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Synopses & Reviews
Publisher Comments:
Grasp the principles and concepts you need to score high in pre-calculus
Getting ready for calculus but feel confused? Have no fear! This un-intimidating guide walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. You'll understand the concepts — not just the number crunching — and see how to perform all the tasks you need to score high at exam time.
Pre-calculus 101 — get a review of the Algebra II you need to know, real numbers, and how to graph, solve, and perform operations with functions
What's your angle? — take a tour of the essentials of trigonometry, from angles, right triangles, and trig ratios to graphing the parent graph of the six basic trig functions
Keep it simple — discover how to simplify trig expressions and solve for an unknown variable using formulas and identities (and solve triangles that aren't right triangles using Law of Sines and Law of Cosines)
Not just plane thinking — delve into analytic geometry and system solving with the understanding of complex numbers, polar-coordinate graphing, conics, systems of equations, sequences, and more
Open the book and find:
An overview of pre-calculus
Tips on graphing trig functions like a pro
How to apply the major theorems and formulas
The lowdown on analytic geometry
Guidance on identifying limits and continuity
The 4-1-1 on working with a graphing calculator
The laws for solving oblique triangles
Everything you need to prepare for calculus
Learn to:
Grasp essential pre-calculus topics
Apply the major theorems and formulas
Tackle proofs with confidence and ease
Synopsis:
The fun and easy way to learn pre-calculusAbout the Author
Yang Kuang, PhD, is a professor of mathematics at Arizona State University. He currently serves on the calculus committee where he and other members discuss what and how to teach calculus to students majoring in math and physical sciences. Elleyne Kase is a professional writer. | 677.169 | 1 |
Access Math Tasks, Solutions, Videos and Khan Academy Practice
Welcome Teachers and Students! This MFM1P Grade 9 Applied Math Help Resource has been compiled to assist in closing the gap that exists between academic and applied student achievement in the province of Ontario. All resources include math tasks, solutions, videos, practice links and more to ensure every student can achieve at the highest level in their Ontario grade 9 applied math course.
If you have resources you would be willing to share, please contact me so I can add it to the database. I hope you find these resources useful!
Many of these resources were modified from the TIPS4RM resource by great math teachers and friends, Dave Bracken and Michael Smith with further additions and modifications by Kyle Pearce.
MFM1P Specific Expectations
NA1.04 - Make comparisons using unit rates (e.g., if 500 mL of juice costs $2.29, the unit rate is 0.458¢/mL; this unit rate is less than for 750 mL of juice at $3.59, which has a unit rate of 0.479¢/mL);
MFM1P Specific Expectations
LR2.03 - Identify, through investigation, some properties of linear relations (i.e., numerically, the first difference is a constant, which represents a constant rate of change; graphically, a straight line represents the relation), and apply these properties to determine whether a relation is linear or non-linear.
MFM1P Specific Expectations
LR4.07 - – select a topic involving a two-variable relationship, pose a question on the topic, collect data to answer the question, and present its solution using appropriate representations of the data.
MFM1P Specific Expectations
LR1.04 - Describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses (e.g., describe the trend observed in the data. Does a relationship seem to exist? Of what sort? Is the outcome consistent with your hypothesis? Identify and explain any outlying pieces of data. Suggest a formula that relates the variables. How might you vary this experiment to examine other relationships?).
MFM1P Specific Expectations
MG1.03 - Solve problems that require maximizing the area of a rectangle for a fixed perimeter or minimizing the perimeter of a rectangle for a fixed area (Sample problem:You have 100 m of fence to enclose a rectangular area to be used for a snow sculpture competition. One side of the area is bounded by the school, so the fence is required for only three sides of the rectangle. Determine the dimensions of the maximum area that can be enclosed.).
Course Description - Grade 9 Applied Math
This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. | 677.169 | 1 |
Middle School Math Grade: 6
Prerequisite: Placement by district assessment
A grade level course designed to provide students with sufficient mathematical foundation to meet 6th grade state and district standards.
Advanced Middle School Math Grade: 6
Prerequisite: Placement by district assessment Designed for students who have demonstrated an exceptionally high level of understanding and proficiency of 5th grade standards.
This course covers the same concepts as the grade level class but with greater depth, complexity, and pace.
Pre-Algebra Grade: 7
Prerequisite: Completion of Middle School Math
A grade level course designed to provide students with sufficient mathematical foundation to meet 7th grade state and district standards. Successful completion of this course adequately prepares students for Algebra 1.
Algebra Foundations Grade: 8
Prerequisite: This course is for students who have not met the prerequisites for
Algebra 1.
A course designed to introduce key Algebra concepts and skills in depth. This course will not cover all Algebra 1 standards. Successful completion will result in preparedness for, and placement in, Algebra 1.
Algebra 1 Grade: 8
Prerequisite: In addition to completion of Pre-Algebra, prerequisites may include district placement test, state test results, semester grades, and teacher recommendation.
A grade level course designed to provide students with sufficient mathematical foundation to meet Algebra 1 standards. This course meets the UC/CSU criteria for first year Algebra. Successful completion will result in placement in Geometry. | 677.169 | 1 |
The Four Pillars of Geometry
by John Stillwell Publisher Comments
For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra... (read more)
Fractals
by John Briggs Publisher Comments
Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them... (read more)
Riemannian Geometry
by Manfredo P. Do Carmo Publisher Comments
Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese)... (read more)
A Vector Space Approach to Geometry
by Melvin Hausner Publisher Comments
This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to... (read more)
Complex Spaces in Finsler, Lagrange and Hamilton Geometries
by Gheorghe Munteanu Publisher Comments
This book presents the most recent advances in complex Finsler geometry and related geometries: the geometry of complex Lagrange, Hamilton and Cartan Spaces. The last three spaces were initially introduced to and have been investigated by the author of... (read more)
Modern Geometry / With CD (02 Edition)
by David A. Thomas Publisher Comments
MODERN GEOMETRY was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics... (read more)
Convex Polyhedra (Springer Monographs in Mathematics)
by A. D. Alexandrov Publisher Comments
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems... (read more)
Analytic Geometry (7TH 92 Edition)
by Gordon B. Fuller Publisher Comments
Tailored for a first course in the study of analytic geometry, the text emphasizes the essential elements of the subject and stresses the concepts needed in calculus. This new edition was revised to present the subject in a modern, updated manner. Color... (read more)
Analytical Conics
by Barry Spain Publisher Comments
This concise text introduces students to the elements of analytical geometry, covering basic ideas and methods. Topics include transformation of axes, the line at infinity, conics and pencils of conics, homographic correspondence, line-coordinates, and... (read more)
Elementary Geometry for College Students (5TH 11 Edition)
by Daniel C. Alexander Publisher Comments
Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new... (read more)
Three Lectures on Fermat's Last Theorem
by Louis Joel Mordell Publisher Comments
Attempted by the greatest mathematicians including Euler, Legendre, Gauss, Abel, Dirichlet, Cauchy, and Kummer, and here is Mordell. Considered a classic, and unabridged.... (read more)
Geometric Analysis and Applications to Quantum Field Theory
by Peter Bouwknegt Publisher Comments
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Synopsis:
Table of Contents
What Do I Need to Know?- Complex Numbers.- Prelude to Complex Analysis.- Differentiation.- Complex Integration.- Cauchy's Theorem.- Some Consequences of Cauchy's Theorem.- Laurent Series and the Residue Theorem.- Applications of Contour Integration.- Further Topics.- Conformal Mappings.- Final Remarks.- Solutions to Exercises.- Bibliography.- Index.
"Synopsis"
by Springer, | 677.169 | 1 |
Navigate the rest of the site at your leisure. If you think this course can help
benefit you in any way, why not improve your chances of maths success and enrol today.
If you have any further questions contact our friendly team on 01745 832211
Do you want to make your IGCSE maths studies as painless and as successful as possible?
We can help. Igcsemaths.co.uk is a new division of the well established Nationwide
Home Study Publications. Our aim is to help you pass the International GCSE (IGCSE)
mathematics exam. Since 1990, through our sister site maths4all.co.uk we have helped
thousands of students like you, achieve maths success. Whatever your level, we can
help you. Introduced as an alternative to the GCSE and taken in well over 100 countries,
the IGCSE combines the best of the GCSE and the old O level. Because it is said to
stretch the more able student, many private and international schools have adopted
the IGCSE. Ideal for students who want to go on to take either AS or A level maths,
or science subjects such as physics.
• You may need to sit an examination which is recognised throughout the world.
• Perhaps you prefer an exam which is entirely calculator based.
• You may be about to relocate or already living outside the UK, and wish to pursue
you or your child's studies.
• Work commitments make it impossible for you to study full time at a school or
college.
• You cannot afford to give up your job in order to study.
• In order to work or study abroad you may need to pass this vital qualification.
Whatever your dream - you may want to become a teacher, join the police, become a
nurse or any career needing mathematics - we can help with all of these things. Our
courses use the well-proven "distance learning" method of study. This allows you
to continue with your usual job, career or lifestyle whilst spending a short time
studying whenever and wherever you want, using quality teaching materials. Study
at home, at work, on the bus, in the car - anywhere! With the added bonus of support
available by post phone or email should you need it, you cannot fail but to improve
your knowledge. You are in complete control of your studies.
Start to study for the global IGCSE mathematics exam (suitable for both UK and overseas
students) and enrol today. | 677.169 | 1 |
mediate Algebra: Concepts and Applications
The Bittinger Concepts and Applications Program delivers proven pedagogy, guiding students from skills-based math to the concepts-oriented math ...Show synopsisThe Bittinger Concepts and Applications Program delivers proven pedagogy, guiding students from skills-based math to the concepts-oriented math required for college courses.Hide synopsis
Description:Good. Used-Good Hardcover. Annotated instructor's edition. Book...Good. Used-Good Hardcover. Annotated instructor's edition. Book contains same material as original text, but includes the answers or additional annotations. 9th | 677.169 | 1 |
and Intermediate Algebra for College Students
The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated ...Show synopsisThe Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process16287561628756Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321628756This book is a good book to start off with if you don't really understand math that well. the only problem with the book i reviced was the teacher edition and i asked for the student. but everything else | 677.169 | 1 |
Real World Math: Engaging Students through Global Issues promotes student engagement by providing real-world data on global issues with a focus on practical solutions. The student workbook and corresponding teacher's guide concentrate on foundational algebra and geometry concepts. All lessons are aligned with National Council of Teachers of Mathematics Standards and Expectations. Topics range from climate change to financial literacy and build both mathematical knowledge and global perspective. Complementary datasets are also available to download for free. Learn more about Real World Math | 677.169 | 1 |
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses. | 677.169 | 1 |
Edexcel GCSE 2012 Maths Linked Pair Pilot reforms The Edexcel GCSE 2012 linear Maths Linked Pair Pilot specification is now available to download for first teaching in September 2012 (for two-year courses) and first assessment in June 2014.
The main changes are:
No content change to the specification
Linear assessment structure: all units are taken at the end of the course*
*Please see the FAQs with specific details to how linear rules operate with the linked pair.
Background to the Linked Pair Pilot
The 'linked pair' pilot began in September 2010, and consists of two GCSEs:
Methods which looks at the pure aspects of mathematics
Applications, which includes using mathematics in everyday contexts including "financial applications" and problem-solving in real-life scenarios
The 'linked pair' pilot is worth two GCSEs and is being piloted at the same time as our single Edexcel GCSE Mathematics specifications. Jointly, the linked pair GCSEs cover the rigorous core national curriculum programme of study, which is also assessed by the single GCSE. The pair, in addition, give a broader grounding in both methods in mathematics and applications of mathematics. | 677.169 | 1 |
Description
This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals First Course in Probability: SOLUTIONS MANUAL (7th Edition | 677.169 | 1 |
An Edge in Education: Advancing Math Courses with Mathematica (Spanish)
Dana Vazzana
This video features Dana Vazzana, an associate professor of mathematics at Truman State University, who explains why integrating Mathematica into her university-level math classes helps students gain deeper understanding of concepts and insights into real-world applications. Includes Spanish audio. | 677.169 | 1 |
...
Show More students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites | 677.169 | 1 |
Calculus is the study of functional relationships and how related quantities change witheach other. In your first exposure to calculus, the primary focus of your attention wason functions involving a single independent variable and a single dependent variable. Forsuch a function
f
, a single real number input
x
determines a unique single output value
f
(
x
). However, many of the functions of importance both within mathematics itself aswell as in the application of mathematics to the rest of the world involve many variablessimultaneously. For example, frequently in physics the function which describes the forceacting on an object moving in space depends on three variables, the three coordinateswhich describe the location of the object. If the force function also varies with time,then the force depends on four variables. Moreover, the output of the force function willitself involve three variables, the three coordinate components of the force. Hence theforce function is such that it takes three, or four, variables for input and outputs threevariables. Far more complicated functions are easy to imagine: the gross national productof a country is a function of thousands of variables with a single variable as output, anairline schedule is a function with thousands of inputs (cities, planes, and people to bescheduled, as well as other variables like fuel costs and the schedules of competing airlines)and perhaps hundreds of outputs (the particular routes flown, along with their times).Although such functions may at first appear to be far more difficult to work with thanthe functions of single variable calculus, we shall see that we will often be able to reduceproblems involving functions of several variables to related problems involving only singlevariable functions, problems which we may then handle using already familiar techniques.By definition, a function takes a single input value and associates it with a singleoutput value. Hence, even though in this book the inputs to our functions will ofteninvolve several variables, as will the outputs, we will nevertheless want to regard the inputand output of a function as single points in some multidimensional space. This is naturalin the case of, for example, the force function described above, where the input is a pointin three dimensional space, four if we need to use time, but requires some mathematicalabstraction if we want to consider the input to the gross national product function as apoint in some space of many thousands of dimensions. Because even the geometry of two-and three-dimensional space may be in some respects new to you, we will use this chapterto study the geometry of multidimensional space before proceeding to the study of calculusproper in Chapter 2.Throughout the book we will let
R
denote the set of real numbers.
Definition
By
n
-dimensional Euclidean space
we mean the set
R
n
=
{
(
x
1
,x
2
,...,x
n
) :
x
i
∈
R
,i
= 1
,
2
,...,n
}
.
(1.1.1)1
Copyrightc
by Dan Sloughter 2001
2
Introduction to
R
n
Section 1.1
x x x
123
x
1
( , , )
x
2
x
3
Figure 1.1.1 A point in
R
3
That is,
R
n
is the space of all ordered
n
-tuples of real numbers. We will denote a point inthis space by
x
= (
x
1
,x
2
,...,x
n
)
,
(1.1.2)and, for
i
= 1
,
2
,...,n
, we call
x
i
the
i
th
coordinate
of
x
.
Example
When
n
= 2, we have
R
2
=
{
(
x
1
,x
2
) :
x
1
,x
2
∈
R
}
,
which is our familiar representation for points in the Cartesian plane. As usual, we willin this case frequently label the coordinates as
x
and
y
, or something similar, instead of numbering them as
x
1
and
x
2
.
Example
When
n
= 3, we have
R
3
=
{
(
x
1
,x
2
,x
3
) :
x
1
,x
2
,x
3
∈
R
}
.
Just as we can think of
R
2
as a way of assigning coordinates to points in the Euclideanplane, we can think of
R
3
as assigning coordinates to three-dimensional Euclidean space. Topicture this space, we must imagine three mutually perpendicular axes with the coordinatesmarked off along the axes as in Figure 1.1.1. Again, we will frequently label the coordinatesof a point in
R
3
as, for example,
x
,
y
, and
z
, or
u
,
v
, and
w
, rather than using numberedcoordinates.
Example
If an object moves through space, its location may be specified with fourcoordinates, three spatial coordinate, say,
x
,
y
, and
z
, and one time coordinate, say
t
.Thus its location is specified by a point
p
= (
x,y,z,t
) in
R
4
. Of course, we cannot drawa picture of such a point.Before beginning our geometric study of
R
n
, we first need a few basic algebraic defini-tions.
Section 1.1 Introduction to
R
n
3
Definition
Let
x
= (
x
1
,x
2
,...,x
n
) and
y
= (
y
1
,y
2
,...,y
n
) be points in
R
n
and let
a
be a real number. Then we define
x
+
y
= (
x
1
+
y
1
,x
2
+
y
2
,...,x
n
+
y
n
)
,
(1.1.3)
x
−
y
= (
x
1
−
y
1
,x
2
−
y
2
,...,x
n
−
y
n
)
,
(1.1.4)and
a
x
= (
ax
1
,ax
2
,...,ax
n
)
.
(1.1.5)
Example
If
x
= (2
,
−
3
,
1) and
y
= (
−
4
,
1
,
−
2) are two points in
R
3
, then
x
+
y
= (
−
2
,
−
2
,
−
1)
,
x
−
y
= (6
,
−
4
,
3)
,
y
−
x
= (
−
6
,
4
,
−
3)
,
3
x
= (6
,
−
9
,
3)
,
and
−
2
y
= (8
,
−
2
,
4)
.
Notice that we defined addition and subtraction for points in
R
n
, but we did not definemultiplication. In general there is no form of multiplication for such points that is usefulfor our purpose. Of course, multiplication is defined in the special case
n
= 1 and for thespecial case
n
= 2 if we consider the points in
R
2
as points in the complex plane. Weshall see in Section 1.3 that there is also an interesting and useful type of multiplicationin
R
3
. Also note that (1.1.5) does provide a method for multiplying a point in
R
n
by aa real number, the result being another point in
R
n
. In such cases we often refer to thereal number as a
scalar
and this multiplication as
scalar multiplication
. We shall providea geometric interpretation of this form of multiplication shortly.
Geometry of
R
n
Recall that if
x
= (
x
1
,x
2
) and
y
= (
y
1
,y
2
) are two points in
R
2
, then, using thePythagorean theorem, the distance from
x
to
y
is
(
y
1
−
x
1
)
2
+ (
y
2
−
x
2
)
2
.
(1.1.6)This formula is easily generalized to
R
3
: Suppose
x
= (
x
1
,x
2
,x
3
) and
y
= (
y
1
,y
2
,y
3
) aretwo points in
R
3
. Let
z
= (
y
1
,y
2
,x
3
). Since the first two coordinates of
y
and
z
are thesame,
y
and
z
lie on the same vertical line, and so the distance between them is simply
|
y
3
−
x
3
|
.
(1.1.7)Moreover,
x
and
z
have the same third coordinate, and so lie in the same horizontal plane.Hence the distance between | 677.169 | 1 |
Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and plain English *Author: Taylor, Paul/ Paul, Taylor/ Bollobas, Bela *Series Title: Cambridge Studies in Advanced Mathematics (Hardcover) *Series Number: 59 *Binding Type: Hardcover *Number of Pages: 588 *Publication Date: 1999/05/13 *Language: English *Dimensions: 9.36 x 5.92 x 1.71 inches
From the Publisher: Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and "plain English"
Description:
This Computer Algebra Handbook gives a comprehensive snapshot of this
field at the intersection of mathematics and computer science with applications in physics, engineering and education. It contains both theory, systems and practice of the discipline of symbolic computation ...
Description:
This book introduces stochastic processes and their applications for students
in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time dependent random phenomena encountered in these disciplines. Through numerous science ... | 677.169 | 1 |
Math 9 is the first step in preparing students for the study of calculus by providing important skills in algebraic manipulation and interpretation at the college level. Topics will include a review of basic algebraic concepts; lines; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions, identities, inverse functions and equations; applications of trigonometry; systems of equations and matrices; conic sections; sequences, series and combinatorics. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous.
Math 10 prepares students for the study of calculus by providing important critical thinking and problem solving skills. The central theme of the course is the analysis of mathematical functions as models of change. Families of functions - linear, exponential, logarithmic, power, periodic, polynomial, rational - will be introduced, compared and contrasted. Course content will include an introduction to functions and functional notation; transformation of functions; composite, inverse and combinations of functions; vectors and polar coordinates; series; parametric equations; complex numbers. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous.
Prerequisite:
Mathematics 9 and proficiency with the TI-83 graphing calculator as gained from, for instance, Math 209.
This course is intended for students preparing for a career in elementary school teaching. Emphasis will be on the structure of the real number system, numeration systems, elementary number theory, and problem solving techniques. Technology will be integrated throughout the course.
