world applications through word problems such as those involving compound interest and exponential growth and decay that they will find on their homework. |
I'm starting an undergrad. course in Mathematical Physics in September and I'm gonna want to study some extra maths in the mean time I think. I figure it might as well be something useful, so my question is basically whether or not studying the old Edexcel "pure" units would be useful/helpful come September?
I'm asking about the old pure units and not more mechanics/further pure units (I've only done M1 and FP1 at A-level o: ) or some such because these are the textbooks that I'll be able to keep. My school was getting rid of a load of old textbooks recently so I figured I might as well take a few off their hands, but I've only managed to get P1-5 so far. I'm hoping to get P6 and if I'm lucky I might be able to get some of the older application textbooks as well, but I really don't know.
So yeah, would studying this stuff be a good idea or is there something else that'd be more worthwhile?
Thanks
EDIT: I just realised it sounds like I've stolen the textbooks haha. I asked first!
(Original post by TenOfThem)
Depending on your board more FP might be good
AQA have downloadable FP2 and FP3 books on their website
Their FP3 is all about differential equations which may be of use
I'm not actually going to be taking any exams so the board only matters if the textbooks will assume I know stuff that I don't know e.g. if AQA FP2 assumes I know stuff from AQA FP1 that isn't in Edexcel FP1. I'll have a look on the website, thank you downloadable textbooks sound perfect haha!
But yeah, do you reckon more pure would be more useful than more mechanics then? |
Algebra at Cool math .com Hundreds of free Algebra 1, Algebra 2 and Precalcus Algebra lessons. Great to share with students and serve as extra information. Some contain some great animation related to the topics presented. Bored with Algebra? Confused by Algebra? Hate Algebra? We can fix that. Coolmath Algebra has hundreds of really easy to follow lessons and examples. Algebra 1, Algebra 2 and Precalculus Algebra. with system:unfiledby 2 users
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Algebrator A software program to help students learning Algebra. A student must purchase to use. with algebrator
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Math Foundation Math Foundation is an award-winning program which features interactive e-learning tools to help you master the concepts of mathematics quickly and easily. The courseware is highly effective for adult learners, homeschool and traditional students. with foundationhomelearningmathtutorial |
Specific course objectives
Learn how to work in the complex framework, evaluate integrals of olomorphic functions, manipulate power and Fourier series, adopt the point of view of signal theory, calculate and operate with Fourier and Laplace transforms, solve simple ordinary differential equations with constant coefficients, understand convolutions.
Course programme
The language of signals
Continuous and discrete signals.
Basic operations on signals: sum and linear combinations of signals, traslation and rescalings. |
Friday, May 25, 2012
A Mathematical Orchard and the End of May Sale
A collection of 208 challenging, original problems with carefully worked solutions. In addition to problems from The Wohascum County Problem Book, there are about 80 new problems, many of which involve experimentation and pattern finding.
The problems are intended for undergraduates; although some knowledge of linear or abstract algebra is needed for a few of the problems, most require nothing beyond calculus. In fact, many of the problems should be accessible to high school students. On the other hand, some of the problems require considerable mathematical maturity, and most students will find few of the problems routine.
Over four-fifths of the book is devoted to presenting instructive, clear, and often elegant solutions. For many problems, multiple solutions are given. Appendices list the prerequisites for individual problems and arrange them by topic. This should be helpful to classes on problem solving and to individuals or teams preparing for contests such as the Putnam. The index can help, as well, in finding problems with a specific theme, or in recovering a half-remembered problem. |
TEXTBOOK*
Lie Groups: A Problem-Oriented Introduction via Matrix Groups
Harriet Pollatsek
Can be used as supplementary reading in a linear algebra course, or as a primary text in a bridge course that helps students make the transition to courses that emphasize definition and proofs, as well as for an upper level elective.
The work of the Norwegian mathematician Sophus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the "objects" in Lie's theory (Lie groups and Lie algebras) requires extensive mathematical prerequisites beyond the reach of the typical undergraduate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and important material becomes accessible even to college sophomores. Working with Lie's ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world.
Lie Groups is an active learning text that can be used by students with a range of backgrounds and interests. The material is developed through 200 carefully chosen problems. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers.
An Instructor's Manual is available to teachers who adopt Lie Groups as a text. Contact our Service Center for details at 1-800-331-1622.
A hardcover version of this book is available in our regular store.
* As a textbook, Lie Groups does have DRM. Our DRM protected PDFs can be downloaded to three computers. |
Exploring Multivariable Calculus is an excellent tool which a student can use to visualize surfaces in 3D. A student can enter up to four equations where some of them can be in another coordinate system such as cylindrical or spherical or even implicit. The graphs are rendered in an easy to visualize manner. The wide variety of menu options allows a student to grab and turn the graphs until they are easy to visualize. |
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 |
Minnesota High School Mathematics 5-12
Achieve excellent results on the Minnesota certification exam with the help of XAMonline. This study guide specializes in high school mathematics and covers 15 competencies and 65 skills while also concisely reviewing five content categories including Number Sense; Functions, Algebra and Calculus; Measurement and Geometry; Data, Probability and Discrete Math; and Mathematical Processes. For an extra boost of confidence, the study guide includes a 100-question sample test to give you the skills you need to succeed!
More study tools, more practice. Check out these additional products |
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Dragon Maths 4 is a write-on student workbook that contains a full mathematics programme for most Year 6 students. It gives comprehensive coverage of work at mathematics curriculum Level 3. It guides students through the Advanced Additive/ Early Multiplicative Stage (stage 6) of ...
Dragon Maths 2 is a write-on student workbook that contains a full mathematics programme for most Year 4 students. It gives comprehensive coverage of work at mathematics curriculum Level 2. It covers Stage 5 of the number framework.
Dragon Maths 6 is a write-on student workbook that contains a full mathematics programme for most Year 8 students. It gives comprehensive coverage of work at mathematics curriculum Level 4. It fully covers the Advanced Multiplicative / Early Proportional Stage (stage 7) of the Nu ...
Written by leaders in the field, this best-selling book will guide teachers as they help all Pre-K -- 8 learners make sense of math by supporting their own mathematical understanding and effective planning and instruction. Elementary and Middle School Mathematics: Teaching Develo ...
Gamma Fundamentals covers nine achievement standards. It is the ideal text for students who want to gain NCEA Level 1 credits early, or who are not continuing with Maths after Year 11. The material in Gamma Fundamentals is internally assessed at NCEA.
Gamma Mathematics covers nine of the Achievement Standards, including all the externally assessed material. It is the ideal text for students continuing on to do NCEA at Level 2 in Year 12. Gamma Mathematics has an associated Workbook with 80 self-contained assignments. |
Solution Solver 2.0 description
Solution Solver Features include: 10 master calculators with up to 7 sub calculators per master, access to internet scientific databases for data look up purposes, adjustable views and significant digit selections,and more. |
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. |
Mathematics for Plumbers and Pipe Fitters
Mathematics for Plumbers and Pipe Fitters
Mathematics for Plumbers and Pipefitters
Mathematics for Plumbers and Pipefitters
Summary
Fully updated for optimal learning, Mathematics for Plumbers and Pipefitters, 7E remains a trusted resource for essential math concepts in the plumbing and pipefitting trades. With an emphasis on real-world examples that will prepare readers to successfully transfer their knowledge to on-the-job situations, this book utilizes the most currently used fitting materials to demonstrate key concepts. Simplified, clear explanations and a straightforward approach, combined with new units on changes of state, pressure and heat, and mechanical advantage, make this an ideal tool for anyone entering the field. |
Linear Algebra Labs with MATLAB 3rd Edition
0131432745
9780131432741 setting. The LABS and Projects are meant to supplement a standard sophomore level course in linear algebra. They follow the general outline for such a course, introducing instructional routines and appropriate MATLAB commands to solve problems related to each concept. Our primary goal is to use the laboratory experiences to aid in understanding the basic ideas of linear algebra. As such we use instructional M-files that provide a tool kit for working with linear algebra without the need for programming in the MATLAB command set. Although no programming background is assumed, those students with computing skills can further enhance their skills within MATLAB. We have found that students initially rely on the tool kit, but many quickly begin to use MATLAB commands directly, even though we provide little formal instruction in this area. We recommend an instructional approach that integrates the language and terminology of computing within the lecture format. In addition, when possible and appropriate, computer demonstrations and experiments should be used in lectures. Three of the LABS are different from the others. LAB 5 examines sets with addition and scalar multiplication and investigates the defining properties of a vector space in a pedagogical way. LAB 8 presents the defining properties of the determinant in such a way that a considerable amount of class time can be saved on this topic. Also, LAB 11 presents an independent supplement to the standard classroom coverage of linear transformations by examining the geometry of plane linear transformations. New Section 11.2 introduces homogeneous coordinates to incorporate translations. The LABS are not self contained. Except for LABS 8 and 11, they assume that the material has already been presented in the classroom. Sometimes, however, it is expedient to discuss a topic using a fresh, computational approach. New material has been added to this third addition, both in the LABS and in the accompanying instructional M-files. The modifications to the LABS provide a number of alternate approaches to topics some of which use more graphically oriented M-files to provide visualization of concepts. Many of the instructional M-files have been enhanced to take advantage of the graphical user interface (GUI) available in MATLAB . In addition we have included instructional files that use the Symbolic Math Toolbox. These sections can be omitted without loss of continuity if this toolbox is not available. A detailed list of new features is on page viii and a short description of all the instructional files is on page x. A full description of the instructional files is available by printing alldesc.txt that accompanies the tool kit of instructional files. We extend our sincere gratitude to the National Science Foundation (ILI #DMS-9051282) for providing the funds for implementing a mathematics laboratory at Temple University. This facility provided the educational arena necessary to develop the laboratory materials and extend our instructional M-files for MATLAB from 1990 to 1993. We thank the many students who were patient with and receptive to using the laboratory to aid in the development and understanding of the concepts of linear algebra. A special thanks to our colleague Dr. Nicholas Macri for his valuable assistance in designing and preparing this manual. David R. Hill David E. Zitarelh May, 2003 «Show less... Show more»
Rent Linear Algebra Labs with MATLAB 3rd |
This set accompanies Saxon Math's Saxon's Algebra 1 curriculum. Ideal for extra students, this set includes 30 test forms with full, step-by-step test solutions. The answer key features answers to all student textbook practices and problem sets Saxon Algebra 1, Answer Key Booklet & Test Forms
Review 1 for Saxon Algebra 1, Answer Key Booklet & Test Forms
Overall Rating:
5out of5
Date:November 4, 2011
jan123
Location:AZ
Age:35-44
Gender:female
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
The only disadvantage in this booklet is not enough tests. For couple of chapters only one test. Even-though each chapter keeps repeating the questions fro previous chapter its just not enough practice. The test are very well made. They cover those chapters of the text book they specify. I like those test for my child.
Share this review:
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Review 2 for Saxon Algebra 1, Answer Key Booklet & Test Forms
Overall Rating:
3out of5
This is included in the home study kit!
Date:November 29, 2010
Juliana Lyon
Age:25-34
Gender:female
Quality:
3out of5
Value:
1out of5
Meets Expectations:
1out of5
I did not realize it was included in the home study kit. Just wanted to warn others ;) |
Addition and subtraction within 5, 10, 20, 100, or 1000. Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a subtraction within 20, and 55 – 18 = 37 is a subtraction within 100.
Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team. Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.1
Commutative property. See Table 3 in this Glossary.
Complex fraction. A fraction A/B where A and/or B are fractions (B nonzero).
Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. See also: computation strategy.
Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. See also: computation algorithm.
Congruent. Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).
Counting on. A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on—pointing to the top book and saying "eight," following this with "nine, ten, eleven. There are eleven books now."
Dot plot.See: line plot.
Dilation. A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.
Expanded form. A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.
