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presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. The fundamentals of MATLAB are illustrated throughout with many examples from a wide range of familiar scientific and engineering areas, as well as from everyday life. The new edition has been updated to include coverage of Symbolic Math and SIMULINK. It also adds new examples and applications, and uses the most recent release of Matlab. 4e is an ideal textbook for a first course on Matlab or an engineering problem solving course using Matlab, as well as a self-learning tutorial for professionals and students expected to learn and apply Matlab for themselves. · New chapters on Symbolic Math and SIMULINK provide complete coverage of all the functions available in the student edition of Matlab.* New: more exercises and examples, including new examples of beam bending, flow over an airfoil, and other physics-based problems* A new bibliography provides sources for the engineering problems and examples discussed in the text · A chapter on algorithm development and program design · Common errors and pitfalls highlighted · Extensive teacher support on solutions manual, extra problems, multiple choice questions, PowerPoint slides · Companion website for students providing M-files used within the book |
Video Summary: This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations |
best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the social sciences, business, nursing and allied health fields. Let us introduce you to the practical, interesting, accessible, and powerful world of mathematics today—the world of A Survey of Mathematics with Applications, 8e. |
Course Description
MA 1025
Mathematical Problem Solving
Prerequisite: C or above in MA1000. Topics in algebra including exponents and their properties, and addition, subtraction, and multiplication of variable expressions. Solving and applying linear equations and applying exponential equations are studied. Graphing lines and linear inequalities using slope-intercept form and solving systems of equations and inequalities as they relate to business, social sscience and finance applications and displaying data are also covered. Throughout the course application problems and appropriate technology will be emphasized. |
Yes, you can...
Master math and science!
Succeed with Math: Every Student's Breaking the Science Barrier: How to
Guide to Conquering Math Anxiety Explore and Understand the Sciences
By Sheila Tobias, author of the By Sheila Tobias and Carl T. Tomizuka
best-selling Overcoming Math Anxiety
Understanding science isn't just for science majors.
Succeed with Math is the ground-breaking practical
guide that enables you to conquer math anxiety and Successful people in fields as diverse as law, architecture,
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Breaking the Science Barrier will help you understand:
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A NEW MATH LANGUAGE FOR BLIND STUDENTS
Summary: Introducing a new language for easily and effectively
communicating mathematics information between blind students
and their teachers and fellow students not familiar with Braille.
The author's objective is to introduce the audience to a new and
simple language for communicating mathematics information
between blind students familiar with Braille and their teachers,
fellow students, and parents who may not be familiar with and not
able to use Braille.
Those of you who are blind or are teachers or parents of blind
students are strongly encouraged to experiment with this new
language, improve it over time, and in the process increase the
mathematical knowledge of blind students. Mathematics is the
language of science and technology. With this necessary
knowledge of mathematics, blind students will develop into even
more capable, self-sufficient, contributing citizens of the twenty-
first century.
There are just two major requirements for this new mathematics
language. First the language must be the same when spoken as
when written. And second the language must be the same when
written in Braille as when printed.
While these two requirements sound simple they require
fundamental changes in the way mathematics expressions are
written. Fortunately these changes impact only the form of written
mathematics and not its underlying meaning. By analogy,
mathematics is fundamentally the same whether written in the
German, French, Arabic, Chinese, Spanish, Greek, or English
language.
For the past several hundred years mathematics has been typically
presented on the printed page in a two dimensional format with
symbols printed not only horizontally left to right across the page
but also vertically above and below in superscripts, subscripts, and
sub-subscripts. Admittedly this allows the traditional printed form
of mathematical expressions to be quite compact. However,
because speech is restricted by time to a single linear dimension, it
is necessary to similarly restrict this new mathematics language
when written to a single horizontal linear dimension across the
page so that the language is the same when spoken as when
printed.
The second requirement, that mathematical expressions are the
same when written in Braille as when printed, is accomplished by
limiting the number of single character symbols in the new
language to only sixty-four, the number of six-dot Braille
characters. Traditional mathematics uses nearly a thousand special
symbols developed over several hundred years, many of which are
retained to this day in their original form in honor of the famous
mathematicians that first published those particular mathematical
ideas.
This new mathematical language for blind students uses for
simplicity the sixty-four characters of ASCII Braille. ASCII is the
abbreviation for the American Standard Code for Information
Interchange. Those interested in but unfamiliar with ASCII Braille
are referred to the Internet where searching on the words "ASCII
Braille" will provide multiple hits illustrating the specific
relationship between the sixty-four six-dot ASCII Braille symbols
and their printed equivalents. During the presentation of this paper
handouts describing ASCII Braille will be available to the
audience and a transparency will be projected using the overhead
projector.
Briefly ASCII Braille includes the same twenty-six lower case
English alphabetic characters as all other American and English
Braille. However, the fifth character line of ASCII Braille is
allocated to the ten digits one through nine and zero rather than
adding a prefix character to the alphabetic characters a through j of
the first Braille character line. Having unique Braille symbols for
the ten digits is very useful and makes numerical expressions
written in ASCII Braille much simpler. This new math language
writes whole and decimal fraction numbers in the usual way where
four hundred eighty three and a quarter is written as 483.25 and
spoken as four, eight, three, point, two, five with no spaces
between these six characters.
Besides the twenty-six alphabetic characters, the ten digits, and the
all important blank space character, ASCII Braille includes twenty-
seven common printed symbols usually found on most American
typewriter and computer keyboards. These printed symbols and
their spoken names are more than sufficient to write and speak all
mathematical expressions provided one follows the same writing
style as a novelist. The novelist is required to name and introduce
the characters in the story before using their names or nicknames
to subsequently and efficiently refer to these people. While several
of the twenty-seven symbols such as the plus sign and the equal
sign will have well understood global definition, many of the other
symbols must be defined locally by the writer before their use in
mathematical expressions for the mutual understanding of the
writer and reader.
Just as taught in high school algebra, one can use an alphabetic
character to represent a variable, an element of a set, or a set of
elements. When properly predefined, the twenty-six lower-case
alphabetic characters can be used to represent any mathematical
expression. And just as in narrative writing, one can use predefined
pronounceable single or multi-syllable combinations of ASCII
Braille characters (often referred to as words or nicknames) to
provide all the mathematical symbols one may ever need.
To avoid confusion one must separate every mathematical symbol
or word from its neighbors with the all important blank space
character. Therefore the product of the two variables x and y
cannot be written in the usual way by placing the x next to the y
without a space between them, but must be written as x space star
space y where the asterisk, nicknamed star, represents the
multiplication symbol.
In the following examples the symbols for the four operations of
addition, subtraction, multiplication and division will be given the
nicknames of plus, minus, star (for the asterisk), and slash
respectively. Also the left and right parentheses, nicknamed open
and close respectively, are used to specify the order in which one
does the operations starting first with the inner most parenthetical
expression. In order to handle exponents while remaining on a
single printed line one can use the caret or up-arrow and the
underscore symbols, nicknamed up and down respectively.
At the presentation of this paper the author will write out the
following two expressions for the audience on the easel paper pad.
To express four plus one-half, one uses the following sequence of
symbols: 4 + ( 1 / 2 ) which is spoken with pauses replacing the
spaces as "four plus open one slash two close". To express that the
square root of sixty four equals eight one may write the following
sequence of symbols: ( 64 ^ ( 1 / 2 ) _ ) = 8 which is spoken with
pauses replacing the spaces as "open six four up open one slash
two close down close equals eight".
Yes, these linear representations are unable to utilize the
compactness of traditional two-dimensional mathematical
expressions; however this minor disadvantage is greatly over
overcome by the feature of this new mathematics language that the
spoken, printed, and Braille forms are identical, which allows blind
students and their teachers to be able to communicate any and all
types of mathematical expressions as long as they have locally
predefined the elements of their expressions.
Several types of moderately priced equipment on display here at
the CSUN Technology and Persons with Disabilities Conference
are available to assist blind students and teachers in converting
narrative text and mathematical expressions between their spoken,
printed, and Braille forms. Where graphs or drawings are helpful in
understanding mathematical expressions and concepts, these must
be drawn as very simple tactile drawings and complete narrative
descriptions of these drawings must precede each tactile drawing.
Equipment on display here at the conference is also available for
converting between tactile and printed drawings.
It is also strongly recommended that authors of written
mathematics learning material for blind students limit their
vocabulary to the one to two thousand words used both by Voice
of America to communicate with listeners with limited knowledge
of English and used by sign language to communicate with those
with hearing and speaking disabilities. While it is important to
familiarize students with the traditional and historical terms for
mathematical concepts, after introducing these complex terms
authors should substitute common nicknames for them from the
above-mentioned limited vocabularies.
Because change is always difficult, it is anticipated that some
traditional mathematicians may resist using this new mathematics
language and may even be offended by it.
The author of this paper is currently working on developing a
textbook for blind students covering arithmetic and algebra using
this new mathematics language and has coined a nickname for the
language. The language is called "mith" spelled m, i, t, h, which
stands for Mathematics In The Head.
Stop and realize that you, the audience, have learned this new
language, mith, in less than a half hour. Please use it and improve
upon it to help blind students learn mathematics.
Permission is granted by the author to reproduce this paper in any
form for any purpose that will contribute in any way toward
helping blind students learn mathematics. |
Schaum's has Satisfied Students for 50 Years.
Now Schaum's Biggest Sellers are in New Editions!
For, and completely updated information to conform to the latest developments in every field of study.
Schaum's Outlines-Problem Solved
Schaum's Outline of Mathematics for Liberal Arts Majors helps students understand basic concepts and offer extra practice on such topics as logic, truth tables, axiom statements, consumer mathematics, probability and counting techniques, the real number system, and more. Each chapter offers clear concise explanations of topics and include hundreds of practice problems with step-by-step solutions. |
The Math Class that's Right for You
Developmental mathematics is a sequence of pre-college level math courses designed to prepare students for college level mathematics.The developmental mathematics program at Weber State University offers Pre-algebra (Math 0950), a First Course in Algebra (Math 0990) and Intermediate Algebra (Math 1010), as well as Pathway to Contemporary Math (Math 810). Many students entering an open enrollment institution like Weber State University need developmental mathematics courses for a variety of reasons.It is the goal of the WSU Developmental Mathematics program to assist students in gaining the math skills they need for success in college level mathematics in as short a time as possible.
Weber State University is a leader in the state when it comes to developmental mathematics reform.Traditional developmental mathematics programs only provide lecture courses, shown by research to be the least effective method of instruction.
Choose From These Options:
Course Type
Basic Format
Who should take this
class?
How to register
in Banner?
Pathway to Contemporary Math*:
*This course is only for students who plan to take Math 1030, this course will not be a pre-req for any other Math QL course. |
Mathematics - Algebra (529 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
Isaac Todhunter's Algebra for Beginners: With Numerous Examples is a mathematics textbook intended for the neophyte, an excellent addition to the library of math instructionals for beginners. Todhunter's textbook has been divided into 44 chapters. Early chapters highlight the most basic principles of mathematics, including sections on the principal signs, brackets, addition, subtraction, multiplication, division, and other topics that form the foundation of algebra. Simple equations make up the large majority of the material covered in this textbook. Later chapters do introduce quadratics, as well as other more advanced subjects such as arithmetical progression and scales of notation. It is important to note that Todhunter sticks very much to the basics of algebra. The content of this book lives up to its title, as this is very much mathematics for beginners. The content is provided in an easy to follow manner. This book could thus be used for independent learning as well as by a teacher. A great deal of focus has clearly been given to providing examples. Each concept is accompanied by numerous sample questions, with answers provided in the final chapter of the book. The example questions are every bit as important as the explanations, as one cannot begin to grasp mathematical concepts without having the opportunity to put them into practice. The basics of algebra are explained in an easy to follow manner, and the examples provided are clear and help to expand the knowledge of the learner. If given a chance, Isaac Todhunter's Algebra for Beginners: With Numerous Examples can be a valuable addition to your library of mathematics textbooks.
Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections.
Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
The present work is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, which in the former work were treated in an elementary manner; and we have here introduced theorems and examples which are unsuitable for a first course of reading.<br><br>From this point the work covers ground for the most part new to the student, and enters upon subjects of special importance: these we have endeavoured to treat minutely and thoroughly, discussing both bookwork and examples with that fulness which we have always found necessary in our experience as teachers.<br><br>It has been our aim to discuss all the essential parts as completely as possible within the limits of a single volume, but in a few of the later chapters it has been impossible to find room for more than an introductory sketch; in all such cases our object has been to map out a suitable first course of reading, referring the student to special treatises for fuller information.<br><br>In the chapter on Permutations and Combinations we are much indebted to the Rev. W. A. Whitworth for permission to make use of some of the proofs given in his Choice and Chance.