Prerequisite:
Mathematics 208, or successful completion of a high school geometry course and Mathematics 233.
Survey of selected topics from contempory mathematics to introduce the student to mathematical thinking for the nonspecialist. Topics include systems of numeration, algebraic modeling, linear programming, trigonometry, math of finance, probability and statistics, and an introduction to calculus.
Operations with signed numbers, evaluation of expression containing numbers and letters, simplifying algebraic expressions, equations, word problems, exponents, polynomials, factoring and special products, fractions, graphing, systems of equations, radicals, and quadratic equations. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205B or 206 with a grade of "C" or better. This course may be taken for Mathematics 205B credit (2.5 units) by those students who have successfully completed Mathematics 205A with a grade of "C" or better.
The course contains the material covered in the first half of the Mathematics 205 course. It will cover signed numbers, evaluation of expressions, solving linear equations and inequalities, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205 or 206 with a grade of "C" or better.
Advisory:
Completion of Mathematics 402. Concurrent enrollment in Guidance 563A is advised. Students who were previously unsuccessful in Mathematics 205 are encouraged to attend.
A survey of practical geometry with an emphasis on applications to other disciplines and everyday life. Parallel lines, triangles, circles, polygons, three dimensional figures, vectors, and right triangle trigonometry will be covered. There will be a weekly lab.
This course is a remedial, modular, self-paced course. Application and critical thinking skills are developed in each module. Module A covers operations with whole numbers, equivalent fractions, multyplying self | 677.169 | 1 |
ALEX Lesson Plans
Title: Predict the Future?
Description:
Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.
Standard(s): 7: Utilize advanced features of database software, including merging data, sorting, filtering,
querying, and creating reports.
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Predict the Future? Description: Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.
Title: Show Me The Money - Saving and Investing
Description:
Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan AL1 (9-12) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1 Information Literacy (K - 12), or Mathematics (7 - 12) Title: Show Me The Money - Saving and Investing Description: Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan. domain Exponential Growth and Decay
Description:
ThisStandard(s): [MA2010] AL1 (9-12) 7: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2010] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This
Title: Density
Description:
DStandard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] CHE (9-12) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (9-12) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] [MA2010] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)
Subject: Mathematics (9 - 12), or Science (8 - 12) Title: Density Description: D
Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Subject: Mathematics (8 - 12) Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Title: Finding the Slope of a Line
Description:
ThisStandard(s): (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]
Subject: Mathematics (8 - 12) Title: Finding the Slope of a Line Description: This
Title: Math is Functional
Description:
This ( ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Math is Functional Description: This
Thinkfinity Lesson Plans
Title: Apple Pie Recording Chart
Description:
This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
Standard(s): [MA2010] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1] 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7-SP1] [MA2010] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Building Bridges
Description:
In 28: Understand that patterns of association can also be seen
Subject: Mathematics,Professional Development Title: Building Bridges Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Gallery Walk
Description:
In coordinate Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Age vs. Mileage
Description:
In
Subject: Mathematics Title: Automobile Mileage: Age vs. Mileage Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: The Centroid and the Regression Line
Standard(s): 44: AL2 (9-12) 21: Create equations in two or more variables to represent relationships
Subject: Mathematics Title: The Centroid and the Regression Line Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2010] (6) 17: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6] 10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7-EE4 Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Least Squares Regression
Description:
In Least Squares Regression
Title: Graph Chart
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): 2: Recognize and represent proportional relationships between quantities. [7-RP2 of 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2010] AL2 (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Bathtub Water Levels
Description:
In table Bathtub Water Levels Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: The Effects of Outliers 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3
Subject: Mathematics Title: The Effects of Outliers Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exploring Linear Data
Description:
In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation Exploring Linear Data Description: In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Title: Traveling Distances
Description:
In Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Linear Alignment
Description:
In
Standard(s): Linear Alignment Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Title: Make a Conjecture
Description:
In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2010] AL2 (9-12) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] [MA2010] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1T (9-12) 37: [S-ID4 ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2010] ALT (9-12) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7 Health,Mathematics Title: Make a ConjectureTitle: Exact Ratio
Description:
This
Standard(s): [MA2010] AL1 (9-12) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9 Mathematics Title: Exact Ratio Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Interactives/Games where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]
Learning ActivitiesThinkfinity Learning Activities
Title: Tube Viewer Simulation
Description:
This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change.
Standard(s): Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Flowing Through Mathematics
Description:
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
Standard(s): cases GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3
Subject: Mathematics Title: Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 | 677.169 | 1 |
Combining scientific inquiry with advanced mathematics, SC1117 is a stimulating, two-semester course for high-school students that will challenge learners to understand and explain how energy, matter, and motion are all related. Engaging lessons introduce theories and experiments and encourage students to develop the knowledge and understanding necessary to support conclusions with numerical results. | 677.169 | 1 |
It provides a full set of commonly used scientific calculation functions and supports the following unique features:
- Check history results for re-editing purposes; - Draw graphs corresponding to the math equations you input, such as Cartesian y(x) and x(y), parametric x(t), y(t) and polar r(θ)equations; - Allow users to choose from the variable bounds and background color to give a vivid display for a deeper understanding of the equations.
Still hesitate? Try the lite version to verify whether it meets your needs fully.
Kindly take note that the lite version has some restrictions, such as complicated scientific functions like sin, log are not supported.
1. Added sound effect, which can be disabled in the Settings 2. Optimized translation algorithm, allowing the graph to move and zoom in/out more fluently 3. Changed coordinate calculation algorithm, making the coordinate easily readable (Coordinate is marked via the multiples of 5.) 4. Fixed the bug that a tiny coordinate would be displayed at the origin under some circumstances 5. Operating system requirement: Android 2.2 and above
Comments and ratings for Scientific Graphing Calculator
(43 stars)
by Danny Kezar on 04/06/2013
Difficult to use...
(43 stars)
by dan driggers on 29/01/2013
It doesn't zoom x and y axis independently
(43 stars)
by A Google User
(43 stars)
by Melanie | 677.169 | 1 |
Introduction
The Mathematics Department hopes that all students will take mathematics courses. This said, be careful to take only those courses that are appropriate for your level of experience. Incoming students should take advantage of Harvards Mathematics Placement Test and of the science advising available in the Science Center the week before classes begin. Members of the Mathematics Department will be available during this period to consult with students. Generally, students with a strong precalculus background and some calculus experience will begin their mathematics education here with a deeper study of calculus and related topics in courses such as Mathematics 1a, 1b, 18,19a,b, 21a,b, 23a,b and 25a,b. The Harvard Mathematics Placement Test results recommend the appropriate starting level course, either Mathematics Ma, 1a, 1b, or 21. Recommendation for Mathematics 21 is sufficient qualification for Mathematics 18, 19a,b, 21a, 23a, and 25a.
What follows briefly describes these courses: Mathematics 1a introduces the basic ideas and techniques of calculus while Mathematics 1b covers integration techniques, differential equations, and series. Mathematics 21a covers multi-variable calculus while Mathematics 21b covers basic linear algebra with applications to differential equations. Students who do not place into (or beyond) Mathematics 1a can take Mathematics Ma, Mb, a two-term sequence which integrates calculus and precalculus material and prepares students to enter Mathematics 1b.
There are a number of options available for students whose placement is to Mathematics 21. For example, Mathematics 19a,b are courses that are designed for students concentrating in the life sciences. (These course are recommended over Math 21a,b by the various life science concentrations). In any event, Math 19a can be taken either before or after Math 21a,b. Math 19b should not be taken with Math 21b. Math 19a teaches differential equations, related techniques and modeling with applications to the life sciences. Math 19b teaches linear algebra, probability and statistics with a focus on life science examples and applications. Mathematics 18 covers selected topics from Mathematics 1b and 21a for students particularly interested in economic and social science applications.
Mathematics 23 is a theoretical version of Mathematics 21 which treats multivariable calculus and linear algebra in a rigorous, proof oriented way. Mathematics 25 and 55 are theory courses that should be elected only by those students who have a strong interest in mathematics. They assume a solid understanding of one-variable calculus, a willingness to think rigorously and abstractly about mathematics, and to work extremely hard. Both courses study multivariable calculus and linear algebra plus many very deep related topics. Mathematics 25 differs from Mathematics 23 in that the work load in Mathematics 25 is significantly more than in Mathematics 23, but then Mathematics 25 covers more material. Mathematics 55 differs from Mathematics 25 in that the former assumes a very strong proof oriented mathematics background. Mathematics 55, covers the material from Mathematics 25 plus much material from Mathematics 122 and Mathematics 113. Entrance into Mathematics 55 requires the consent of the instructor.
Students who have had substantial preparation beyond the level of the Advanced Placement Examinations are urged to consult the Director of Undergraduate Studies in Mathematics concerning their initial Harvard mathematics courses. Students should take this matter very seriously. The Mathematics Department has also prepared a pamphlet with a detailed description of all its 100-level courses and their relationship to each other. This pamphlet gives sample lists of courses suitable for students with various interests. It is available at the Mathematics Department Office. Many 100-level courses assume some familiarity with proofs. Courses that supply this prerequisite include Mathematics 23, 25, 55, 101, 112, 121, and 141. Of these, note that Mathematics 101 may be taken concurrently with Mathematics 1, 18, 19, or 21.
Mathematics 113, 114, 122, 123, 131, and 132 form the core of the departments more advanced courses. Mathematics concentrators are encouraged to consider taking these courses, particularly Mathematics 113, 122 and 131. (Those taking 55a,b will have covered the material of Mathematics 113 and 122, and are encouraged to take Mathematics 114, 123, and 132.)
Courses numbered 200-249 are introductory graduate courses. They will include substantial homework and are likely to have a final exam, either in class or take home. Most are taught every year. They may be suitable for very advanced undergraduates. Mathematics 212a, 230a, 231a and 232a will help prepare graduate students for the qualifying examination in Mathematics. Courses numbered 250-299 are graduate topic courses, intended for advanced graduate students.
The Mathematics Department does not grant formal degree credit without prior approval for taking a course that is listed as a prerequisite of one you have already taken. Our policy is that a student who takes and passes any calculus course is not normally permitted to then take a more elementary course for credit. A student who has passed Mathematics 21a, for example, will normally not be allowed to take Mathematics 1a, or 1b for credit. The Mathematics Department is prepared to make exceptions for sufficient academic reasons; in each case, however, a student must obtain written permission from the Mathematics Director of Undergraduate Studies in advance.
In the case of students accepting admission as sophomores, this policy is administered as follows: students counting one half course of advanced standing credit in mathematics are deemed to have passed Mathematics 1a, and students counting a full course of advanced standing credit in mathematics are deemed to have passed Mathematics 1a and 1b.
Primarily for Undergraduates
Mathematics Ma. Introduction to Functions and Calculus I
Catalog Number: 1981 Enrollment: Normally limited to 15 students per section.
Meghan Anderson, Melody Chan, Peter M. Garfield, Meredith Hegg, and members of the Department
Half course (fall term). Section meeting times: Section I: M., W., F., at 10; Section II: M., W., F., at 11; Section III: M. W. F., at 12 (with sufficient enrollment); and a twice weekly lab session to be arranged. EXAM GROUP: 3
The study of functions and their rates of change. Fundamental ideas of calculus are introduced early and used to provide a framework for the study of mathematical modeling involving algebraic, exponential, and logarithmic functions. Thorough understanding of differential calculus promoted by year long reinforcement. Applications to biology and economics emphasized according to the interests of our students. Note: Required first meeting: Tuesday, September 3, 8:30 am, Science Center D. Participation in two, one hour workshops are required each week. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. This course, when taken for a letter grade together with Mathematics Mb, meets the Core area requirement for Quantitative Reasoning.
Mathematics Mb. Introduction to Functions and Calculus II
Catalog Number: 3857 Enrollment: Normally limited to 15 students per section.
Meredith Hegg, Meghan Anderson, Sarah Chisolm, Peter M. Garfield, and members of the Department
Half course (spring term). Section I: M., W., F., at 10; Section II: M. W., F., at 11; Section III: M., W., F., at 12 (with sufficient enrollment); and a twice weekly lab session to be arranged. EXAM GROUP: 1
Continued investigation of functions and differential calculus through modeling; an introduction to integration with applications; an introduction to differential equations. Solid preparation for Mathematics 1b. Note: Required first Meeting in spring: Monday, January 27, 8:30 am, Science Center A . Participation in two, one hour workshops are required each week. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. This course, when taken for a letter grade together with Mathematics Ma, meets the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics Ma.
Mathematics 1a. Introduction to Calculus
Catalog Number: 8434 Enrollment: Normally limited to 30 students per section.
Peter M. Garfield, Janet Chen, Sarah Chisolm, Sukhada Fadnavis, and members of the Department (fall term); Oliver Knill (spring term)
Half course (fall term; repeated spring term). Fall: Section I, M., W., F., at 9 (with sufficient enrollment); Section II, M., W., F., at 10; Section III, M., W., F., at 11; Section IV, M., W., F., at 12; Section V, Tu., Th., 10-11:30; Section Vl, Tu., Th., 11:30-1. Spring: Section I, M., W., F., at 10, and a weekly problem section to be arranged. EXAM GROUP: 1
The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. This course will help you see why by introducing: how differential calculus treats rates of change; how integral calculus treats accumulation; and how the fundamental theorem of calculus links the two. These ideas will be applied to problems from many other disciplines. Note: Required first meeting in fall: Wednesday, September 4, 8:30 am, Science Center C . This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: A solid background in precalculus.
Mathematics 18 (formerly Mathematics 20). Multivariable Calculus for Social Sciences
Catalog Number: 0906
Meredith Hegg
Half course (fall term). M., W., F., at 9. EXAM GROUP: 2
Focus on concepts and techniques of multivariable calculus most useful to those studying the social sciences, particularly economics: functions of several variables; partial derivatives; directional derivatives and the gradient; constrained and unconstrained optimization, including the method of Lagrange multipliers. Covers linear and polynomial approximation and integrals for single variable and multivariable functions; modeling with derivatives. Covers topics from Math 21a most useful to social sciences. Note: Should not ordinarily be taken in addition to Mathematics 21a or Applied Mathematics 21a. Mathematics 21b can be taken before or after Mathematics 18. Examples draw primarily from economics and the social sciences, though Mathematics 18 may be useful to students in certain natural sciences. Students whose main interests lie in the physical sciences, mathematics, or engineering should consider Math or Applied Mathematics 21a. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. Prerequisite: Mathematics 1b or equivalent, or a 5 on the BC Advanced Placement Examination in Mathematics.
Mathematics 19a. Modeling and Differential Equations for the Life Sciences
Catalog Number: 1256
John Hall (fall term) and John Wes Cain (spring term)
Half course (fall term; repeated spring term). M., W., F., at 1, and a weekly discussion section to be arranged. EXAM GROUP: 6
Considers the construction and analysis of mathematical models that arise in the life sciences, ecology and environmental life science. Introduces mathematics that include multivariable calculus, differential equations in one or more variables, vectors, matrices, and linear and non-linear dynamical systems. Taught via examples from current literature (both good and bad). Note: This course is recommended over Math 21a for those planning to concentrate in the life sciences and ESPP. Can be taken with or without Mathematics 21a,b. Students with interests in the social sciences and economics might consider Mathematics 18. This course can be taken before or after Mathematics 18. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.
Mathematics 19b. Linear Algebra, Probability, and Statistics for the Life Sciences
Catalog Number: 6144
Peter M. Garfield
Half course (spring term). M., W., F., at 1, and a weekly problem section to be arranged. EXAM GROUP: 6
Probability, statistics and linear algebra with applications to life sciences, chemistry, and environmental life sciences. Linear algebra includes matrices, eigenvalues, eigenvectors, determinants, and applications to probability, statistics, dynamical systems. Basic probability and statistics are introduced, as are standard models, techniques, and their uses including the central limit theorem, Markov chains, curve fitting, regression, and pattern analysis. Note: This course is recommended over Math 21b for those planning to concentrate in the life sciences and ESPP. Can be taken with Mathematics 21a. Students who have seen some multivariable calculus can take Math 19b before Math 19a. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.
Mathematics 23a. Linear Algebra and Real Analysis I
Catalog Number: 2486
Paul G. Bamberg
Half course (fall term). Tu., Th., 2:30-4. EXAM GROUP: 16, 17
A rigorous, integrated treatment of linear algebra and multivariable differential calculus, emphasizing topics that are relevant to fields such as physics and economics. Topics: fields, vector spaces and linear transformations, scalar and vector products, elementary topology of Euclidean space, limits, continuity, and differentiation in n dimensions, eigenvectors and eigenvalues, inverse and implicit functions, manifolds, and Lagrange multipliers. Note: Course content overlaps substantially with Mathematics 21a,b, 25a,b, so students should plan to continue in Mathematics 23b. See the description in the introductory paragraphs in the Mathematics section of the catalog about the differences between Mathematics 23 and Mathematics 25. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics 1b or a grade of 4 or 5 on the Calculus BC Advanced Placement Examination, plus an interest both in proving mathematical results and in using them.
Mathematics 25a. Honors Linear Algebra and Real Analysis I
Catalog Number: 1525
Benedict H. Gross
Half course (fall term). M., W., F., at 10. EXAM GROUP: 3
A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness. Note: Only for students with a strong interest and background in mathematics. There will be a heavy workload. May not be taken for credit after Mathematics 23. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: 5 on the Calculus BC Advanced Placement Examination and some familiarity with writing proofs, or the equivalent as determined by the instructor.
Mathematics 25b. Honors Linear Algebra and Real Analysis II
Catalog Number: 1590
Noam D. Elkies
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
A rigorous treatment of basic analysis. Topics include: convergence, continuity, differentiation, the Riemann integral, uniform convergence, the Stone-Weierstrass theorem, Fourier series, differentiation in several variables. Additional topics, including the classical results of vector calculus in two and three dimensions, as time allows. Note: There will be a heavy workload. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics 23a or 25a or 55a.
*Mathematics 55a. Honors Abstract Algebra
Catalog Number: 4068
Dennis Gaitsgory
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
A rigorous treatment of abstract algebra including linear algebra and group theory. Note: Mathematics 55a is an intensive course for students having significant experience with abstract mathematics. Instructors permission required. Every effort will be made to accommodate students uncertain of whether the course is appropriate for them; in particular, Mathematics 55a and 25a will be closely coordinated for the first three weeks of instruction. Students can switch between the two courses during the first three weeks without penalty. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.
*Mathematics 55b. Honors Real and Complex Analysis
Catalog Number: 3312
Dennis Gaitsgory
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
A rigorous treatment of real and complex analysis. Note: Mathematics 55b is an intensive course for students having significant experience with abstract mathematics. Instructors permission required. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.
*Mathematics 60r. Reading Course for Senior Honors Candidates
Catalog Number: 8500
Peter B. Kronheimer
Half course (fall term; repeated spring term). Hours to be arranged.
Advanced reading in topics not covered in courses. Note: Limited to candidates for honors in Mathematics who obtain the permission of both the faculty member under whom they want to work and the Director of Undergraduate Studies. May not count for concentration in Mathematics without special permission from the Director of Undergraduate Studies. Graded Sat/Unsat only.
*Mathematics 99r. Tutorial
Catalog Number: 6024
Peter B. Kronheimer and members of the Department
Half course (fall term; repeated spring term). Hours to be arranged.
Supervised small group tutorial. Topics to be arranged. Note: May be repeated for course credit with permission from the Director of Undergraduate Studies. Only one tutorial may count for concentration credit.
For Undergraduates and Graduates
See also Applied Mathematics and Statistics.
Mathematics 101. Sets, Groups and Topology
Catalog Number: 8066
Adam Jacob
Half course (fall term). M., W., F., at 11. EXAM GROUP: 4
An introduction to rigorous mathematics, axioms, and proofs, via topics such as set theory, symmetry groups, and low-dimensional topology. Note: Familiarity with algebra, geometry and/or calculus is desirable. Students who have already taken Mathematics 23a,b, 25a,b or 55a,b should not take this course for credit. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: An interest in mathematical reasoning.