Expected value. For a random variable, the weighted average of its possible values, with weights given by their respective probabilities.
First quartile. For a data set with median M, the first quartile is the median of the data values less than M. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the first quartile is 6.2See also: median, third quartile, interquartile range.
Fraction. A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.
Identity property of 0. See Table 3 in this Glossary.
Independently combined probability models. Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair.
Integer. A number expressible in the form a or –a for some whole number a.
Interquartile Range. A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9. See also: first quartile, third quartile.
Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.3
Mathematics of Information Processing and the Internet (IA). The Internet is everywhere in modern life. To be informed consumers and citizens in the information-dense modern world permeated by the Internet, students should have a basic mathematical understanding of some of the issues of information processing on the Internet. For example, when making an online purchase, mathematics is used to help you find what you want, encrypt your credit card number so that you can safely buy it, send your order accurately to the vendor, and, if your order is immediately downloaded, as when purchasing software, music, or video, ensure that your download occurs quickly and error-free. Essential topics related to these aspects of information processing are basic set theory, logic, and modular arithmetic. These topics are not only fundamental to information processing on the Internet, but they are also important mathematical topics in their own right with applications in many other areas.
Mathematics of Voting (IA). The instant-runoff voting (IRV), the Borda method (assigning points for preferences), and the Condorcet method (in which each pair of candidates is run off head to head) are all forms of preferential voting (rank according to your preferences, rather than just voting for your single favorite candidate).
Mean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.
Mean absolute deviation. A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.
Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.
Midline. In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values. Multiplication and division within 100. Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 ÷ 8 = 9.
Multiplicative inverses. Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 × 4/3 = 4/3 × 3/4 = 1.
Number line diagram. A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.
Percent rate of change. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year.
Probability distribution. The set of possible values of a random variable with a probability assigned to each.
Properties of operations. See Table 3 in this Glossary.
Properties of equality. See Table 4 in this Glossary.
Properties of inequality. See Table 5 in this Glossary.
Properties of operations. See Table 3 in this Glossary.
Probability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).
Probability model. A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.
Random variable. An assignment of a numerical value to each outcome in a sample space. Rational expression. A quotient of two polynomials with a non-zero denominator.
Rational number. A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers.
Rectilinear figure. A polygon all angles of which are right angles.
Rigid motion. A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions are here assumed to preserve distances and angle measures.
Repeating decimal. The decimal form of a rational number. See also: terminating decimal.
Sample space. In a probability model for a random process, a list of the individual outcomes that are to be considered.
Scatter plot. A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.5
Similarity transformation. A rigid motion followed by a dilation.
Tape diagram. A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.
Terminating decimal. A decimal is called terminating if its repeating digit is 0.
Third quartile. For a data set with median M, the third quartile is the median of the data values greater than M. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15. See also: median, first quartile, interquartile range.
Transitivity principle for indirect measurement. If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies to measurement of other quantities as well.
Vector. A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers.
Vertex-Edge Graphs (IA). Vertex-edge graphs are diagrams consisting of vertices (points) and edges (line segments or arcs) connecting some of the vertices. Vertex-edge graphs are also sometimes called networks, discrete graphs, or finite graphs. A vertex-edge graph shows relationships and connections among objects, such as in a road network, a telecommunications network, or a family tree. Within the context of school geometry, which is fundamentally the study of shape, vertex-edge graphs represent, in a sense, the situation of no shape. That is, vertex-edge graphs are geometric models consisting of vertices and edges in which shape is not essential, only the connections among vertices are essential. These graphs are widely used in business and industry to solve problems about networks, paths, and relationships among a finite number of objects – such as, analyzing a computer network; optimizing the route used for snowplowing, collecting garbage, or visiting business clients; scheduling committee meetings to avoid conflicts; or planning a large construction project to finish on time.
Visual fraction model. A tape diagram, number line diagram, or area model.
Whole numbers. The numbers 0, 1, 2, 3,....
Tables
Table 1. Common addition and subtraction situations. 6
Result Unknown
Change Unknown
Start Unknown
Add to
Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now? 2 + 3 = ?
Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two? 2 + ? = 5
Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? ? + 3 = 5
Take from
Five apples were on the table. I ate two apples. How many apples are on the table now? 5 – 2 = ?
Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat? 5 – ? = 3
Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before? ? – 2 = 3
Total Unknown
Addend Unknown
Both Addends Unknown1
Put Together/ Take Apart2
Three red apples and two green apples are on the table. How many apples are on the table? 3 + 2 = ?
Five apples are on the table. Three are red and the rest are green. How many apples are green? 3 + ? = 5, 5 – 3 = ?
1These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as.
2Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than or equal to 10.
3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other versions are more difficult.
Table 2. Common multiplication and division situations.7
Unknown Product
Group Size Unknown (How many in each group? Division)
Number of Groups Unknown (How many groups? Division)
3 x ? = 18, and 18 ÷ 3 = ?
? x 6 = 18, and 18 ÷ 6 = ?
Equal Groups
There are 3 bags with 6 plums in each bag. How many plums are there in all?
Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?
If 18 plums are shared equally into 3 bags, then how many plums will be in each bag?
Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?
If 18 plums are to be packed 6 to a bag, then how many bags are needed?
Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?
Arrays,4 Area5
There are 3 rows of apples with 6 apples in each row. How many apples are there?
Area example. What is the area of a 3 cm by 6 cm rectangle?
If 18 apples are arranged into 3 equal rows, how many apples will be in each row?
Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?
If 18 apples are arranged into equal rows of 6 apples, how many rows will there be?
Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?
Compare
A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?
Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?
A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost?
Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?
A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue at?
Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?
General
a × b = ?
a × ? = p, and p ÷ a = ?
? × b = p, and p ÷ b = ?
4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.
5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations.
Table 3. The properties of operations. Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system.
Associative property of addition
(a + b) + c = a + (b + c)
Commutative property of addition
a + b = b + a
Additive identity property of 0
a + 0 = 0 + a = a
Existence of additive inverses
For every a there exists –a so that a + (–a) = (–a) + a = 0.
Associative property of multiplication
(a × b) × c = a × (b × c)
Commutative property of multiplication
a × b = b × a
Multiplicative identity property of 1
a × 1 = 1 × a = a
Existence of multiplicative inverses
For every a ≠ 0 there exists 1/a so that a × 1/a = 1/a × a = 1.
Distributive property of multiplication over addition
a × (b + c) = a × b + a × c
Table 4. The properties of equality. Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems.
Reflexive property of equality
a = a
Symmetric property of equality
If a = b, then b = a.
Transitive property of equality
If a = b and b = c, then a = c.
Addition property of equality
If a = b, then a + c = b + c.
Subtraction property of equality
If a = b, then a – c = b – c.
Multiplication property of equality
If a = b, then a × c = b × c.
Division property of equality
If a = b and c ≠ 0, then a ÷ c = b ÷ c.
Substitution property of equality
If a = b, then b may be substituted for a in any expression containing a.
Table 5. The properties of inequality. Here a, b and c stand for arbitrary numbers in the rational or real number systems.
Exactly one of the following is true: a < b, a = b, a > b.
If a > b and b > c then a > c.
If a > b, then b < a.
If a > b, then –a < –b.
If a > b, then a ± c > b ± c.
If a > b and c > 0, then a × c > b × c.
If a > b and c < 0, then a × c < b × c.
If a > b and c > 0, then a ÷ c > b ÷ c.
If a > b and c < 0, then a ÷ c < b ÷ c.
1Adapted from Wisconsin Department of Public Instruction, standards/mathglos.html, accessed March 2, 2010.
2Many different methods for computing quartiles are in use. The method defined here is sometimes called the Moore and McCabe method. See Langford, E., "Quartiles in Elementary Statistics," Journal of Statistics Education Volume 14, Number 3 (2006).
3Adapted from Wisconsin Department of Public Instruction, op. cit.
4To be more precise, this defines the arithmetic mean.
5Adapted from Wisconsin Department of Public Instruction, op. cit.
6Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).
77The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. |
For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and pro...
For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text... |
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Normal 0 false false false Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps students explore key concepts and push their understanding to new heig...
Normal 0 false false false For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet... |
Division Practice Book 2, Grades 4-5 by Ned Tarrington
Price: $0.99 USD. 2890 words.
Language: English. Published on July 24, 2011. Nonfiction » Children's Books » Science.Elementary Algebra Expression Practice Book 2, Grades 4-5 by Ned Tarrington
Price: $0.99 USD. 2140 words.
Language: English. Published on July 29, 2011. Nonfiction » Children's Books » Mathematics / Algebra.
Enhance essential elementary algebra skills with these twenty-one practice problems. Each problem has an expression with mixed operators to reinforce the concept of operator precedence and use of parentheses. Choose a problem from the problem list, and then confirm your answer by easily navigating the link to the complete instructive solution. Most appropriate for 4th and 5th grade students.
Middle School Math Solution: Algebra and Number by Jing Guan
Price: $39.99 USD. 77460 words.
Language: English. Published on October 27, 2011. Nonfiction » Science and Nature » Mathematics.
Math is a special and important learning in education. Even though Math is hard to some people, it is not hard to learn if you follow a good guide. This book is a good guide that will help high/middle school students learn basic and advanced skills with important concepts and skills carefully designed into questions and solution for students to master. This book will escort you to your success.
Catch Up With Your Kid in Middle School Math in a Day by A. Datta
Price: $3.53 USD. 21480 words.
Language: English. Published on January 1, 2012. Nonfiction » Science and Nature » Mathematics.
This book is for you if you would like to be involved in your school-going kid's math education and need to get your own basics right, or if you decided to extend your education, may be involving some computer programming, or statistics and want to be up to speed in junior high school math before taking the next step. This is not on teaching techniques.
Multiplication Practice Book 2, Grades 4-5 by Ned Tarrington
Price: $0.99 USD. 2890 words.
Language: English. Published on July 20, 2011. Nonfiction » Children's Books » Science. 4th and 5th grade students.
Subtraction Practice Book 1, Grade 3 by Ned Tarrington
Price: $0.99 USD. 2870 words.
Language: English. Published on July 8, 2011. Nonfiction » Children's Books » Science.
Practice and hone important subtraction skills. Select one of twenty math problems with complete solutions that educate the student in the subtraction process. The book also includes four bonus word problems with complete explanations and answers. Easily navigate the links from the problem list to view the solution. Most appropriate for 3rd grade students.
Fruitful Addition by Ned Tarrington
Price: $1.99 USD. 16470 words.
Language: English. Published on August 21, 2011. Nonfiction » Children's Books » Science.
Learn important math skills by using pictures to supplement addition concepts. Choose between 45 basic addition problems, work the problem, and then follow the link to the complete answer. Each problem and also the answer have corresponding fruit pictures for the student to view. The math level of this book is most appropriate for children in kindergarten. |
Description
For introductory sophomore-level courses in Linear Algebra or Matrix Theory.
This text presents the basic ideas of linear algebra in a manner that offers students a fine balance between abstraction/theory and computational skills. The emphasis is on not just teaching how to read a proof but also on how to write a proof.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
1 - Linear Equations And Matrices
2 - Solving Linear Systems
3 - Determinants
4 - Real Vector Spaces
5 - Inner Product Spaces
6 - Linear Transformations and Matrices
7 - Eigenvalues and Eigenvectors
8 - Applications of Eigenvalues and Eigenvectors (Optional)
9 - MATLAB for Linear Algebra
10 - MATLAB Exercises
A P P E N D I X A Preliminaries
A P P E N D I X B Complex Numbers
A P P E N D I X C Introduction to Proofs |
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Mathematics
Mathematics Department
Teachers: Jose Tajeda, Roy Sam, Borges Rafael
All students must complete 4 years of Mathematics. Regents exams are generally taken at the student's third year. Freshmen must pass the Math A Regents or Intergrated Algebra Regents for a Regents Diploma and either: -Both Math A and Math B for an Advenced Regents Diploma -OR Intergrated Algebra AND Geometry AND Trigonometry Regents.