There are many men and women who, from lack of opportunity or some other reason, have grown up in ignorance of the elementary laws of science. They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge.<br><br>Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance.<br><br>To meet this double need - the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him - is the aim of the "Thresholds of Science" series.<br><br>This series consists of short, simply written monographs by competent authorities, dealing with every branch of science - mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics Avhich the engineer must emphasize, such as numerical com)utations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid. The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject. The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytical geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of eii ort. The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value.
The Directly Useful Technical Series requires a few words by way of introduction. Technical books of the past have arranged themselves largely under two sections: the theoretical and the practical. Theoretical books have been written more for the training of college students than for the supply of information to men in practice, and have been greatly filled with problems of an academic character. Practical books have often sought the other extreme, omitting the scientific basis upon which all good practice is built, whether discernible or not. The present series is intended to occupy a midway position. The information, the problems, and the exercises are to be of a directly useful character, but must at the same time be wedded to that proper amount of scientific explanation which alone will satisfy the inquiring mind. We shall thus appeal to all technical people throughout the land, either students or those in actual practice.
Already Published Anthropology By R.R. Makett An Introduction To Science By J.Arthuk Tnousos Evolution By J, Abthuk Thohson am The Animal World By F.W. Gakele Introduction To Mathe-Matics By A.N. Whitehead Astronomy By A. R.Hinks Psychical Research. By W.F. Eabbett The Evolution Of Plants By D.H. Scott Crime And Insanity. By C.A. Mebcieb Matter And Energy. By F.Sodd Psychology By W.McDouoau. Principles Of Physiology By J.G. McKendrick The Making Of The Earth By J.W. Gregoev Electricity By Gisbest Kapp The Human Body By A.Kiitb Future Issues Chemistry By R.Meldola The Mineral World. By SiT.
The work on Algebra of which this volume forms the first part, is so far elementary that it begins at the beginning of the subject. It is not, however, intended for the use of absolute beginners. The teaching of Algebra in the earlier stages ought to consist in a gradual generalisation of Arithmetic; in other words, Algebra ought, in the first instance, to be taught as Arithmetica Universalis in the strictest sense. I suppose that the student has gone in this way the length of, say, the solution of problems by means of simple or perhaps even quadratic equations, and that he is more or less familiar with the construction of literal formulae, such, for example, as that for the amount of a sum of money during a given term at simple interest Then it becomes necessary, if Algebra is to be anything more than a mere bundle of unconnected rules, to lay down generally the three fundamental laws of the subject, and to proceed deductively in short, to introduce the idea of Algebraic Form, which is the foundation of all the modern developments of Algebra and the secret of analytical geometry, the most beautiful of all its applications.
This tract is intended to give an account of the theory of equations according to the ideas of Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of Abel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations.<br><br>More than to any other treatise, I feel indebted to Professor H. Weber's invaluable Algebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit.<br><br>I am obliged to Mr Morris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with Art. 52.
The subject-matter of this book is a historical summary of the development of mathematics, illustrated by the lives and discoveries of those to whom the progress of the science is mainly due. It may serve as an introduction to more elaborate works on the subject, but primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know.<br><br>The first edition was substantially a transcript of some lectures which I delivered in the year 1888 with the object of giving a sketch of the history, previous to the nineteenth century, that should be intelligible to any one acquainted with the elements of mathematics. In the second edition, issued in 1893, I rearranged parts of it, and introduced a good deal of additional matter. The third edition, issued in 1901, was revised, but not materially altered; and the present edition is practically a reprint of this, save for a few small corrections and additions.
This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission:<br><br>A. Makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or<br><br>B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report.<br><br>As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission to the extent that such employee or contractor prepares, handles or distributes, or provides access to, any information pursuant to his employment or contract with the Commission.
Edward Everett Whitford was bom in Brookfield, N.Y., January 31, 1865;graduated from Brookfield Academy in 1881; received the degree of A.B. from Colgate University in 1886 and of A.M. in 1890. He taught in Colbj Academy, New London, N.H., Keystone Academy, Factorjrville, Pa., Shamokin (Pa.) High School, Commercial High School and Pratt Institute, Brooklyn, N.Y. He was principal of Brookfield High School, 1900-1. He is now instructor in mathematics in the College of the City of New York with which institution he has beei connected since 1905. He has been a graduate student in Coliunbia University since February, 1904, and is a member of the American Mathematical Society. The writer takes this opportunity of expressing hithanks to Professor David Eugene Smith for fruitfnsuggestions and able and helpful criticism.523 West ISIbt Str., New Yobk, December, 1911.
The Principles of Mathematics: Vol. 1 is a terrific introduction to the fundamental concepts of mathematics. Although the book's title involves mathematics, it is not a textbook packed with equations and theorems. Instead philosopher Bertrand Russell uses mathematics to explore the structure of logic. Russell's ultimate point is that mathematics is logic and logic itself is truth. The book is substantial and covers all subjects of mathematics. It is divided into seven sections: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. Russell covers all the major developments of mathematics and the contributions of important figures to the field. His sharp mind is evident throughout The Principles of Mathematics, as he challenges established rules and teachers readers how to think through difficult problems using logic. Russell was one of the great minds of the 20th Century. In this book he discusses how his ideas were influenced by the logician Peano. He also debates other philosophers and mathematicians, and even anticipates the Theory of Relativity, which had not yet been published by Einstein. One does not need to love mathematics to gain insights from The Principles of Mathematics: Vol. 1. Those who are interested in logic, intellectualism, philosophy or history will find significant insights into logical principles. Readers who desire an intellectual challenge will truly enjoy The Principles of Mathematics: Vol. 1.
Counting a series of things and keeping tally of the tens on the fingers were processes used by primitive peoples. From the ten fingers arose ultimately the decimal system of numeration. Recording the results of counting was done by the Egyptians and other ancient nations by means of strokes and hooks; for one thing a single stroke | was made, for two things two strokes || were used, and so on up to ten which was represented by Π. Then eleven was written |Π, twelve ||Π, and so on up to twenty, or two tens, which was represented by ΠΠ. In this way the numeration proceeded up to a hundred, for which another symbol was employed.<br><br>Names for ||, |||, ||||, ΠΠ, etc., appear in the Egyptian hieroglyphics, but a special symbol for each name is not used. Probably the Hindoos first invented such symbols, and passed them on to the Arabs, through whom they were introduced into Europe.<br><br>2<br><br>Greek Notation<br><br>The Greeks used an awkward notation for recording the results of counting.
In preparing the present work, the author has endeavored to meet the needs of colleges and scientific schools of the highest rank.<br><br>The development of the subject follows in the main the author's College Algebra; but numerous improvements have been introduced.<br><br>Attention is especially invited to the following:<br><br>1. The development of the fundamental laws of Algebra for the positive and negative integer, the positive and negative fraction, and zero, in Chaps. I and II.<br><br>In the above treatment, the author has followed to a certain extent The Number System of Algebra, by Professor H. B. Fine; who has very courteously permitted this use of his treatise.<br><br>2. The development of the principles of equivalence of equations, and systems of equations, both linear and of higher degrees; see 116-123, 182, 233-6, 396, 442, 470, 477, and 478.<br><br>3. The prominence given to graphical representation.<br><br>In Chap. XIV, the student learns how to obtain the graphs of linear equations with two unknown numbers, and of linear expressions with one unknown number. He also learns how to represent graphically the solution of a system of two linear equations, involving two unknown numbers, and sees how indeterminate and inconsistent systems are represented graphically.<br><br>The graphical representation of quadratic expressions, with one unknown number, is taken up in 465; and, in 467, the graphical representation of equal and imaginary roots.
This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and tio?oxt 3 xaAwafcaxs.- ing the principles of a few.
The object of what are here called mathematical essays is to co-ordinate a pupils knowledge on certain subjects which are not specially dealt with in text-books. The essays, of which outlines are given in the first part of this book, are of the following types: (i) A group of theorems on one subject, the theorems in ordinary text-books being often scattered in one or several volumes (e.g., Essays 19, 26, 70, 91);(ii) A series of questions leading up to the solution of an important problem (e.g., Essays 79, 87, 90, 93);(iii) A collection of different methods of proving the same theorem (e.g., Essays 28, 61, 75, 78);(iv) A series of applications- of the same theorem (e.g., Essays 37, 48, 75); (v)A classification of tests of the same geometrical condition (e.g. Essays 3, 4, 40, 41).The subjects given in the first part (Essays1-100) are, as a rule, of an elementary character. In several of these, a question, which throws light on different subjects, is repeated, Those given in the second part (Essays101-200) are taken from papers set for entrance scholarships in the Trinity and Pembroke groups of Cambridge colleges from 1905 and 1907 respectively. I should be grateful for notices of any errors that may be found in the text or answers, and for any suggestions from teachers for the improvement of the book. Charles Davison. Birmingham, November, 1914.
Teacher's Manual for First-Year Mathematics is a book written by George William Myers, a Professor of the Teaching of Mathematics and Astronomy at the University of Chicago. The book is intended as a teaching manual for teachers instructing their students using a textbook called First Year Mathematics. Myers' book is intended as a companion piece to the textbook First Year Mathematics, released by the same publishing company, The University of Chicago Press. The book makes effort to assist the teacher by providing them with a detailed how-to regarding teaching the specific problems presented in the textbook. Teacher's Manual is presented in chapters, each corresponding to a chapter in First Year Mathematics. Specific references are made to page numbers and problems presented in the textbook. In total, the book contains fourteen different chapters. Teacher's Manual for First-Tear Mathematics can only be used in conjunction with the appropriate textbook. Without access to First Year Mathematics, the book is of no use. It is however an excellent companion piece to the textbook, and those able to access the original textbook will surely find this text to be highly beneficial. While a well-written teacher's manual, George William Myers' book assumes the reader has access to the original textbook. If you are interested in making use of this manual, do ensure that you are also able to access First Year Mathematics.
It is the purpose of this work to present a through investigation of the various systems of Symbolic Reasoning allied to ordinary Algebra. The chief examples of such systems are Hamilton's Quaternions, Grassmann's Calculus of Extension and Boole's Symbolic Logic. Such algebras have an intrinsic value for separate detailed study; also they are worthy of a comparative study, for the sake of the light thereby thrown on the general theory of symbolic reasoning, and on algebraic symbolism in particular.<br><br>The comparative study necessarily presupposes some previous separate study, comparison being impossible without knowledge. Accordingly after the general principles of the whole subject have been discussed in Book I. of this volume, the remaining books of the volume are devoted to the separate study of the Algebra of Symbolic Logic, and of Grassmann's Calculus of Extension, and of the ideas involved in them. The idea of a generalized conception of space has been made prominent, in the belief that the properties and operations involved in it can be made to form a uniform method of interpretation of the various algebras.<br><br>Thus it is hoped in this work to exhibit the algebras both as systems of symbolism, and also as engines for the investigation of the possibilities of thought and reasoning connected with the abstract general idea of space. A natural mode of comparison.between the algebras is thus at once provided by the unity of the subject-matters of their interpretation. The detailed comparison of their symbolic structures has been adjourned to the second volume, in which it is intended to deal with Quaternions, Matrices, and the general theory of Linear Algebras. This comparative anatomy of the subject was originated by B. Peirce's paper on Linear Associative Algebra, and has been carried forward by more recent investigations in Germany.
This text presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and of students in the first year of a junior college. The material of the text includes the essential and vital features of the work commonly covered in the past in separate courses in college algebra, trigonometry, and analytical geometry.<br><br>The fundamental idea of the development is to emphasize the fact that mathematics cannot be artificially divided into compartments with separate labels, as we have been in the habit of doing, and to show the essential unity and harmony and interplay between the two great fields into which mathematics may properly be divided; viz., analysis and geometry.<br><br>A further fundamental feature of this work is the insistence upon illustrations drawn from fields with which the ordinary student has real experience. The authors believe that an illustration taken from life adds to the cultural value of the course in mathematics in which this illustration is discussed. Mathematics is essentially a mental discipline, but it is also a powerful tool of science, playing a wonderful part in the development of civilization. Both of these facts are continually emphasized in this text and from different points of approach.<br><br>The student who has in any sense mastered the material which is presented will at the same time, and without great effort, have acquired a real appreciation of the mathematical problems of physics, of engineering, of the science of statistics, and of science in general.<br><br>A distinctly new feature of the work is the introduction of series of "timing exercises" in types of problems in which the student may be expected to develop an almost mechanical ability. The time which is given in the problems is wholly tentative; it is hoped, in the interest of definite and scientific knowledge concerning what may be expected of a freshman, that institutions using this text will keep a somewhat detailed record of the time actually made by groups of their students. |
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Mathematics Courses
Math placement test. To enroll in courses marked with a star (*) below, you must take the math placement test. For test dates, see the math placement test information. Starred courses begin Tuesday, June 26.