Mathematics 116. Real Analysis, Convexity, and Optimization
Catalog Number: 5253
Paul G. Bamberg
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Develops the theory of convex sets, normed infinite-dimensional vector spaces, and convex functionals and applies it as a unifying principle to a variety of optimization problems such as resource allocation, production planning, and optimal control. Topics include Hilbert space, dual spaces, the Hahn-Banach theorem, the Riesz representation theorem, calculus of variations, and Fenchel duality. Students will be expected to understand and invent proofs of theorems in real and functional analysis. Prerequisite: Mathematics 23ab, 25ab, or 55ab, or Mathematics 21ab plus at least one other more advanced course in mathematics.
Mathematics 117. Probability and Random Processes with Economic Applications
Catalog Number: 45584
Sukhada Fadnavis
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
A self-contained treatment of the theory of probability and random processes with specific application to the theory of option pricing. Topics: axioms for probability, calculation of expectation by means of Lebesgue integration, conditional probability and conditional expectation, martingales, random walks and Wiener processes, and the Black-Scholes formula for option pricing. Students will work in small groups to investigate applications of the theory and to prove key results. Note: A problem-solving section is required MW 2-3 or Th 7:30-9:30 PM Prerequisite: A thorough knowledge of single-variable calculus and infinite series, plus at least one more advanced course such as MATH E-23a that provides experience with proofs and elementary real analysis. Acquaintance with elementary probability is desirable.
[Mathematics 141. Introduction to Mathematical Logic]
Catalog Number: 0600
Instructor to be determined
Half course (fall term). M., W., F., at 11. EXAM GROUP: 4
An introduction to mathematical logic with applications to computer science and algebra. Formal languages. Completeness and compactness of first order logic. Definability and interpolation. Decidability. Unsolvable problems. Computable functions and Turing machines. Recursively enumerable sets. Transfinite induction. Note: Expected to be given in 2014–15. Prerequisite: Any mathematics course at the level of Mathematics 21a,b or higher, or permission of instructor.
Mathematics 143. Set Theory
Catalog Number: 6005
Peter Koellner
Half course (fall term). W., 1–3. EXAM GROUP: 6, 7
An introduction to set theory covering the fundamentals of ZFC (cardinal arithmetic, combinatorics, descriptive set theory) and the independence techniques (the constructible universe, forcing, the Solovay model). We will demonstrate the independence of CH (the Continuum Hypothesis), SH (Suslins Hypothesis), and some of the central statements of classical descriptive set theory. Note: An additional hour of lecture will be scheduled independently. Prerequisite: Any mathematics course at the level of Mathematics 21a or higher, or permission of instructor.
Mathematics 145. Set Theory II - (New Course)
Catalog Number: 19964
Peter Koellner
Half course (spring term). W., 1–3, and an additional hour of lecture will be scheduled independently. EXAM GROUP: 6, 7
An introduction to the hierarchy of axioms of infinity in set theory, their applications and their inner models. Note: An additional hour of lecture will be scheduled independently.
[Mathematics 152. Discrete Mathematics]
Catalog Number: 8389
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Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
An introduction to finite groups, finite fields, finite geometry, discrete probability, and graph theory. A unifying theme of the course is the symmetry group of the regular icosahedron, whose elements can be realized as permutations, as linear transformations of vector spaces over finite fields, as collineations of a finite plane, or as vertices of a graph. Taught in a seminar format, and students will gain experience in presenting proofs at the blackboard. Note: Expected to be given in 2014–15. Students who have taken Mathematics 23a,b, 25a,b or 55a,b should not take this course for credit.
Mathematics 154. Probability Theory
Catalog Number: 4306
Clifford Taubes
Half course (fall term). M., W., F., at 12. EXAM GROUP: 5
An introduction to probability theory. Discrete and continuous random variables; distribution and density functions for one and two random variables; conditional probability. Generating functions, weak and strong laws of large numbers, and the central limit theorem. Geometrical probability, random walks, and Markov processes. Note: This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning and the Core area requirement for Quantitative Reasoning. Prerequisite: A previous mathematics course at the level of Mathematics 19ab, 21ab, or higher. For students from 19ab or 21ab, previous or concurrent enrollment in Math 101 or 112 may be helpful. Freshmen who did well in Math 23, 25 or 55 last term are also welcome to take the course.
[Mathematics 168. Computability Theory]
Catalog Number: 31297
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Half course (spring term). M., W., F., at 12. EXAM GROUP: 5
An introduction to computability theory (also known as recursion theory). A discussion of the problem of determining what it means for a set or function to be computable, including primitive recursion, Turing machines, and the Church-Turing Thesis. The theory of Turing degrees and the computably enumerable sets. Topics: the halting set, Turing reducibility and other reducibilities, Posts problem, the Recursion Theorem, priority arguments, and more. Note: Expected to be given in 2014–15. Prerequisite: The student must have the ability to read and write mathematical proofs.
Mathematics 233a. Theory of Schemes I
Catalog Number: 6246
Igor Andreevich Rapinchuk
Half course (fall term). M., W., F., at 11. EXAM GROUP: 4
An introduction to the theory and language of schemes. Textbooks: Algebraic Geometry by Robin Hartshorne and Geometry of Schemes by David Eisenbud and Joe Harris. Weekly homework will constitute an important part of the course. Prerequisite: Mathematics 221 and 232a or permission of instructor.
Mathematics 265x. Reasoning via Models - (New Course)
Catalog Number: 73059 Enrollment: Limited to 20.
Eric S. Maskin, Barry C. Mazur, and Amartya Sen
Half course (fall term). Tu., 2–4. EXAM GROUP: 15, 16, 17
An examination of how formal models are used in different disciplines. Examples will be taken from economics, mathematics, physics and philosophy, among other fields. Note: This course may not be counted towards the required eight letter-graded half-courses in mathematics for the concentration requirement 1a, but may be counted as one of the four half-courses in mathematics or related fields, requirement 1b. This is cross-listed in Economics, History of Science, and Philososphy. Prerequisite: There are no specific course prerequisites, but ease and familiarity with formal reasoning is essential.
Mathematics 270x. Topics in Automorphic Forms - (New Course)
Catalog Number: 70229
Benedict H. Gross
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
We will give an introduction to the theory of modular and automorphic forms, with an emphasis on applications to algebraic number theory. Topics to be covered include the formalism of L-groups, functoriality, trace formulae, and the construction by Chenevier and Clozel of number fields with limited ramification.
Nature of Evidence
Professor Noah Feldman, FAS Professor Barry Mazur
Fall 2012 Seminar
Meets: Th 1:00pm - 3:00pm in WCC Room 3008
2 classroom credits
Co-taught with mathematician Barry Mazur, this interdisciplinary,
cross-listed class will explore and compare the nature of evidence
and proof in a number of different fields: law, mathematics, the
sciences, social sciences, and humanities. It will ask: What is
considered evidence? How does what counts as evidence illuminate
what it means to say we want to know and understand the truth? How
can we communicate it across disciplines and contexts? Permission of
instructors required. Single paper. Background in allied fields
helpful but not required. | 677.169 | 1 |
Key Features
KEY FEATURES: · This is a more accessible version of Arfken and Weber's blockbuster reference, Mathematical Methods for Physicists, 5th Edition · Many more detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems · More frequent and thorough explanations help readers understand, recall, and apply the theory · New introductions and review material provide context and extra support for key ideas · Many more routine problems reinforce basic concepts and computations
Description
This new adaptation of Arfken and Weber's bestselling Mathematical Methods for Physicists, Fifth Edition, is the most comprehensive, modern, and accessible text for using mathematics to solve physics problems. Additional explanations and examples make it student-friendly and more adaptable to a course syllabus.
Readership
Juniors and Seniors in Physics, Engineering, Applied Mathematics, Chemistry and Environmental Sciences; also practitioners and researchers in these fields.
Quotes and reviews
"True to the title, this new text achieves a comprehensive coverage of the 'essential' topics in mathematical physics at the undergraduate level. This new version is filled with enlightening examples, which is the key to undergraduate teaching. More importantly, many examples are real problems from various fields of physics." - David Hwang, University of California at Davis
"The book contains many worked out problems some of which are solved in more than one way to accommodate different learning needs and styles of different students. Particularly, the chapters on vector analysis, determinant and matrices, Fourier series, and probability are extremely well written and will be an instant success with the students." - Amit Chakrabati, Kansas State University | 677.169 | 1 |
Product Description
The quadratic formula is demystified as students piece together and match up the various parts - vertex, axis of symmetry, discriminant, and quadratic formula. The goal is to match these cards to the factor, root, point pair, and graph cards to discover the connections to the quadratic equation. All decks have a sampling of non-function parabolas and include several parabolas that are in translated positions. Makes pattern recognition and relational thinking easy to teach. One repair deck included for lost or damaged cards. Includes nine card decks and a 60-page teacher's manual. Grade 8 and up.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. | 677.169 | 1 |
Description
Used by more than 6 million math students, MyMathLabThis–42% of the 452 examples are new or revised, and 31% of the 3,741 exercises are new or revised.
Table of Contents
Chapter 1: Algebra and Equations
1.1 The Real Numbers
1.2 Polynomials
1.3 Factoring
1.4 Rational Expressions
1.5 Exponents and Radicals
1.6 First-Degree Equations
1.7 Quadratic Equations
Chapter 1 Summary
Chapter 1 Review Exercises
Case Study 1: Consumers Often Defy Common Sense
Chapter 2: Graphs, Lines, and Inequalities
2.1 Graphs
2.2 Equations of Lines
2.3 Linear Models
2.4 Linear Inequalities
2.5 Polynomial and Rational Inequalities
Chapter 2 Summary
Chapter 2 Review Exercises
Case Study 2: Using Extrapolation to Predict Life Expectancy
Chapter 3: Functions and Graphs
3.1 Functions
3.2 Graphs of Functions
3.3 Applications of Linear Functions
3.4 Quadratic Functions
3.5 Applications of Quadratic Functions
3.6 Polynomial Functions
3.7 Rational Functions
Chapter 3 Summary
Chapter 3 Review Exercises
Case Study 3: Architectural Arches
Chapter 4: Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Applications of Exponential Functions
4.3 Logarithmic Functions
4.4 Logarithmic and Exponential Equations
Chapter 4 Summary
Chapter 4 Review Exercises
Case Study 4: Characteristics of the Monkeyface Prickleback
Chapter 5: Mathematics of Finance
5.1 Simple Interest and Discount
5.2 Compound Interest
5.3 Annuities, Future Value, and Sinking Funds
5.4 Annuities, Present Value, and Amortization
Chapter 5 Summary
Chapter 5 Review Exercises
Case Study 5: Continuous Compounding
Chapter 6: Systems of Linear Equations and Matrices
6.1 Systems of Two Linear Equations in Two Variables
6.2 Larger Systems of Linear Equations
6.3 Applications of Systems of Linear Equations
6.4 Basic Matrix Operations
6.5 Matrix Products and Inverses
6.6 Applications of Matrices
Chapter 6 Summary
Chapter 6 Review Exercises
Case Study 6: Matrix Operations and Airline Route Maps
Chapter 7: Linear Programming
7.1 Graphing Linear Inequalities in two Variables
7.2 Linear Programming: The Graphical Method
7.3 Applications of Linear Programming
7.4 The Simplex Method: Maximization
7.5 Maximization Applications
7.6 The Simplex Method: Duality and Minimization
7.7 The Simplex Method: Nonstandard Problems
Chapter 7 Summary
Chapter 7 Review Exercises
Case Study 7: Cooking with Linear Programming
Chapter 8: Sets and Probability
8.1 Sets
8.2 Applications of Venn Diagrams
8.3 Introduction to Probability
8.4 Basic Concepts of Probability
8.5 Conditional Probability and Independent Events
8.6 Bayes' Formula
Chapter 8 Summary
Chapter 8 Review Exercises
Case Study 8: Medical Diagnosis
Chapter 9: Counting, Probability Distributions, and Further Topics in Probability
9.1 Probability Distributions and Expected Value
9.2 The Multiplication Principle, Permutations, and Combinations
9.3 Applications of Counting
9.4 Binomial Probability
9.5 Markov Chains
9.6 Decision Making
Chapter 9 Summary
Chapter 9 Review Exercises
Case Study 9: QuickDraw® from the New York State Lottery
Chapter 10: Introduction to Statistics
10.1 Frequency Distributions
10.2 Measures of Central Tendency
10.3 Measures of Variation
10.4 Normal Distributions
10.5 Normal Approximation to the Binomial Distribution
Chapter 10 Summary
Chapter 10 Review Exercises
Case Study 10: Statistics in the Law—The Castañeda Decision
Appendixes
Appendix A: Graphing Calculators
Appendix B: Tables
Table 1: Formulas from Geometry
Table 2: Areas under the Normal Curve
Table 3: Integrals
Answers to Selected Exercises
Index of Applications
Index
Purchase Info
ISBN-10: 0-321-70893-8
ISBN-13: 978-0-321-70893-9
Format: Alternate Binding
$194.67
We're temporarily out of stock, but order now and we'll send it to you later. | 677.169 | 1 |
Summary: As in previous editions, the focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of ''active participant'' is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar problems, he...show morelps them build their confidence and eventually7073 +$3.99 s/h
Good
One Stop Text Books Store Sherman Oaks, CA
2010-02-16 Paperback Good Good.35.08 978143904695173 | 677.169 | 1 |
This book fills a gap in the linear programming literature, by explaining the steps that are illustrated but not always fully explained in every elementary operations book '" the steps that lead from the elementary and intuitive graphical method of solution to the more advanced simplex tableau method.Most of the world, even those technically trained, can get along very well by seeing a few illustrations of simple linear programming problems solved graphically, followed by instruction in the use of computer software for solving real-world problems. But there needs to be a coterie of initiates who understand the process well enough to explain it to others, to know what the pitfalls,More... ramifications and special cases are, and to provide further developments. I have used an informal narrative style with a number of worked out examples and detailed explanations, to put the topic within reach | 677.169 | 1 |
Math Textbooks and Resources
Math and Science Services has current textbooks for all mathematics courses in the Liberal Arts Core. Students can use them in the lab only, with a current University of Northern Iowa Identification card.
We also have
old textbooks and math-topic books, which students may borrow for up to one week with a current UNI ID card. Math topic books include
Winning at Math; Math Study Skills Workbook; Multiculturalism in Mathematics,
Science and Technology; and The Dell Book of Logic Problems.
In addition
to textbooks, Intelligent Tutor is available for students to
complete interactive computer-aided instruction on specific math content.
Statistical software, SPSS is also available on Math and Science Services computers. | 677.169 | 1 |
This eBook introduces the subject of measures and measurement, and looks at both metric and imperial units of measurement, the process and accuracy of reading scales, limits on the accuracy of measurements and compound measurements. More
This eBook introduces the subject of measures and measurement, and looks at both metric and imperial units of measurement, the process and accuracy of reading scales, limits on the accuracy of measurements and compound measurements.
This eBook is part of our range of Key Stage 3 (KS3) maths eBooks that are fully aligned with the UK Governments national curriculum.
OurMeasures and Measurement is a module within the Geometry and Measures principle section our Key Stage 3 (KS3) publications. It is one module out of a total of six modules in that principle section, the others being: • 2D Shapes and 3D Solids • Loci, Constructions and 3D Co-ordinates • Angles, Bearings and Scale Drawings • Transformations • Pythagoras' Theorem, Trigonometry and Similarity | 677.169 | 1 |
Precalculus with Unit-Circle Trigonometry - 3rd edition
Summary: This book introduces trigonometry through the unit circle. Cohen emphasizes graphing to explain complex concepts in an uncomplicated style, and provides supplementary graphing-calculator exercises at the end of most sections for additional perspective and reinforcement.
Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
PART X. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
PART XI. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
PART XII. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations : The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.6.49 +$3.99 s/h
Acceptable
AlphaBookWorks Alpharetta, GA
05343527586.99 | 677.169 | 1 |
This collection features resources produced by Shirley Fall designed to enable high ability GCSE students to explore further mathematical topics beyond the scope of the syllabus thus bridging the gap between GCSE and AS level. The resources could also be used as introductory work at AS level in preparation for more in depth study.…
This collection contains all twelve issues of iSquared magazine. The magazine is edited by Sarah Shepherd whose aim is to bring together a collection of articles that reflect the wide range of modern-day applications of mathematics. Many people are unaware that maths is more than just abstract concepts, inaccessible to all but thoseInquiry maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement called a prompt. Inquiries can involve a class on diverse paths of exploration or in listening to a teacher's exposition. In inquiry maths, students take responsibility for directing the lessonThis collection of resources, produced by the O.R. Society, supports the teaching and learning of decision mathematics. The collection contains seven short films explaining what operational research is, how it is used in a variety of every day situations and what career opportunities the study of operational reasearch affords.
TheThis collection of resources from Nuffield are designed to improve the ability of students to analyse and present data, ask questions about and find meaning in data and discuss critically the interpretation of data. 'Exploratory Data Analysis' emphasises getting to know the data, analysing and finding meaning, simple disciplines Centre for Innovation in Mathematics Teaching (CIMT) was established in 1986. The centre is a focus for research and curriculum development in mathematics teaching and learning, with the aim of unifying and enhancing mathematical progress in schools and colleges.
This collection contains resources for use in the teaching of | 677.169 | 1 |
Cartesian Coordinate
Little Hopper's Treasure Hunt is a fun introduction to graphing and the Cartesian coordinate system. Learn to read and identify points on a graph using the Cartesian coordinate system while searching the ocean for treasure and surprises.
Smart Algebra builds graphs of any complexity (including the implicit functions) in polar and Cartesian coordinate systems, quickly draws the image on the screen, allows the analysis of the function (search for extremum, integral in the interval,
Demonstrates the use of a square proximity algorithm. Draws squares on a form using some techniques from the Drawing.Drawing2D namespace. Also demonstrates how to open a particular directory folder using Windows Explorer. | 677.169 | 1 |
This course applies the principles of geometry and trigonometry and the computing of compound angles to situations encountered in the machining industry. It also gives a brief introduction to the calculations required in computer numerical control programming. Two classroom, two lab hours per week.
Prerequisite:
CAM 1141
Booklist for CAM 11420189417
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Section = 333 335 337 339*Term designations represent when courses are typically offered. They are included for planning purposes only and subject to change. Refer to the current schedule for actual course offerings. | 677.169 | 1 |
PrecalRECALCULUS, Fourth Edition focuses on teaching the essentials of what a student needs to fulfill their PreCalculus requirement and to fully prepare them to succeed in calculus. It provides students with an integrated review of algebra and trigonometry while focusing on essential calculus concepts. Faires and DeFranza prepare students for calculus by providing a solid grounding in analysis and graphing, tools necessary to make a successful transition to calculus. This streamlined text provides all the mathematics that students need?it doesn't b... MOREog them down in review, or overwhelm them with too much, too soon. The authors are careful to keep this book, unlike many of the PreCalculus books on the market, at a length that can be covered in one term. Get a better grade with PRECALCULUS! With a focus on teaching the essentials, this mathematics text provides you with the fundamentals necessary to be successful in this course and your future calculus course. Exercises and examples are presented the way that you will encounter them in calculus so that you are truly prepared for your next course. Learning tools found throughout the text such as exercises, calculus connections, and true and false questions help you master difficult concepts. | 677.169 | 1 |
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From the Back Cover- An expanded section on encryption
- Additional examples of the ways in which theory can be applied to problems in computing
- Many more exercises covering a range of levels, from the basic to the more advanced
This book is ideal for students taking a one-semester introductory course in discrete mathematics, particularly for first year undergraduates studying Computing and Information Systems. | 677.169 | 1 |
Cliffs Quick Review for Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.
A used copy at a fantastic price | 677.169 | 1 |
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Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics | 677.169 | 1 |
See the Pathways
Pathways for The New Mathways Project
The three mathematics pathways serve students who are placed into developmental math at the Beginning/Introduction to Algebra or Intermediate Algebra level or who have completed Basic Arithmetic. Each pathway leads to completion of a college-level, transferable math course.
The pathways are anchored in college-level transferable mathematics courses with outcomes compatible with those for courses listed in the Texas Academic Course Guide Manual, such as Introductory Statistics (MATH 1342) and Contemporary Mathematics (MATH 1332).