Integrated Algebra (1&2): This course is an in-depth study of algebraic principles, conceptual understanding, procedural fluency and problem solving. This is the first course of the new NYS High School Mathematics Regents sequence. This coourse culiminates ina Regents Exam.
Geometry (1&2): This is a three semester course in which students learn how to construct geometric proofs and logic proofs. Students also further develop their skills in algebra and are introduced to key concepts in the following areas: trigonometry; logarithms; probability, and statistics. |
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MAC 1108 - Applications of College Algebra
This course is team-taught with biology, chemistry and physics faculty. How concepts from college algebra are applied to the fields of biology, chemistry and physics will be examined.
Corequisite: MAC 1105. Terms Offered: Fall, |
AS/A2 Mathematics (level 3)
Develop an understanding of coherence and progression in mathematics and extend your range of skills and techniques
Is it for me?
If you want to learn more about maths and its applications and appreciate the support it offers to other subjects then this is the course for you. Assessment is exam based.
What's involved?
AS
Core Mathematics 1
Extend your knowledge of polynomials and the use of both algebraic and graphical techniques for their resolution. You will meet the foundations of calculus, exploring such techniques as differentiation and integration.
Decision Mathematics 1
Learn what an algorithm is and develop skills in various sorting algorithms. Graphs and networks form the major part of this unit. The application of mathematical modelling will be covered leading to linear programming which has many applications.
Core Mathematics 2
This unit introduces sequences and series and develops the concept of limits. You will meet exponentials and logarithms which have practical importance to 'real world' situations. Your knowledge of trigonometry will be extended as will your skills in calculus.
A2
Core Mathematics 3
You will look at functions and their notation and how they can be represented graphically. In trigonometry you will look at inverse graphs, solve trigonometric equations and meet some more identities.
Core Mathematics 4
Develop your algebraic skills by simplifying expressions, performing algebraic division and working with partial fractions. Working in the (x,y) plane you will use cartesian and parametric equations to represent curves. Binomial series will be investigated as will their validity. Trigonometry will be developed to include compound angle and double angle formulae and other identities that are useful in calculus.
Statistics 1
Using calculators to obtain mean and standard deviation values from data sets. You will assess the appropriateness of numerical measures such as mean, median, mode, range and interquartile range. You will use probability and look at the concept of random events. You will adopt correct notation and apply probability laws. You will work with the Binomial distribution and Normal distribution and their properties. You will look at samples and make predictions about populations to include confidence intervals.
Entry Requirements:
A minimum of 5 GCSEs at grades A* to C, with:
grade B or above in Maths
grade C or above preferred in English Language.
Which courses go well with this?
This course combines well with all science subjects but especially Further Maths and Physics. It can also be used as a broadening subject alongside non-science subjects e.g. Economics.
Progression:
Mathematics A2 can lead to many mathematics, science and engineering related courses in higher education. |
This course provides the underlying mathematical concepts and processes applied in the fields of science and the technologies. Topics include scientific notation, the U.S. and metric systems of measurement, solving equations and graphing functions, perimeters, areas, volumes, the Pythagorean Theorem, logarithms, and right triangle trigonometry. A scientific calculator is required for this course. A (F, Sp) |
Do the Math: Secrets, Lies, and Algebra
In the eighth grade, 1 math whiz < 1 popular boy, according to Tess's calculations. That is, until she has to factor in a few more variables, like:
1 stolen test (x),
3 cheaters (y),
and 2 best friends (z) who can't keep a secret.
Oh, and she can't forget the winter dance (d)!
Then there's the suspicious guy Tess's parents know, but that's a whole different problem.—
Allie (Forest Hill, MD)
This was a very interesting book. It had a new way of looking at life: through math. As the main character discovers, math is so logical that it can often help to solve problems in real life--and she has some big ones. Any math lover would instantly love this book, and anyone else would love it also for its unique perspective on life. I would highly recommend it to anyone, even those who think math is useless (maybe this will change their minds).
—
Molly (Agua Dulce, CA)
This wonderful, witty book puts things in a refreshingly new perspective, relating everyday things to math in a way that will have you thinking. This book evokes an interest in math without being a textbook and also allows us to enter the world of a typical teenage girl. This book combines typical teenage life and math in a way that will make you excited for math class.
—
Darcy (Hudson, WI)
Do the Math: Secrets, Lies, and Algebra is a light-hearted read, perfect for a breezy summer day and a cold glass of pink lemonade. Tess, a self-proclaimed "math lover" finds ways to relate her real-life eighth grade situations to (what else?) algebra. For once, Tess must question everything- even math. She soon learns the true value of friends, family, and algebra.
Do the Math #2: The Writing on the Wall |
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DescriptionFeatures & benefits
Key features
Contents address the syllabus topics studied at year 10.
A theme-based exercise at the end of each chapter, called Application, provides a set of exercises to show the practical application of the maths learned in the chapter.
Written in straightforward language to ensure ease of comprehension.
Each chapter opens with a problem to illustrate the relevance of the maths to be learned. This problem is reviewed at the end of the chapter.
The chapter-opening page also includes a list of the key concepts to be covered in the chapter plus a clear reference to the relevant syllabus outcome so that students know exactly what they will be studying.
A background quiz, Before you start, to test that students have the skills to complete the chapter, immediately follows the chapter-opening page.
Plenty of clear worked examples and well-graded exercises - each question is coded to indicate the level of difficulty.
Did you know? boxes in the margin provide interesting snippets of information to stimulate students' interest.
Language references in the margin explain key terms and other language features to address maths literacy.
Hints remind students of key points to remember when tackling specific questions; Error Alerts! remind students of common mistakes.
Many practical and group activities are included throughout the text.
Visually appealing design with not too much material on each page, enlivened by frequent use of cartoon-style illustrations.
Each chapter concludes with Test Yourself! which reviews the work of the chapter. |
An Introduction to Optimization, 2nd Edition
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business |
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DescriptionExamining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions:
What mathematical knowledge and skills matter for the world of work today?
How does information technology change the necessary knowledge and the ways in which it is encountered?
How can we develop these essential new skills in the workforce?
With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.
Contents
Acknowledgements
1. Introduction
1.1 New Demands on Commerce and Industry
1.2 Information Technology and the Changing Nature of Work
1.3 Background to the Research
1.4 A Description of Key Ideas
1.5 Aims and Methods
2. Manufacturing 1: Modelling and Improving the Work Process in Manufacturing Industry
2.1 Process Improvement in Manufacturing
2.2 Workplace Observations of Process Improvement
2.3 Learning Opportunities for Process Improvement
2.4 Outcomes for Learning and Practice
2.5 Conclusions
3. Manufacturing 2: Using Statistics to Improve the Production Process
3.1 Process Control and Improvement Using Statistics
3.2 Workplace Observations of Statistical Process Control
3.3 Learning Opportunities for Statistical Process Control
3.4 Outcomes for Learning and Practice
3.5 Conclusions
4. Financial Services 1: Pensions and Investments
4.1 The Techno-Mathematics of Pensions and the Work of Customer Services
Related Subjects
Name: Improving Mathematics at Work: The Need for Techno-Mathematical Literacies (Paperback) – Routledge
Description: By Celia Hoyles, Richard Noss, Phillip Kent, Arthur Bakker. Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the twenty-first century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies...
Categories: Adult Education and Lifelong Learning, Educational Research, Post-Compulsory Education, Teaching & Learning, Education Policy, Work-based Learning, Operational Research / Management Science |
Discovering Geometry Intro
Discovering Geometry began in my classroom over 35 years ago. During my first ten years of teaching I did not use a textbook, but created my own daily lesson plans and classroom management system. I believe students learn with greater depth of understanding when they are actively engaged in the process of discovering concepts and we should delay the introduction of proof in geometry until students are ready. Until Discovering Geometry, no textbook followed that philosophy.
I was also involved in a Research In Industry grant where I repeatedly heard that the skills valued in all working environments were the ability to express ideas verbally and in writing, and the ability to work as part of a team. I wanted my students to be engaged daily in doing mathematics and exchanging ideas in small cooperative groups.
The fourth edition of Discovering Geometry includes new hands-on techniques, curriculum research, and technologies that enhance my vision of the ideal geometry class. I send my heartfelt appreciation to the many teachers who contributed their feedback during classroom use. Their students and future students will help continue the evolution of Discovering Geometry. |
sophomore/junior-level courses in Merchandising Problems, Retailing Mathematics, and Merchandising Mathematics. Reflecting the authors' extensive practical experience in the world of retailing, this text provides students with a basic knowledge of the principles and techniques of real-world merchandising mathematics and explains how to apply these fundamentals to solving specific, everyday retail merchandising problems. Instructor- and student-friendly, the text features clear, concise explanations of concepts followed by exam... MOREple problems, and practice problems using realistic industry figures. This book provides readers with a firm foundation in the principles and techniques ofreal-world merchandising mathematics and shows them how to apply these fundamentals to solving specific, everyday retail merchandising problems. Throughout, clear, concise explanations of concepts are followed by step-by-step example problems, practice problems using realistic industry figures, and selected answers. Includes suggestions for working some problems on a computer spreadsheet. Features a review of basic mathematics, decimals, percents, fractions, and highlighted formulas. Basic Merchandising Mathematics. Profitability. Cost of Merchandise Sold. Markup as a Merchandising Tool. Retail Pricing for Profit. Inventory Valuation. The Collar Merchandise Plan. Dollar Open-to-Buy. Performance Measures. For Retail Executives and Buyers in training and Small Storeowners. Concepts are followed by step by step example problems, practice problems using realistic industry figures, and selected answers. For retail executives and buyers in training and small storeowners. Softcover. |
Increasing our awareness of why we have math anxiety and an appreciation of our own attitudes can actually help us to learn anxiety management tools and strategies to learn math. An emphasis is placed on understanding problem solving techniques and math assertiveness.
Prerequisite: MATH 075 with a minimum grade of C or MATH 085 (may be taken concurrently). |
Calculus - an Introduction
By M. Bourne
Founders
of Calculus
Sir Isaac Newton
Gottfried
Leibniz
The volume of wine
barrels was one of the problems solved using the
techniques of calculus. See a solution at Volumes by Integration.
Calculus is concerned with comparing quantities which
vary in a non-linear way. It is used extensively in
science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit)
do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.
Calculus was developed independently by the Englishman, Sir
Isaac Newton, and by the German, Gottfried Leibniz. They were both working on problems of motion towards
the end of the 17th century. There was a bitter dispute between the men over who developed calculus first.
Because of this independent development, we have an unfortunate mix of notation and vocabulary that is used in calculus.
From Leibniz we get the dy/dx and ∫ signs.
The development of an accurate clock in the 17th century led to significant developments in science and mathematics, and amongst the greatest of these was the calculus.
For scientists, it was very important to be able to predict the
positions of the stars, to help in maritime navigation. The greatest challenge was to determine longitude when a ship was at sea.
Whichever nation could send ships to the New World and
successfully bring them back laden with goods, would become a
rich country.
Newton and Leibniz built on the algebraic and geometric work
of Rene Descartes, who developed the Cartesian co-ordinate system, which we met before.
There are two main branches of calculus.
The first is differentiation (or derivatives), which helps us to find a rate of change of one quantity compared to another.
The second is integration, which is the reverse of differentiation.
We may be given a rate of change and we need to work backwards to find the original relationship (or equation) between the two quantities.
Calculus in Action 1
Solar Two sustainable energy project in
California.
A power tower produces electricity from sunlight
by focusing thousands of sun-tracking mirrors, called
heliostats, on a single receiver sitting on top of a
tower. The receiver captures the thermal energy of the
sun and stores it in tanks of molten salt (to the right
of the tower) at temperatures greater than 500 degrees
centigrade.