Prerequisites are important in
mathematics, especially in the calculus sequence that includes courses through MATH S-21b. Courses numbered MATH S-101 and above do not require calculus.
Calculators. MATH
S-Y, S-Ar, S-1a, S-1b, and S-1ab use graphing calculators. They are not required for the placement test. Ask your instructor on the first day of class about which models are most conveniently
supported.
*MATH S-Y
Mathematical Models and Expressions (31920)
The course explores basic mathematical models as they arise in real-world situations with the goal of understanding the meaning behind mathematical expressions and functional relationships. The course
encourages independent thinking while rigorously reviewing basic algebraic and statistical techniques and notation as needed. This course provides preparation for statistics courses as well as for
quantitative reasoning components of standardized tests at the secondary school level. Prerequisites: arithmetic and algebra. Placement test required. (4 credits)
A review of algebra is integrated into the study of rational, exponential, logarithmic, and trigonometric functions. Taught in small sections, the course emphasizes applications and problem solving
and provides preparation for calculus and basic science. Graphing calculators are used, though no previous calculator experience is required. Prerequisite: a good working knowledge of algebra, as
demonstrated by a satisfactory score on the placement test. Students without the prerequisite placement test score are
withdrawn from the course. (4 credits)
This course covers differential and integral calculus in one variable, with applications. We aim to develop conceptual understanding, computational skills, and the students' ability to apply the
material to science. The topics covered overlap with the advanced placement calculus curriculum to a large extent. A graphing calculator can occasionally be useful. Students enrolling for graduate
credit participate in weekly pedagogical seminars investigating current research in mathematics education. Prerequisites: a good working knowledge of algebra, functions, logarithms, trigonometry, and
analytic geometry. Placement test required. The graduate-credit option is intended for students in the Extension School
graduate program in mathematics for teaching. Please contact the Mathematics for Teaching Office for details. (4 credits)
Galileo wrote that "the book of the universe is written in the language of mathematics." Speaking the language of modern mathematics requires fluency with the topics of this course: infinite series,
integration, and differential equations. The course aims to balance applications and theoretical understanding. Graphing calculators can help with understanding certain concepts and are recommended,
but exams do not require them. The topics covered are not identical to those of a BC advanced placement class, but do overlap with the advanced placement calculus curriculum to a large extent.
Students enrolling for graduate credit participate in weekly pedagogical seminars investigating current research in mathematics education. Prerequisite: a good working knowledge of differentiation and
an acquaintance with integration, as demonstrated by a satisfactory score on the placement test. The graduate-credit
option is intended for students in the Extension School graduate program in mathematics for teaching. Please contact the Mathematics for Teaching Office for details. (4 credits)
*MATH S-1ab
Calculus I and II (30390)
This is a very intensive course covering differential and integral calculus in one variable, including series and some differential equations. We aim to develop theoretical understanding and practical
skills. Some students leave prepared for multivariable calculus; others leave having previewed one-variable calculus. Graphing calculators are recommended but are not used in exams. The topics covered
are not identical to those of a BC advanced placement class but do overlap to a large extent. Prerequisite: a strong interest in mathematics plus an excellent facility with geometry, algebra, and
analytic geometry, including functions, graphs, exponentials and logarithms, and trigonometric functions. Placement test
required. (8 credits)
MATH S-21a
Multivariable Calculus (30189)
To see how calculus applies in situations described by more than one variable, we study vectors, lines, planes, and parameterization of curves and surfaces; partial derivatives, directional
derivatives, and gradients; optimization and critical point analysis, including the method of Lagrange multipliers; integration over curves, surfaces, and solid regions using Cartesian, polar,
cylindrical, and spherical coordinates; vector fields, and line and surface integrals for work and flux; and the divergence and curl of vector fields together with applications. Prerequisite: two
semesters of calculus. Placement test recommended. (4 credits)
Ever wonder where a theorem comes from or why you should believe it? There is much more to mathematics than learning formulas and procedures: studying mathematics is about building and describing
mathematical structures, discovering their properties (your theorems), and convincing yourself and others of your discoveries (by writing proofs). In this class, we start from some basic assumptions
(no calculus necessary) and reason our way together until we have built and described some important concrete and abstract structures. Along the way, students learn the subtle art of mathematical
reasoning, and we convince ourselves of some surprising and sophisticated conclusions, including beautiful results from basic number theory, group theory, and topology. Prerequisites: imagination, a
solid mastery of precalculus, as well as a serious interest in making and critiquing arguments. Placement test
recommended. (4 credits)
Is mathematics invented or discovered? Is its language that of the mind or of the world? How does one actually go about exploring a mathematical topic? Questions such as these inform this course as we
develop a specific branch of mathematics—graph theory—and apply it to a vast spectrum of subjects, from algebra, topology, and computer science to tournaments and transportation. What, for
example, is the most efficient street cleaning system for New York City? The course interests those who teach or are thinking of teaching math, or those who want to help improve the way it is taught
now. Prerequisite: Placement test recommended. (4 credits) |
9780534338Concepts of Intermediate Algebra: An Early Functions Approach
This comprehensive book from Dave Gustafson is perfect for a one-semester course where early coverage of graphing and functions is used to explore the mathematics and applications. All the topics generally found in a one-semester intermediate algebra course are here, but with a modern twist: Gustafson emphasizes conceptual understanding, early treatment of graphing, problem solving, and use of technology (graphing calculators).
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Advanced Algebra II: Conceptual Explanations
Collection Properties
Summary: This is the Conceptual Explanations part of Kenny Felder's course in
Advanced Algebra II. It is intended for students to read on their
own to refresh or clarify what they learned in class. This text
is designed for use with the "Advanced Algebra II: Homework and Activities"
and the "Advanced Algebra II: Teacher's Guide" collections (coming soon) to make up the entire course.
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Students explore the concept of piecewise functions. In this piecewise functions lesson, students graph piecewise functions by hand and find the domain and range. Students make tables of values given a piecewise function. Students write piecewise functions given a graph.
Eleventh graders explore the TI-InterAcitve!. In this Algebra II lesson, 11th graders examine features of the TI-InterActive! including drawing on a Graph, using Stat Plots, exploring the syntax for piecewise functions, and using sliders in order to obtain parametric variations. The lesson is designed to encourage students' creativity.
Students explore the concept of piecewise functions. In this piecewise functions lesson, students find the derivatives of piecewise functions. Students determine points of discontinuity and jumps in the graph using their Ti-89 calculator.
Students explore the concept of piecewise functions. In this piecewise functions lesson, students write functions to represent the piecewise function graphs on their Ti-Nspire calculator. Students determine the formula given the piecewise function graph.
Young scholars explore piecewise functions. In this Algebra II/Pre-calculus lesson, students write formulas for piecewise functions and check their work on the calculator. The lesson assumes that young scholars have seen piecewise functions prior to this activityCalculus students find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise functions.
Learners investigate how to use piecewise functions to describe various situations in everyday life. They explore scenarios such as the intensity of workout routines, the rise and decline of reported cases of malaria, and the varying rate of two hikers on a camping trail. Tasks include writing and graphing a piecewise function to describe a situation, writing a piecewise function when given the function's graph, and interpreting information about the graph of a piecewise function in the context of the problem.
A hands-on lesson using the TI-CBR Motion Detector to provide information to graph and analyze. The class uses this information to calculate the slope of motion graphs and differentiate scalar and vector quantities. There is a real-world activity of a Roof Manufacturer's Test in regards to the pitch of roofs, as well as several other real-world scenarios.
Eighth graders, after researching the properties of graphs of conic sections, absolute value and inverse relations, make a drawing of precise functions and relations from a specified list of equations. The final design should analyze the domains needed for the equations. In addition, they explain completely what was done and why it was done.
Students investigate sonar technology. In this Algebra II lesson, students explore use sound waves to measure distance. The students conduct several experiments with a CBR 2 unit to collect data and graph distance vs. time. Students model the data with piecewise functions.
Students investigate semiconductor chips and its technological use. In this algebra lesson, students use the semiconductor chip as a real life application tool to study functions, linear equations and quadratic equations. They relate the growth in technology because of the conductor chip to exponential functions.
In this solar flare reconstruction worksheet, students read about the 'saturation' point of satellite detectors when solar flares are at their most intense phase of brightness. Kids are given x-ray flare data and they re-plot the data to estimate the peak of intensity. They create 2 exponential functions to fit the data and estimate the peak intensity and time. Students use calculus to integrate one of the functions and calculate the total energy radiated by the flare.
Graph piecewise functions as your learners work to identify the different values that will make a piecewise function a true statement. They identify function notations and graph basic polynomial functions. This lesson includes a series of critical thinking questions and vocabulary.
Learners collect data using the CBL. In this statistics lesson, students predict the type of graph that will be created based on the type of activity the person does. The graph represents heart rate depending the level of activity.
Students discover piecewise functions and analyze slope. In this algebra lesson, students explore slopes through stories and motion based scenario. This activity leads up to constraints being put on the function.
Students investigate piecewise functions. In this algebra activity, students model piecewise functions in the real world. They graph the parts of the functions following the restrictions of the domain |
534469 / ISBN-13: 9780198534464
Visual Complex Analysis
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the ...Show synopsisThis radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.Hide synopsis
Visual Complex Analysis
This book is an exceptional example of the way a fully realized alternate approach to a body of knowledge can reveal new truths about that knowledge and, even more important, a deeper understanding of new ways of approaching knowledge. One of the best books on mathematics I know, and that's not just ...
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The current crop of mathematicians are growing up in a more "visual" world and while the different texts of Brown/Churchill and Bressoud are very good, Needham does an excellent job with visualization of the principles and showing how the pieces fit together from a time-line perspective |
Chapter 3: Graphs, Linear Equations, and Functions 3.1 The Rectangular Coordinate System 3.2 The Slope of a Line 3.3 Linear Equations in Two Variables Summary Exercises on Slopes and Equations of Lines 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Functions
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MATHEMATICS 091
Intermediate Algebra, Individualized - Module 1 (1)
On-campus computer-based instruction. Simplifying and evaluating rational expressions, solving equations involving rational expressions, applications. This is the 1st92
Intermediate Algebra, Individualized - Module 2 (1)
On-campus computer-based instruction. Functions, linear models and graphs, solving linear inequalities, solving absolute value equations and inequalities. The 291 is required. Mandatory P/NC grading.
MATHEMATICS 093
Intermediate Algebra, Individualized - Module 3 (1)
On-campus computer-based instruction. Using rational exponents, simplifying radical expressions, and solving radical equations. This is the 3or higher on the Algebra COMPASS test, or a score of 28 or higher on ther College Algebra COMPASS test. Previous credit for or concurrent enrollment in MATH 092 is required. Mandatory P/NC grading.
MATHEMATICS 094
Intermediate Algebra, Individualized - Module 4 (1)
On-campus computer-based instruction. Solving quadratic equations by completing the square & the quadratic formula, graphing quadratic functions, applications. The 4th btter), or a score of 51 or higher on the Algebra COMPASS test, or a score of 28 or higher on the College Algebra COMPASS test. Previous credit for or concurrent enrollment in MATH 093 is required. Mandatory P/NC grading.
MATHEMATICS 095
Intermediate Algebra, Individualized - Module 5 (1)
On-campus computer-based instruction. Evaluating exponential and logarithmic expressions, solving these types of equations. This is the 5th in a sequence of 5 self-paced courses, MATH 091-095. The 5-course sequence is equivalent to MATH 099. Students must complete the entire MA94 is required. Mandatory P/NC grading.
MATHEMATICS 096
Intermediate Algebra, Individualized - Modules (5)
On-campus computer-based sequence of 1-credit self-paced modules. MATH 091-095. Rational, radical, and quadratic expressions and equations. Introduction to functions: linear, quadratic, exponential, and logarithmic. MATH 081-085 and MATH 091-095 together are equivalent to MATH 080 and MATH 099. Must be completed within one year. Prerequisite: MATH 080 (2.0 or better),99
Intermediate Algebra II (0)
Simplifying and evaluating linear, quadratic, polynomial, radical, rational, exponential, and logarithmic expressions. Solving these same types of equations and inequalities with graphs and applications to real world modeling and investigating functions. Prerequisite: MATH 098 (2.0 or better), or a score of 51 or higher on the Algebra Compass test, or a score of 28 or higher on the College Algebra COMPASS test. Student Option Grading.