The pathways will include a Frameworks for Mathematics and Collegiate Learning course (EDUC 1300 or PYSC 1300) to be taken in conjunction with the studentís first math course in the pathway. The mathematics courses and the student success course will form an interconnected experience enabling students to succeed in mathematics and build the skills they need to complete a degree or certificate program in their chosen field of study. | 677.169 | 1 |
In this article, we explain what we mean by an "interactive mathematics text"; we describe its goals, contents, and pedagogical methods; and we explain the thinking that went into in writing our text, Visual Linear Algebra.
This simple Javascript-enhanced web page leads students on an exploration of the "Josephus Problem," a classic problem of recreational mathematics involving the elimination of people arranged in a circle. | 677.169 | 1 |
it would probably be best if you did list which books you have, considering I'm pretty sure the number of classes offered at UTD far exceeds the number for which you have text books, that way no one has to waste their time asking whether or not you have a specific book.
I don't know the title or author, the professor hasn't posted anything about it yet. It's the book for Math 2420, right? It's most likely the same book, I don't think they switch math texts very often. | 677.169 | 1 |
9780321523105
ISBN:
0321523105
Pub Date: 2008 Publisher: Addison Wesley Higher Education
Summary: Addison-Wesley, James S. is the author of Elementary Algebra Worksheets for Classroom or Lab Practice for Elementary Algebra, published 2008 under ISBN 9780321523105 and 0321523105. Three hundred thirty two Elementary Algebra Worksheets for Classroom or Lab Practice for Elementary Algebra textbooks are available for sale on ValoreBooks.com, one hundred four used from the cheapest price of $2.39, or buy new starting a...t $14.48.[read more]
Ships From:Georgetown, KYShipping:StandardComments: 0321523105 Good title in good condition. Pages are clean and tight. Covers have some shelf wear.... [more] 0321523105 Good title in good condition. Pages are clean and tight. Covers have some shelf wear. Satisfaction guaranteed. If item not as described, return for refund of purchase price. [less | 677.169 | 1 |
factoring or if there is a good site which can assist me.
Algebrator is a useful software to solve igcse maths worksheets free download problems . It gives you step by step answers along with explanations. I however would warn you not to just paste the answers from the software. It will not help you in understanding the subject. Use it as a guide and solve the questions yourself as well.
I used Algebrator also , especially in Basic Math. It helped me a great deal , and you won't believe how simple it is to use! It solves the tasks and it also explains everything step by step. Better than a teacher!
Check out at the tutorials available at You have ample information on Algebra 1, particularly on function domain, side-side-side similarity and leading coefficient. Good luck!
I remember having often faced problems with algebra formulas, converting fractions and exponential equations. A truly great piece of algebra program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Algebra 2, Algebra 1 and Intermediate algebra. I greatly recommend the program. | 677.169 | 1 |
Hi, I am a freshman in high school and I am having trouble with my homework. One of my problems is dealing with fourth grade factor problems; can anyone help me understand what it is all about? I need to complete this asap. Thanks for helping.
I really don't know why God made algebra, but you will be delighted to know that a group of people also came up with Algebrator! Yes, Algebrator is a program that can help you crack math problems which you never thought you would be able to. Not only does it provide a solution the problem, but it also explains the steps involved in getting to that solution. All the Best!
I am a frequent user of Algebrator and it has really helped me comprehend math problems better by giving detailed steps for solving. I recommend this online tool to help you with your algebra stuff. You just need to follow the instructions given there.
Algebrator is the program that I have used through several algebra classes - Algebra 1, Basic Math and Algebra 1. It is a really a great piece of algebra software. I remember of going through problems with perpendicular lines, relations and dividing fractions. I would simply type in a problem homework, click on Solve – and step by step solution to my math homework. I highly recommend the program. | 677.169 | 1 |
Introductory Algebra for College Students -With CD - 5th edition
Summary: KEY BENEFIT: TheBlitzer Algebra Seriescombines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student appeal. Blitzerrsquo;s E...show morequations and Inequalities in One Variable; Problem Solving; Linear Equations and Inequalities in Two Variables; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations and Introduction to Functions. MARKET: for all readers interested in algebra Books Will Follow Kansas City, MO
2008 Hardcover Fair100.00 +$3.99 s/h
Acceptable
TextbookFetcher Cortland, NY
Hardcover Fair 0132356791 | 677.169 | 1 |
Summary: This user-friendly workbook improves both student understanding and retention of algebra concepts through a series of activities and guided explorations using the graphing calculator. An ideal supplement for any college algebra or trigonometry course, EXPLORATIONS IN PRECALCULUS, Third Edition is a useful tool for integrating technology without sacrificing content. By clearly and succinctly teaching keystrokes, class time is devoted to investigations instead of how t...show moreo use a graphing calculator. Arranged by topics, this workbook enables the instructor to assign the appropriate Explorations Unit's that correlate's with the topic under discussion in the classroom. The workbook has a flexible organization. Each unit has one or more prerequisite units that are required for student success in working the assigned unit. This allows the use of this ancillary text with any core course textbook62 | 677.169 | 1 |
Students are asked to minimize the labor costs of hiring different numbers of workers for different shifts at different hourly wages in a pizza shop. Students use the graph of a system of linear inequalities to solve this linear programming problem geometrically. Activity sheets guide students step by step through the basic process. Homework problems, extension problems, and problem solutions are included. Teacher materials are available only through Key Curriculum Press, but the essence of the lesson is incorporated in the student activity sheets. (sw/js)
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.
Grade Level Indicators (Grade 10)
6.
Solve equations and inequalities having rational expressions as coefficients and solutions.
7.
Solve systems of linear inequalities.
10.
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
11.
Solve real-world problems that can be modeled, using systems of linear equations and inequalities.
Grade Level Indicators (Grade 11)
9.
Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).
Mathematical Processes Standard
Benchmarks (8–10)
B.
Apply mathematical knowledge and skills routinely in other content areas and practical situations.
F.
Use precise mathematical language and notations to represent problem situations and mathematical ideas.
Benchmarks (11–12)
J.
Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation.
Principles and Standards for School Mathematics
Algebra Standard
Represent and analyze mathematical situations and structures using algebraic symbolsUse mathematical models to represent and understand quantitative relationshipsmodel and solve contextualized problems using various representations, such as graphs, tables, and equations.identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts;
draw reasonable conclusions about a situation being modeled.
Connections Standard
Recognize and apply mathematics in contexts outside of mathematics
Representation Standard
Use representations to model and interpret physical, social, and mathematical phenomena | 677.169 | 1 |
Mathematics Honours 4210
Introduces students to the investigative and research aspects of mathematical knowledge. It prepares students for further postgraduate study in mathematics (PhD or Masters) either in Australia or overseas. Alternatively, it provides valuable additional training for those students wishing to enter the workforce. Employers particularly appreciate the communication, report writing, problem-solving and research skills developed in the Honours program. Honours is a coordinated programme spanning two semesters of full-time study or four semesters of part-time study. The Honours program requires students to study 6 advanced topics together with a project done under the supervision of an academic staff member. For administrative purposes students enrol in each of the 20 unit semester length subjects: MATH4110, MATH4120, MATH4210, MATH4220.
Not available in 2014
Previously offered in 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004
Objectives
1. To deepen understanding of a particular area of mathematics, while at the same time broadening knowledge of related areas 2. To develop the capability of understanding mathematical, and mathematically based technical literature 3. To develop writeen and oral communication skills 4.To develop research skills
Students intending to pursue Honours in Mathematics should consult with Head of School or the Mathematics Honours Coordinator prior to their commencement. In general a credit level average in a mathematics major at the 3000 level is required for entry into Honours.
Modes of Delivery
Internal Mode
Teaching Methods
Lecture Individual Supervision Student Projects
Assessment Items
Examination: Class
Essays / Written Assignments
Projects
Contact Hours
Lecture: for 4 hour(s) per Week for Full Term
Compulsory Components
Requisite by Enrolment
This course is only available to students enrolled in the Bachelor of Science (Honours), Bachelor of Science (Professional) (Honours) or Bachelor of Mathematics (Honours) programs. | 677.169 | 1 |
The Math Learning Center, or MLC for short, was created to help FAU
students develop their math problem solving skills so they have the
confidence and ability to solve math problems on their own.
The MLC offers FREE walk-in group
tutoring any time the center is
open:
Monday - Thursday: 9am - 6pm
Friday: 9am - 4pm
The MLC offers FREE one-on-one tutoring for
most undergraduate courses in
mathematics. Please read the policy
for this service by clicking the
link in the left menu bar.
The MLC is beginning to offer
online "eTutoring" services during
the Fall 2013 semester. Please use
the link in the left menu bar to
visit the Remote MLC webpage. Here,
you can access the dates/times/URLs
for any etutoring being offered.
Tutoring is available for most
undergraduate mathematics courses: Intermediate and College Algebra, Math
for
Liberal Arts, Statistics, Pre-calculus, Trigonometry, and all Calculus
courses.
Exam review sessions are offered as well. You
can check out the schedules for tutoring and exam review sessions by
clicking on the related links in the left menu bar.
The Math Learning Center is
certified with the College Reading
and Learning Association (CRLA). See
more about the CRLA. | 677.169 | 1 |
A Tribute to Paul Erdős(
Book
) 5
editions published
between
1990
and
2008
in
English
and held by
320
libraries
worldwide
More sets, graphs, and numbers a salute to Vera Sós and András Hajnal(
Book
) 6
editions published
in
2006
in
English
and held by
284
libraries
worldwide
Discrete mathematics, including (combinatorial) number theory and set theory has always been a stronghold of Hungarian mathematics. The present volume honouring Vera Sos and Andras Hajnal contains survey articles (with classical theorems and state-of-the-art results) and cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers inspire further research. The volume is recommended to experienced specialists as well as to young researchers and students.
Set theory by A Hajnal(
Book
) 8
editions published
in
1999
in
English and Undetermined
and held by
278
libraries
worldwide
This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.
Combinatorics(
Book
) 12
editions published
between
1976
and
1988
in
English and Undetermined
and held by
270
libraries
worldwide | 677.169 | 1 |
Chapter 7 Resource Masters | Keyword: chapter resource masters iv Teacheru0027s Guide to Using the Chapter 7 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often.
Glencoe Texas Mathematics, Course 3 | Keyword: glencoe texas mathematics Chapter 2 54 Glencoe MAC 3 For Exercises 1 and 2, look for a pattern. Then use the pattern to solve the problem. 1. GEOMETRY Draw the next two angles in the pattern.
Skills Practice Workbook | Keyword: skills practice workbook Copyright by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be ... | 677.169 | 1 |
Online Math Homework Help
This tool provides more than 100 textbooks** via instant and free access to Hotmath—a subscription worth up to $49
per year. Students get help solving a specific problem from their textbook by selecting the:
Code:
Subject
Publisher
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Page
Specific problem number
A full-featured 2D and 3D graphing calculator
This powerful tool functions more efficiently than many stand-alone calculators costing up to $100. Work can be
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Triangle Solver
This tool develops Geometry skills. Now students can easily input their own values.
The calculator:
Determines the missing information
Draws the triangle to scale
Provides the math rules it used to compute the missing values
Equation Library
Equation Library contains more than 125 interactive common math equations and formulas. Students can type in live
inputs and the Library will provide the missing variable—and in some cases even graph the equation!
Unit Conversion Tool
This tool is extremely useful in both math and sciences by making it easy for students to quickly convert units of | 677.169 | 1 |
50
Total Time: 6h 49m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 05/18/2010
Last Updated At: 05/18/2010
In this 50-lesson algebra series, we'll look at equations and inequalities. We'll start out looking at word problems dealing with linear equations. Then, we'll move on to look deeply at quadratic equations and how to approach and solve them. Next up, we'll transition back to word problems to really cement our quadratic equation knowledg. After that, we'll look at radical equations and variation before starting a study of inequalities. Within the videos on inequalities, we'll look at basic and advanced techniques for manipulating and solving inequalities, including those that contain quadratics, rational numbers, radicals and absolute valueCollege Algebra: Introduction to Solving Linear Equations with Rationalsation with at Word Problems
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Beginning Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers linear equations, inequalities, polynomials, rational expressions, relations and functions, roots and radicals, quadratic equations and systems of equations. Perimeter Linear for Consecutive Numbers
Professor Burger walks you through a word problem to find consecutive numbers. First, you will read the problem and then define a variable for the numbers you need to find. Using this variable, you will write an equation to solve for the variable. Then, you can replace this variable in the equation and determine the consecutive numbers sum Finding an Average
In this lesson, you will learn how to approach word problems that involve averages or means that involve averages or means (many of which include grades or scores Constant Velocity Problem about Work Mixture Problem
In this lesson, you will learn how to approach word problems that involve equalities and ratios or fractions that involve percentages, ratios, recipes, mixes, etc an Investment Business Quadratics by Factoring
In this lesson, you will learn to solve quadratic equations by factoring. Quadratic equations involve factors that are now squared, which could give us more than one possible answer. To discover if an equation has more than one answer, you need to set the equation equal to zero and factor. You will discover that if your quadratic equation factors into a perfect square, it will have only one solutionInt Algebra: Solving by Completing the Square This lesson will teach you how to find solutions by completing the square. In this technique, you'll start by isolating all constants on one side of the equation and all variable terms on the other side. Then, you'll add or subtract something to both sides to complete the square. In this case, you'll end up with x^2+6+9 = 9-1. This equation will be easier to evaluate given that you can simplify it to (x+3)^2 = 8. When you finally get to a solution value for x using this approach, you may need to rationalize a denominator (take radicals out of it), and Professor Burger will review this in the lesson, too Completing the Square: An Example In this lesson, you will learn more advanced techniques to use when solving an equation by completing the square. This lesson will cover what to do when the initial x^2 term contains a coefficient, how to solve problems that involve fractions, how to handle denominators with fractions, etc. This technique is the basis for the quadratic formula, which can always been used to solve quadratic equations Proving the Quadratic Formula Using the Quadratic Formula
The quadratic formula is used to solve for x in quadratic equations, which come in the form ax^2+bx+c=0. This formula is most commonly used when the expression can't be easily factored for evaluation. Oftentimes, this is because the two solutions to the equation are not real numbers. In this lesson, Professor Burger will walk you through when to use the formula, what the alternatives to the formula are and how to apply the formula. He will also explain how and why the formula can give imaginary numbers as solutions and what that means Predict Solution Type by Discriminant
When working with quadratic equations and the quadratic formula, there is a way to determine what type of solutions you will find and how many there will be (2 real solutions or 2 complex solutions or 1 solution) by looking at the coefficients of the quadratic formula. In this lesson, you will learn how to do this by calculating and evaluating the discriminant (d) of the quadratic formula (equal to b^2-4ac, which is a component of the quadratic formula a Squared Variable Finding Real Number Fancy Word Problems with Quadratic Pythagorean Theorem referees Motion Projectile Other Determining Extraneous Roots theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Int Algebra: Solving Equations Containing Radicals
When working with equations, you often end up with a radical of some sort (like a square root) on one side of the equation. These type of equations are called radical equations because they contain a square root. To evaluate this type of equation, you'll want to get rid of the radical. This lesson will show you how to approach and solve this type of equation by getting rid of the radical (by isolating the radical alone on one side of the equals sign and then squaring both sides of the equation). When evaluating this type of equation, you will always want to check your solutions in the original equation to make sure that you don't end up with an extraneous root as a solution. Even if the equation solves to give you an extraneous root, it is not a valid solution. An extraneous root is something that is a root to the quadratic but not to the original equation Equations with Two Radicals
In this lesson, Professor Burger will show you how to solve equations that contain two radicals (roots). When you have an equation with two square roots, you'll want to have them on opposite sides of the equal sign. Then, you'll square both sides of the equation. If there is still a radical remaining, you'll have to isolate it on one side of the equation and then square both sides once again. There will be several examples included in this lesson that will show you how to approach this type of problem and then how to check your work Rational Exponent Vari systems Direct Proportion
In order to explain direct proportionality, Professor Burger uses a real-world example of a spring and Hooke's Law. Hooke's law states that the distance a spring stretches varies directly to the force applied. If force, f, is directly proportional to distance, d, then d~f or d=kf. This equation allows us to find the constant, k, of how much the spring stretches when force is applied. After we have found this number, we can determine the distance the spring will stretch with varying forces applied.
A lesson on inverse proportions can be found here Inverse Proportion
In this lesson, inverse proportionality is explained using light as a real-world example. The illumination of a light source varies inversely to the square of the distance from the source, or I=k/(d^2). So, to find the illumination of a particular light source, you will need to find the constant, k, of that source, and then divide by the distance squared.
An introduction to direct proportion can be seen here:
This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth! Inequalities
Professor Burger discusses solving inequalities for one variable. He begins with reminders about adding, subtracting, multiplying, and dividing with both positive and negative numbers and the effect on the inequality sign. Then he demonstrates solving for a variable within an inequality, using the inequality 2(x + 3) < 4x + 10. You will then review interval notation (covered in a previous lesson) and three different ways to write the answer Mathematics More On Inequality Word Quadratic Inequalities
In this lesson, Professor Burger will teach you how to solve quadratic (non-linear) inequalities. In a quadratic inequality, there are things like x^2 included. To evaluate these inequalities, we once again start by factoring. Next, you'll find the values for x, for which the quadratic inequality is positive such that you will be able to make a sign chart and then determine the sign (positive or negative) for ech interval delineated on the sign chart. Once you have identified the intervals that satisfy the equation, Professor Burger will show how to properly denote the answer using correct notation including Quadratic Domains of Radical Express Burger Number Lines & Absolute Values Equations
In this lesson, Professor Burger discusses solving problems with absolute values. Remember that the absolute value of a number includes both the positive and negative value of that number. This means that an equation involving an absolute value means that you will have to solve for two equations, one equal to a positive value, and one equal to the negative value Equations with 2 Absolute Values
In this lesson, you will learn how to solve an equation that has two absolute values. When beginning any equation with an absolute value, remember that, by definition, the absolute value of a number has both a positive and negative answer. You will also go over how to work an equation with a fraction inside an absolute value.
For a refresher on equations with one absolute value, see this lesson Inequalities
Reminding us of its definition, Professor Burger demonstrates how to work an inequality with an absolute value. You will need to convert the inequality from the absolute value to an inequality encompassing both the positive and negative points of that absolute value. This will look different, depending on whether the absolute value is < or >. Prof. Burger walks you through several examples.
For an introduction to inequalities, see this lesson:
And for more on absolute values:
functions Absolute Value Inequality | 677.169 | 1 |
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We are sorry for any inconvenience.
Mathematicians in industry and commerce, and also those entering postgraduate study, are expected to possess a range of mathematical abilities from knowledge and implementation of mathematical and computational techniques to the development of mathematical skills. Within nearly all mathematics degree programmes in the UK the acquisition of subject-specific knowledge, essential IT skills, and the use of mathematical and statistical software, as well as subject-specific skills of logical thought and analysis and problem solving, are well embedded in the curriculum (Quality Assurance Agency for Higher Education, 2000). Typically, these are delivered through formal lectures supported by tutorials and/or seminars, problem classes and practical workshop sessions; while assessment is normally heavily weighted to formal examinations. Increasingly it is recognized that some variety of teaching and learning experience helps students to develop both subject-specific and transferable skills, and in many instances these can be accommodated through activities loosely grouped as 'mathematical modelling'. Associated assessments and feedback designed around project-based work, from more extensive coursework assignments through to substantial reports, can allow students to demonstrate their understanding and problem-solving abilities, and enhance both their mathematical and key skills. Often quoted attributes gained by graduates are the subject-specific, personal and transferable skills gained through a mathematics-rich degree. Increasingly, students are selecting their choice of degree to meet the flexible demands of a changing workplace and well-designed Mathematics, Statistics and Operational Research (MSOR) programmes have the potential to develop a profile of the knowledge, skills abilities and personal attributes integrated alongside the more traditional subject-specific education. | 677.169 | 1 |
See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.
Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:
Understanding and using rati Author(s): No creator set
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One-Sided Limits - Free Math Video by Brightstorm A limit is the value that a function approaches as the input of that function approaches a certain value. In Calculus, sometimes functions behave differently depending on what side of the function that they are on. This video explains how a one-sided limit is the behavior on one only one side of the value where the function is undefined. (3:02) Author(s): No creator setPearl River, China (with window) Zoom down to land reclamation from the river delta. Dissolve between data collected in 1988, 1992, and 1995. Author(s): No creator set
Social Media + Job Search Conference Meet with social media experts who can help you develop your online presence to make connections, job search, demonstrate advocacy, expressions of your interest or establish your personal brand. Register in Gilmour Hall 110. $10 conference registration fee. Join the conversation #SMedia4Jobs To access the conference site visit Author(s): No creator set
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Why Give - Elena Fedyszyn Having volunteered during all four of her undergrad years with the Girl Scouts, Elena Fedyszyn '09 describes why she also now chooses to give monetarily every year to Johns Hopkins. Author(s): No creator set
English Conference: Medical Writing John Smieska, a Physician Assistant, explains the structure and importance of the SOAP note and SBAR formats, for medical communication and record keeping. Author(s): No creator set
Logarithm Rule - Problem 2 This video is a continuation of the logarithm rule and works through another example where this rule is used to find the derivative of the natural logarithm of a function. The logarithm rule is a special case of the chain rule. (2:13) Author(s): No creator set
Africa Speaks, America Answers In Bedford-Stuyvesant, Brooklyn, pianist Randy Weston and bassist Ahmed Abdul Malik celebrated with song the revolutions spreading across Africa. In Ghana and South Africa, drummer Guy Warren and vocalist Sathima Bea Benjamin fused local musical forms with the dizzying innovations of modern jazz. These four were among hundreds of musicians in the 1950s and '60s who forged connections between jazz and Africa that definitively reshaped both their music and the world.
In this video, as in his new Author(s): No creator set
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Programs of Distinction - Flannery O'Connor Studies Short biographical introduction to this famous Southern writer best known for eccentric, even grotesque characters and her wry, satiric style. O'Connor's Catholocism informs her writing on multiple levels. (1:28) Author(s): No creator set | 677.169 | 1 |
Mathematica Basics
Jon McLoone
This screencast helps you to get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions. | 677.169 | 1 |
Thinkfinity Podcasts
Title: Art Algorithms
Description:
In
Standard(s): [MA2010] ALC (9-12) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2010] DM1 (9-12) 7: Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. (Alabama) [MA2010] DM1 (9-12) 8: Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama) [MA2010] DM1 (9-12) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms. (Alabama) [MA2010] MI1 (9-12) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Arts, Mathematics, Science Title: Art Algorithms Description: In | 677.169 | 1 |
Student and tutor module reviews
Discovering mathematics
Student reviews
Very good course. No matter how good you think you are at maths, this course shows how you can still improve your written skills.
I took this course as a filler, but it opened my eyes to the bad habits which I had picked up. As an introductory course to maths, it is brilliant. Would well recommend.
Course starting: February 2013
Review posted: November 2013
I would highly recomend this course to any forty something "mature" students like myself. I really had a strong aversion to Mathematics at high school, I think this can be fairly attributed to poor teachers who probably did not fully understand the subject themselves. This course however was extremely well structured in my opinion for beginers or people like myself who use a lot of general Mathematical principles in their everyday job but have picked up bad techniques from fellow workers along the way. The tutor was always available to answer questions via email.
Course starting: October 2012
Review posted: November 2013
This was a wonderful experience and a dream come true doing this course. I left school with no knowledge of mathematics or examinations so this course was an eye opener. I have always wanted to understand mathematics, and I found it fascinating. I did find it hard at times but that may be because I was also doing a language course at the same time. I surprised myself in getting reasonable results for my TMAs and EMA.
Also I am hearing impaired and had to rely on online tutorials because of the area I live in, which was hard because of not being able to understand 100% of what went on with the tutorials but my tutor and others were very good and helped a lot.
I would like to thank the OU for making this happen for me. One day who knows I may carry on with mathematics but at the moment I'm going towards language courses which is also a challenge for me and once again something I always wanted to learn.
Course starting: October 2012
Review posted: September 2013
I enjoyed this course very much and the learning of algebra was fascinating. I would have preferred just one big textbook rather than all the books as I kept having to find them all the time for referring back. The TMAs are not easy and take a lot of studying but all in all it is a worthy course for anyone who wants to understand maths. It has helped me also to engage with the children with their homework especially algebra!
Course starting: February 2012
Review posted: August 2013
Lovely course. Material was easy to understand and TMA easy to do. I had great support from tutor as well. It is a revision if you had math few years ago and do not feel confident in the subject. I feel that I should have done MS121 rather then mu123 as I found it too easy for me.
Course starting: February 2012
Review posted: July 2013
The perfect course for anyone who was told they were useless at maths at school! The course books were fun and lively (not two adjectives I would previously have thought appropriate to maths books)and my tutor was excellent. I also really enjoyed using the online resources such as dataplotter and graphplotter, which certainly beat drawing graphs by hand.
This course certainly boosted my confidence - if I can complete (and pass) a maths course, anything is possible! My only slight criticism was that the EMA came rather hard on the heels of the last TMA, so that my EMA was rather more rushed than I would have liked. All in all, a thoroughly enjoyable introduction to OU Maths - highly recommended.
Karen Thomas
Course starting: October 2012
Review posted: July 2013
The course is very enjoyable and very helpful to refresh high school math. However, if you are looking for a challenge and you were good at math in high school, then MU123 is probably not a good choice for you.
The course material is very well written and enjoyable, and our tutor was very professional and prepared. Overall, I am satisfied with the course.
Course starting: February 2012
Review posted: July 2013
An easy one. A pleasure to study it. The course is for beginners and the material is easy to read and understand. If you have studied math before you should skip it but if you have not then do it as it is good preparation for MST121. I would definitely recommend it.
Emil Eftimov
Course starting: October 2011
Review posted: April 2013
Far too easy for me. I wish I started straight on MST121 (Using Mathematics). If you've studied GCSE maths or something at a similar level then this should be easy enough for you. If you haven't then it shouldn't tax your brain cells too much. But everything is clearly explained and there's plenty of worked examples which show you how the problems are solved.
It's an easy 30 credits towards your degree though; ideal if you've other modules/courses that are taking up most of your time.
Course starting: October 2011
Review posted: August 2012
A very rewarding course! I hadn't studied mathematics since last taking this subject(at GCSE in 1996)and I was pleased to find that any gaps in my knowledge were more than covered in the available course Books A-D. There are also two additional books, supplementing the units including a glossary, summaries of maths concepts and calculator exercises. It is worth cross-checking with these as you progress through the units as they help to reinforce your learning.
The tutorials were held approximately once a month with interspersed Elluminate-Live online tutorials, which were also very useful. I have to say, my tutor was absolutely excellent and replied to any of my queries within a couple of hours and the tutorials always addressed any concerns students had.
Completing this course and achieving 95 percent was largely due to the professional way in which the literature was presented; it was very comprehensive, varied and enjoyable. Although some students disliked the iCMAs (interactive computer marked assignments) I gained a lot from them as you have ample opportunity to test yourself via online (end of unit)Practice Quizzes, which are also interactive - they test your recently learned knowledge and you gain instant feedback once you have completed the end of unit quiz.
Many of the earlier concepts, which are often not covered in basic maths qualifications, such as surds made this course much more interesting and algebra(the part I most feared), was by the end my strongest area-thanks largely to the way it was taught in the materials.
Finally, for any prospective MU123 students; have faith in the course materials and cover as much of the subject content as possible, the effort is worth it!
Hilary Jane Kitching
Course starting: February 2011
Review posted: August 2012
This was my first introduction to studying with the Open University and I thoroughly enjoyed it. I came into it having not done any maths for 20+ years.
It starts with a very gentle approach and constantly builds upon what you have learned previously. The learning curve does tend to get a little sharper towards the latter end of the units but it is definitely manageable. I managed very high marks throughout.
The course materials were excellent, as was my tutor. I would highly recommend this module to anyone.
Craig Cope
Course starting: October 2011
Review posted: August 2012
I was a little nervous before starting this course as I have avoided maths like the plague in the past, but needed it for career purposes. But I worried for nothing because the maths is so well explained throughout.
Initially the maths was very basic, a bit like brushing up on old school skills and gradually built up along with my confidence in my ability. Very soon I was solving problems I would not have even attempted in the past and I find that I still use the skills learned in this course in everyday situations.
The course books are excellent, taking you through each area of maths step by step, giving plenty of examples and opportunities to practice throughout, linking the topics to real life situations. I was also very fortunate to have an excellent tutor.
Course starting: October 2010
Review posted: August 2012
Really enjoyed this module. My tutor was fantastic, and the materials were well put together, and explained things well. The practice quizes which accompanied each unit were invaluable, as you could do them as many times as you wanted and they really helped me get my head around things from time to time.
There is a learning curve, but because of the excellence of the materials it is almost unnoticeable till you get to the end and look back and see how far you have come!
One of the most pleasurable OU modules I have ever done. Would recommend to anyone.
Louise Grassie
Course starting: October 2011
Review posted: July 2012
MU123 is a very good course to prepare for further study in mathematics or do it just as a refresher. The material is taught using real world examples and is easily applied everywhere around you.
I really liked the statistics part and started collecting data everywhere to work with.
The TMA were very manageable, I also took the opportunity to learn some LaTeX doing them (which is not required by the course at all). You can also do everything by hand and there is no need to use word processor or anything. TMAs are handwritten or printed and send by post, whereas CMA are done online in a web browser.
In fact, everything is available online in form of websites to produce graphs for example. There is no need to install any additional software.
The tutor was great! I really enjoyed doing the course.
Marcus Becker
Course starting: October 2010
Review posted: June 2012
Great Module. Eases you into the course so well. A fantastic tutor. What can I say about this course other than it worked well.
I got a bit lazy around the middle of the course but with some encouragement from the tutor I was back on track and was able to easily pass.
The books and information provided were spot on.
I loved Maths in school but this really reminded me of how difficult it can be. But don't be alarmed, the coursework will lead you right into it so you can't go wrong if you read it.
I would definitely recommend this module to ANYONE. It was my first module with OU and a great introduction Thanks
Patrick Byrne
Course starting: February 2011
Review posted: May 2012Enter a module code to find a review
To send us reviews on modules you have
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National 2.5% also qualify for the AIME.
The Mathematical Association of America wants to increase interest in mathematics and to develop problem solving through a friendly and fun competition. The purpose of the AMC 8 is to demonstrate the broad range of topics available for the junior high school mathematics curriculum. The AMC 12 covers the high school mathematics curriculum, excluding calculus. The AMC 10 covers subject matter normally associated with grades 9 and 10. Site includes past AMC Archives.
Math Contests contains the actual math contests given to students participating in Math League Contests, Grades 4, 5, and 6, School Years 1979-1980 through 2010-2011, and Grades 7, 8, and Algebra Course 1, School Years 1996-1997 through 2010-2011. The contests are designed to build student interest and confidence in mathematics.
The USAMO provides a means of identifying and encouraging the most creative secondary mathematics students in the country. It serves to indicate the talent of those who may become leaders in the mathematical sciences of the next generation. The USAMO is part of a worldwide system of national mathematics competitions. Sponsored by MAA American Mathematics Competitions. | 677.169 | 1 |
AP Calculus
Through intensive research and development, Agile Mind Calculus was created for teachers, administrators, and schools seeking to offer this central college-level course to a broad cross-section of students.
Calculus AB follows the well-respected AP® syllabus and emphasizes algebraic, numerical, and graphical representations throughout. Students will be prepared for success on the AP Calculus exam and in college, with thorough grounding in:
Functions, inverse functions, and limits of functions
Differentiation
Integration
The fundamental theorem
More than one hundred real-world applications
Talk with us about working together to close the achievement gaps in math and science. For all students.
AP-style multiple-choice practice exams, written by past members of the College Board AP Calculus Test Development Committee to mirror the content and structure of the two-part multiple choice portion of the AP Calculus AB exam
Real-time reporting of progress that allows students to take responsibility for their own learning
Robust Supports for Teachers
In addition to Internet-delivered services, educators and administrators also receive face-to-face seminars, mentoring, and high-quality support materials to help them manage their demanding workloads, enhance their expertise, and dramatically improve outcomes for their students.
Online and face-to-face professional development seminars and mentoring directly tied to practice
Day-by-day lesson support with advice and classroom strategies, equipping teachers to enact each day of instruction to achieve success for all students
Collaboration with Leading Educational Research Center
Our mathematics and academic youth programs are developed in collaboration with the Charles A. Dana Center at the University of Texas at Austin. Working with leading educators throughout the country, we have developed mathematics programs for middle school, Algebra I, Geometry, Algebra II, Precalculus, Calculus, and AP Statistics. These programs build on the Dana Center's trusted work with more than 100,000 teachers over the past decade and on the core belief that all students can succeed in mathematics if given the opportunity. | 677.169 | 1 |
In this unit students will build on the work they have already done with linear relationships.While they will see and work with other function families, the emphasis will be on linear and exponential families.They will compare and contrast the properties of linear and exponential functions. They will spend time working to understand functions as an important mathematical structure by examining function characteristics, notation, representations, and operations of specific function families.Students will practice building functions that describe the relationship between two quantities from a context.They will look at multiple ways to apply functions to solve problems and represent situations.They will also work with sets of order pairs that do not represent functions.
Next Generation Content Standards and Objectives:
Objectives Directly Taught or Learned Through Inquiry/Discovery
Evidence of Student Mastery of Content
M.1HS.LER.1 understand
M.1HS.LER.2 explain
M.1HS.LER.3 graph
Determine a feasible region of solution (Lesson 13)
M.1HS.LER.4 understand
M.1HS.LER.7 for
M.1HS.LER.8 relate
M.1HS.LER.9 calculate
M.1HS.LER.11 compare.
M.1HS.LER.12 write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
M.1HS.LER.13 write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.)
M.1HS.LER.14 identify
M.1HS.LER.16 construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two input-output pairs (include reading these from a table).
M.1HS.LER.17 observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (Limit to comparisons between exponential and linear models.)
Lesson 14:Copies of the following for each student:Attachments for Part 1 (Attachment 1A, Attachment 1B, Attachment 1C), index cards, and centimeter cubes available for each student who wants to use them (optional).
Each lesson contains the possibility for both formative and summative assessment.The lessons have been written with a concern for providing teachers with the flexibility to make decisions that will best meet their students' needs.See evidence of student mastery.For the unit assessment students are asked to find two functions that are important to a specified topic and discuss its use and representations in both a paper and presentation.
Major Products:
Lesson 6Presentation (Group)
Lesson 10Presentation (Group)
Lesson 15Newspaper Article (Individual)
UnitFunction Presentation and Paper (Individual)
Unit Reflection:
Teachers need to consider the level of understanding students have achieved relative to the cluster topics.Can students represent and solve equations and inequalities graphically?Do students understand the concept of function and the use of function notation?Can students interpret functions that arise in the context of an application?Can students analyze functions using different representations?Can students build a function that models a relationship between two quantities?Can students build new functions from existing functions?Can student construct and compare linear and exponential models and solve related problems?Can students interpret expressions for functions in terms of the situation they model?
Tagged Next Generation Content Standards and Objectives
NxG ID
NxG Objectives
M.1HS.LER.1
understand(CCSS.Math.Content.HSA-REI.D.10)
M.1HS.LER.2
explain(CCSS.Math.Content.HSA-REI.D.11)
M.1HS.LER.3
graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (CCSS.Math.Content.HSA-REI.D.12)
M.1HS.LER.4
understand (CCSS.Math.Content.HSF-IF.A.1)
M.1HS.LER.5
use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. (CCSS.Math.Content.HSF-IF.A.1)
for(CCSS.Math.Content.HSF-IF.B.4)
M.1HS.LER.8
relate(CCSS.Math.Content.HSF-IF.B.5)
M.1HS.LER.9
calculate(CCSS.Math.Content.HSF-IF.B.6)
M.1HS.LER.10
graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
graph linear and quadratic functions and show intercepts, maxima, and minima.
compare.(CCSS.Math.Content.HSF-IF.C.9)
M.1HS.LER.12
write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations.
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.(CCSS.Math.Content.HSF-BF.A.1)
M.1HS.LER.13
write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.)(CCSS.Math.Content.HSF-BF.A.2)
M.1HS.LER.14
ident.(CCSS.Math.Content.HSF-BF.B.3)
M.1HS.LER.15
distinguish between situations that can be modeled with linear functions and with exponential functions.
recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. (CCSS.Math.Content.HSF-LE.A.1)
M.1HS.LER.16
construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)
M.1HS.LER.17
observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (Limit to comparisons between exponential and linear models.)(CCSS.Math.Content.HSF-LE.A.3)
M.1HS.LER.18
interpret the parameters in a linear or exponential function in terms of a context. (CCSS.Math.Content.HSF-LE.B.5) | 677.169 | 1 |
Solutions To Complex Analysis Ahlfors
An Introduction to Complex Analysis and Geometry John P. D. when viewed from the perspective of complex analysis. My own of elementary complex analysis and geometry. a solution in Z unless b is an even number.
4. CHAPTER 1. THE HOLOMORPHIC FUNCTIONS operations: both the inner. Z = (t0x, t0y,1 ? t0) with t0 being the solution of t2. papers were not widely known - even Cauchy who has obtained numerous fundamental results in complex analysis considered early in his career the complex numbers simply as symbols
analysis to advanced undergraduate and graduate Principle.- Sequences and Series of Numbers.-. Sequences and Series of Functions. ISBN 978-88-470- 1940-9 bounds to the solutions of the above equations. The last chapter, which includes many examples,. exercises 7 The 6th edition includes a systematic
How is real analysis and complex analysis different? 1. 2. Applications of complex analysis. 3. What is complex analysis? If forced to give a one-sentence description, many math-. applications of complex analysis in physics and engineering.
deep appreciation of complex analysis and how this perspectrve of complex analysrs The book begins at an elementary solutions at regular singular pornts Bessel functrons, of linear functional analysis as related to fundamental aspects
Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners. | 677.169 | 1 |
Computer explorations with a computer algebra system (CAS) can be used to illuminate ideas in analytic geometry and calculus. Given five points in a plane, a unique conic section will pass through them, but the details of finding it are overwhelming to do by hand. The computer algebra system Mathematica is used to assist with these computations which are suitable for an undergraduate computer laboratory exercise. | 677.169 | 1 |
John E. Freund's Mathematical Statistics with Applications, Eighth Edition, provides a calculus-based introduction to the theory and application of statistics, based on comprehensive coverage that reflects the latest in statistical thinking, the teaching of statistics, and current practices.
A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probabThis is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their w development...
Statistics and data for the non-specialistAt university you may be expected to analyse complex data and present your findings, whatever your area of study. Collins Academic Skills Series: Numbers gives you the skills you need to make sense of data and numbers and the confidence to use them effective...
Most people remember chemistry from their schooldays as a subject that was largely incomprehensible, fact-rich but understanding-poor, smelly, and so far removed from the real world of events and pleasures that there seemed little point, except for the most introverted, in coming to terms with its g...
One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such...
Astronomy has made enormous progress over the past decades and engages public and media interest as never before. IAU Symposium 260, held at the start of the IAU-UNESCO International Year of Astronomy 2009, addresses questions relevant to the role of astronomy in the modern world and its links to cu...
16.
[직수입양서] The Joy of X : A Guided Tour of Math, from One to Infinity(Paperback)
A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times.
The fun and easy way to get down to business with statistics Stymied by statistics? No fear this friendly guide offers clear, practical explanations of statistical ideas, techniques, formulas, and calculations, with lots of examples that show you how these concepts apply to your everyday life.
Cultural geography is a major, vibrant subdiscipline of human geography. Cultural geographers have done some of the most important, exciting and thought-provokingly zesty work in human geography over the last half-century.This book exists to provide an introduction to the remarkably diverse, controv...
The computational education of biologists is changing to prepare students for facing the complex datasets of today's life science research. In this concise textbook, the authors' fresh pedagogical approaches lead biology students from first principles towards computational thinking. A team of renown... | 677.169 | 1 |
Not So Special Anymore by R.M. Barron
Price:
$0.99 USD.
Approx. 18,400 words.
Language:
English.
Published on May 29, 2012.
Category:
Nonfiction.