When
electricity is needed, the energy in the molten salt is used
to create steam, which drives a conventional electricity-generating
turbine (to the left of the tower).
Calculus (in this case, differentiation) is used to maximise
the efficiency of the process.
Calculus in Action 2
Calculus is used to improve the efficiency of hard drives and other computer components.
Differentiation
The 3 sections on differentiation in Interactive Mathematics are as follows:
Differentiation, which introduces the concept of the derivative and gives examples of the basic techniques for differentiating. |
Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering. |
Science, Technology, and Mathematics > Mathematics
This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.
Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece.
In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.
Revving engines, smoking tires, and high speeds. Car racing enthusiasts and race drivers alike know the thrill of competition, the push to perform better, and the agony—and dangers—of bad decisions. But driving faster and better involves more than just high horsepower and tightly tuned engines. Physicist and amateur racer Chuck Edmondson thoroughly discusses the physics underlying car racing and explains just what's going on during any race, why, and how a driver can improve control and ultimately win.
The world of motorsports is rich with excitement and competition—and physics. Edmondson applies common mathematical theories to real-world racing situations to reveal the secrets behind successful fast driving. He explains such key concepts as how to tune your car and why it matters, how to calculate 0 to 60 mph times and quarter-mile times and why they are important, and where, when, why, and how to use kinematics in road racing. He wraps it up with insight into the impact and benefit of green technologies in racing. In each case, Edmondson's in-depth explanations and worked equations link the physics principles to qualitative racing advice.
From selecting shifting points to load transfer in car control and beyond, Fast Car Physics is the ideal source to consult before buckling up and cinching down the belts on your racing harness.
As anyone from cold climates knows, frequently occurring ice and snow lead to a special appreciation of sports such as skiing, sledding, and skating. Prolific physics popularizer Mark Denny's take on winter athletics lays out the physical principles that govern glaciated game play.
After discussing the physical properties of ice and snow and how physics describes sliding friction and aerodynamic drag, Denny applies these concepts to such sports as bobsledding, snowboarding, and curling. He explains why clap skates would only hinder hockey players, how a curling rock curls, the forces that control luge speed, how steering differs in skiing and snowboarding, and much more. With characteristic accuracy and a touch of wit, Denny provides fans, competitors, and coaches with handy, applicable insight into the games they love. His separate section of technical notes offers an original and mathematically rigorous exploration of the key aspects of winter sports physics.
A physics-driven exploration of sports played on ice and snow that is truly fun and informative, Gliding for Gold is the perfect primer for understanding the science behind cold weather athletics.
Why does a harpsichord sound different from a piano? For that matter, why does middle C on a piano differ from middle C on a tuning fork, a trombone, or a flute? Good Vibrations explains in clear, friendly language the out-of-sight physics responsible not only for these differences but also for the whole range of noises we call music.
The physical properties and history of sound are fascinating to study. Barry Parker's tour of the physics of music details the science of how instruments, the acoustics of rooms, electronics, and humans create and alter the varied sounds we hear. Using physics as a base, Parker discusses the history of music, how sounds are made and perceived, and the various effects of acting on sounds. In the process, he demonstrates what acoustics can teach us about quantum theory and explains the relationship between harmonics and the theory of waves.
Peppered throughout with anecdotes and examples illustrating key concepts, this invitingly written book provides a firm grounding in the actual and theoretical physics of music. |
Fundamentals of Precalculus is designed to review the fundamental topics that are necessary for success in calculus. Containing only five chapters, this text contains the rigor essential for building a strong foundation of mathematical skills and concepts, and at the same time supports student... |
Contents
Linear Algebra is the Small Scale Theory of Everything
To study the large, start with the small.
In small scales, every space is a vector space.
Indeed if you walk a mile east, a mile north, a mile west and a mile south, you're back were you started, but if you fly a 1,000 miles east, a 1,000 miles north, a 1,000 miles west and a 1,000 miles south, you're not back were you started (where will you be?).
Some Technical Remarks
The Term Test
Our one and only Term Test is coming up. It will take place in class on Tuesday October 24 2006, starting promptly at 1:10PM and ending at 3:00PM sharp. It will consist of 4-5 questions (each may have several parts) on everything that we will have covered in class by October 18: the axiomatic definition of fields and vector spaces, and other examples, spans, linear combinations and linear equations, linear dependence and independence, bases, the replacement lemma and its consequences, a bit about linear transformations and a few smaller topics that we touched but don't deserve their own headers.
Extra Class Time
On Thursday, October 26th, we will have a 2-hour class (1-3PM) to make up for the class time lost on the Term Test, and just one hour of tutorials (3-4PM) as no HW assignment is due on that week anyway. |
Prealgebra - With Cd - 4th edition
Summary: For courses in Basic College Mathematics, Introductory Algebra, and Intermediate Algebra, and combined Beginning and Intermediate Algebra.
This engaging workbook series presents a student-friendly approach to the concepts of basic math and algebra, giving students ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the worktexts are to build confidence, increase motivation, and encourage ...show moremastery of basic skills and concepts. Martin-Gay ensures that students have the most up-to-date, relevant text preparation for their next math course; enhances students' perception of math by exposing them to real-life situations through graphs and applications; and ensures that students have an organized, integrated learning system at their fingertips. The integrated learning resources program features text-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5 |
UA preparatory math goes virtual
Apr 26, 2011 By La Monica Everett-Haynes
Is this what flashes across your mental screen when you think about math? The UA's mathematics department is piloting a new course, Math 100, which is designed to help students who struggle with university-level math. The course provides personalized instruction with a heavy emphasis on tutoring, peer support and the use of technology.
The University of Arizona's math department is experimenting with a novel approach to early math instruction – one with a heavy emphasis on technology and peer-to-peer tutoring.
Arguably, few other required college-level courses elicit the same frustration or the intimidation factor as mathematics.
Some commonly talk about holding a hatred for math, believe they are no good at it or think up strategies to avoid it all together.
But one University of Arizona team is working to unravel the enigmatic nature of math for the very students who struggle the most with it – those who do not test into college-level math.
Math 100, now in the second semester of its pilot phase, has a heavy emphasis on both self-paced progress and peer-to-peer support while being offered through Elluminate, a web-conferencing system.
"Students are so used to being online. We thought that if we put the course online we could interact more," said Michelle Woodward, who coordinates the pilot course being offered by the UA mathematics department.
The number of section offerings will be expanded during the fall to accommodate more UA students who do not test into algebra-level mathematics.
Woodward said the course is being emphasized and expanded because it is especially important for new students to grasp college math, especially algebra – a curricular core – early.
Algebraic skills have long been associated with giving students the ability to think in more complex ways. A student's ability to comprehend algebra has long been upheld as an indication of college-readiness, particularly for study in science and engineering-related disciplines.
"It's the foundational material they need to be prepared for college algebra," Woodward said.
"My whole goal in this is to make an online environment that is as close to what students would do in person. I want the environment to be as interactive as possible," Woodward said, adding that another program, the ALEKS Learning Module, provides both structure and flexibility while also offering the course content.
"I have done a lot of work with students who needed individualized plans. ALEKS does that for me," she said. "I could not do that for 300 students, it doesn't replace me – it frees me up to work with students individually, the kind of work I didn't have time to do before."
Over the course of the semester, the 300 students currently enrolled in one dozen Math 100 sections meet three hours weekly, receiving self-paced instruction mediated by Elluminate. Students complete assignments, learning to master algebraic expressions and graphing techniques and, all the while, ALEKS tracks their progress.
"We are able to personalize the lessons much better than we have. It's been wonderful," said Cheryl Ekstrom, a mathematics lecturer who initiated the idea to incorporate Elluminate. "You aren't stuck listening to a lecture on things you already know or breezing by things you don't understand."
This is in direct contrast to more established and traditional ways of teaching math.
"In a traditional class, it doesn't matter if it's hard for you," said Shailendra Simkhada, an electrical engineering senior also studying math.
"Each day in a regular class, you might get a new chapter or deadline to meet but, here, they can work at their own pace," he said.
"It's not that they do less work, but if you don't understand something you get more information and one-on-one help so that they stay on track," he added.
If fact, students designate their goals at the start of the class, deciding what sections they want to master and what math class they hope to test into at the end of the term.
Students also engage in weekly virtual classroom meetings, sharing their computer screens and conversing online with student leads and support staff – UA students who are advanced in math and receive more than 15 hours of training.
Kirandeed Banga, a UA sophomore studying biology, is a member of the student lead and support staff.
Each week, Banga joins the other leads and support staff members in a classroom in the Math Building where they each log online to tutor and monitor student work.
"With it being completely online, it's hard to get their trust. But we try to talk to them as much as possible," said Banga who, like others on the team, also offer office hours.
"And we put them into virtual groups, so they are also able to help one another," she added. "They obviously are used to the technology, so they can adapt to it."
Also built into the design of the course is extensive support to the UA students facilitating the class.
Ivvette Rios, a UA math and French major, observes the virtual sessions and conducts weekly meetings with all of the students offering tutoring and support. Her role is to ensure that the leads and support staff have everything they need to appropriately help the hundreds of students enrolled.
Rios said the time for self-evaluation and self-reflection is critical for those involved, and helps to ensure that the structure is working well for all involved.
"We are always thinking of ways we can do this better; to make it more and more like our everyday experience," Rios said. "It's work out way better than we thought it would."
Leo Shmuylovich knows a lot about how tutoring can take a student from confused to confident. The Washington University graduate student has worked as a tutor for several test preparatory companies over the years, helping ...
(PhysOrg.com) -- New research from the University of Notre Dame suggests that even though adults tend to think in more advanced ways than children do, those advanced ways of thinking don't always override old, incorrect"Considering how many fools can calculate, it is surprising that it should be thought either a difficult or tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the text-books of advanced mathematics-and they are mostly clever fools-seldom take the trouble to show you how easy the calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way." Calculus Made Easy, Silvanus P. Thompson, Prologue, 1910 Diet |
A First Book in Algebra
"A First Book in Algebra" will give you the confidence to tackle mathematical, science or social research problems using the power of algebra. Contains extensive worked examples and over 1400 exercises - with answers of course!First published over 100 years ago, this volume remains the definitive guide to applying elementary algebra to real-world problems, whether for everyday use or exam preparation.
show more show less
A FIRST BOOK IN ALGEBRABYWALLACE C. BOYDEN, A.M.
Edition:
N/A
Publisher:
CreateSpace Independent Publishing Platform
Binding:
Trade Paper
Pages:
180
Size:
8.00" wide x 10.00" long x 0.41 Book in Algebra - 9781463706470 at TextbooksRus.com. |
Course in Enumeration
9783540390329
ISBN:
3540390324
Pub Date: 2007 Publisher: Springer
Summary: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more ...about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result |
Curve *A 38-digit precision math emulator for properly fitting high order polynomials and rationals. *A robust fitting capability for nonlinear fitting that effectively copes with outliers and a wide dynamic Y data range.
Graphically Review Curve Fit Results: Once CurveCompact Calculator - CompactCalc - CompactCalc is an enhanced scientific calculator for Windows with an expression editor.CompactCalc is an enhanced scientific calculator for Windows with an expression editor. It embodies generic floating-point routines, hyperbolic and...Desktop Calculator - DesktopCalc - DesktopCalc is an enhanced, easy-to-use and powerful scientific calculator with an expression editor, printing operation, result history list and integrated help.DesktopCalc is an enhanced, easy-to-use and powerful scientific calculator with an... |
Math of Finance is a course approved by the State Department of Education to count as a math credit if it is taught at the rigor of Algebra I or above. The course teaches about aspects of personal income, wages, and tax deductions. Areas of home buying, renting, bill paying, and auto purchases are also covered. Lastly, the course will conclude with personal retirement accounts, planning for the future, and Federal Income Tax filings.