MATHEMATICS & 107
Math in Society (5)
Practical applications of mathematics as they arise in everyday life.Includes finance math, probability & statistics, and a selection of other topics. Designed for students who are not preparing for calculus.Prerequisite: MATH 098 (2.0 or better), MATH 099 (2.0 or better), MATH 095 (2.0 or better), or a score of 69 or higher on the Algebra COMPASS test or a score of 35 or higher on the College Algebra COMPASS test. Student Option Grading.
MATHEMATICS 111
Elements of Pre-Calculus (5)
Algebra topics including mathematical modeling, graphing & problem solving w/ polynomial, rational, exponential & logarithmic functions. Applications. Topics from mathematics of finance. Intended for students in business, social sciences & some biological sciences 141
Precalculus I (5)
The elementary functions and their graphs, with applications to mathematical modeling. Examples include linear, quadratic, polynomial, rational, exponential and logarithmic functions, composite functions, inverse functions and transformation of graphs 146
Introduction to Stats (5)
Analysis of data through graphical and numerical methods, linear regression, the Normal distribution, data collection, elementary probability, confidence intervals and hypothesis testing. Emphasis on applications. Prerequisite: MATH 098 (2.0 or better), MATH 099 (2.0 or better),MATH 095 (2.0 or better), or a score of 69 or higher on the Algebra COMPASS test or a score of 35 or higher on the College Algebra COMPASS test, AND placement in ENGL 100 or ESL 100. Student Option Grading.
MATHEMATICS & 148
Business Calculus (5)
Differential and Integral Calculus of elementary functions with an emphasis on business and social science applications. Designed for students who want a brief course in Calculus. (No credit given to those who have completed MATH& 151.) Prerequisite: MATH 111 preferred (2.0 orbetter) or MATH& 141 (2.0 or better), or a score of 70 or higher on the College Algebra COMPASS test. Student option grading.
MATHEMATICS & 151
Calculus I (5)
Definition, interpretation and applications of the derivative. Derivatives of algebraic and transcendental functions. Prerequisite: MATH& 142 (2.0 or better), or a score of 70 or higher on both the College Algebra and Trigonometry COMPASS Tests. Student option grading.
MATHEMATICS & 171
Math for Elem Ed I (5)
Fundamental concepts of numbers and operations related to topics taught at the K-8 level. Topics include problem solving, algebraic thinking, numberation, and arithmetic with rational numbers. Recommended for future elementary teachers. Prerequisite: MATH 098 (2.0 or better), MATH 099 (2.0 or better), or MATH 095 (2.0 or better), or a score of 69 or higher on the Algebra COMPASS test or a score of 35 or higher on the College Algebra COMPASS test, AND placement into ENGL 100 or ESL 100. Student Option Grading.
MATHEMATICS 297
Individual Project in Mathematics (1)
Individual project in a specific area of mathematics. By arrangement with instructor. Prerequisite: Instructor permission, based on evaluation of student's educational and work experience. Student option grading.
MATHEMATICS 298
Individual Project in Mathematics (2)
Individual project in a specific area of mathematics. By arrangement with instructor. Prerequisite: Instructor permission, based on evaluation of student's educational and work experience. Student option grading.
MATHEMATICS 299
Individual Project in Mathematics (3)
Individual project in a specific area of mathematics, by arrangement with instructor. Prerequisite: Instructor permission based on evaluation of student's educational and work experience. Student option grading. |
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry.... more...
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making... more...
The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers.... |
Minimum dimensions (W x D x H)
What's in the box
Calculator Specifications
Auto power off
Approximately 5 minutes
Entry system logic
Algebraic
Graphing Functions
2D plots: function, polar, parametric sequence plots: cobweb, stairstep split screen: plot and table, before-and-after zoom statistical plots: scatter, histogram, box and whisker, normal probability, line, bar, pareto for functions: intersection, extremum, slope, area under a curve and between two curves zoom to a point on a graph or row in a table |
offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and...
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This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems |
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10 Recommended Open Textbooks for College Math Students
Open-source textbooks are popular today especially among students who need to be more practical due to budget constraints. College students who need resource materials in math can check out any of the following books available online for free.
Open-source textbooks are gaining popularity these days. Many students are given the freedom to choose the books they would use when taking college courses. The idea is to enable them to find more practical yet effective resource materials. To date, there are numerous open source books available for free in online and/or PDF versions. Here are 10 of the most recommended for college mathematics courses.
Abstract Algebra: Theory and Applications by Tom Judson. The textbook teaches abstract algebra principles and theory specifically to college students in their junior and senior years. The strengths include a broad range of exercises (computational and theoretical) with nontrivial applications.
Fundamentals of Mathematics by Denny Burzynski and Wade Ellis. As a work text, this book covers traditional topics in modern pre-algebra courses. It also tackles other important topics like elementary analytic geometry, estimation, and introductory algebra.
A Gentle Introduction to the Art of Mathematics by Joseph Fields. This is one of the most popular free open-source math textbooks for obvious reasons. The content focuses on foundations of the subject and introduces students to many important techniques about mathematical proof. Amusing quotations are provided at the start of every chapter.
A First Course in Linear Algebra. The introductory textbook is designed specifically for college sophomores and juniors. The content includes discussions about systems of linear equations. From there, other concepts are covered like matrix algebra.
Analysis 1 by Jairus M. Khalagai. The material is divided into three units. The first consists of analysis on real line; the second is about vector analysis; and the third covers complex analysis. The book is written based on the fact that mathematics is about analysis.
Calculus by Ralph W.P. Masenge. The four-unit module covers everything students should learn about calculus. The first two parts cover basic concepts of integral and differential calculus. The third unit is about sequences of numbers and infinite series. The last is about integral and differential calculus of functions of variables.
Understanding Algebra by James W. Brennan. The book is highly recommended to college students who need a refresher about algebra. This is for those who are preparing for more complex college-level mathematics and who are into homeschooling.
Probability and Statistics by Paul Chege. Students who are studying statistics will find this book most helpful. The three units consist of descriptive statistics, random variables, and probability theory.
Numerical Methods with Applications by Autar K. Kaw. Like many open-source math textbooks, this one is designed to integrate math concepts with practical applications. There are chapters about approximation and errors, differentiation, nonlinear equations, interpolations, and more.
A Modern Formal Logic Primer by Paul Teller. The book has associated solutions manual to serve as guide for students when solving given mathematical exercises. This textbook was originally published by Prentice Hall in 1989 but was pulled out when Pearson Education bought the company. The author was given the right to publish it on his own and so he did but as an open-source materialPerhaps you could write next articles referring to this article. I desire to read more things about it! Great post. I was checking constantly this blog and I am impressed! Extremely useful info particularly the last part
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Summary: CONTEMPORARY BUSINESS MATH FOR COLLEGES, 15th Edition presents an arithmetic-based, basic approach to business math. It emphasizes a practical, skill-building approach to prepare students for careers in business through step-by-step development of concepts, numerous practice exercises, and real-world application of techniques. The text progresses from the most basic to more complex business math topics |
Summary: INT94JV: The Beauty of Mathematics Freshman seminar
Thursdays, 2-2:50pm
Santa Rosa
Instructor: Daryl Cooper
Office Hours: MWF 12-1 or by appointment.
This is a 1 unit class which is graded Pass/No-Pass.
To get a Pass grade you should attend regularly. If you miss a class email me to explain
why. There is no homework. There are no exams. There is reading assigned which you may
choose to do or not. You may if you wish write a paper. You are strongly encouraged to ask
questions.
Some topics we will cover:
various sizes of infinity
fourth dimension
curved space
how can we know some things are impossible, now and for ever?
what is mathematical proof and why is it important?
irrational numbers and music
how many prime numbers are there?
and many other things.
I can lend you a copy of books 1 or 2, but you must pay a deposit which will be returned in |
Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Mathematical achievements of pre-modern Indian mathematicians
Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17th Century of the Christian era. It provides an examination of pre-Modern Indian mathematical contributions that can be valuable to mathematicians and mathematical historiansReviews
Editorial reviews
Publisher Synopsis
"This substantial volume offers a wide selection of demonstrations and examples of the methods of pre-modern Indian mathematics, especially those dealing with indeterminate equations. Readers interested in the worldwide development of mathematics will find this book's abundance of detailed source material, presented in modern notation, a welcome change from the scantiness of the chapters on India in most general histories of mathematics."--Mathematical Association of America online, November 5, 2013 "The book is unique in that its theme is mathematics and only mathematics."--Zentralblatt MATH, 1263.01003Read more... |
A group of related
subjects, such as Algebra, Geometry, Trigonometry, Calculus and
others that concern with the study of number, quantity, shape, and
space, and their inter-relationships, applications, generalizations
and abstractions.
Max
Abbreviate for
maximum.
Maximum
The largest
element of a set.
Mean
Average
Meter
A measure of
length in Metric System. 1 m = 3.28 ft.
Metric
system
Any physical
measuring system of which the units and subunits are related by
multiples of ten .
Micro
Meter
1 micro meter
= m
Midpoint
The point on
a line segment that is equidistant from its endpoints.
Minimum
The least element
of a set. It's abbreviated as Min.
Minus
operation
Subtracting
operation.
Minus
sign
The symbol '-',
indicating subtraction or a negative quantity.
Monomial
An one term
expression.
Multiple
Any number or
polynomial that is the product of a given number or polynomial and
an integral multiplier.
Multiplication
sign
The symbol ·
placed between numbers to be multiplied. In Algebra the multiplication
sign is omitted, we only use it between two numbers. For
example we write 2·3 or (2)(3), ,
,.
Multiplicative
identity
Multiply
To combine two
expressions by multiplication. If the expression has more than one
term, you may use the distributive law. |
Mathematical Palette
THE MATHEMATICAL PALETTE makes mathematics enjoyable, relevant, understandable, and informative for students. Visually engaging, the text features ...Show synopsisTHE MATHEMATICAL PALETTE makes mathematics enjoyable, relevant, understandable, and informative for students. Visually engaging, the text features full color pictures of fine art to bring mathematical concepts to life for the liberal arts student. The text emphasizes problem solving through discovery and applications, encouraging students to become active participants and instilling a rich understanding and appreciation for the beauty of mathematics. Along with its emphasis on writing and critical thinking skills, the text presents the history of mathematicians with numerous, everyday applications to illustrate the evolution and practicality of math and parallel the creativity of liberal arts majors. The Third Edition of THE MATHEMATICAL PALETTE also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes BCA/iLrn Testing and Tutorial, vMentor live online tutoring, and a Book Companion Web Site featuring online graphing calculator |
Essentials of Mathematics for Elementary Teachers: A Contemporary Approach
About this title: The "Essentials" version of Musser, Burger & Peterson's best-selling textbook it brings together the many facets of elementary and middle school mathematics in one concise volume. With a focus on providing a complete understanding of mathematics that translates immediately into the classroom, the authors use their proven formula to present all the core subjects, including: Introduction to Problem SolvingSetsWhole NumbersNumerationNumber TheoryFractionsDecimalsRatioProportionPercentIntegersRational NumbersReal NumbersAn |
Mathematical Discovery 2
Continues the development of linear algebra and calculus from MATH1210. In algebra, students learn how matrices may be simplified by an appropriate choice of coordinates. Known as the eigenvalue technique, this is a very powerful mathematical tool and is used throughout Science and Engineering. In calculus, students learn the mathematics behind algorithms used in calculators for computing exponential, trigonometric and other functions. They are also introduced to functions of several variables and to the notion of a differential equation, which are key concepts in mathematical modelling.
This course is a sequel to MATH1210 and is likewise intended for prospective mathematics majors and those who have a strong background in mathematics. There is substantial overlap with MATH1120; students' performance on this common material is compared and used to scale the marks to ensure that comparable students achieve comparable grades. |
Now available! The Information Literacy User's Guide
Good researchers have a host of tools at their disposal that make navigating today's complex information ecosystem much more manageable. Gaining the knowledge, abilities, and self-reflection necessary to be a good researcher helps not only in academic settings, but is invaluable in any career, and throughout one's life. The Information Literacy User's Guide will start you on this route to success.
The Information Literacy User's Guide is based on two current models in information literacy: The 2011 version of The Seven Pillars Model, developed by the Society of College, National and University Libraries in the United Kingdom and the conception of information literacy as a metaliteracy, a model developed by one of this book's authors in conjunction with Thomas Mackey, Dean of the Center for Distance Learning at SUNY Empire State College. These core foundations ensure that the material will be relevant to today's students.