A commentary on Special Education in the United States, this work offers anyone with an interest in education an inside look at how IDEA is implemented, or not implemented, on some campuses. Not an academic work, the author offers insight based on 17 years experience as a Spec Ed Teacher and as a Spec Ed parent. The short work also includes contributions from other teachers.
Be Your Child's Maths Tutor Book 2 - Algebra by Angie Fish
Series: Be Your Child's Tutor Series, Book 2.
Price:
$2.99 USD.
Approx. 10,820 words.
Language:
English.
Published on June 6, 2012 by
Angelfish eBooks.
Category:
Nonfiction.
This book was written by an experienced maths tutor to help parents and carers to be able to tutor their child in algebra and equations. This book contains 10 lesson plans for hourly tuition sessions, which would cost £20-£25 if you paid a tutor. Written in Plain English so that even the most nervous adult can understand the concepts before explaining it to their childMATLAB for Beginners: A Gentle Approach - Revised Edition by Peter Kattan
Price:
$9.99 USD.
Approx. 35,420 words.
Language:
English.
Published on June 10, 2012.
Category:
Nonfiction.
This book is written for beginners and students who wish to learn MATLAB. The material presented is very easy and simple to understand - written in a gentle manner. The topics covered in the book include arithmetic operations, variables, mathematical functions, complex numbers, vectors, matrices, programming, graphs, solving equations, and an introduction to calculus. | 677.169 | 1 |
Precalculus
9780077221294
ISBN:
007722129X
Edition: 3 Pub Date: 2008 Publisher: McGraw-Hill Companies, The
Summary: The Barnett Graphs & Modelsseries in college algebra and precalculus maximizes student comprehension by emphasizing computational skills, real-world data analysis and modeling, and problem solving rather than mathematical theory. Many examples feature side-by-side algebraic and graphical solutions, and each is followed by a matched problem for the student to work. This active involvement in the learning process helps... students develop a more thorough understanding of concepts and processes. A hallmark of the Barnett series, the function concept serves as a unifying theme. A major objective of this book is to develop a library of elementary functions, including their important properties and uses. Employing this library as a basic working tool, students will be able to proceed through this course with greater confidence and understanding as they first learn to recognize the graph of a function and then learn to analyze the graph and use it to solve the problem. Applications included throughout the text give the student substantial experience in solving and modeling real world problems in an effort to convince even the most skeptical student that mathematics is really useful.
Barnett, Raymond A. is the author of Precalculus, published 2008 under ISBN 9780077221294 and 007722129X. Five hundred twenty six Precalculus textbooks are available for sale on ValoreBooks.com, one hundred ninety four used from the cheapest price of $9.95, or buy new starting at $172.39.[read more | 677.169 | 1 |
Based on feedback from users of first edition, COMAP has completed a major
revision of Course 1, now available on CD-ROM.
• Some chapters are completely rewritten (i.e., Pick a Winner and Landsat, which is
now titled Scene from Above). Other chapters are streamlined while retaining the
thematic, modeling approach. • Most chapters are shorter. The revised Course 1 has a total of 57 Activities—
a 39% reduction from first edition's 93.
• Each Activity and Individual Work has a clear statement of purpose in the
student edition and in the teacher materials.
• Lesson structure is more consistent than in the first edition from chapter to chapter.
• Many activities are shorter than in first edition; they are designed for
completion in one 45-minute class period.
• Individual Work offers more mathematical practice problems.
• Both quantity of reading and reading level are reduced.
• FYI, Take Note, and Modeling Note features call attention to key facts.
• Teacher Notes indicate which Individual Work questions are essential to future
development work and which are calculator related.
• Chapter summaries are clearer and more succinct in their review of important mathematics.
Calculator and computer software written specifically for Mathematics: Modeling Our World (MMOW). With software programs for each chapter allows students to explore real-world themes with the same tools used by scientists, technicians, and business people. The software includes graphing calculator programs, specialty computers, spreadsheet template, data sets, and geometric drawing utility sketches.
DVD Video
Video segments accompany each chapter and are used to motivate students as they begin a chapter, or to provide additional information for a specific problem.
Teacher Development
Teacher training and support available through COMAP staff trainers, through a toll-free support line (1-800-772-6627), and via our Teacher Support Website. | 677.169 | 1 |
More About
This Textbook
Overview
Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections.
Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn's Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area.
Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.
Related Subjects
Meet the Author
John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor's Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who's Who Among America's Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one | 677.169 | 1 |
This lesson contains real numbers - difference between the set and the period. Union and intersection, difference –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains –periods of numbers-intersection, Union and difference- absolute values - analysis of quadratic equations and finding the zeroes of equations-distance between two points–with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains a slope of straight line -equation of the straight line - perpendicular and parallel lines –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains-trigonometric functions trigonometric ratios for many special angles - relationship between the trigonometric ratios of complementary angles –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains -types of functions - domain and range of these functions- increasing and decreasing - even and odd functions –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains – new functions from old functions and the domain and range of the resulting function –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains - General and natural exponential functions-domain and range -solving equations containing exponential function –with many questions and different applications with the explanation in detail step by step*view sample lesson
This lesson contains-one side limit-limit of piecewise function–limit at infinity-horizontal asymptote - limit of trigonometric functions–with many questions and different applications with the explanation in detail step by step*view sample lesson | 677.169 | 1 |
Pre-Algebra DemystSay goodbye to dry presentations, grueling formulas, and abstract theories that would put Einstein to sleep -- now there's an easier way to master the disciplines you really need to know. McGraw-Hill's "Demystified Series" teaches complex subjects in a unique, easy-to-absorb manner, and is perfect for users without formal training or unlimited time. They're also the most time-efficient, interestingly written "brush-ups" you can find. Organized as self-teaching guides, they come complete with key points, background information, questions at the ... MOREend of each chapter, and even final exams. You'll be able to learn more in less time, evaluate your areas of strength and weakness and reinforce your knowledge and confidence. A self-teaching guide to basic arithmetic, covering whole numbers, fractions, percentages, ratio and proportion, basic algebra, basic geometry, basic statistics and probability.
Three Types of Percent Problems
Word Problems
UNIT 5 – RATIO AND PROPORTIONS
Ratio
Proportions
Word Problems
UNIT 6 – BASIC ALGEBRA
Integers
Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Solving Basic Equations
Word Problems
UNIT 7 – BASIC GEOMETRY
Basic Geometric Figures
Perimeter
Area
Volume
Word Problems
UNIT 8 – BASIC STATISTICS AND PROBABILITY
Graphs
Finding Averages
Probability
Word Problems
FINAL EXAM
ANSWERS TO ALL QUESTIONS
Allan G. Bluman taught mathematics and statistics in high school, college, and graduate school for 39 years. He received his Ed.D. from the University of Pittsburgh and has written three mathematics textbooks published by McGraw-Hill. Mr. Bluman is the recipient of "An Apple for the Teacher Award" for bringing excellence to the learning environment and the "Most Successful Revision of a Textbook" award from McGraw-Hill. His biographical also record appears in Who's Who in American Education, Fifth Edition. | 677.169 | 1 |
GeMy original degree is Political Science. Basically...I LOVE this stuff! The Virgina SOL standard questions require students to extrapolate information before being able to answer the question in front of them.
...Prealgebra is a great way to understand just how important it is to evaluate an unknown quantity. Thus, 2x+4=8 can best be understood as 2x=4 and x=2. Testing that unknown quantity by replacing the variable with a 2 shows you can check your work quite rapidly. | 677.169 | 1 |
Frequently Asked
Questions About Math
Why is math so important? graduation, high school students need to be
Sources The more your child knows about math, the
educated to a comparable level of math skills in
algebra, geometry, data analysis and statistics.2
more options he or she will have in life. Studies
1. The American Diploma
show that higher-level math skills mean an But I didn't need math for my
Project, 2004
increased ability to succeed in college and career, so why does my child?
work. For example, a majority of workers who
2. ACT Study, Ready for The workforce of the 21st century is not the
earn more than $40,000 annually have two or
College and Ready for same as it was even a decade ago. Nationwide,
more high school credits at the algebra 2 level
Work: Same or Different?, the number of jobs requiring technical training
or higher. 1
2006 is growing five times faster than other occupa-
3. Prosperity Partnership, Why is middle school math so tions. Here in Washington, our state leads the
2007 important? nation in jobs for people with bachelor degrees
in science and engineering, but is 38th in the
Research indicates that proficiency in algebra number of students graduating with these de-
4. Achieve, Inc., Do All by the end of 8th grade is critical for success in grees.3 And according to the Associated Gen-
Students Need Challeng- higher level mathematics classes. eral Contractors of America, electricians, pipe
ing Math in High School? Unfortunately, middle school is where the fitters, sheet metal workers, draftsmen and
cracks begin to show. Unknowingly, they enroll surveyors need algebra, geometry, trigonom-
in a lower-level math track that proves difficult etry and physics to be successful on the job.4
to get out of once they're in high school.
What if my child just isn't good at
Does my child really need to take math?
Algebra II?
While it's true that some students may like
To secure a job that will eventually support a math more than others, all students are capable
family, students will need at least 1-2 years of of learning math at higher levels. Some students
education or training beyond high school. Stu- may be more successful in math if it is taught in
dents planning to attend a 2-year community a more hands-on way. Increasingly, career and
or technical college or 4-year baccalaureate technical education programs offer rigorous
institution must take a placement test in math. math- and science-based programs in path-
Those who don't pass must enroll in remedial, ways such as nursing, veterinarian sciences,
or "pre-college," classes. Students don't receive computer programming and robotics. To make
All students credit for pre-college classes, but they do have sure your children keep all of their options
to pay for them. That means paying for classes
are capable of your child could have taken for free in high
open, make sure these courses cover skills
through advanced algebra and geometry.
learning math at school.
higher levels. What can I do to make sure my child
What if my child doesn't plan on go- is well prepared in math?
ing to college? Does he/she still need
math? Studies show that having high expectations
has a great impact on student success, so be
In today's world, math is no longer just for sure to encourage your child to take the high-
college-bound students. A 2006 study by ACT est level math possible. Actively participate in
examined the skills needed to succeed as a your child's course selection each semester
freshmen in college and compared them to and encourage them to take math all four
skills needed for job-training programs that years of high school. If your child struggles in
earn a sufficient wage to support a family of math class, ask the teacher about after school
four. ACT found that whether planning to enter support programs or online tutorials. Being
college or workforce training programs after involved can make a world of difference!
College Work Ready Agenda • • Partnership for Learning | 677.169 | 1 |
Why Mathematica and Why Now?
Cliff Hastings
Mathematica offers an interactive classroom experience that helps students explore and grasp concepts. Topics covered in this screencast include getting started, interactivity, and cross-discipline uses. | 677.169 | 1 |
Peer Review
Ratings
Overall Rating:
This is a comprehensive set of online tutorials and self-tests covering the fundamental topics of mechanics. Topics include vectors, 1D and 2D kinematics, Forces and Dynamics, and Work and Energy (under construction). These tutorials provide introductions to the concepts, illustrated by animations and graphs. Quantitative measurements can be taken as well. Instructions and text help explain the purpose of each simulation, how it works, and the physics involved. The user is able to enter responses to specific questions and receive immediate confirmation of the answer. Many demonstrations are provided as well.
Learning Goals:
Provide an introduction and reinforce conceptual learning of students in introductory mechanics, and have them test their understanding.
Target Student Population:
Introductory physics classes in high school and college. Some sections may be suitable for physical science classes.
Prerequisite Knowledge or Skills:
Students should have a general introduction to mechanics. This material does not constitute a complete course. Math through algebra and trigonometry is required for some of this material. Calculus is not required.
Type of Material:
Tutorials with interactive Java simulations
Recommended Uses:
Tutorial, Self-test, and Drill and Practice.
Technical Requirements:
Standard web browser with Sun Java Plug-in version 1.4 or later.
Evaluation and Observation
Content Quality
Rating:
Strengths:
These excellent tutorials cover some of the most fundamental, and for many students difficult, aspects of introductory mechanics. Having this online resource allows students to work at their own pace outside of class, covering topics that they are having the most difficulty understanding. They are able to visualize the concepts in many different formats such as position, velocity, acceleration, and energy graphs, animated pictures, motion diagrams, and force diagrams. Students are asked to interpret graphs, diagrams, and physical situations.
The author uses a spiral approach in his learning materials. For example, kinematics is discussed exclusively in the first two sections but also appears later in the dynamics section.
Concerns:
It is sometimes difficult to make accurate measurements to obtain the answers to quantitative questions. The scales are a little obscure and can result in an incorrect answer.
The "Work and Energy" illumination is still under construction.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The site is very comprehensive, thereby allowing an instructor to use it for several weeks or more of a typical first semester course. An instructor could use this site exclusively for Mechanics, so that searching for other sites is not needed. It is designed so the student can proceed at a slow, steady pace. It may be used as an in-class activity or for homework.
This material is interactive and provides immediate feedback to students. The activities that the students have to perform range from fairly simple and straight forward to very challenging, thus making them useful for a wide range of student background and skills. It is designed so a student can proceed at a slow, steady pace if needed. It may be used as an in-class activity or for homework.
The connection between the tutorial materials and the student activities,
using the same interface and language, creates a coherent and extensive resource. However, because of the modular nature of the exercises, single exercises or illustrations can be used stand-alone very effectively. This makes these resources very flexible in their instructional uses.
The fact that this program allows instructors to track the student usage and grades for these exercises is important. Students can be motivated by having their use of this material be a part of their grades.
Concerns:
The responses to some of the questions only inform the student as to weather or not the answer is correct. There is no feedback to help the student determine the cause of their mistake. As a result, the student will need to seek help from the instuctor or some other resource.
Some of the illuminations are a bit repetitive. Although this is important for learning, some students might not appreciate it.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The interface to the illuminations is simple and straight forward.
Instructions and tips for running the applets and solving the problems are avialable on the pages. Each section starts with a brief description of that particular topic along with a question mark (?) tab to click on if one has questions on how to proceed. Most sections have a separate window at the bottom that lists all the physics concepts and definitions.
<
The author provides a link to download the Sun Java Plug-in (J2SE JRE) required for running these simulations.
Concerns:
Students may find the graphics somewhat bland.
Some of the simulations in the Dynamics and Work & Energy sections are still under construction.
Other Issues and Comments:
Reviews of some of the individual illuminations are available on MERLOT, although some are for earlier versions of the resources | 677.169 | 1 |
Principles of Mathematical Modeling
By
Clive Dym, Harvey Mudd College, Claremont, California, U.S.A.
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.
Audience Students in Mathematical Modeling courses taught in either mathematics or engineering departments; also professional engineers and mathematicians.
Reviews
"It is one of the best introductory texts in mathematical modeling which the reviewer warmly recommends to anyone who wishes to learn the foundations of mathematical modeling with enjoyment." -Yuri V. Rogovchenko, in ZENTRALBLATT FUR MATHEMATIK, 2005 "Principles of Mathematical Modeling is a delightfully readable, well-written account of the way engineers look at the world. It covers a surprizingly wide range of topics...The many examples treated in the text are drawn from the practical world that engineers inhabit, with some surprises thrown in for good measure..." - Robert Borelli, Harvey Mudd College "The book itself is marvelously interdisciplinary, treating biological and human designed systems in addition to physical systems. These examples show that engineers can do more than simply analyze simple physical systems with known, exact solutions." - Bill Wood, University of Maryland at Baltimore | 677.169 | 1 |
The capstone process begins in MATH 300. Students develop library research, scholarly reading, writing, and collaboration skills needed to develop, implement, and complete their capstone projects. Students develop a learning plan that integrates their Mathematics concentration,capstone interests, and personal and professional goals. | 677.169 | 1 |
Book Description: The notion of symmetry is important in many disciplines, including physics, art, and music. The modern mathematical way of treating symmetry is through transformation groups. This book offers an easy introduction to these ideas for the relative novice, such as undergraduates in mathematics or even advanced undergraduates in physics and chemistry. The first two chapters provide a warm-up to the material with, for example, a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. The notions of a transformation group and of an abstract group are then introduced. Group actions, orbits, and invariants are covered in the next chapter. The final chapter gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations. Throughout the text, examples are drawn from many different areas of mathematics. Plenty of figures are included, and many exercises with hints and solutions will help readers master the material | 677.169 | 1 |
Center for Quantitative Education
"Mathematics is the language in which God has written the Universe" &mdash Galileo
At the Q-Center, we believe in teaching mathematics as a language. Students need to learn the grammar and vocabulary of mathematics - the skills of solving particular equations and the like. Beyond that, they need to learn to use the language to interpret the world as they need to be successful in their chosen path. Finally, learning a different language should provide an insight into new ways of thinking, and students should gain a cultural understanding of how mathematics fits into the world.
Of course, since it is their learning that matters, we can't do it for them. We can only provide the situation and support that they need to develop their own understandings. However, as we are paid to teach them, we take responsibility for their learning by
determining what they need to learn,
providing a situation in which they can and will develop this understanding,
letting them struggle so that they make the learning their own, but to provide support so they don't give up and succeed in their struggle, and
providing honest feedback so we know what we have accomplished and what we still need to work on.
The Q-Center was formally established in January 2006 with the initial charge to
make College Algebra a modern, technologically rich course where more students are successful and satisfied;
pursue extramural funding and continue our research program on undergraduate education in quantitative disciplines, with an emphasis on the effective use of technology; and
maintain an outreach program to share our work with K-12 schools to help them better prepare students. | 677.169 | 1 |
Iteration A Tool Kit of Dynamics Activities
9781559533546
ISBN:
1559533544
Publisher: Key Curriculum Press
Summary: Iteration: A Tool Kit of Dynamics ActivitiesIterationis a time-honored process in mathematics, but recent technology allows us to look at iteration with a fresh eye. Share the astounding discoveries scientists and mathematicians have made in recent years and how those discoveries are used in many different areas of study. The book can be used in many mathematics courses, but is especially suited to an algebra class. ...Grades 7-12
Choate, Jonathan is the author of Iteration A Tool Kit of Dynamics Activities, published under ISBN 9781559533546 and 1559533544. Seventeen Iteration A Tool Kit of Dynamics Activities textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $2.39, or buy new starting at $19.64 137 p. Contains: Illustrations.[less] | 677.169 | 1 |
"MATH A"
Although a statement that Harvard gives fourteen different courses in elementary mathematics--all called "Math A"--would be gross exaggeration, nevertheless present lack of uniformity among the sections gives just that impression. Resolving not to permit the slightest hint of regimentation to cast its ominous shadow over their fair course, the men in charge of "Math A" have allowed the fourteen sections to become, in practice, almost wholly independent of one another. Not only teaching methods, but organization of material, examinations, and grading standards vary from section to section, and as a result men undertaking "Math A" can never be sure of what they are in for. While initiative of individual instructors, especially of young instructors, must never be destroyed, its scope should be kept within clearly defined limits.
The problem of defining the field in which initiative is to be exercised is a difficult one. There is at present a rather definite syllabus provided for all the instructors, but many proceed to disregard it. Since each section has its own examinations, there is no effective way for preventing this; could the whole course be given identical exams the problem would be solved. This is not possible for an interesting reason. Teaching "Math A" are a number of the country's leading experts in the field, and they simply cannot agree as to the best methods of presentation; indeed, they cannot agree entirely as to what an elementary course in mathematics should contain. Thus there can be no one examination that will be fair to every student.
However, simply because there can be no single examination, there need not be fourteen different ones. If each of the three or four experts would draw up a syllabus containing what he believes to be the essentials of the course, in the order in which they should be presented, and if every section were required to follow one of these plans, the number of examinations necessary would be reduced to three, or four, as the case might be. Although this would not be a complete solution, it would be a long step toward a much-needed reform. | 677.169 | 1 |
SOS 10th Grade Math allows student's to study shapes focusing on the deeper dimensions of their real-world use and purpose. Rich and rewarding, this course also offers an individual-based, step-by-step learning system and integrated solution keys from the SOS Teacher application! Additional topics are congruent triangles, quadrilaterals, similar polygons, and circles. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
Optimization is concerned with finding the best (optimal) solution to mathematical problems that may arise in economics, engineering, the social sciences and the mathematical sciences. As is suggested by its title, this book surveys various ways of penetrating the subject. The author begins with a selection of the type of problem to which optimization can be applied and the remainder of the book develops the theory, mainly from the viewpoint of mathematical programming. To prevent the treatment becoming too abstract, subjects which may be considered 'unpractical' are not touched upon. The author gives plausible reasons, without forsaking rigor, to show how the subject develops 'naturally'. Professor Ponstein has provided a concise account of optimization which should be readily accessible to anyone with a basic understanding of topology and functional analysis. Advanced students and professionals concerned with operations research, optimal control and mathematical programming will welcome this useful and interesting book.