Algebra A&B
Semesters: 1 or 2
Grade level: 9 - 12 Prerequisite: None Description:
The students will explore expressions, equations, functions and rational numbers, learn basic algebraic procedures for solving equation and inequalities, also learn proportional reasoning, graphing techniques, factoring polynomials, and explore rational expressions and equations. Upon completion of this course students will take a state mandatory Instruction Test and that score will be posted on their transcripts.
This course is designed to reinforce and continue using skills learned in Algebra I. Students will explore the language of algebra in verbal, tabular, graphical, and symbolic forms. Upon completion of this course students will take a state mandatory Instruction Test and that score will be posted on their transcripts.
Precalculus explores topics in algebra, trigonometry, and analytic geometry to prepare the students for calculus. Precalculus provides an extensive review of algebra before introducing functions and their graphs. The use of technology is made in many examples and exercises. All exercises, applications, and examples have been selected for their relevance to calculus.
Calculus challenges students to apply math principles to real-life situations and to develop their capacity for problem solving. The skills and lessons in the course will aid the student in the retention of important concepts, reinforce concepts through practice, apply concept in variety of contexts, promote student collection of data, develop logical thinking skills, and improve usage of math theory in proofs.
This course challenges students to develop their capacity for problem solving. The skills and lessons in the course will aid the student in the retention of important concepts, reinforce concepts through practice, apply concepts in a variety of contexts, promote student collection of data, develop logical thinking skills, and improve usage of math theory in proofs. Upon completion of this course students will take a state mandatory Instruction Test and that score will be posted on their transcripts.
The Stigler Public Schools website is under the supervision of Linda Henderson, Web Page Advisor. The Web Page team each year at Stigler High School is responsible for updating and maintaining all information. This team is also under the direct supervision of Linda Henderson, Web Page Advisor. Any questions or comments regarding our Web Site should be directed, through email, to [email protected]. Any technical questions should be directed, through email, to our technical director [email protected]. We do not believe that anything on this web site is copyright protected. If you find something that is copyrighted, please tell us, and it will be removed as quickly as possible. All content has been checked for suitability. However, the Stigler School District is not responsible for the accuracy, nature, or quality of the information on any page not constructed by the Stigler Web Design Class. |
Manhattan Beach ACT MathAs a radar and satellite systems engineer, algebra is key to understanding basic principles of each subject. I |
Mathematics (MAT)
Precalculus Algebra
This is the first of two courses designed to emphasize topics which are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and predictions. |
This course is designed for students who have successfully completed the standards for Algebra I. The course, among other things, includes properties of geometric figures, trigonometric relationships, and reasoning to justify conclusions. Methods of justification will include paragraph proofs, flow charts, two-column proofs, indirect proofs, coordinate proofs, and verbal arguments. A gradual development of formal proof is encouraged. Inductive and intuitive approaches to proof as well as deductive axiomatic methods should be used.
This set of standards includes emphasis on two- and three-dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving techniques should be used to implement these standards, including algebraic skills. Calculators, computers, and graphing utilities (graphing calculators or computer graphing simulators), dynamic geometric software, and other appropriate technology will be used as tools to assist in teaching and learning. Any technology that will enhance student learning should be used.
The information contained in this curriculum applies to both single and double blocked classes. |
Mathematics
The general goals of the program are to provide all students with knowledge of the basic facts, principles and methods of mathematics, and the computational skills needed to apply them. Seventh graders are grouped according to placement test results. A two-track sequence, chosen by the student and parent(s) with advice from teachers, starts in grade 8. An honors program is offered in grades 11 and 12. |
Fundamentals of Elementary Calculus The Real Number System Continuous Functions Extensions of the Law of the Mean Functions of Several Variables The Elements of Partial Differentiation General Theorems of Partial Differentiation Implicit-Function Theorems The Inverse Function Theorem with Applications Vectors and Vector Fields Linear Transformations Differential Calculus of Functions from Rn to Rm Double and Triple Integrals Curves and Surfaces Line and Surface Integrals Point-Set Theory Fundamental Theorems on Continuous Functions The Theory of Integration Infinite Series Uniform Convergence Power Series Improper Integrals Answers to Selected Exercises |
256 October 10 & 14, 2008Mathematical Induction (Rosen 4.1) Mathematical induction is a form of proof that is used to prove statements of the following structure: n Z+ P (n), where P (n) is some statement about the positive integer n. A
Mathematics 256, Final Exam 9:00 a.m.12:00 noon, December 18, 2008The nal exam will be comprehensive. Approximately 40% of the exam will cover discrete mathematics and 60% will cover linear algebra. Your nal exam score may replace one of the two tes
Euclids Algorithm and Solving Congruences Mathematics 100 A September 22, 2006Denition. The greatest common divisor of two natural numbers a and b, written gcd(a, b), is the largest natural number that divides both a and b. Middle School Algorithm.
36243_1_p1-2912/8/97 8:39 AM Page 23MORE ABOUT FUNCTION PARAMETERSDefault Values for Parameters in FunctionsProblem. We wish to construct a function that will evaluate any real-valued polynomial function of degree 4 or less for a given real val
36243_2_p31-3412/8/97 8:42 AMPage 3136243AdamsPRECEAPPENDIX 2 JA ACS11/17/97pg 31CODES OF ETHICSThe PART OF THE PICTURE: Ethics and Computing section in Chapter 1 noted that professional societies have adopted and instituted codes
14.4 The STL list<T> Class Template114.4 The STL list<T> Class TemplateIn our description of the C+ Standard Template Library in Section 10.6 of the text, we saw that it provides a variety of other storage containers besides vector<T> and that o
15.4 An Introduction to Trees1TREES IN STLThe Standard Template Library does not provide any templates with Tree in their name. However, some of its containers - the set<T>, map<T1, T2> , multiset<T>, and multmap<T1, T2> templates - are generall
10.2 C-Style Arrays1VALARRAYSAn important use of arrays is in vector processing and other numeric computation in science and engineering. In mathematics the term vector refers to a sequence (one-dimensional array) of real values on which various
15.3 Recursion Revisited1EXAMPLE: DRY BONES!The Old Testament book of Ezekiel is a book of vivid images that chronicle the siege of Jerusalem by the Babylonians and the subsequent forced relocation (known as the exile) of the Israelites followin
10.7 An Overview of the Standard Template Library1STL Iterators. The Standard Template Library provides a rich variety of containers:vector list deque stack queue priority_gueue map and multimapset and multiset The elements of a vector<T> can
5.5 Case Study: Decoding Phone Numbers15.5 Case Study: Decoding Phone NumbersPROBLEMTo dial a telephone number, we use the telephones keypad to enter a sequence of digits. For a long-distance call, the telephone system must divide this number i
1.3 Case Study: Revenue Calculation11.3 Case Study: Revenue CalculationPROBLEMSam Splicer installs coaxial cable for the Metro Cable Company. For each installation, there is a basic service charge of $25.00 and an additional charge of $2.00 for
7.7 Case Study: Calculating Depreciation17.7 Case Study: Calculating DepreciationPROBLEMDepreciation is a decrease in the value over time of some asset due to wear and tear, decay, declining price, and so on. For example, suppose that a company
1From Paraconsistent Logic to Universal LogicJean-Yves Bziau"The undetermined is the structure of everything" AnaximanderAbstract During these last years I have been developed a general theory of logics that I have called Universal Logic. In t |
This text is designed to help teachers work with beginning ESL students in grades 5 to 12. It provides lessons and activities that will develop the students' vocabulary, English usage, and mathematical understanding. A balance of high-interest activities,
Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.Digital Dice will appeal to anyone who enjoys popular math or computer science.
This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.
A thorough and highly accessible resource for analysts in a broad range of social sciences. Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include: More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aid users of computer programs Extensive appendices containing mathematical details important for a thorough understanding of the topic With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Uses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations.
New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include: Contributions from eleven of the world??'s leading figures in time series Shared balance between theory and application Exercise series sets Many real data examples Consistent style and clear, common notation in all contributions 60 helpful graphs and tables Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
This book provides a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students. The book alternates between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. It covers topics ranging from classical cellular biophysics and proceeding up to systems level neuroscience. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combined with earlier ones. Each chapter includes a comprehensive series of exercises with solutions, taken from the set developed by the authors in their course lectures. MATLAB code is included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen the reader's understanding or to introduce basic concepts for less mathematically inclined readers completes each chapter.A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscienceProvides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processesIntroduces numerical methods used to implement algorithms related to each mathematical conceptIllustrates numerical methods by applying them to specific topics inneuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to desc Sec
Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions—and inspire more love and hatred—than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life.These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment—as well as of those rare individuals driven to insanity and even murder by an obsession with math.This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.In this best-selling classic, George Pólya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Pólya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. How to Solve It popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages.P—he taught until he was ninety—and maintained a strong interest in pedagogical matters throughout his long career. In addition to How to Solve It, he published a two-volume work on the topic of problem solving, Mathematics of Plausible Reasoning, also with Princeton.Pólya is one of the most frequently quoted mathematicians, and the following statements from How to Solve It make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till
Leonhard Euler's polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists—who include mathematicians and scientists—examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.Classroom-tested activities and problem solvingAccessible problems that move beyond regular art school curriculumMultiple solutions of varying difficulty and applicabilityAppropriate for students of all mathematics and art levelsOriginal and exclusive essays by contemporary artistsSolutions manual (available only to teachers)
The Handbook Philosophy of Technology and Engineering Sciences addresses numerous issues in the emerging field of the philosophy of those sciences that are involved in the technological process of designing, developing and making of new technical artifact
Computational science is a quickly emerging field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. However, limited educational materials exist in this field. Introduction to Computational Science fills this void with a flexible, readable textbook that assumes only a background in high school algebra and enables instructors to follow tailored pathways through the material. It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.The text embraces two major approaches to computational science problems: System dynamics models with their global views of major systems that change with time; and cellular automaton simulations with their local views of how individuals affect individuals. While the text is generic, an extensive author-generated Web-site contains tutorials and files in a variety of software packages to accompany the text.Generic software approach in the textWeb site with tutorials and files in a variety of software packagesEngaging examples, exercises, and projects that explore scienceAdditional, substantial projects for students to develop individually or in teamsConsistent application of the modeling processQuick review questions and answersProjects for students to develop individually or in teamsReference sections for most modules, as well as a glossaryOnline instructor's manual with a test bank and solutions |
Sharp Math
Building Better Math Skills
A 10-question diagnostic quiz in every chapter to show readers where they need the most help.
Math from basic arithmetic to Algebra 2, broken down by subject and then building up from chapter to chapter so readers can group concepts together for easier learning.
A variety of practice exercises with detailed answer explanations for every topic.