The Information Literacy User's Guide introduces students to critical concepts of information literacy as defined for the information-infused and technology-rich environment in which they find themselves. This book helps students examine their roles as information creators and sharers and enables them to more effectively deploy related skills. This textbook includes relatable case studies and scenarios, many hands-on exercises, and interactive quizzes.
Real Analysis Textbook
How We got from There to Here: A Story of Real Analysis
Robert Rogers, Eugene Boman
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
Dr. Diane Kiernan, SUNY ESF
Natural Resources Biometrics
Diane Kiernan
Natural Resources Biometrics begins with a review of descriptive statistics, estimation, and hypothesis testing. The following chapters cover one- and two-way analysis of variance (ANOVA), including multiple comparison methods and interaction assessment, with a strong emphasis on application and interpretation. Simple and multiple linear regressions in a natural resource setting are covered in the next chapters, focusing on correlation, model fitting, residual analysis, and confidence and prediction intervals. The final chapters cover growth and yield models, volume and biomass equations, site index curves, competition indices, importance values, and measures of species diversity, association, and community similarity. |
Developmental Mathematics
MAT - 098 Pre-Algebra This is a developmental course in pre-algebra skills. It includes addition, subtraction, multiplication, and division of whole numbers, fractions, decimals, and real numbers. Also covered is a study of percent, the metric system, data analysis, geometry, signed numbers, and equations. Approximately three additional hours per week should be expected using MathXL to complete online homework and tutorial programs. Students in this course may be required to attend the Learning Support Center[1] for additional instruction and skill-building exercises. Semesters offered: Fall, Spring, Summer. 3 Credits
MAT - 099 Elementary Algebra This is a developmental course covering the standard topics in a high school Algebra I course. Included are units on the properties of the real number system, solving linear and quadratic equations, linear inequalities, operations with algebraic expressions, factoring, exponents, and radicals. Simple relations, the concept of a function, and an introduction to graphing are also included. Approximately three additional hours per week should be expected using MathXL to complete online homework and tutorial programs. Students in this course may be required to attend the Learning Support Center[1] for additional instruction and skill-building exercises. Prerequisite: MAT 098 or appropriate score on placement test. Semesters offered: Fall, Spring, Summer. 3 Credits
MAT - 100 Intermediate Algebra This is a developmental course covering the topics course. It includes units on sets and their properties, the real number system, operating with algebraic expressions, factoring, exponents, and radicals. Students solve linear and quadratic equations, and inequalities. There are also units on the properties and graphs of functions and relations including lines, the conic sections centered at the origin, and the exponential and logarithmic functions. Math XL is required. Approximately three additional hours per week should be expected using MathXL to complete online homework and tutorial programs. Students in this course may be required to attend the Learning Support Center[1] for additional instruction and skill building exercises. Prerequisite: MAT 099 or appropriate score on placement test. Semesters offered: Fall, Spring, Summer. 3 Credits |
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Show More enhanced to create a better overall learning experience for the reader. Technology integrated throughout the text helps readers interpret real-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops readers' mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines.Key Topics: Whole Numbers and Problem Solving; Variables and Problem Solving; Problem Solving with Rational Number: Addition and Subtraction of Integers, Fractions, and Decimals; Adding and Subtracting Integers; Adding and Subtracting Fractions; Adding and Subtracting Decimals; Multiplication and Division of Rational Numbers; Multiplying and Dividing Integers; Multiplying and Dividing Fractions; Multiplying and Dividing Decimals; Problem Solving with Ratios, Proportions, and Percents; Problem Solving with Geometry; The Geometry of Two-Dimensional Plane Figures; The Geometry of Three-Dimensional Space Figures; More Problem Solving with Algebra and Models; Mathematical Modeling and Problem Solving Involving Solution of EquationsMarket: For all readers interested in Prealgebra, Algebra |
Keywords: Bounds (3)
An interactive applet and associated web page that show the definition and ...
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An interactive applet and associated web page that show the definition and properties of the bounding box of a polygon or set of points. The bounding box is used in other entries to find area using the so-called box method. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a bounding box when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry and a worked example. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at
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This course is designed to introduce the student to the rigorous examination ...
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This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics algebra, analysis, and topology because it is where the other two fields meet. Upon successful completion of this course, the student will be able to: Use set notation and quantifiers correctly in mathematical statements and proofs; Use proof by induction or contradiction when appropriate; Define the rational numbers, the natural numbers, and the real numbers, and understand their relationship to one another; Define the well-ordering principle the completeness/supremum property of the real line, and the Archimedean property; Prove the existence of irrational numbers; Define supremum and infimum; Correctly and fluently manipulate expressions with absolute value and state the triangle inequality; Define and identify injective, surjective, and bijective mappings; Name the various cardinalities of sets and identify the cardinality of a given set; Define Euclidean space and vector space and show that Euclidean space is a vector space; Define the complex numbers and manipulate them algebraically; Write equations for lines and planes in Euclidean space; Define a normed linear space, a norm, and an inner product; Define metric spaces, open sets; define open, closed, and bounded sets; define cluster points; define density; Define convergence of sequences and prove or disprove the convergence of given sequences; Prove and use properties of limits; Prove standard results about closures, intersections, and unions of open and closed sets; Define compactness using both open covers and sequences; State and prove the Heine-Borel Theorem; State the Bolzano-Weierstrass Theorem; State and use the Cantor Finite Intersection Property; Define Cauchy sequence and prove that specific sequences are Cauchy; Define completeness and prove that Euclidean space with the standard metric is complete; Show that convergent sequences are Cauchy; Define limit superior and limit inferior; Define convergence of series using the Cauchy criterion and use the comparison, ratio, and root tests to show convergence of series; Define continuity and state, prove, and use properties of limits of continuous functions, including the fact that continuous functions attain extreme values on compact sets; Define divergence of functions to infinity and use properties of infinite limits; State and prove the intermediate value property; Define uniform continuity and show that given functions are or are not uniformly continuous; Give standard examples of discontinuous functions, such as the Dirichlet function; Define connectedness and identify connected and disconnected sets Construct the Cantor ternary set and state its properties; Distinguish between pointwise and uniform convergence; Prove that if a sequence of continuous functions converges uniformly, their limit is also continuous; Define derivatives of real- and extended-real-valued functions; Compute derivatives using the limit definition and prove basic properties of derivatives; State the Mean Value Theorem and use it in proofs; Construct the Riemann Integral and state its properties; State the Fundamental Theorem of Calculus and use it in proofs; Define pointwise and uniform convergence of series of functions; Use the Weierstrass M-Test to check for uniform convergence of series; Construct Taylor Series and state Taylor's Theorem; Identify necessary and sufficient conditions for term-by-term differentiation of power series. (Mathematics 241)
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Abstracts
Since 2002, Sweet Briar College has received three National Science Foundation awards for developing curricular materials for undergraduate mathematical biology education. A distinctive feature of the materials is their connection with current and ongoing medical and molecular biology research as well as their emphasis on the critical role mathematics now plays in achieving significant breakthroughs. Partnering with researchers and educators from the University of Virginia, Virginia Tech, and Western Michigan University for the various components of the three projects, we developed a team-taught course in biomathematics, followed by a textbook and a laboratory manual for the course published in 2007. We are now developing a collection of modules for conventional mathematics and biology courses that highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. Calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. This work attempts to address a critical national need for introducing students to mathematical methods beyond the interface of biology with calculus. Our talk presents a summary of the progress we have made since 2002, highlights what we consider to be our strongest accomplishments and weakest points, and maps out steps for further advancing mathematical biology education into the next decade.
Infusing Quantitative Approaches into the Undergraduate Biology Curriculum Kären C. Nelson, University of Maryland
Katerina V. Thompson, University of Maryland
James Sniezek, Montgomery College
William F. Fagan, University of Maryland
A major curriculum redesign effort at the University of Maryland (UM) has brought together teams of faculty, postdoctoral fellows, and graduate students to infuse all levels of our undergraduate biological sciences curriculum with innovative pedagogies, current research approaches, and increased emphasis on interdisciplinary connections and quantitative approaches. Our efforts have largely been guided by the recommendations in the NRC report BIO 2010 (2003) and have resulted in revisions to courses in biology, biochemistry, chemistry, mathematics, and physics. Our MathBench initiative addresses the need for enhancing quantitative proficiency through a series of interactive, web‐based modules that are used to supplement existing course content across the biological sciences curriculum. UM introductory biology students using MathBench showed significant increases in quantitative skills that were independent of previous math coursework, and they were also more willing to attempt to solve quantitative problems, whether or not they ultimately arrived at the correct answer. UM graduates who had used MathBench in their coursework reported a greater appreciation for the essential role of mathematics in modern biology compared to those who had not. We are currently collaborating with faculty at Montgomery College, a nearby 2-year institution, to implement MathBench in introductory biology courses there to ease the transition of the students who subsequently transfer to UM. MathBench modules allow students from diverse educational backgrounds to hone their quantitative skills, preparing them for more complex mathematical approaches that represent the future of modern biology.
Developing Research Skills in Theoretical Ecology: A Research-based Course for Young Undergraduates and High School Students Glenn Ledder, University of Nebraska-Lincoln
Brigitte Tenhumberg, University of Nebraska-Lincoln
As part of an interdepartmental effort to attract promising students to research at the interface between mathematics and biology, we created a course in which a group of recent high school graduates and first-year college students conducts a challenging research project in insect population dynamics. The students set up experiments, collect data, use the data to develop mathematical models, test their models against further experiments, and prepare their results for dissemination. The course is self-contained in that the lecture portion develops the mathematical, statistical, and biological background needed for the research. A special writing component helps students learn the principles of scientific writing and presentation. The course has been very successful and can serve as a prototype for similar courses at other institutions.
An Initiative to Broaden Diversity in Undergraduate Biomathematics Training Gregory Goins, Department of Biology, North Carolina A&T State University
C. Dinitra White, Department of Biology, North Carolina A&T State University
At North Carolina A&T State University (NCATSU), there is critical need to better coordinate genuine research and classroom experiences for undergraduates early in their academic career. Here we describe the development and implementation of an faculty alliance that culminated in a NSF-supported undergraduate biomath (UBM) award (iBLEND). The fundamental purpose of the iBLEND alliance was to inspire under-represented minorities to pursue research careers by increasing the visibility of research conducted at the interface of math and biology at NCATSU. The iBLEND initiative increased exposure and extended benefits to a larger number of our students and faculty, who might otherwise have disregarded research at the interface of biology and mathematics. Because of the many positive impacts, iBLEND gained significant buy-in from administration, faculty, and students by: (1) working from the ground-up with administration to promote campus-wide biomathematics research and training; (2) fostering associations between research and regular undergraduate academic courses; (3) creating and disseminating biomathematics teaching and learning modules and (4) enhancing learning community support at the interface of mathematics and biology. Currently, iBLEND is viewed as a productive site for graduate schools to recruit underrepresented minority students having specific competencies related to mathematical biology.
A Collaborative, Project-Based Approach to Biomathematics at Utah State University Brynja Kohler, Utah State University
In this presentation, I will describe some history of the collaboration among colleagues in Biology and Mathematics and our efforts to integrate mathematics into the laboratory education of biologists. To overcome the passivity and isolation typical of lecture oriented mathematics instruction, colleagues have developed a Biology/Applied Mathematics Instruction Model and a variety of projects in biology to engage students in observation, data collection, mathematical modeling, and the application of mathematics. I will describe one project in detail in which students investigate the diffusion model using brine shrimp from the Great Salt Lake, and share some of the pedagogical aspects of instruction that lead to the successful implementation of these projects.
In response to the call of Bio 2010 for integrating quantitative skills into undergraduate biology education, 30 HHMI program directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI funded mini-grant, led by Karl Joplin of East Tennessee State University, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative approach to undergraduate biology education. This presentation summarizes the results of the 2007 and 2008 summer institutes and a 2009 workshop on using problem based learning to integrate mathematics, biology and computational methods. The consortium developed four draft white papers, a wiki site and a listserv.
One major outcome of these three meetings is a special issue of Cell Biology Education-Life Science Education, that will emerge this fall. Many of the papers in this issue emerged from or were influenced by these meetings. This presentation calls on mathematicians, computer scientists, and life scientists to join us in completing the inventory of resources that can be used in integrating biology, mathematics, and computation and seek to inspire collaborators to develop a single database or digital library that will allow instructors to find resources that they can adopt and adapt to their own institution and students, evaluate resources and share their own resources with the community. The report suggests that the community develop lists of quantitative competencies for entry into graduate programs in the life sciences that parallel the recommendations for future physicians found in Scientific Foundations for Future Physicians: Report of the AAMC-HHMI Committee (AAMC and HHMI, 2009) and calls for new quantitative competencies for all undergraduates that will allow them to become scientifically literate citizens who are able to weigh competing claims and make responsible decisions.