Synopsis:
A concise account which finds the optimal solution to mathematical problems arising in economics, engineering, the social and mathematical sciences.
Table of Contents
Preface; List of symbols; 1. Approaching optimization by means of examples; 2. An intuitive approach to mathematical programming; 3. A global approach by bifunctions; 4. A global approach by conjugate duality; 5. A local approach for optimization problems in Banach spaces; 6. Some other approaches; 7. Some applications; Appendices; Comments on the text and related literature; References; | 677.169 | 1 |
Mathematics for Materials Scientists and Engineers
Parabolic approximation to a surface and local eigenframe. The surface on the left is a second-order approximation of a surface at the point where the coordinate axes are drawn. The surface has a local normal at that point which is related to the cross product of the two tangents of the coordinate curves that cross at the that point. The three directions define a coordinate system. The coordinate system can be translated so that the origin lies at the point where the surface is expanded and rotated so that the normal n coincides with the z-axis as in the right hand curve. (Image by Prof. W. Craig Carter.) | 677.169 | 1 |
Prealgebra, Third Edition, is a significant revision of the second It is our belief that the third edition will continue to help today's students through pedagogical use of full color and updated applications. As part of MathMax: The Bittinger System of Instruction, a comprehensive and well-integrated supplements package provides maximum support for both instructor and student. MathMax: The Bittinger System of Instruction offers a completely integrated package of four-color text, multimedia CD-ROM, interactive tutorial software and videos that guide students successfully through developmental math. Key elements of the MathMax system include learning objectives keyed to the exposition, exercises, and examples; a hallmark five-step problem-solving process; and modern, interesting applications and problems. [via]
This all new edition of Trigonometry, derived from the authors popular Algebra & Trigonometry, Third Edition, helps students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, a variety of new tools help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material. [via] | 677.169 | 1 |
You are here
Mathematics for the Environment
Publisher:
Chapman & Hall/CRC
Number of Pages:
653
Price:
89.95
ISBN:
9781439834725
This book is a combination of mathematics with social and political commentary, but the connection is not always smooth. Such a combination is fine when there is a discussion of an ecological or environmental issue followed by an explanation of the mathematics needed to understand it. However, when it reaches the point where Walter delves into U. S. government intervention in the lives of the citizenry, a line is crossed where it becomes a book on the current state of the relationship between the federal government and the populace. In chapter 22, "Surveillance, Spies, Snitches, Loss of Privacy and Life" Walter sounds very much like a conspiracy theorist.
When it appears, the mathematics is not very difficult; nearly all of it can be understood by anyone in the last year of a college-prep high school mathematics program. The book is heavily referenced and one positive characteristic is that there are many detailed exercises designed to highlight how mathematics can be used to explain natural phenomena and human behavior and its consequences. Topics such as global climate change, the concept of money, centralized decision-making, the power of corporations to control the economy and political activity and energy use are some of the issues examined and mathematically dissected.
Walter clearly has a political and social agenda that is wrapped within the mathematics. While this book could serve as a text for courses in applied mathematics and a resource for study material in many other subject areas, the material of Walter's agenda has the potential to be distracting at best and controversial at worst.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.
MATHEMATICS IS CONNECTED TO EVERYTHING ELSE Earth's Climate and Some Basic Principles One of the Greatest Crimes of the 20th Century Feedback Edison's Algorithm: Listening to Nature's Feedback Fuzzy Logic, Filters, the Bigger Picture Principle Consequences of the Crime: Suburbia's Topology A Toxic Consequence of the Crime Hubbert's Peak and the End of Cheap Oil Resource Wars: Oil and Water The CO2 Greenhouse Law of Svante Arrhenius
What Is Mathematics? More Basics The Definition of Mathematics Used in This Book The Logic of Nature and the Logic of Civilization Box-Flow Models Cycles and Scales in Nature and Mathematics The Art of Estimating
We All Soak in a Synthetic Chemical Soup Thomas Latimer's Unfortunate Experience What's in the Synthetic Chemical Soup? Synthetic Flows and Assumptions The Flow of Information about Synthetic Flows You Cannot Do Just One Thing: Two Examples
Mathematics and Energy How Much Solar Energy Is There? Solar Energy Is There, Do We Know How to Get It? Four Falsehoods Nuclear Power: Is It Too Cheap to Meter? Net Primary Productivity and Ecological Footprints NPP, Soil, Biofuels, and the Super Grid
The Brower–Cousteau Model of the Earth How Heavily Do We Weigh upon the Earth? Mining and Damming: Massive Rearrangements Fish, Forests, Deserts, and Soil: Revisited The Cousteau–Brower Earth Model
The Dunbar Number The Sustainability Hypothesis: Is It True? The Dunbar Number Public Relations, Political Power, and the Organization of Society Political Uses of Fear Confronting Fear (and Apathy): Organizing Your Community for Self-Preservation and Sustainability
MATH AND NATURE: THE NATURE OF MATH One Pattern Viewed via Geometry and Numbers: Mathese The Square Numbers of Pythagoras The Language of Mathematics: Mathese A General Expression in Mathese: A Formula for Odd Numbers An Important Word in Mathese: Σ Sentences in Mathese: Equations with Σ and a Dummy Variable Induction, Deduction, Mathematical Research, and Mathematical Proofs What Is a Mathematical Proof? What Is a Deductive System? Originalidad es volver al Origen
Axioms and Atoms Molecules and Atoms; the Atomic Number and the Atomic Mass Number of an Atom Scaling and Our First Two Axioms for Numbers Our First Axiom for Numbers Number 1: Its Definition, Properties, Uniqueness The Definition of Multiplicative Inverse Our Second Axiom for Numbers If … , Then … . Our First Proofs Return to the Problem: How Many Protons in One Gram of Protons? What Is a Mole? Scaling Up from the Atomic to the Human Scale
Five More Axioms for Numbers Associativity, Identity, and Inverses for + Commutativity of + and * Distributivity
What Patterns Can Be Deduced in Our Deductive System? Playing the Mathematics Game Rules for Playing the Mathematics Game The Usual Rules for Fractions Are Part of Our Deductive System Can You Tell the Difference between True and False Patterns? More Exercises
ONE OF THE OLDEST MATHEMATICAL PATTERNS A Short Story and Some Numberless Mathematics Relations Defined as Collections of Ordered Pairs Symmetric Relations Transitive and Reflexive Relations Equivalence Relations Relations That Are Functions
A Set of Social Rules for the Warlpiri People The Section Rule The Mother Relation Rules The Marriage Rules The Father Relation Rules Cultural Contexts in Which Mathematics Is Done
COUNTING Counting Exactly Numeracy Counting Social Security Numbers among Other Things Permutations: Order Matters There Are n! Permutations of n Distinct Objects Counting Connections: Order Does Not Matter
Equivalence Relations and Counting Using Equivalence Relations to Count Combinations: Order Does Not Matter Additional Counting Problems DNA Computing More Exercises
BOX MODELS: POPULATION, MONEY, RECYCLING Some Population Numbers Counting People in the World A Fundamental Axiom of Population Ecology Counting People in the United States
Basic Mathematical Patterns in Population Growth Schwartz Charts Are Box-Flow Models Our First Population Model: Simple Boxes and Flows Three Basic Operations: Addition, Multiplication, and Exponentiation Defining Logarithm Functions Computing Formulas for Doubling Times Natural Logarithms Logarithms to Any Base Further Study: More Complicated Models and Chaos Theory The World's Human Population: One Box
Box Models: Money, Recycling, Epidemics Some Obvious Laws Humans Continue to Ignore A Linear Multiplier Effect: Some Mathematics of Money Multiplier Effects Arising from Cycles: The Mathematics of Recycling A Simple Model of an Influenza Epidemic
CHANCE: HEALTH, SURVEILLANCE, SPIES, AND VOTING Chance: Health and News If You Test HIV Positive, Are You Infected? Chance and the "News
Surveillance, Spies, Snitches, Loss of Privacy, and Life Is Someone Watching You? Why? Living with a Police Escort? I'm Not Worried, I've Done Nothing Wrong
Voting in the 21st Century Stealing Elections Is a Time Honored Tradition A Simple Solution Exists Two Modest Proposals
ECONOMICS What Exactly Is Economics? It Takes the Longest Time to Think of the Simplest Things A Preview of Two Laws of Nature Three Kinds of Economists The Human Economy Depends on Nature's Flows of Energy and Entropy Nature's Services and Human Wealth: Important Calculations How We Treat Each Other: How We Treat Nature — The Tragedy of the Commons
The Concept of Money Financial Wealth and Real Wealth Is Financial Collapse Possible Now? Follow the Money Are You Paying More or Less Than Your Fair Share of Taxes? Financial Growth vs. Fish Growth Fractional Reserve Banking: An Amazing Mathematical Trick
Distributed vs. Centralized Control and Decision Making Farms: To Be Run by Few or by Many? Utilities: MUNI or Investor-Owned? Linux vs. Microsoft Medicine for People or for Profit or Both? A Little History An Example of the Need for Fuzzy Logic: The Definition of Poverty
Energy and Thermodynamics Energy and the First Law of Thermodynamics The First Law of Thermodynamics Entropy and the Second Law of Thermodynamics Early Statements of the Second Law of Thermodynamics Algebraic Statement of the Second Law of Thermodynamics So What Is Entropy and Can We Measure It? Some Applications of the Second Law of Thermodynamics: Power Plants and Hurricanes Hiking up a Mountain Understanding Entropy with a Little Mathematics
The Financial Mathematics of Loans, Debts, and Compound Interest Simple and Compound Interest: A Review How Much Does a Debt Really Cost You? Buying on Time and/or Installment Plans. Amortization. The Four Important Numbers: P, R, r, n Examples of Individual Debt: Rent-to-Own, Credit Cards, and Loans
MEDIA LITERACY Information Flow in the 21st Century Investigative Journalism Requires Cash Thesis: The Range of Debate is Too Narrow Now Time Series Test and Multiple Source Test Measuring the Range of Debate Distractions and Illusions
Media Literacy: Censorship and Propaganda Filters and Censors Censorship: External and Internal Conclusion and Epilog: Where Are the Adults? | 677.169 | 1 |
Beast Academy
3A Guide and Practice Bundle:Guide 3A delivers complete lessons to the students of Beast Academy in an
engaging comic-book style. The companion book, Practice 3A, provides over 400 problems ranging from introductory level
exercises to very challenging puzzles and word problems, to reinforce the
lessons in the Guide. Beast Academy 3A covers the following topics:
Shapes: Angles, triangles, quadrilaterals, other polygons, puzzles with
polyominoes. Skip-Counting: Patterns with repeated addition, arithmetic
sequences, foundations for understanding multiplication, distribution, and
factoring. Perimeter and Area: Perimeter and area of rectangles, polygons,
and rectilinear shapes.
9781934124420
$27.00
Beast Academy
3B Guide and Practice Bundle : Guide 3B delivers complete lessons to the
students of Beast Academy in an engaging comic-book style. The companion
book, Practice 3B, provides over 400 problems ranging
from introductory level exercises to very challenging puzzles and word
problems, to reinforce the lessons in the Guide. Beast Academy 3B covers
the following topics: Multiplication: The times table, the commutative and
associative properties, multiplying numbers that end in one or more
zeroes. Perfect Squares: Squaring a number that ends in 5, finding the
next perfect square, multiplying nearby numbers using perfect squares. The
Distributive Property: Order of operations, area models of the
distributive property, multiplying multi-digit numbers.
Prealgebra
Textbook and Solutions Manual : Prealgebra
prepares students for the rigors of algebra, and also teaches students
problem-solving techniques to prepare them for prestigious middle school
math contests such as MATHCOUNTS, MOEMS, and the AMC 8. Topics covered in
the book include the properties of arithmetic, exponents, primes and
divisors, fractions, equations and inequalities, decimals, ratios and
proportions, unit conversions and rates, percents, square roots, basic
geometry (angles, perimeter, area, triangles, and quadrilaterals),
statistics, counting and probability, and Prealgebra
course. Our site includes a free innovative online learning system, Alcumus,
and a free collection of videos, both aligned to this textbook.
9781934124147
$59.00
Introduction
to Algebra Textbook and Solutions Manual
: Learn the basics of algebra from
former USA Mathematical Olympiad winner and Art of Problem Solving founder
Richard Rusczyk. Topics covered in the book include linear equations,
ratios, quadratic equations, special factorizations, complex numbers,
graphing linear and quadratic equations, linear and quadratic
inequalities, functions, polynomials, exponents and logarithms, absolute
value, sequences and series, and much Algebra I
course, and also includes many concepts covered in Algebra II. Middle
school students preparing for MATHCOUNTS, high school students preparing
for the AMC, and other students seeking to master the fundamentals of
algebra will find this book an instrumental part of their mathematics
libraries.
9781934124109
$42.00
Introduction
to Counting and Probability Textbook and Solutions Manual: Learn the basics of counting
and probability from former USA Mathematical Olympiad winner David
Patrick. Topics covered in the book include permutations, combinations,
Pascal's Triangle, basic combinatorial identities, expected value,
fundamentals of probability, geometric probability, the Binomial Theorem,
and much more. The text is structured to inspire the reader to explore and
develop new ideas. Each section starts with problems, so the student has a
chance to solve them without help before proceeding. The text then
includes solutions to these problems, through which counting and
probability techniques are taught. Important facts and powerful problem
solving approaches are highlighted throughout the text. In addition to the
instructional material, the book contains over 400 problems. The solutions
manual contains full solutions to all of the problems, not just answers.
This book is ideal for students who have mastered basic algebra, such as
solving linear equations. Middle school students preparing for MATHCOUNTS,
high school students preparing for the AMC, and other students seeking to
master the fundamentals of counting and probability will find this book an
instrumental part of their mathematics libraries. Our site includes a free
innovative online learning system, Alcumus, and a free collection
of videos, both aligned to this textbook.
9781934124086
$57.00
Introduction
to Geometry Textbook and Solutions Manual
: Learn the fundamentals of geometry
from former USA Mathematical Olympiad winner Richard Rusczyk. Topics
covered in the book include similar triangles, congruent triangles,
quadrilaterals, polygons, circles, funky areas, power of a point,
three-dimensional geometry, transformations, and much more. The text is
structured to inspire the reader to explore and develop new ideas. Each
section starts with problems, so the student has a chance to solve them
without help before proceeding. The text then includes solutions to these
problems, through which geometric techniques are taught. Important facts
and powerful problem solving approaches are highlighted throughout the
text. In addition to the instructional material, the book contains over
900 problems. The solutions manual contains full solutions to all of the
problems, not just answers. This book can serve as a complete geometry
course, and is ideal for students who have mastered basic algebra, such as
solving linear equations. Middle school students preparing for MATHCOUNTS,
high school students preparing for the AMC, and other students seeking to
master the fundamentals of geometry will find this book an instrumental
part of their mathematics libraries.
9781934124123
$47.00
Introduction
to Number Theory Textbook and Solutions Manual
: Learn the fundamentals of number
theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew
Crawford. Topics covered in the book include primes & composites,
multiples & divisors, prime factorization and its uses, simple
Diophantine equations, base numbers, modular arithmetic, divisibility
rules, linear congruences, how to develop number sense, and much more. The
text is structured to inspire the reader to explore and develop new ideas.
Each section starts with problems, so the student has a chance to solve
them without help before proceeding. The text then includes motivated
solutions to these problems, through which concepts and curriculum of
number theory are taught. Important facts and powerful problem solving
approaches are highlighted throughout the text. In addition to the
instructional material, the book contains hundreds of problems. The
solutions manual contains full solutions to nearly every problem, not just
the answers. This book is ideal for students who have mastered basic
algebra, such as solving linear equations. Middle school students
preparing for MATHCOUNTS, high school students preparing for the AMC, and
other students seeking to master the fundamentals of number theory will
find this book an instrumental part of their mathematics libraries.
9781934124048
$64.00
Intermediate
Algebra Textbook and Solutions Manual
: A comprehensive textbook
covering Algebra 2 and topics in Precalculus. This book is the follow-up
to the acclaimed Introduction to Algebra textbook. Topics
covered in this book include a review of basic algebra topics, complex
numbers, quadratics and conic sections, polynomials, multivariable
expressions, sequences and series, identities, inequalities, exponents and
logarithms, piecewise-defined functions, functional equations, and much
more. As with all of the books in Art of Problem Solving's Introduction
and Intermediate series, the text In addition to the
instructional material, the book contains over 1600 problems. The
solutions manual contains full solutions to all of the problems, not just
answers.
9781934124062
$47.00
Intermediate
Counting and Probability Textbook and Solutions Manual
: Continue your exploration of
more advanced counting and probability topics from former USA Mathematical
Olympiad winner David Patrick. This book is the follow-up to the acclaimed Introduction
to Counting & Probability textbook. Topics covered in this book
include inclusion-exclusion, 1-1 correspondences, the Pigeonhole
Principle, constructive expectation, Fibonacci and Catalan numbers,
recursion, conditional probability, generating functions, graph theory,
and much more. As with all of the books in Art of Problem Solving's
Introduction and Intermediate series, the text is structured to inspire
the reader to explore and develop new ideas. Each section starts with
problems, so the student has a chance to solve them without help before
proceeding. The text then includes solutions to these problems, through
which counting and probability techniques are taught. Important facts and
powerful problem solving approaches are highlighted throughout the text.
In addition to the instructional material, the book contains over 650
problems. The solutions manual contains full solutions to all of the
problems, not just answers.
9781934124161
$53.00
Precalculus
Textbook and Solutions Manual
: Precalculus is part of the
acclaimed Art of Problem Solving curriculum designed to challenge
high-performing middle and high school students. Precalculus covers
trigonometry, complex numbers, vectors, and matrices. It includes nearly
1000 problems, ranging from routine exercises to extremely challenging
problems drawn from major mathematics competitions such as the American
Invitational Mathematics Exam and the USA Mathematical Olympiad. Almost
half of the problems have full, detailed solutions in the text, and the
rest have full solutions in the accompanying Solutions Manual. As with all
of the books in Art of Problem Solving's Introduction and Intermediate
series, Precalculus
9781934124185
$49.00
Calculus
Textbook and Solutions Manual : Calculus is
part of the acclaimed Art of Problem Solving curriculum designed to
challenge high-performing middle and high school students. Calculus covers
all topics from a typical high school or first-year college calculus
course, including: limits, continuity, differentiation, integration, power
series, plane curves, and elementary differential equations. The text is
written to challenge students at a much deeper level than a traditional
high school or first-year college calculus course. The book includes
hundreds of problems, ranging from routine exercises to extremely
challenging problems drawn from major mathematics competitions such as the
Putnam Competition and the Harvard-MIT Math Tournament. Many of the
problems have full, detailed solutions in the text, and the rest have full
solutions in the accompanying Solutions Manual. | 677.169 | 1 |
New. Essential Calculus: Early Transcendental Functions...New. Essential Calculus: Early Transcendental Functions responds to the growing demand for a more streamlined and faster paced text at a lower price for students. This text continues the Larson tradition by offering instructors proven pedagogical techniqu. | 677.169 | 1 |
Pre-Algebra
Description
This pre-algebra work-text gives a brief but complete review of all arithmetic topics, broadening many topics to include more than one approach to the correct solution. Much of the text is devoted to algebra and related topics, scientific notation, geometry, statistics, and trigonometry. Problem-solving strategies help students apply mathematical skills to word problems. Students build confidence in their mathematical potential as they successfully work in advanced topics that are presented in an understandable and interesting style | 677.169 | 1 |
algebra
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Algebra is one of the basic building blocks to learning mathematics at a higher level.
According to Answers.com, the primary definition of algebra is "A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set." Within algebra, there are several categories within the discipline, including elementary algebra, abstract algebra, linear algebra, universal algebra, algebraic number theory, algebraic geometry, and algebraic combinatorics.