A 15-20 question recognition and recall practice set that includes material from the entire chapter (and a few questions that cover material from the previous chapters), to once again reinforce what the reader has learned on a larger scale. Detailed answer explanations follow the practice set. |
As I've traveled around to smaller four-year schools, community colleges and precollege schools, faculty are always amazed at some of the simplest aspects of Mathematica. The fact that you can have Mathematica "look" like math consistently now and now have point-and-click palettes available make getting started with it easier than ever before. Are there specific features or functional questions that you have if you're just getting started? |
Algebra And Trigonometry - 01 edition
ISBN13:978-0534434120 ISBN10: 0534434126 This edition has also been released as: ISBN13: 978-0534380298 ISBN10: 0534380298
Summary: Algebra and Trigonometry was designed specifically to help readers learn to think mathematically an...show mored to develop true problem-solving skills. Patient, clear, and accurate, the text consistently illustrates how useful and applicable mathematics is to real life. The new book follows the successful approach taken in the authors' previous books, College Algebra, Third Edition, and Precalculus, Third Edition. ...show less
The text has light marking, the cover has a small "slit" on the upper back edge and several tiny soil marks on the back cover, otherwise in nice condition. Quantity Available: 1. ISBN: 0534434126. IS...show moreBN/EAN: 9780534434120. Inventory No: 1560779853. ...show less
0534434126 |
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MAT A26 Lecture 451Power Seriesdefinition 1.1.A power series is a series of the formk=0ak (z - a)k ,where ak is a sequence and a is a constant. The power series can be a real or complex depending on whether ak and a are real or complex.corollary 1
MAT A26 Lecture 461Differentiating and Integrating Power Seriesproposition 1.1. Letn=0an xn be a real power series with radius of con-vergence R, defining a function f (x) for |x| < R. Then (a) the power seriesnan xn-1n=0obtained by differentiati
Physical Sciences Division University of Toronto at ScarboroughMATA26Y TERM TEST I [20]October 28, 1996 110 minutes1. (a) Compute the derivative f (x) for each of the following functions f (x). Note: Simplification of your answer is not required. 5x +
UBC Calculus Online Course Notes Equations of Straight LinesA Review of Lines and SlopesThis page serves as a quick review of straight lines and their important features. Many of these features are fundamental to a mathematical understanding of Calculus
Test! UBC Calculus Online Course NotesComposite FunctionsComposite functions are so common that we usually don't think to think to label them as composite functions. However, they arise any time a change in one quantity produces a change in another whic
5.05 - Principles of Inorganic Chemistry III - Spring 2005Professor Christopher Cummins, Copyright 2005.MIT Department of Chemistry5.05 2005 Exam 1.INSTRUCTIONSThis exam is not open-book, so do not take answers directly from the reading.Rather, you
Introduction to Archaeology: Class 1Introduction Copyright Bruce Owen 2002Anthropology 324: Introduction to ArchaeologyIm Bruce OwenI am an archaeologist who works in Peru; Ive spent over 5 years there since 1983I work on the far south coastal regio
Introduction to Archaeology: Class 2What archaeology is and how it got that way Copyright Bruce Owen 2002Dating conventionsB.C./A.D. = Before Christ, Anno Domini ("Year of our Lord")based on the conventional birth of Christ, which may or may not have
Introduction to Archaeology: Class 3What we want to learn - and how Copyright Bruce Owen 2002A little more on what archaeology is Archaeology is generally defined either by its data or by its goalsDefined by data: Archaeology is the study of the mate
Introduction to Archaeology: Class 4Archaeological -isms and the nature of the world Copyright Bruce Owen 2002Archaeologists, like all anthropologists and other humans, have various different general waysof thinking about the worldsomething like the
Introduction to Archaeology: Class 8Types, seriation, components, and culture history Copyright Bruce Owen 2002Types, or typologyNecessary for basic description of what was found (often before you know anything else)For artifacts: Morphological types
Introduction to Archaeology: Class 11Digging square holes Copyright Bruce Owen 2002OK, we have mapped the site, made and analyzed systematic surface collections, and maybedone some remote sensing. We still have questions about what went on there, so w
Introduction to Archaeology: Class 12Site formation, linking arguments, and ethnoarchaeology Copyright Bruce Owen 2002So now we are digging.We want to know about people, cultures, and societiesbut we are digging up layers of dirt and garbage.how can
Introduction to Archaeology: Class 13Experimental archaeology and faunal analysis Copyright Bruce Owen 2002Today we cover two basically unrelated topics: experimental archaeology and faunal analysisdo the readings to get more of the story!Experimenta
Introduction to Archaeology: Class 14Archaeobotany and Bioarchaeology Copyright Bruce Owen 2002Today we once again cover two basically unrelated topics: archaeobotany (also calledpaleoethnobotany) and an introduction to bioarchaeologydo the readings
Introduction to Archaeology: Class 16Social groups, status, gender, and inequality Copyright Bruce Owen 2002Anthropologists and archaeologists often talk about "groups" of people. What do we mean by"groups"?this is a slippery concept, more than it in
Introduction to Archaeology: Class 17Cognitive archaeology Copyright Bruce Owen 2002Cognitive archaeology is a hot topic, but no one is exactly sure what it isBasically: What people thought in the past, when they thought it, how they came to think it, |
"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." -Aristotle
The mission of the Mathematics Department of Miami Dade College, Kendall Campus, is to support the college in its efforts to provide a high quality education by keeping the diversity of our learners and their needs at the center of our decision-making with regard to curriculum, instruction, support, and assessment. Specifically, the Kendall Campus Mathematics Department supports a vision that is based upon the vital importance of the first years of collegiate mathematics education-an education that prepares the learner for a future role in society by engaging him or her in instruction that includes fluency, understanding, reasoning, and communication skills needed to comprehend mathematics and its applications. Scientifically and technologically literate, the learner becomes a resourceful problem solver ready to make educated personal and professional decisions, and amply prepared to contribute to the improvement of our global society.
"Transire Summ Pectus Mundoque Potiri"
(Transcend Human Limitations and Master the Universe)
Our faculty and staff are here to assist students in every possible way. Please feel free to browse through our department site and find out about the services we provide for students |
Math Content Standard A: Content of Math
Key Element 2. Measurement
A student who meets the content standard should select
and use appropriate systems, units and tools of measurement,
including estimation.
Measurement For All
Students make measurement decision such as which units
are most appropriate for the context, what degree of accuracy
should be measured, and how much confidence can be put
into interpretations about variations of measurement.
The same measurement concepts that are learned as primary
students apply throughout our mathematical education in
high school, college, and the work place.
Measurement extends beyond length, area, volume, temperature,
and weights as attributes of objects. It includes brightness,
relations, pulse, speed, radioactivity, sound, pressure
and many other attributes. It can be expressed as a direct
physical measurement or as a rate. Technology (probe-ware
and computer based labs) helps extend the concepts of
measurement to complex interactions and abstract measurements,
all requiring an understanding of measurement concepts
above and beyond the old-fashioned skills of using non-technical
measuring tools. |
Product Description
From Amazon.ca
Help your child build Math skills with fun and engaging activities. Packed with lessons and exercises from Elementary School to High School, each designed to prepare students for success in state standards testing.
An engaging 3D interface and easy-to-understand examples help algebraic concepts come to life.
Packed with lessons and exercises from Elementary School to High School, each designed to prepare students for success in state standards testing.
Learn how to collect, analyze and present masses of data in a clear and concise manner.
Build fundamental skills with Basic Math, including addition, subtraction, multiplication and division. Expand your horizons with Pre-Algebra, Algebra and Geometry. Prepare for High School and College with Trigonometry, Pre-Calculus, Calculus and Statistics.
Students also receive Microsoft Excel Tutor for the PC, a student organizer and iPod study materials. After School Extras include music downloads, ringtones and mobile games. Also perfect for adults who want to brush up on Math.
The Math Advantage Edge:
PC/Mac hybrid for the first time ever
All on DVD--no more disc swapping
Improved user experience with an all-in-one installer that makes using the programs easy
Student Benefits
Master the Fundamentals
Overcome Challenging Topics
Realize Academic Potential
Prepare for College
Basic Math Detailed explanations and creative lessons will make it easy to grasp key concepts and develop a strong math foundation.
Counting Techniques
Factor Trees
Fractions & Decimals
Perimeter & Area
Systems of Measurement
Pre-Algebra Get a head start on Algebra with an engaging introduction to algebraic symbols, variables and expressions.
Mixed Numbers
Ratios & Proportions
Scientific Notation
Order of Operations
Formulas & Substitution
Algebra I & II An engaging 3D interface and easy-to-understand examples help algebraic concepts come to life.
Expressions & Equations
Absolute Values
Lines, Slopes & Intercepts
Proportions & Inequalities
Polynomials & Functions
Geometry Learn and apply Geometry concepts at your own pace with a detailed lessons and follow-up activities that reinforce learned skills.
Statistics & Probability Learn how to collect, analyze and present masses of data in a clear and concise manner.
Mean, Median & Mode
Standard Deviation
Sampling Theory
Correlation & Regression
Plots & Graphs
Calculus Master the fundamentals of Calculus through simplified explanations and examples.
Limits & Continuity
Derivatives
Sequences & Series
Common Graphs
Functions & Equations
The--OR--if for any reason you are not completely satisfied with this product, return this product within 30 days of the date of purchase and the company will refund your money. See complete details inside.
Product Description
Help your child build critical Math skills. Hundreds of Math lessons and exercises from Elementary School to High School prepare students to succeed on state standards testing.
I bought this program to brush up on my math skills for a test I plan to take shortly. This is a great program if you just want a quick overview of algebra, geometry. trig and statistics. The calculus program is a joke.
If you actually want to be able to solve math problems I'm sure there must be better programs out there. There aren't any practice questions for what you are learning. Just information, an example or two and a short test at the end of a section.
The program isn't horrible. It just isn't good. It does serve my purposes though..
are virtually useless for learning on one's own.
Then I tried the Princeton Review Math Library CD ROM set, which was fantastic. The subject matter was logically organized and the presentation was clear and concise. The first level was a single mathematical principal which, if you were already familiar with it, you could pass and move on to the next. If it was something you were not familiar with you could click on it and get a detailed explanation of that concept (for example a rule of exponents) and, if that wasn't quite enough, you could click a button for an animated walk-through of a problem that shows you how that concept is used. At the end of each section was a self-test with ten questions that gave you practice and confidence using the principals given. Unfortunately as PC operating systems and hardware have moved on my disks became unplayable as the animation audio would 'stick' and repeat infinitely.
Searching for an alternative I purchased 'Math Advantage' hoping it was another Princeton Review but alas, as many of the reviews I read indicated, it is really a poorly written textbook shoved onto a disk. Most of the material is simply long text expositions with a video 'example' here and there where the legal disclaimer that runs before it plays is longer than than the scant and poorly presented 'information' it contains. Since I purchased it, it has been collecting dust and I have gone back to scrounging for a decently written textbook. Overall, very disappointing. I neither recommend this for adults nor for children.
8 of 9 people found the following review helpful
5.0 out of 5 starsGood supplement for higher mathJan 6 2009
By L. V. Davis - Published on Amazon.com
I bought this for my 9th grade daughter. She struggled at first to figure out how to use it and get used to what was expected. She had a C average in Algebra but used this as a tutorial for her final exam and made an A on the last test and final exam, giving her a B for a final grade. It really helped! Another reason I like this software is I paid one price for tutorials that will take her through Calculus. Big bonus! I'm looking forward to this helping in her upcoming Geometry class.
4 of 4 people found the following review helpful
1.0 out of 5 starsVery mediocreDec 1 2008
By chaz - Published on Amazon.com
This has plenty of information, but lacks exercises and practice problems - the stuff one needs to do to actually learn math. It's a hassle to navigate between subjects as you have to, for example, quit and close the Algebra program to look at Geometry, so cross-referencing is difficult. |
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 |
In the context of very bright high school students with strong mathematics backgrounds, it is typical to teach discrete math to students without requiring calculus as a prerequisite. In particular, this is the norm both at the Ross program (where 2nd year students often had a combinatorics class) and at Mathcamp (where many discrete math classes are often taught without calculus as a prerequisite). Both summer programs avoid teaching calculus because it messes up highschool students who are going to be stuck taking calculus whether they already know it or not.
In particular, it's quite possible to teach formal differentiation and integration of power series in order to do generating functions without discussing traditional differentation or limits. In fact, the Ross problem sets had a problem set developing the basics of calculus for polynomials (linearity, Leibniz rule, etc.) without ever discussing limits. I'd already learned calculus at that point, but not all the students had. And the students who didn't know calculus didn't have too much of a difficulty with that problem set. It's certainly easier than proving that the group of units modulo p is cyclic.