Bio2010 catalyzed a national discussion on how best to prepare future biomedical researchers. How people learn and the need for interdisciplinary approaches to solving complex problems were the basis for recommendations that called for a stronger foundation in mathematics, physical, and information sciences Many colleges and universities reformed their biology curriculum, integrated active learning and inquiry-based laboratory experiences. The report has influenced subsequent reports on preparing students for careers in the life or health sciences, including the AAMC/HHMI Scientific Foundations for Future Physicians report, the Vision and Change report, and the revision of AP Biology. We will review the more recent reports and discuss the need to go beyond current recommendations in light of the information revolution and the urgent need to solve complex problems that our society is facing. We will present some examples of a quantitative curriculum that introduces quantitative concepts through case studies based on authentic data sets.
The Division of Human Resource Development (HRD) of the National Science Foundation is located within the Directorate for Education and Human Resources. The Division's programs aim to increase the participation and advancement of underrepresented minorities and minority-serving institutions, women and girls, and persons with disabilities at every level of the science and engineering enterprise. Programs within HRD have a strong focus on partnerships and collaborations in order to maximize the preparation of a well-trained scientific and instructional workforce for the new millennium.
As the U.S. seeks to strengthen its STEM enterprise as outlined in the America COMPETES Act, the effort demands new resources and tactics for professional STEM workforce development, especially among populations historically underrepresented in STEM fields. Three current programs — the Louis Stokes Alliances for Minority Participation (LSAMP), the Historically Black Colleges and Universities Undergraduate program (HBCU-UP) and Tribal Colleges and Universities Program (TCUP) — have established records of facilitating learning and research by tens of thousands of underrepresented minority undergraduate students pursuing STEM careers.
HRD promotes excellence in STEM education through its highest priorities: the development of a diverse and well-prepared workforce of scientists, technicians, engineers, mathematicians, and educators; creation of a well-informed citizenry; and the design, development, and evaluation of new tools, approaches, and models for learning. Those priorities support access to the ideas and tools of science and engineering for all. EHR's investment in education, research, and infrastructure enhances the quality of life of all citizens and the health, prosperity, welfare, and security of the Nation while educating the STEM workforce of the future.
The mission of the NIH is to improve human health. NIH's ability to carry out this mission rests, in part, on training the next generation of biomedical scientists. Currently, too few quantitatively trained young American researchers are coming into the field. To address this need, the National Institute of General Medical Sciences through its MARC-USTAR program followed the recommendations of Bio2010, a groundbreaking report from the National Academy of Sciences, to enhance undergraduate biology education. To systematically implement Bio2010 recommendations, the MARC Branch provides a competitive funding opportunity that focuses on transformative curricular improvement activities to integrate the quantitative sciences (mathematical, physical, engineering and information) into the study of biology at the undergraduate level.
For the past 6 years the College Board, working directly with teachers, educators, researchers and scientists has been working on development of a new Advanced Placement Biology Curriculum. The work has been guided by evidenced centered design research and is now close to being implemented in AP Biology classes. The content of this new curriculum is structured around four "Big Ideas" of biology—one of which is evolution. The focus on only four "Big Ideas" limits the breadth of material covered in the curriculum while emphasizes the depth of content understanding. For the student this means more of a focus on a broad, but rigorous, conceptual understanding instead of focusing on largely disconnected specifics of biology as so many do in today's classrooms. Importantly, this broad conceptual approach to biology content is coupled with an increased emphasis on the process and skills of doing biology which includes explicit application of mathematical tools and techniques. This is reflected in the content part of the curriculum but should be very apparent in the laboratory component that is currently under development.
Something Like a New Sense: The Biological ESTEEM Collection Anton Weisstein, Truman State University
Gretchen Koch, Goucher College
How can we effectively convey to students the power and utility of quantitative approaches in studying biological systems? In this presentation, we introduce the philosophy and scope of the Biological ESTEEM Project, an open collection of Excel-based curricular modules. After illustrating three pedagogical approaches to integrating math and biology in the classroom, we will demonstrate a sample lesson plan for a pharmacokinetics module.
"It takes a village" – Curricular revision for biology majors at the University of Puerto Rico Michelle Borrero and Migdalisel Colon, University of Puerto Rico-Rio Piedras
The Department of Biology at University of Puerto Rico- Rio Piedras Campus has been conducting an on-going comprehensive curricular revision through which it has delineated several strategies to incorporate quantitative and informatics concepts and skills. With the support of an administrative supplement for curricular improvement in MARC U*STAR Institutions (from NIGMS) we have implemented a course sequence that promotes the development of quantitative skills in biology majors and are revising all medullar courses and laboratories for the integration of the aforementioned skills. Our new curricular sequence takes into account the mathematical content that is required to develop important concepts in our biology courses, and includes it as a pre-requirement for them. As part of this effort, we have assessed the effect of making a statistics course a pre-requirement for Genetics. We developed an assessment instrument that measures student's knowledge of basic statistical and probability concepts and other quantitative concepts applied to Genetics. Using this instrument, as a pre- and post survey, we identified concepts that students are not proficient even after they approve the statistics course. We will present our efforts to achieve student learning of these concepts in the Genetics course. In addition, we will discuss the progress made so far in the curricular revision of the undergraduate laboratory courses as a medium to help our students develop quantitative skills through research-like activities. Finally, we will present the challenges that we have encountered throughout this process and strategies that we have identified to address them.
An Open Source, Open Science Pedagogy for Computational Biology Kam D. Dahlquist and John David N. Dionisio, Loyola Marymount University
One way to attract undergraduates from traditional biology and computer science majors into bioinformatics and to prepare them for future research in this field is to explicitly teach them how to carry out interdisciplinary research within the context of an undergraduate course. From the biology side, open access to large scientific data sets enables students to tackle authentic research problems to solve with software, problems large enough to require team effort. From the computer science side, open source principles, culture, and tools can be leveraged to teach best practices to solve these problems, including up-front project design, program and process documentation, quality control, standards, and project management. Our effort to implement this with computer science majors can be found at We close the loop of this open source, open science pedagogy by releasing the results and products of the research back to the community at large as a resource for further development, analysis, and curricular improvement. We have implemented this pedagogy in a Biological Databases course that is team-taught by a biologist and a computer scientist and is cross-enrolled by both biology and computer science majors. The course culminates in a final project where the students are grouped in teams to create GenMAPP-compatible Gene Databases for new species that are not yet available, using XMLPipeDB, an open source tool chain for building relational databases from XML sources. Each team is divided into the assigned roles of project manager, coder, ID minder, and GenMAPP user. Each team creates a database, uses it to analyze publicly-available microarray data for their species, writes technical documentation and a scientific paper, and releases the database and code back to the community. The students each contribute their domain-specific skills in biology and computer science, while learning how to work with colleagues from the complementary discipline.
Looking back at six years of support of undergraduate biomathematics at Geneseo, we have an opportunity to evaluate our experience and suggest lessons that might help similar institutions as they improve the quality of the experiences that they provide their students. We have found that maintaining our emphasis on the student research experience, combined with targeted institutional curricular change, has allowed the impact of the NSF grant money to be felt more broadly across the campus. Focusing on providing intense undergraduate research opportunities has given us the flexibility to adapt to changes in personnel and research interests over the years, and has put us in a position where we feel that the changes in the campus culture that we have fostered will bring long-lasting benefit to the institution.
BioMaPS at Murray State University: A Collaborative Research Experience Terry Derting and Renee Fister, Murray State University
We will highlight the progress made at addressing research problems at the intersection of biology and mathematics in the context of an NSF-UBM program, BioMaPS (Biology and Mathematics in Population Studies) at Murray State University. The program involves teams of biology and mathematics students with biology and mathematics faculty working collaboratively through a year-long research initiative. Discussion will involve the successes and challenges involved in providing and assessing an integrative program that captures the creativity of research, introduces an interdisciplinary biomathematics course curriculum, and produces collaborative results. The skills that the students gain allow them to connect their separate disciplines into a complementary biomathematical whole. Assessment related to the educational gains of students and contributions of the program to training future STEM professionals will be presented.
The goal of the REBMI program is to prepare undergraduate students to work on interdisciplinary teams that tackle "translational", real-life challenges at the interface between biology and mathematics. By creating "unstructured, open-ended" environments within active research laboratories, we leverage the strong and uncommonly open-mindedness of liberal arts students while at the same time exposing them to "real world" research experiences. In our presentation we review the successes and failures of our program and how our experiences are re-shaping the ways we think about preparing biologists and mathematicians to work together. Our observations emphasize that the effectiveness of team research depends not only on the individual expertise of the team members, but also on basic project management skills, for example, work scheduling, identified roles, meetings, priorities, deliverables, problem anticipation, and deadlines. Thus it will be necessary to modify undergraduate curricula to include team project management skills such as these so that the promise of MATH-BIO 2010 initiatives can be realized in the workplace.
Blending Biology and Math is not a one-time intervention. Students need to utilize math in their biology courses and see biological applications in their math courses. We have produced a range of curricular materials to blend math and biology. Using research as a motivating force, we have mentored interdisciplinary math-biology team projects that stimulate students to take courses outside their major. The Genome Consortium for Active Teaching (GCAT; has empowered over 300 teachers to bring genomics into their curriculum through DNA microarrays. Now GCAT is bringing synthetic biology to faculty through investigative lab modules and faculty workshops. The last major obstacle to genuine reform is the traditional introductory biology course. We are implementing a new course that revives biology as a science, unifies small and big biology and highlights the role of math. We have applied the advice in How People Learn to produce a fresh approach to biology that will change the way you teach and how your students learn. All of our advances in education have been part of a new concentration in genomics, which formally recognizes the accomplishment of students who integrate their education with biology and math.
Getting Ahead in Math Bio Ed: towards a National Plan for Undergraduate Quantitative Life Science Education Louis J. Gross, Professor of Ecology and Evolutionary Biology and Mathematics Director
National Institute for Mathematical and Biological Synthesis (NIMBioS.org) University of Tennessee, Knoxville
Despite several decades of efforts to develop and encourage quantitative components in life science undergraduate programs, there remains a disconnect between the formal mathematics education that most undergraduate biology students are exposed to and the direct application of this in their life science instruction. A variety of recent reports as well as expected modifications to the main test used in the US medical school admission process present a unique opportunity to develop a national-scale initiative to assist a broad array of institutions to enhance the mathematics components of their biological sciences curriculum, as well as the biological components of their mathematics curriculum. Such a plan necessarily should incorporate the needs of differing institutions, the variety of curricular trajectories of students, and a method to assess these efforts. I will discuss the NIMBioS plans for this initiative and the potential for collaborations with many stakeholders. |
text on linear algebra is split into two parts. The first treats the subject at an elementary level, although it does not compromise on the development of theory. Acquaintance with the basic matrix computations would be an advantage, but is not assumed. Throughout, Jacob emphasizes the "the reasons why" rather than simply "how to compute". The second part deals with more advanced topics. |
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Logic I - Tools for Thinking Student text
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316 pages
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reusable—not a workbook
Logic I: Tools for Thinking is used as an introductory or second-year textbook for students in grades 8 or 9 and above (and some 7th graders), in homeschool, co-op, and Christian school settings. Logic I: Tools for Thinking covers a wide range of topics in both formal and informal logic accurately and engagingly. Humorous and serious examples are drawn from a wide range of subject areas: religion, history, politics, literature, science, taxes, and more. If you're looking for in-depth coverage at a sensible pace—with no logic background required—and you want a thoroughly Christian perspective on logic, then Logic I: Tools for Thinking is for you.
Scope of Logic I: Tools for Thinking
Logic I begins with vital foundational topics: thinking and reasoning, what logic is, language and how it relates to logic.
The course then moves on to statements and logical operators, along with various tools to use on them. Topics include negation, contradiction, conjunction, disjunction, equivalence, and implication.
On this foundation one of the most useful modern formal (or deductive) logic systems, the sentential calculus, is developed in detail. Formal logic has broad application in such areas as mathematics and computer programming.
The book closes with a substantial section devoted to informal (or inductive) logic. Informal logic encompasses the types of arguments students encounter on a daily basis.
This combination of formal and informal logic topics makes Logic I: Tools for Thinkingunusual in its breadth and usefulness. If you're looking for a substantial, year-long course which will strengthen your child's thinking skills (and stimulate yours too!), this course is for you.
What do I order?