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Overview: Ratios and proportions are common ways to compare numbers. They have many mathematical applications, such as scale models, percentages, and interest. Ratios and proportions can be set up with variables, and solved for those variables. What Is a Ratio? A ratio is a comparison of two numbers byHigh failure rates in remedial math have prompted Illinois community college teachers to develop "math literacy" courses for students in non-STEM majors. A remedial revolution will hit Florida next fall: Most state college students will not be required to take remedial courses, regardless of their collegeOVERVIEW Fairly straightforward radical equation in the title but there is so much hidden potential here for students in Alg 2/Precalculus. REFLECTIONS • The solutions to the equation above are -1 and 0. No big deal, right? The usual algorithm --- just square both sides and solve the resulting quadratic by any ...
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The totality of rational expression addition and subtraction problems in Wentworths New School Algebra (published in 1898) vs. the University of Chicago School Mathematics Project Algebra (published in 2002) . I. From Wentworths New School Algebra , pp. 133, 134, 135, 137 [click to enlarge]:—
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"The world as we have created it is a process of our thinking. It cannot be changed without changing our thinking."― Albert Einstein The only way we can change our child's future is by changing the way how Algebra is perceived. I have been doing a lot of research on this problem and have realized that ...
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Overview: Triangles have many different properties. For example, the sum of all three angles is always equal to 180 o . The area of a triangle is equal to 1/2 times the base times the height. The triangle inequality property is another property that can be used in real-world situations. Straight Lines andIf you ask a 5 year old, ' What do you want to become when you grow up? ' The would say a lawyer, doctor, scientist, the president or any other career that they are passionate about. They will tell you their dreams with certainty , determination and belief as if no obstacle could ever prevent them from ...
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Chapter 11: Algebra and Geometry Connections; Working with Data
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This chapter covers graphing and comparing square root functions, solving radical equations, using the Pythagorean theorem and its converse, using the distance formula, and making & interpreting stem-and-leaf plots & histograms. | 677.169 | 1 |
Linear Algebra - A free textbook by Prof. Jim Hefferon of St. Michael's College. This wikibook began as a wikified copy of Prof. Hefferon's text. Prof. Hefferon's book may differ from the book here, as both are still under development.
A Course in Linear Algebra - A free set of video lectures given at the Massachusetts Institute of Technology by Prof. Gilbert Strang. Prof. Strang's book on linear algebra has been a widely influential book and it is referenced many times in this text.
Octave a free and open soure application for Numerical Linear Algebra. Uses of this software is referenced several times in the text. There is also an Octave Programming Tutorial wikibook under development.
A toolkit for linear algebra students - An online software resource aimed at helping linear algebra students learn and practice a basic linear algebra procedures, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence. This software was produced by Przemyslaw Bogacki in the Department of Mathematics and Statistics at Old Dominion University.
Wikipedia is frequently a great resource that often gives a general non-technical overview of a subject. Wikipedia has many articles on the subject of Linear Algebra. Below are some articles about some of the material in this book. | 677.169 | 1 |
This course is deigned for students who need additional time to understand and develop mathematical concepts. In addition to their regular Math class, students will use an online computer program called ALEKS to support and strengthen their math skills. This is a course designed to help students pass and excel in their regular math course. In addition to working with ALEKS, students will prepare and study for the Oregon State Assessment Test in Mathematics.
State Standards:
Math Skills is aligned to state standards for your math course. See your math course syllabus for details. ALEKS is aligned to CCSS (Common Core State Standards) and teaches the necessary skills for the State Assessment OAKS exam as well.
Guidelines:
1. Students will be courteous and respectful to others.
2. Do not disrupt the learning process.
3. Students will be prepared for class!!!
4. Show P.R.I.D.E
Important:
Cell phones may not be used during class time. Cell phones may not be used as calculators.
Music Playing devices will be left to teacher discretion.
No FOOD or DRINK will be allowed in the computer lab.
Materials: Needed every day for class!
Calculator – Scientific Calculator is required for this course! There are not enough computers for every student, so please bring a calculator as you may be working on homework part of the period.
Pencils w/erasers
Planner
Grading Procedures;
Assignments: No homework!
A minimum of 90 minutes of ALEKS is recommended per week so that students are prepared to test on ALEKS every two weeks.
Students must work on Math Homework, when not working on the ALEKS program.
***Some days all students will be required to participate in a review or assessment activities.
***On Fridays, math practice web sites may be an option (including math games related to the current topics of your math class), IF the student is caught up with course requirements for Math Skills and your regular class.
***If a student works on math daily and is earning at least a C in both Math Skills and their math course, he or she may be eligible to complete other course work one day a week.
***If it is convenient for the student and their math teacher students are ENCOURAGED to review for and retake tests for their MATH class during math skills.
Tests:
Once every two weeks, students will be assessed in the Aleks program. Each assessment will be worth a total of 10 points. Students will be awarded points for showing improvement from the previous assessment. At the end of the course, a final assessment will be given in the Aleks program.
Students may request an Aleks retake test if desired. If a student shows a very strong gain one week and a weak gain the week previous, the gain will be averaged over the two week thereby improving the student's grade.
Quizzes may be given to highlight current or review skills needed in your math skill class (5 points). Students may request a quiz over a topic they feel they need to review.
Students needing to complete work sample tasks (scored with the state rubric) may complete one as a 10 point test.
Alternative assessments may be assigned as needed to assist a student in understanding current or review topics (10 points). Students may request alternative assessments when they assess the need to study and review a topic.
Student requests will be honored to the extent possible given the constraints of the course.
Attendance Policy:
Academic Behavior Expectations: Math Skills is Sophomore/Junior/Senior level course. I expect that each student will attend all class sessions and will come prepared and ready to learn. This means that each student will be in his or her seat by the start of the class period with a sharpened pencil, eraser, paper, a scientific calculator and a textbook; and will remain in their seats until the bell signals the end of class. Additionally, I expect that students will conduct themselves maturely and will respect their own right and the rights of their classmates to a sound math education.
Make-up test/work: It is your responsibility to make-up the work you have missed. ALEKS tests will be taken the next day the student logs into the program at school.
Grading Procedure: Your grade for this class will be determined by:
100% tests, projects, and work samples on which students may not use notes/assignments
Scale:
100-90% A 89-80% B 79-70% C 69-60% D
59-0% F
Except for meetings your teacher is available to help you before and after school daily. You are welcome to schedule ahead or you may simply drop by.
To be eligible to earn credit recovery by proficiency through the Math Skills class, a student must be identified by their Algebra I teacher as knowing a sufficient number of standards and having the workplace skills necessary to learn the remaining objectives by the end of the semester or year. The ALEKS program will assess the student's progress toward proficiency in Algebra I. When all objectives for one or both Semesters have been met, the student will be given a passing grade. Each semester a student is eligible to earn a letter grade for Math Skills OR a passing/ not passing grade for Algebra I Credit Recovery by Proficiency, NOT BOTH. | 677.169 | 1 |
Computer-Based Tutorial Programs
Computer programs that provide students additional practice with selected topics in the secondary school curriculum can be developed or purchased. With these programs, the computer can drill students in algebra, geometry, and trigonometry as well as in arithmetic. Moreover, the computer can do more than just acknowledge a correct answer and generate another problem (or indicate "error" and repeat the same problem). The software can indicate where an error was made or offer suggestions for reaching a correct answer based specifically on the student's incorrect answer.
Computers can be used for tutorial, drill, and practice in a number of ways. The software should be adjustable in terms of level of difficulty, number of problems, and mastery level. The software should be intelligent; it should sense when a student is having difficulty with a particular operation or concept and automatically branch to a tutorial with another set of problems. Software that includes a classroom management component and a record-keeping facility is helpful in planning lessons and tracking students' progress.
One of the major problems for a teacher of a large class is not being able to provide adequate individual instruction, even with an aide or teacher's assistant. Weaker students often require considerable attention. A computer with appropriate software can help these students work on their deficiencies, of which they usually are acutely aware, without taking up significant teacher or class time. The argument that computers are nonthreatening, noncritical, and nonjudgmental is certainly valid, especially if the software includes positive reinforcers or if the mathematics is presented in the context of a game or a challenge. | 677.169 | 1 |
Walk through Combinatorics An Introduction to Enumeration and Graph Theory
9789812568861
9812568867
Summary: This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. | 677.169 | 1 |
Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. more...
Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies... more...
The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection... more...
Boost Your grades with this illustrated quick-study guide. You will use it from high school all the way to graduate school and beyond. FREE first 3 chapters in the trial version. Includes both Algebra I and II. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Search for the words... more...
Examines a Tractatus algorismi written in 1307 in Montpellier by Jacopo da Firenze. It is one of the earliest surviving "abbacus" treatises and the first to contain a presentation of algebra. This book includes the text in late medieval Italian with an English translation. It discusses the contents and its place within early abbacus culture. more...
Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must rely on approaches that include semiotic concepts and analyses that recall the history of algebraic ideas, among others. Educational Algebra: A Theoretical and Empirical Approach deals with a theoretical... more...
The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has become prominent. This book focuses on the broader interface of number theory, geometry, and physics. It is presented in three parts: Conformal Field Theories, Discrete Groups, and Renormalization. more... | 677.169 | 1 |
Mathematics for Elementary Teachers: A Conceptual Approach
9780073519579
ISBN:
007351957X
Publisher: McGraw-Hill
Summary: Would you like to rent Mathematics for Elementary Teachers: A Conceptual Approach online from Valore Books now? If you would like to take advantage of discounted prices on pre-owned copies of this book published by McGraw-Hill, look at our selection now. Written by Albert B Bennett, Laurie J Burton and Leonard T Nelson, you can find the cheapest copies of this text book by using our site now. Buy Mathematics for Elem...entary Teachers: A Conceptual Approach online from us today and find out why so many people rent and buy books for college from us. Try our website now for the cheapest deals.
Bennett, Albert B. is the author of Mathematics for Elementary Teachers: A Conceptual Approach, published under ISBN 9780073519579 and 007351957X. Six hundred fifty Mathematics for Elementary Teachers: A Conceptual Approach textbooks are available for sale on ValoreBooks.com, two hundred nineteen used from the cheapest price of $90.09, or buy new starting at $99 | 677.169 | 1 |
224.85,"ASIN":"039504636X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":35.95,"ASIN":"0881332674","isPreorder":0}],"shippingId":"039504636X::OCmPlMC%2B9zD%2Fab43FQz%2BY99daOqjPpCQ9ppZ63ECMLedNpCD%2BZYq8YQUKLFXZ%2BM%2FdFFwvlHJIGPfgUuNE%2FPDCBsik7kkIqFsLL3eQbo0pao%3D,0881332674::83PCK03zQrResAaVKRFd4CJ1Jh3WFtDj2VH6tgsEfGzu3qlts%2FpLpqTYAjzPJdPdq8DG7su6PK86%2BjJ%2Bs0A%2BuPYHUSanECvKn9T%2Fb%2Bz%2Bd book used in the standard upper-division probability course at UC Berkeley when I took it 18 years ago. In my opinion it is still the best. I have since taught the subject myself and was forced to use other books, with many more pages and fancy pictures than Hoel's book. Yet those books do not do anywhere near as good a job of teaching probabilistic *thinking* as well as Hoel. This is what causes the most problems for students of probability, and Hoel does it the right way in Chapters 1 and 2, which are key. The basic explanations are clear and concise, with many instructive examples.
My professor back then told us that if we want to learn probability, then do every exercise in this book. She was absolutely right. The exercises are excellent. Do them, and you will learn a lot.
This used to be *the* book on elementary calculus-based probability theory at most universities. I don't understand why it seems to have fallen out of favor. Perhaps because of its size (it is fairly compact, as it should be) and age, though I fear that it may be because it is a bit more demanding (but worth it) than many of the newer books.
I first noticed this book during the time that I spent at UC Berkeley as an undergraduate applied mathematics major. It was being used for Stat 101, and though I was not taking that course, I bought it because it looked even from casual inspection to be very well laid out, covering important and interesting issues in basic probability.
The strongest feature of this book from my point of view is its conciseness. Much is presented in as short a time as possible, and because of that the book is much more readable than many others of its level. In addition to conciseness, the authors (in my edition Hoel, Port, and Stone) have made a commendable effort to present the reader with clear and concrete definitions, compact theorems (many proven), and abundant useful examples. In the back of the book nearly all of the solutions of the chapter exercises are given, unlike many books where answers to only the odd problems are given. I believe that this book is ideal for self-study, and that much use of it could also be made as a textbook for an undergraduate course in probability. The exercises are not very difficult, but they are by no means trivial, and much can be learned from them. At the end of a close study of this book the reader would be ready to enter into a program of undergraduate level mathematical statistics, or into a further study of probability with the confidence inspired by a firm understanding of the most fundamental and key concepts in probability theory.
This classical text is complete and detailed. I'm an undergraduate and used the book after acquiring the basics of multiple integration as an introduction to the calculus of probability. Plenty of exercises (answers provided) which not only help you understanding the theory but are also complementary to the text. (This is a "non-measure" text on probability theory.) Well written!!!! (see also Hoel at al., 'Int. to Stochastic Processes', and Taylor, 'An Int. to Measure and Probability',(Springer-Verlag)).
This is a fantastic book. It is a pleasure to read and learn from. I know is an expensive text but it is worth its weight in gold, even if used. I have quite a few books on probability and, had I known about this one before, I would have never bothered looking at the others. This is the type of text to bring along if you were to be dropped onto an island in the middle of the Pacific.
This book is an excellent choice for anyone who is interested in learning the elementary probability theory(i.e. calculus-based probability rather than measure theoretic probability). The book assumes the readers have no prior exposure to this subject. However, the readers are expected to have a working knowledge of calculus. While there are many textbooks of the same nature, this book stands out by its clarity, completeness and elegance. The authors present the material in an extremely clear way that any serious reader is able to follow from the beginning to the end. It is absolutely a first-class textbook! A must for anyone interested in elementary probability. The only part I don't like is that the authors use "density function" instead of "probability mass function" for discrete random variable.
I picked up this book for free in a library give away and didn't realize my good fortune until I read the first chapter. My undergrad probability class used Sheldon Ross's Intro To Probability Models book, which certainly contains interesting examples but lacks the intuitive explanation and rigorous (enough for an undergraduate at least) derivations of this book. Chapter 2 alone provided a better treatment of counting and combinatorics than any book I've seen. Most of the exercises have solutions in the back, which are very convenient for self-study, and the exercises themselves range from straightforward to slightly tricky, although all are very manageable. I am looking forward to tackling HPS's Stochastic Processes book next. | 677.169 | 1 |
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The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations | 677.169 | 1 |
math (algebra) Hi. At the sit for mcgraw hills algebra 1 book (website URL is obvious), but don't have a name or password! Could somebody please lend me theres? post it here! Viit Viit! Your teacher needs to register you.
Thursday, September 7, 2006 at 3:09pm by JeremyDRWLS,MATH,ALGEBRA Drawls, How did you get 2h. and then the 2a/h from.Can you help me understand it when you get a chance. Directions: Solve each literal equation for the indicated variable. A=1/2h(B+b) (For b) Area of a trapezoid For Further Reading math,algebra - drwls, Monday, December 18, ...
Monday, December 18, 2006 at 1:30pm by jasmine20
math, algebra what are some challenges about working with rational expressions? Math is a language. Getting it precisely right is a lot easier than describing it in a vague statement in English such as you ask. Is there a chance you can change teachers? If so, I recommend it. THe focus of ...
Tuesday, March 6, 2007 at 12:41am by jas20 | 677.169 | 1 |
ABC Phonics Chant With Musical Accompaniment This video is a phonics chant to help students practice and review their phonics and alphabet at home. Each letter is shown on the screen first in upper and lower case. Then the sound of each letter is made. Finally, the letter name and sound are stated with a picture of an item beginning with the designated letter and sound. For example, M, /m/, mouse. The letters are easy to see and the sounds are clearly made, making this great for phonics practice. Author(s): No creator set
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Basic Math: Lesson 2 - Equalities & Inequalities This lesson consists of providing you with a Self-Tutorial on the basics of equalities and inequalities. I go over how to write results in interval notation, inequality notation, and set (set-builder) notation. I also explain in the printed notes how to use your graphing calculator to help you make comparisons between numbers. Author(s): No creator set
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Solving Inequalities in One Variable: Part 1 of 2 The instructor uses an electronic sketchpad to demonstrate how to solve linear inequalities in one variable. This video is part 1 of 2 and several problems are solved and plotted on a number line.
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Graphing Linear Inequalities in Two Variables This video begins with a simple inequality, then explains how to graph the inequality. The instructor begins by showing how to graph the boundary line, then tells how to show the correct solution set on the graph by shading.
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Graphing Linear Inequalities from Standard Form Instructor uses power point to demonstrate how to graph linear inequalities in standard form. Examples model finding the x- and y-intercepts, drawing a line through the two intercepts and forming a boundary line. The instructor then discusses whether the boundary line is dashed or solid and which way to shade the inequality, above or below the boundary line Systems of Inequalities, Part 2 The instructor in this video, Sal Khan, in an easy, conversational tone, continues to discuss how to graphGraphing Inequalities with Two Variables Just like equations, sometimes we have two variables in an inequality. Graphing inequalities with two variables involves shading a region above or below the line to indicate all the possible solutions to the inequality. This video clip explains how to graph inequalities with two variables by using some of the same techniques used when graphing lines to find the border of our shaded region. (1:42) Author(s): No creator set
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Jesse Owens, Berlin '36, Historic Olympic Run This brief video has been taken from a vintage reel and shows Jesse Owens in Berlin '36, during the Olympics during his historic run. The images are slightly blurred, but this is understandable as the images are more than 70 years old. The video is in German. (1:12) Author(s): No creator set
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Olympic Games Though History This is a very good slideshow concerning the Olympic Games. The slides appear a little too fast, but the information contained within the slides is interesting. There is no narration--just music and captions. (2:58) Author(s): No creator set
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Olympics, Ancient Early Games The ancient Olympics began in about the eighth century, B.C. How important were those games to the Greeks? What honors were bestowed on the winning athletes? Why did they end, after twelve hundred years? (9:54)
Take a virtual trip to the ancient world to discover more about it. Move the video forward - to 6:00 - to begin the trip. Author(s): No creator set
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Olympics, Ancient - Honors for the Athletes So highly regarded were winning athletes, in the ancient Olympic games, that their names were used in the Greek calendar. People referenced events by the year that a particular champion prevailed in his sport.
What other honors were bestowed upon winning athletes in the ancient games? Take a look at the very beginning of this clip from Seven Wonders of Ancient Greece. Author(s): No creator set Berlin | 677.169 | 1 |
Elementary and Intermediate Algebra A Combined Course
9780495108511
ISBN:
0495108510
Edition: 3 Pub Date: 2007 Publisher: Thomson Learning
Summary: Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! ELEMENTARY AND help you to move through each new concept with ease. Real-w...orld applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including ThomsonNOW for ELEMENTARY AND INTERMEDIATE ALGEBRA, a personalized online learning companion.
McKeague, Charles P. is the author of Elementary and Intermediate Algebra A Combined Course, published 2007 under ISBN 9780495108511 and 0495108510. Two hundred forty five Elementary and Intermediate Algebra A Combined Course textbooks are available for sale on ValoreBooks.com, one hundred twenty five used from the cheapest price of $1.99, or buy new starting at $48 | 677.169 | 1 |
History of Mathematics An Introduction
9780073051895
ISBN:
0073051896
Edition: 6 Pub Date: 2005 Publisher: McGraw-Hill College
Summary: David Burton covers the history behind the topics typically covered in an undergraduate maths curriculum or in elementary or high schools. He illuminates the people, stories, and social context behind mathematics' greatest historical advances, while maintaining appropriate focus on the mathematical concepts themselves.
Burton, David M. is the author of History of Mathematics An Introduction, published 2005 u...nder ISBN 9780073051895 and 0073051896. One hundred thirty History of Mathematics An Introduction textbooks are available for sale on ValoreBooks.com, twenty three used from the cheapest price of $5.89, or buy new starting at $44 | 677.169 | 1 |
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