So the reason for requiring such a prerequisite for a college course is not that it's actually a logical prerequisite, but instead for sociological reasons along the lines of Alex's answer. |
@book {MATHEDUC.06068645,
author = {Deiser, Oliver},
title = {First aid in analysis. Overview and basic knowledge with numerous illustrations and examples. (Erste Hilfe in Analysis. \"Uberblick und Grundwissen mit vielen Abbildungen und Beispielen.)},
year = {2012},
isbn = {978-3-8274-2994-0},
pages = {246~p.},
publisher = {Berlin: Springer Spektrum},
doi = {10.1007/978-3-8274-2995-7},
abstract = {This book takes up the analysis, as it is normally taught at the pre-university levels, which tends to be a descriptive way to introduce the concepts of analysis. In carefully chosen steps, the author translates these notions into a purely formalistic language, from the basics through to integration. Numerous examples and illustrations help the reader to understand this formal language. This then allows the author to present almost all exotic examples, which can hardly be explained in the descriptive language. The reader will note with comfort that the author also recommends not to forget the intuitive content of this formalism.},
reviewer = {Hansueli H\"osli (Ittigen)},
msc2010 = {I10xx (U20xx)},
identifier = {2013a.00673},
} |
We are moving to our new website at nmss.edu.au soon, you can preview it now.
The National Mathematics Summer School (NMSS) is a program for the discovery and development of mathematically gifted
and talented students from all over Australia. It is a two-week residential summer course held each January at The
Australian National University (ANU) in Canberra.
Students participate in a series of lecture courses from mathematicians in a number of branches of mathematics at a
relatively advanced level. They attend tutorials under the guidance of a range of staff — postgraduate students,
mathematics teachers and academic mathematicians.
The main activity of NMSS is an in-depth study of three or four different
areas of mathematics. Each is very challenging and will extend every
student. On the other hand, the program is non-competitive and very
much hands-on. The emphasis is on doing mathematics, not just on
listening to someone else talking about it.
By the end of the two weeks, most students are amazed at how much they
have accomplished and post-school surveys indicate that the NMSS has
succeeded in raising their intellectual horizons. Almost everyone
returns home with a considerably enhanced view of their own potential. |
Sharp3D.Math contains fundemental classes to dealing with numerics on the .NET platform. It contains various mathematical structures such as vectors, matrices, complex numbers and contains methods for numerical integration, random numbers generation and other object-oriented n... |
ELEMENTARY TECHNICAL MATHEMATICS (10TH 10)
by EWEN
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Elementary Technical Mathematics Tenth Edition was written to help students with minimal math background prepare for technical, trade, allied health, or Tech Prep programs. The authors have included countless examples and applications surrounding such fields as industrial and construction trades, electronics, agriculture, allied health, CAD/drafting, HVAC, welding, auto diesel mechanic, aviation, natural resources, and others. This edition covers basic arithmetic including the metric system and measurement, algebra, geometry, trigonometry, and statistics, all as they are related to technical and trade fields. The goal of this text is to engage students and provide them with the math background they need to succeed in future courses and careers. |
Calculators Are for Calculating, Mathematica Is for Calculus
Andy Dorsett
In this Wolfram Mathematica Virtual Conference 2011 course, learn different ways to use Mathematica to enhance your calculus class, such as using interactive models and connecting calculus to the real world with built-in datasets.
See how Wolfram technologies like Mathematica and Wolfram|Alpha enhance math education. The video features visual examples of course materials, apps, and other resources to help teachers and students cover math from algebra to calculus to statistics and beyond.
Watch an introduction to the Wolfram Demonstrations Project, a free resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a range of other fieldsIn this video, get a quick introduction to the Wolfram Education Portal, which features teaching and learning tools created with Mathematica and Wolfram|Alpha, including a dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more.
computerbasedmath.org is a project to build a new math curriculum with computer-based computation at its heart. In this talk from the Wolfram Technology Conference 2011, Conrad Wolfram discusses the concept, progress, and plans.
Explore the various ways mobile devices can tap into the power of Mathematica and Wolfram|Alpha to enhance learning in math, science, and even music classrooms in this recorded presentation from the Wolfram Technology Conference 2011.
In this Wolfram Mathematica Virtual Conference 2011 course, learn different ways to use Mathematica to enhance your calculus class, such as using interactive models and connecting calculus to the real world with built-in datasets Portuguese audio.
Mathematica can be used to enhance course management systems by helping teachers easily communicate ideas, give students immediate feedback, and link real-world datasets to textbook examples. Learn more in this screencast.
This is the third video in a series showing examples of Mathematica that are features especially useful for K–12 and community college educators. Topics include mathematical typesetting, slide shows, interactive models, and more.
This is the second video in a series showing examples of Mathematica features that are especially useful for K–12 and community college educators. In this video, you'll discover how easy it is to create interactive Demonstrations, lessons, quizzes, and instructional handouts with Mathematica.
This is the first video in a series showing examples of Mathematica features that are especially useful for K–12 and community college educators. In this video, educators share firsthand experiences of teaching with Mathematica Spanish audio. |
Mathematics - Algebra (356 results)
Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college. Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinar processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers. The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value. Webster Wells. Boston, 1886.
In the selection of materials, those articles liave been taken which have a practical application, and which are preparatory to succeeding parts of the mathematics, philosophy, and astronomy. Tlie object has not been to introduce original matler. In the mathematics, which have been cultivated with success from the days of Pythagoras, and in which the principles already established are sufficient to occupy the most active mind for years, the parts to which the student ought first to attend, are not those recently discovered. Free use has been made of the works of Newton, Maclaurin, Saunderspn, Simpson, Euler, Emerson, Lacroix, and others, but in a way that rendered it inconvenient to refer to them, in particular instances. The proper field for the display of mathematical genius is in the region of invention. But what is requisite for an elementary work, is to collect, arrange and illustrate, materials already provided. However humble this employment, he ought patiently to submit to it, whose object is to instruct, not those who have made considerable progress in the mathematics, but those who are just commencing the study. Original discoveries are not for the benefit of beginners though they may be of great importance to the advancement of science. The arrangement of the parts is such, that the explanation of one is not made to depend on another which is to follow. The addition, multiplication, and division of powers for instance, is placed after involution. In the statement of general rules, if they are reduced to a small number, their applications to particular cases may not, always, be readily understood. On the other hand, if they are very numerous, they become tedious and burdensome to the memory. The rules given in this introduction, are most of them comprehensive; but they are explained and applied, in subordinate articles. A particular demonstration is sometimes substituted for a general one, Avhen the application of the principle to other cases is obvious. The examples are not often taken fi om philosophical subjects, as the learner is supposed to be familiar with none of the sciences except arithmetic. In treating of negative quantities, frequent references are made to mercantile concerns, to debt, and credit, c.These are merely for the purpose of illustration.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics Avhich the engineer must emphasize, such as numerical com)utations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid. The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject. The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytical geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of eii ort. The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge. Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance. To meet this double need the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him is the aim of the Thresholds of Science series. This series consists of short, simply written monographs by competent authorities, dealing with every branch of science mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
Advantage has been taken of the issue of a new edition of the Intermediate Algebra to revise the text and to make a number of changes., To meet the wishes of teachers who have used, or propose to use, the book in the advanced classes of the secondary schools, additions have been made in order that the prescribed courses may be formally covered. To the chapter on equations there have been added exercises bearing on or developing further the theory. A chapter on Scales of Notation has been introduced. The note on Annuities, incidental to the Geometrical Progression, has been expanded to constitute a chapter in which are considered the simpler problems of finance related to annuities, and the use of the fundamental tables of Interest and Annuities provided for and explained. The Miscellaneous Examples that were given in the earlier edition have been retained in the hope that the more adventurous students, in particular candidates for Honours at Matriculation, may find in them a help and a stimulus. The chapter on Exponential and Logarithmic Series has been enlarged in order to give prominence to the concrete problem of the construction of tables of logarithmics, it being felt that in this way the significance of the theory is best brought out. Alfred T.DeLURY. Toronto, July 15,
In preparing this second edition the earlier portions of the book have been partly re-written, while the chapters on recent mathematics are greatly enlarged and almost wholly new. The desirability of having a reliable one-volume history for the use of readers who cannot devote themselves to an intensive study of the history of mathematics is generally recognized. On the other hand, it is a difficult task to give an adequate bird s-eye-view of the development of mathematics from its earliest beginnings to the present time. In compiling this history the endeavor has been to use only the most reliable sources. Nevertheless, in covering such a wide territory, mistakes are sure to have crept in. References to the sources used in the revision are given as fully as the limitations of space would permit. These references will assist the reader in following into greater detail the history of any special subject. Frequent use without acknowledgment has been made of the following publications: Annuario Biografico del Circolo MaknuUico di Palermo 1914; Jakrhuch uber die Fortschritte der Mathematiky Berlin;. C.Poggendorffs Biographisch-Literarisckes Handworterbuch, Leipzig; Gedenkkigebuch fur McUhenuUikeTf von Felix Miiller, 3. Aufl., Leipzig und Berlin, i()i 2 Revue SemestrieUe des Publications MathinuUigues, Amsterdam. The author is indebted to Miss Falka M.Gibson of Oakland, Cal. for assistance in the reading of the proofs. Floman Cajori. University of California March, 1919.
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as wellinformed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large safety factor of deud wood in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing. The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
El Preface This book is the result of twenty years of patient experiment in actual teaching. It is intended to be completed in the first year of the high school. It presents algebraic equations primarily as a device for the solution of problems stated in words, and gives a complete treatment of numerical equations such as are usually included in high-school algebra one-letter and two-letter equations, integral and fractional, including one-letter quadratics and the linear-quadratic pair. So much of algebraic manipulation is included as is necessary for the treatment of these equations. The arithmetic in the book is presented from a new point of view that of approximate computation and is utilized in the evaluation of formulas and in the solution of equations throughout the succeeding pages. Geometrical facts are introduced as the basis of many algebraic and arithmetic problems, and wherever they are not intuitively accepted by the pupils they are accompanied by adequate logical demonstration. Proofs, and parts of proofs, are avoided when they seem to the pupils of an unnecessary and hair-splitting kind. Ah problems are carefully graded, for it is by means of problems that each successive algebraic difficulty is introduced. A great deal of pains has been taken to present new topics clearly and concretely, often dividing them into sub-topics each of which is separately illustrated and apphed to practice. Definitions are generally prepared for by such advance work as will cause the student to feel the need of them; and where no need exists, they are omittedIx this text the authors have endeavored to present a course in algebra for the first year of high school which shall be simple, comprehensible to the students, and of high educational and mathematical value. They have made the solution of equations and problems the core of the course; they have emphasized the essentials, avoiding little-used complexities of algebra; they have taught new ideas inductively; they have emphasized thoughtful rather than mechanical solutions of exercises; they have tried to make the course maintain and increase the students efficiency in arithmetic; they have tried to make the course interesting by including varied problem material and historical notes, and valuable by including practical applications. The essential features of the course have been tried out in the classroom by many teachers. The text contains sufficient material to meet the needs of schools whose pupils have studied algebra before entering the high school; the topics have been arranged, however, so that a class may easily cover the essentials of the course in one school year. Attention is directed to the following devices that have been employed to attain the desired ends: Each topic that is taken up is used in the solution of equations. (See 9, 10, 12, 41, 51, 60, 107, etc.) This makes the study of the various topics purposeful, allows for good gradation in the book as a whole, and emphasizes the equation. Problems are introduced at short intervals. Informational, geometric, and physics problems in reasonable number are used. New types of problems are introduced gradually, appearing first in classified lists, are taught with extreme care, and are used thereafter in miscellaneous lists. Experimental verification is suggested for some of the facts from geometry and physics that are used. (See Exercises 7, 25, 28, 29, 38, 39, 49, 106; 13, 142, 143, 190, etc.