If you will be schooling more than one child, order one student book for each child you are teaching, plus one student book and one teacher's manual for yourself.
If you will be schooling just one child and do not mind sharing the student book, then just order one teacher's manual and one student book, total. If you will be schooling just one child but want your own student book, then order one teacher's manual and two student books. (Note that the student book is not a workbook; all exercises are done on separate paper. So sharing the student book is possible even if you, too, wish to do all the exercises.)
Will I need a new book each year for each student?
No, that won't be necessary because of the durable construction (heavy-duty laminated cover with plastic spiral binding, not comb binding). Schools generally get several years' use out of one student book. |
Twelfth graders examine the Taylor Series. In this calculus activity, 12th graders explore the representation of a function as an infinite sum of terms calculated form the values of its derivatives at a single point, hence the Taylor Series. Students use a TI-89 to explore the patterns and the command to compute the Taylor series.
In this calculus worksheet, students find the Taylor series for each function adn give the interval where the series converges. The two page worksheet contains nine questions. Answers are not included.
Students analyze taylor series for convergence. In this calculus lesson, students analyze the graph of a taylor series as it relates to functions. They use the TI calculator to graph and observe the different series.
In this Taylor Series activity, students explore functions with an infinite series. They complete an integral of convergence and explore the degree of the polynomials. This four-page activity contains four multi-step problems.
In this calculus worksheet, students solve various functions for the Taylor Series using a variety of solving methods including the double angle formula, partial fractions, and u substitution. There are 8 questions.
Students find patterns in a sequence. In this sequences and series lesson, students use their calculator to find the sequence of partial sums. They graph functions and explore convergent series. Students approximate alternating series.
In this interval instructional activity, students determine the interval and radius of convergence of given equations. They use the Taylor series to identify points and the radii of convergence. This two-page instructional activity contains 8 multi-step problems.
In this college level calculus worksheet, students compare two series to compute the error given the number of terms added. Students write the Maclaurin and Taylor series for the given functions. The two page worksheet contains seven problems. Answers are not provided.
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a complex number and write a complex number in the form z = r (cos _+isin_), and finally, how to write a complex number in exponential form using EulerÕs relations.
Teaching elastic forces in your physics class is a snap with this resource! Scholars compare the stretch of rubber bands with differing width, then measure the stretch of a spring and calculate force. In a whole-class experiment, wire is attached to the ceiling and stretched by adding weights to the loose end. When the weights are removed, does the wire return to its original length? Materials lists, procedures, background information and assessments are all provided for your convenience.
Help your pupils define a Taylor polynomial approximation to a function f of degree n about a point x = a. After completing several problems with guided practice, individuals graph convergence of Taylor polynomials and use them to approximate function values.
In this Taylor and Maclaurin series learning exercise, students answer 10 questions about Taylor and Maclaurin series. Students find the Taylor and Maclaurin series for trigonometric, exponential, and inverse functions at a given value.
In this calculus worksheet, students solve functions using the derivatives. They calculate the volume where the graph is revolving around the x-axis, a line, the y-axis and where x=e. There are 28 questions.
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Taylor Series |
A Closer Look at Tests of Significance -- Which Test?, A Closer Look at Tests of Significance Algebra I Second Edition is a clear presentation of algebra for the high school student. Volume 1 includes the first 6 chapters and covers the following topics: Equations and Functions, Real Numbers, Equations of Lines, Graphs of Equations and Functions, Writing Linear Equations, and Linear Inequalities 1 includes the first Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equ Probability and Statistics – A Short Course is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transform 2 includes the last Advanced Probability and Statistics-Second Edition is a clear presentation of the basic topics in statistics and probability, but finishes with the rigorous topics an advanced placement course requires. Volume 1 includes the first 6 chapters and covers the following topics: Analyzing Statistical Data, Visualizations of Data, Discrete Probability Distribution, Normal Distribution, and Experimentation Algebra, Volume 2 Of 2 FlexBook covers the following six chapters:Systems of Equations and Inequalities; Counting Methods - introduces students to linear systems of equations and inequalities as well as probability and combinations. Operations on linear systems are covered, including addition, subtraction, multiplication, and division. Exponents and Exponential Functions - covers more complex properties of exponents when used in functions. Exponential decay and growth are considered, as are geometric sequences and scientific notation. Polynomials and Factoring; More on Probability - introduces students to polynomials and their basic operations as well as the process of factoring polynomials, quadratic expressions, and special products. Also considered is probability through compound events. Quadratic Equations and Functions - introduces students to quadratic equations and various methods of solving them. Also considered is the discriminant and linear, exponential, and quadratic models. Radicals and Geometry Connections; Data Analysis - covers the concept of the radical and its uses in geometry, including the Distance and Midpoint Formula and Pythagorean's Theorem. Also considered are methods of analyzing data with charts and graphs. Rational Equations and Functions; Statistics - covers rational functions and the operations of rational expressions. Students learn to graph rational functions, divide polynomials, and analyze surveys and samples.' |
67137 / ISBN-13: 9780321567130
Basic College Mathematics
Normal 0 false false false The Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into ...Show synopsisNormal 0 false false false The Tobey/Slater/Blair/Crawford series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical "building block" organization makes it easy for students to understand each topic and gain confidence as they move through each section. Students will find many opportunities to check and reinforce their understanding of concepts throughout the text. With this revision, the author team has added a new Math Coach feature that provides students with an office hour experience by helping them to avoid commonly made mistakes. With Tobey/Slater/Blair/Crawford, students have a tutor, a study companion, and now a coach, with them every step of the way.Hide synopsis
...Show more Whole Numbers, Fractions, Decimals, Ratio and Proportion, Percent, Measurement, Geometry, Statistics, Signed Numbers, Introduction to Algebra, Consumer Finance Applications, Tables, Scientific Calculators. For all readers interested in basic college mathematics.Hide
Description:Teacher edition in good condition. Pages are clean and the...Teacher edition in good condition Basic College Mathematics
The book was in good condition, as stated by the seller. I looked through it and it seems to be just what I need to help me brush up on the "basics" before I go ahead with an advanced Math class later this year. Thank you!
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61 and taking a Career Readiness class that includes basic math. This book helped me to score in the highest level. Easy to understand, even for a silver hair who embraced her Texas Instruments Calculator decades ago and never let go |
reflects more than 25 years of author involvement with business math education and the business community. The focus of this edition is on linking mathematics with real business practices in real businesses--giving readers a better appreciation for and understanding of the concepts that are vital in the business world.The book is filled with
Table of Contents
1. Whole Numbers. Place Value and Our Number System. Read whole numbers. Write whole numbers. Round whole numbers. Operations with Whole Numbers-Five-Step Problem-Solving Strategy introduced with addition and continued throughout text. Add whole numbers. Subtract whole numbers. Multiply whole numbers. Divide whole numbers. 2. Fractions. Fractions. Identify types of fractions. Convert an improper fraction to a whole or mixed number. Convert a whole or mixed number to an improper fraction. Reduce a fraction to lowest terms. Raise a fraction to higher terms. Adding and Subtracting Fractions. Add fractions with like (common) denominators. Find the least common denominator for two or more fractions. Add fractions and mixed numbers. Subtract fractions and mixed numbers. Multiplying and Dividing Fractions. Multiply fractions and mixed numbers. Divide fractions and mixed numbers. 3. Decimals. Decimals and the Place-Value System. Read and write decimals. Round decimals. Operations with Decimals. Add and subtract decimals. Multiply decimals. Divide decimals. Decimal and Fraction Conversions. Convert a decimal to a fraction. Convert a fraction to a decimal. 4. Banking. Checking Account Forms. Make account transactions. Record account transactions. Bank Statements. Reconcile a bank statement with an account register. 5. Equations. Equations. Solve equations using multiplication or division. Solve equations using addition or subtraction. Solve equations using more than one operation. Solve equations containing multiple unknown terms. Solve equations containing parentheses. Solve equations that are proportions. Using Equations to Solve Problems. Use the problem-solving approach to analyze and solve word problems. 6. Percents. Percent Equivalents. Write a whole number, fraction, or decimal as a percent. Write a percent as a whole number, fraction, or decimal. Solving Percentage Problems. Identify the rate, base, and portion in percent problems. Use the percentage formula to find the unknown value when two values are known. Increases and Decreases. Find the amount of increase or decrease in percent problems. Find the new amount directly in percent problems. Find the rate or the base in increase or decrease problems. 7. Business Statistics. Measures of Central Tendency. < |
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Overview
This text is an unbound, binder-ready edition.
Calculus: Early Transcendentals, 10th Edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. Calculus: Early Transcendentals, 10th Edition excels in increasing student comprehension and conceptual understanding of the mathematics. The new edition retains the strengths of earlier editions: e.g., Anton's trademark clarity of exposition; sound mathematics; excellent exercises and examples; and appropriate level, while incorporating more skill and drill problems within WileyPLUS.
The seamless integration of Howard Anton's Calculus: Early Transcendentals, 10th Edition with WileyPLUS, a research-based, online environment for effective teaching and learning, continues Anton's vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.
Chapter 5 Integration
5.1 An Overview of the Area Problem
5.2 The Indefinite Integral
5.3 Integration by Substitution
5.4 The Definition of Area as a Limit; Sigma Notation
5.5 The Definite Integral
5.6 The Fundamental Theorem of Calculus
5.7 Rectilinear Motion Revisited Using Integration
5.8 Average Value of a Function and its Applications
5.9 Evaluating Definite Integrals by Substitution
5.10 Logarithmic and Other Functions Defined by Integrals
Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering
6.1 Area Between Two Curves
6.2 Volumes by Slicing; Disks and Washers
6.3 Volumes by Cylindrical Shells
6.4 Length of a Plane Curve
6.5 Area of a Surface of Revolution
6.6 Work
6.7 Moments, Centers of Gravity, and Centroids
6.8 Fluid Pressure and Force
6.9 Hyperbolic Functions and Hanging Cables |
Pre-calculus Module 1
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Standards Addressed by this Resource
G.CO.2:Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.4:Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5:Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Submitted by Emily on Tue, 05/14/2013 - 11:14pm
Pre-calculus Module 1: Complex Numbers and Transformations
Module 1 sets the stage for expanding students' understanding of transformations by first exploring the notion of linearity in an algebraic context. This quickly leads to a return to the study of complex numbers and a study of linear transformations in the complex plane. Thus, Module 1 builds on standards N-CN.1 and N-CN.2, introduced in Grade 11, and standards G-CO.2, G-CO.4, and G-CO.5, introduced in Grade 10. |
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This textbook is a well-organized treatise on calculus. The author intuitively provides detailed and intensive explanations fulfilling beginner's needs. The book is both useful as a reference and a self-taught manual of calculus.
Editorial Reviews
Book Description
Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics.
About the Author
Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology and an Honorary Fellow of Balliol College, of the University of Oxford, UK. His current research interests include linear algebra, wavelets and filter banks, applied mathematics, and engineering mathematics. He is the author or co-author of six textbooks and has published a monograph with George Fix titled "An Analysis of the Finite Element Method." Professor Strang served as SIAM's president from 1999-2000, chaired the US National Committee on Mathematics from 2003–2004, and won the Neumann Medal of the US Association of Computational Mechanics in 2005. He is a fellow of the American Academy of Arts and Sciences.
More About the Author
Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004.
Most Helpful Customer Reviews
I used to consider Stewart's Calculus as an ideal beginner text but this book by Gilbert Strang tops it significantly. This is a great book if you have been away from calculus for a number of years and now want a fairly in-depth treatment beyond the "Calculus for Dummies" genere. Things are presented very well and the tone is almost conversational. For the self-learner who has the time and inclination this text is ideal. There are a goodly number of diagrams and examples.
To top it all off this book is available for free at the MIT Open Course website: [...] In addition to the textbook the website has the Instructor's Manual and the Study Guide.
Excellent resource specially considering how expensive even mediocre calculus textbooks are today. I purchased a used copy since I find reading textbooks on the web gets old real quick. A must have.
If you intend to teach yourself calculus, or if you are looking for a text for review, this one would be an excellent choice. The topics are well explained and well motivated by applications. The book covers a wide array of topics and each of them is clearly developed. I would choose this as the text for a class if I were to teach it. I certainly recommend it for those learning outside the structure of a classroom.
I first saw this book as a MIT textbook. Read it briefly and absolutely loved it. I learnt Calculus many years ago and hope I had this book then. The book is so clear written and easy to understand. I am buying this book for my son now. I am sure it will be a great help for anyone reads this.