The main object in preparing this new Algebra has been to simplify principles and give them interest, by showmg niunbers. Each successive process is taken up for the sake of the economy or new power which it gives as compared with previous processes. This treatment should not only make each principle clearer to the pupil, but should give increased unity to the subject as a whole. We believe also that this treatment of algebra is better adapted to the practical American spirit, and gives the study of the subject a larger educational value. Among the special features of this Introductory Algebra, the following may be mentioned: A large nmnber of written problems are given in the early part of the book, and these are grouped in types which correspond in a measure to the groups used in treating original exercises in the authors Geometry. Many informational facts are used in the written problems. The central and permanent numerical facts in various departments of knowledge have been collected and tabulated on pages280-286 for use in niaking problems.
Thi 8 work was commenced sixteen years ago at the earnest solicitation of numerous teachers, who were dissatisfied with the textbooks then in use. That they were not alone in their opinion is evidenced by the number of new treatises, or revisions of old ones, printed since that time, and now used in the schools of this country. The crudeness of even the best Algebras of a quarter-century ago was mainly owing to the fact that, as a rule, mathematicians neglected the elementary branches for the more attractive fields of Higher and Applied Mathematics; hence blunders and inconsistencies were allowed which otherwise would not have been tolerated. The wonderful progress made in the Natural Sciences, and the extended use of Algebra in the treatment of Geometrical Magnitudes, have finally called the attention of educators to the necessity of improving the elementary treatises, and more rigidly limiting the meaning of the signs. That this agitation comes none too soon is evident to every thoughtful teacher, and can be readily seen by auy one who compares the various text-books used in our schools. Note the following inconsistencies: In some text-books now before me, 6 : 7 equals f;in others, 6 : 7 equals. In some, 6 -f 4 X 2 = 20;in others, 6 -- 4 X 2 = 14.Of course, the meaning and use of a sign depend upon agi eement, but it is of extreme importance that we do agree in such matters. In the same work, too, statements incompatible with each other are made; thus, a -i-bc and a -i-b Xc are said to have different values, and yet be and bXc are, in all woi ks, said to have one and the same meaning. Since a-h be and a -ib Xe differ only in She use of bXc for be, it is plainly necessary that one or the other of these two statements be changed. One of the objects in writing this book is to urge the adoption of the following law for Numerical Values; viz.,(l) Find the value of each term separately; thus, 6-f-4X 2 = 6 -f8= 14. (2)In finding the m, lue of a term, begin at the Right and use the signs in their oi der; thus, 6-f-4x 2 = 6-r-8= f.In other words, the jm tion of the term to the left of the division sign is the Dividend, and the part to the right is the divisor.
The main object in preparing this new Algebra has been to simplify principles This treatment should not only make each principle dearer to the pupil, but should give increased unity to the subject as a whole. We beheve also that this treatment of algebra is better adapted to the practical American spirit, and gives the study of the subject a larger educational value. Among the special features of this Introductory Algebra, the following may be mentioned: A large nimiber of written problems are given in the early part of the book, and these are grouped in types which correspond in a measure to the groups used in treating original exercises in the authors Geometry. Many informational facts are used in the written problems. The central and permanent niunerical facts in various departments of knowledge have been collected and tabulated on pages280-286 for use in making problems.
There are two classes of men who might be benefited by a work of this kind, viz., teachers of the elements, who have hitherto confined their pupils to the working of rules, without demonstration, and students, who, having acquired some knowledge under this system, find their further progress checked by the insufficiency of their previous methods and attainments. To such it must be an irksome task to recommence their studies entirely; I have therefore placed before them, by itself, the part which has been omitted in their mathematical education, presuming throughout in my reader such a knowledge of the rules of algebra, and the theorems of Euclid, as is usually obtained in schools. It is needless to say that those who have the advantage of University education will not find more in this treatise than a little thought would enable them to collect from the best works now in use 1831, both at Cambridge and Oxford. Nordo I pretend to settle the many disputed points on which I have necessarily been obliged to treat. The perusal of the opinions of an individual, offered simply as such, may excite many to become inquirers, who would otherwise have been workers of rules and followers of dogmas. They may not ultimately coincide in the views promulgated by the work which first drew their attention, but the benefit which they will derive from it is not the less on that account. I am not.
The present volume contains a Second Course in Algebra adapted to the latter part of the high school curriculum. It covers the topics usually included in Interme Idiate and Advanced Algebra in secondary schools. Hence pupils who have completed it will be prepared in algebra vfor scientific and engineering schools as well as for the rx ordinary academic college. The methods which are characteristic of the authors Algebra, Book One are here continued and developed. The chief aim is to simplify principles and give them interest, by showing more plainly, if possible, than has been done heretofore, the practical or common-sense reason for each step or process. Each new process, for instance, is introduced by what may be termed the efficiency-inductive method. In the Exercises also there are special examples which cause the pupil to realize the efficiency meaning of processes from various points of view. As in the authors other mathematical texts, pivotal and permanently valuable number facts and laws from other branches of study are introduced in various ways. This gives a correlation of algebra with geography, history, and other subjects. A further correlation with physics and engineering is obtained by the use of some of the most important formulas in these branches, and also by familiarizing the pupil with their fundamental concepts and number facts.
The present book is an enlargement of the authors Elements of Algebra. To the end of Chapter XXVIII. it is identical with the latter and the School Algebra. Some revision of the later chapters in the Elements has been incorporated in this book, and a number of new chapters have been added. The scope of the books, amply justified by their successful use in high and normal schools and colleges, is stated in the preface to the Elements: The aim has been to make the transition from ordinary Arithmetic to Algebra natural and easy. Ko efforts.have been spared to present the subject in a simple and clear manner. Yet nothing has been slighted or evaded, and all difficulties have been honestly faced and explained. New terms and ideas have been introduced only when the development of the subject made them necessary. Special attention has been paid to making clear the reason for every step taken. Each principle is first illustrated by particular examples, thus preparing the mind of the student to grasp the meaning of a formal statement of the principle and its proof. Directions for performing the different operations are, as a rule, given after these operations have been illustrated by particular examples. The importance of mental discipline to every student of mathematics has also been fully recognized.
Colleges and Scientific Schools. The first part is simply a review of the principles of Algebra preceding Quadratic Equations, with just enough examples to illustrate and enforce these principles. By this brief treatment of the first chapters, sufficient space is allowed, without making the book cumbersome, for a full discussion of Quadratic Equations, The Binomial Theorem, Choice, Chance, Series, Determinants, and The General Properties of Equations. Every effort has been made to present in the clearest light each subject discussed, and to give in matter and methods the best training in algebraic analysis at present attainable. The work is designed for a full-year course. Sections and problems marked with a star can be omitted, if necessary; and for a half-year course many chapters must be omitted. The author gratefully acknowledges his obligation to Mr. G.W. Sawin of Harvard College, who has contributed the excellent chapter on Determinants, and been of invaluable assistance in revising every chapter of the book. Answers to the problems are bound separately in paper covers, and will be furnished free to pupils when teachers apply to the publishers for them. Any corrections or suggestions relating to the work will be thankfully received. G.A. Wentworth. Phillips Exeter Academy, September, 1888.
The present volume contains a second course in algebra adapted to the latter part of the High School curriculum. The book is divided into two parts, Part One being meant for use in such classes as give only a half year to the second course in algebra, while the entire volume is to be used by classes giving a whole year to the second course. In half-year classes, Part Two will constitute a reservoir of extra work for bright pupils. The features which characterize the authors First Book in Algebra are continued and dievelopediuible numbers, facts and laws from other branches of study are introduced in various ways. This gives a correlation of algebra with geography, history, economics, and other school studies.
The present volume contains a First Course in Algebra adapted to the early part of the high school curriculum. The main purpose in writing the book has been to simplify prinr Among the special features of this Algebra, the following may be mentioned: A large number of written problems are given in the ben collected and tabulated on pages387-390 for use in making problems. Similariy the most important formulas in arithmetic, geometry, physics, and engineering have been tabulated for use by teacher and pupil (pp. 385, 386).
TlHE following manual was prepared for the use- of the students of Columbia College, and in its original form it has been employed as a text-book, not only in that institution, but in various Colleges, Academies, High Schools, and other institutions of learning. The flattering manner in which it has been received by our most successful teachers of Mathematics, has induced the Author to publish it in its present revised form. In preparing it anew for the press, such alterations and improvements have been made as have been suggested by the authors practical experience in its use as a college text-book. The opening chapters have been somewhat simplified, the chapter on logarithms has been extended, a section on inequalities has been added, and the whole has been carefully corrected and revised.
As regards the method of teaching algebra, I would make it, in the earlier stages, as much a generalized arithmetic as possible. Results obtained by algebra would be verified by arithmetical instances; and the use of a formula would be indicated as including any number of instances. Elaborate (and to my mind wearisome) processes, useful for solving artificial combinations of difiiculties, would be at least deferred. With a comparative beginner, progress towards new ideas or new stages of old ideas can, I think, best be made by the simplest instances, and it is on this account that I would build algebra entirely on arithmetical foundations so far as concerns the teaching of beginners. Professor Forsyth, M.A,, D, Sc,, F.Rs., Cambridge. It is assumed that pupils will be required throughout the course to solve numerous problems which involve putting questions into equations. Some oJE these problems should be chosen from mensuration, from physics, and from commercial life. The use of graphical methods and illustrations, particularly in connection with the solution of equations, is also expected. Extract from the Report of the American Mathematical Society,
The present volume contains a First Course in Algebra adapted to the early part of the high school curriculum. The main purpose in writing the book has been to simplify pririr jwwer which it gives as compared with previous processes. Among the special features of this Algebra, the following may be mentioned: A large number of written problems are given in tjije been collected and tabulated on pages387-390 for use in making problems. Similarly the most important formulas in arithmetic, geometry, physics, and engineering have been tabulated for use by teacher and pupil (pp. 385, 386).
The aim of this little book is to provide an introductory course as a foundation to elementary algebra. A minimum number of definitions, an early introduction of the literal symbol in its simplest form, a clear conception of the opposition of positive and negative quantity, and a gradual introduction to the early processes are believed to be the first essentials to successful later work. New elements are introduced as the result of some natural process, the exponent, for example, not being mentioned or used until, in multiplication, the pupil meets the operation that produces it. Certain important topics are given a more extended treatment than is customary in most books prepared for beginners. The application of the equation to the problem is made in a form that experience has shown to give excellent results, and the reasoning powers developed by the limited classifications have been equal to the demands of the general problem. Substitution has a much more important position than is usual in elementary teaching, and its constant applications are designed to meet an actual need felt by teachers in higher grades of work.
The present volume contains a second course in algebra adapted to the latter part of the High School curriculum. Many schools give only one half year to the study of the second course in algebra,, and it is the object of this book to supply material adapted to the needs of such schools. In different parts of the country, tentative syllabi have recently. been worked out for such a briefer study, and these syllabi have been carefully considered by the authors in writing the present volume. The features which characterize the authors First Book in Algebra are continued and developediLable number facts, and laws from other branches of study are introduced in various ways. |
Calculators
ARTICLES ABOUT CALCULATORS
LIKE hundreds of thousands of other high school students, Greg Myers, 16, began using a graphing calculator in freshman algebra. Graphing calculators, which bear little resemblance to their 1970's ancestors, are sophisticated devices that can run small computer programs and draw the graph represented by complex equations in an instant. In the last few years, they have become mandatory in many high school math classes and can be used on the SAT and advanced placement exams and other standardized... |
Intermediate Algebra with Applications & Visualization, 4th Edition
Description
The Rockswold/Krieger algebra series uses relevant applications and visualization to show students why math matters and gives them a conceptual understanding. It answers the common question "When will I ever use this?" It covers the traditional topics, but rather than present them as concepts to memorize, with applications tacked on at the end, it teaches students the math in context. By seamlessly integrating meaningful applications that include real data, along with visuals—graphs, tables, charts, colors, and diagrams—students are able to see how math impacts their lives as they learn the concepts. This conceptual understanding makes them better prepared for future math courses and life. |
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