Clearly, for some people, Strang's book is better than anything else that they've encountered. Good for them. But for me, when reading it, I feel like a schizophrenic person is yelling at me. All the short sentences, exclamation marks, and off-topic tangents make it "conversational" for sure, but they also distract from the concepts and make the book harder to read. Honestly, I tried reading it - I read the introduction, I read different parts throughout the book, but the same thing kept happening. I've gone through many, many calculus books, and yes, many of them are the same, but I don't think that a book being different makes it necessarily better in this case. If Strang's style resonates with you, more power to you, but I must warn all those looking for a "clear" exposition that his writing (at least in the 1st edition) is completely all over the place, and has given me a mini-migraine.
To give a minor example of his machine gun rapid fire style of writing, at the beginning of the derivatives section he writes:
"This chapter begins with the definition of the derivative. Two examples were in Chapter 1. When the distance is t^2, the velocity is 2t. When f(t)=sin t, we found v(t)=cos(t). The velocity is now called the derivative of f(t). ... [and later...] Note that 'f is not ' times f! It is the change in f. Similarly, 'delta t is not ' delta times t. It is the time step, positive or negative and eventually small."
His characteristically short sentences make me feel like I'm reading a genius 4th grader's work. Maybe it helps students who can't read long sentences, but it makes it less conversational for me, and has the effect of making the text feel robotic and jolty.Read more ›
This is a great self-teaching text. I'm currently in high school and I wanted to get a little ahead of the game so I searched for online calculus texts and found this one. The website ( MIT Text Publications) has all the chapters in pdf format complete with the answers to the odd numbered questions. Uses interesting examples such as the application of calculus to physics and economics.
I have read a great many calculus books at all levels. In my opinion, this is the best single book currently in print for a first course in calculus - especially for those who will go into applied mathematics, engineering or physics. Strang is one of the best, if not the best, teachers of mathematics in the United States. The treatment given in this book is physical and brings the subject to life. Strang uses the odometer and speedometer to give an initial motivation for the differential and integral branches of the subject. This is a simply brilliant approach. Although many ivory tower math types might disagree, mathematics is not just a set of formal rules like a game of chess. The true importance of mathematics is to provide a language to describe the physical world around us. Any introductory calculus text that ignores this fact is doing the student a terrible disservice. This is why, although I have much respect for these texts, I would never recommend the treatments by Apostol or Spivak for a first course in Calculus.
This book has excellent explanations, and is well organized. Usefull as a reference, and to teach yourself calculus. I used it all through college as a supplement (and sometimes replacement) for the assigned text. |
Principles of physics designed to provide students with a mathematically based (non-calculus) understanding of electricity, magnetism, optics and modern physics including electric and magnetic fields, DC and AC circuits, geometrical and wave optics, polarization, and an introduction to relativity and quantum mechanics are covered. For students in arts, science, architecture and pre-professional programs. |
Marina Del Rey Physics Chicago, as part of my coursework in graduate school for my Master's degree, we had to use linear algebra and have an advanced knowledge of it to understand astronomy, cosmology, and astrophysics. Star behavior and other astronomical calculations are dependent on the use of |
Contemporary Precalculus: A Graphing Approach
Book Description: Hungerford integrates graphing technology into the course without losing sight of the fact that the underlying mathematics is the crucial issue. Mathematics is presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. The concepts that play a central role in calculus are explored from algebraic, graphical, and numerical perspectives. Students are expected to participate actively in the development of these concepts by using graphing calculators (or computers with suitable software), as directed in the Graphing Explorations, either to complete a particular discussion or to explore appropriate examples |
Mathematics
It is the goal of the mathematics department that every student will develop a competence in fundamental mathematical processes and a foundation for logical thinking. In accordance with the National Council of Teachers of Mathematics Standards, an emphasis is placed on problem-solving techniques. TI-84 Plus graphing calculators are introduced in Algebra I and used extensively beginning in the second year of algebra. In our highly technological society all young women must increase their mathematical sophistication so that their future career options will be kept open.
The study of mathematics is required through the junior year and strongly recommended for senior year. Every student must complete two years of algebra and a year of geometry. The mathematics department places a student in the course and level most appropriate to her aptitude and preparation. Placement in all math classes is based on departmental recommendation and is determined by a student's overall academic performance as well as a good aptitude for mathematical reasoning and active learning.
Courses in this department:
Math
Algebra I
Credit: 1 (if taken in 9th grade or above)
Students entering this class are expected to have already studied positive and negative numbers, the basic properties of numbers, and simple equations. The course covers all topics of elementary algebra, including verbal problems, factoring, graphing of linear equations, radicals, solving linear and quadratic equations, and linear systems.
Honors Algebra I
Credit: 1 (if taken in 9th grade or above)
This course is for students who have a strong background in arithmetic facts and skills and in elementary algebra, including positive and negative numbers, the basic properties of numbers, and simple equations. They must have demonstrated a good aptitude for mathematical reasoning. The course covers all topics of elementary algebra, including verbal problems, factoring, algebraic fractions, graphing of linear functions, radicals, solving linear and quadratic equations, systems of equations, variations, and the quadratic formula.
Geometry
Credit: 1
This course is for students who had had a full year of elementary algebra. Plane geometry relationships are developed as part of a logical system, and the student learns to write short proofs based on these relations. Algebraic and numerical applications are provided, and units on right triangle trigonometry, three-dimensional figures, and coordinate geometry are included.
Honors Geometry
Credit: 1
This course is for students who have a strong mathematical background, good insight, and solid problem solving skills. Plane geometry relationships will be explored in depth with algebraic and numerical applications provided. Units on congruence, similarity, polygons, right triangles, trigonometry, circles, plane and solid figures, and coordinate geometry will be included.
Algebra II
Credit: 1
This course is for students who have had a full year of elementary algebra. The year consists of a review and extension of Algebra I topics including inequalities, linear equations, operations with polynomials, and application of algebraic skills through verbal problems. Additional topics include functions, complex numbers, and quadratics graphs.
Honors Algebra II
Credit: 1
This course is for students who have a strong background in elementary algebra, including systems of equations, radicals, and quadratics. They must have demonstrated a good aptitude for mathematical reasoning. This course begins with an extension of Algebra I topics and continues with the study of complex numbers, quadratic functions, rational and polynomial functions, rational and polynomial functions, exponents, radicals and logarithms.
Trigonometry
Credit: 1
This course consists of a review of advanced algebraic topics as well as an exploration of basic trigonometry. The algebraic topics include quadratic functions and their applications, composite and inverse functions, exponents, radicals and logarithms. The study of trigonometry consists of right triangle and general triangle relationships and applications, the unit circle, and sine and cosine graphs.
Precalculus
Credit: 1
This course is for students who have a strong background in advanced algebraic topics. The transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis is a challenging one that students must make in this challenging course. Students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively in order to make connections and to contribute to class discussions and discoveries. Topics reviewed and studied consist of various functions (including compositions, inverse, polynomial, rational, exponential and logarithmic) and trigonometry.
Honors Precalculus
Credit: 1
This course is for students who have a strong background in advanced algebraic topics and have demonstrated a good aptitude for mathematical reasoning and intellectual curiosity. The transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis is a challenging one that students must make in this challenging course. Precise arithmetic and algebraic skills are essential to ensure accurate data for proper analysis and to attain a strong level of command and understanding of the concepts studied. Students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively in order to make connections and to contribute to class discussions and discoveries. Topics reviewed and studied consist of several types of functions (including compositions, inverse, polynomial, rational, exponential, logarithmic and circular) and an introduction to limits.
Honors Calculus
Prerequisite: Precalculus or Honors Precalculus Credit: 1
This course is a survey of topics in Calculus from limits and continuity to basic differentiation. It is an opportunity for students to integrate ideas from algebra and geometry to do analytical applications of trigonometry, rational functions, compositions and logarithmic functions. It is a course geared toward deeper understanding of the material but without the focus being on preparing for the AP exam. Students enrolled in this course will not be permitted to take the AP Calculus exam.
AP Calculus - AB
All students registered for this course must take the AP exam. The methods and techniques of differential and integral calculus are developed and applied to algebraic, trigonometric, logarithmic and exponential functions. Students are required to use a graphing calculator. A thorough review of the year's work is made in the final weeks before the AP exam.
AP Statistics
Open to Grade 12 Prerequisite: Precalculus Credit: 1
The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:
Students who successfully complete the course and exam may receive credit, advanced placement, or both for a one-semester introductory college statistics course.
Introduction to Computer Science
Open to Grades: 10-12 Spring Semester Credit: .5
This course focuses and engages the entire discipline of computer science. By demystifying computer hardware and how it works, using computer software and exploring design and implementation, problem solving and developing software, and understanding how computers, people and society interoperate in this course, we will look to build quantitative reasoning skills and a basis for future survival and exploration in our advancing world.
AP Computer Science
Advanced Placement Computer Science studies topics commonly found in college courses, and aims to prepare students for taking the Advanced Placement test in the Spring. Topics include: critical thinking and problem solving, algorithm development, data structures, and Object-Oriented programming. The course will be taught using Java.
The Girls' School Advantage
Meet Heejin, '14
Favorite class:
This may sound cliché, but honestly I enjoyed almost all classes offered at Walker's because they all allowed me to mature tremendously both intellectually and spiritually. But if I have to choose one, it would be Honors English 11. Although this class was one of the most demanding courses of my life, it was a pleasure for me to take an advanced English course as an international student. At the beginning of the year, I struggled a lot with much anxiety, but I can certainly say that by the time the year ended, I left the classroom with a smile.
- Heejin, '14
South Korea |
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems...
see more
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems regarding abstract algebra. Included is a Table of Contents that lists the topics such as Integers, Functions, Groups, Polynomials, Galois Theory, Unique Factorization, etc. There is also a link to an online study guide for the topic.
This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" ("...
see more
This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" (" target=״_blank״ as part of the MERLOT Classics Series on Elluminate. It is a good opportunity to explore the site from the authors' eyes and to gain insight into how they use it in classes.It would be good for a faculty development workshop or for individual enjoyment.
This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever...
see more |
calculus : Java Glossary
The mathematics for computing speed given distance at any point (derivative), or distance given speed at any
point (integration), and similar problems. Solutions can be done numerically or sometimes analytically by a
process similar to algebra. Integration in 3D is one of the most satisfying flavours of mathematics. If you ever
get a chance to study it, take it. I remember being amazed when I learned to analytically calculate temperatures
in a complex object given the simple rules of how heat flows. The most complicated thing I ever did
professionally with calculus was compute the volumes of irregular blast regions in a giant bread-shaped cavern at
the Peace River power project. In 2001, I used some elementary calculus to discover the
World Trade towers on 9-11 did not collapse by gravity alone, a fact I consider of paramount political
importance. Unfortunately, the average citizen is so ignorant of mathematics, they don't understand or
trust the argument. |
Contents
The mathematics program at St. Olaf is nationally recognized for innovative and effective teaching, for scholarship, and for service to the profession. We see mathematics as interesting, important, useful, and appropriate for students with a wide variety of interests. Welcome to our mathematical community.
What's Happening in St. Olaf Math?
Watch this spot for news of colloquia and other weekly events.
Every Week!
1. Math Problem Solving Group
Day, Time, Room still to be determined
The Math Problem Solving Group meets weekly to work on a variety of problems, often with a central theme, and to discuss problem-solving strategies. Additionally, students can use the meetings to prepare for the MAA North Central Section Team Contest, the Putnam Exam, the Konhauser Problemfest, the COMAP modeling contest, and other math competitions. This is an excellent exercise for students pursuing careers in math education and for students contemplating graduate mathematical study.
Interested students should contact Prof. Gower (gower@stolaf.edu) by Friday, September 19. Please indicate which night(s) of the week are best for you and any nights that absolutely do not work for you. Please try to be as flexible as possible with scheduling.
2. Weekly MSCS Game Night, Wednesdays 6:45 P.M.
Science Center 188
All game enthusiasts are welcome to come to SC 188 on Wednesday nights at 6:45 PM to play a variety of mathematical and other board games. Past games have included Hawaiian checkers, and Settlers of Catan, to name a few.
Goodies will be served.
Why you should be there:
Lots of Fun
Meet new friends
Improve your reasoning skills
3. GRE Review Sessions
If you are planning to take the GRE Mathematics Subject test this year, now is the time to review. This fall, Professors Gower and Ufferman will be holding evening review sessions for the GRE math subject test. If you are interested in attending the sessions, please email Eric Ufferman (ufferman@stolaf.edu) by Friday, September 12th. Please indicate which night(s) of the week are best for you, any nights that absolutely do not work, and which date you are taking the test. Please try to be as flexible as possible with scheduling.
Department News
Class of 2010: There will be 79 mathematics majors graduating in the class of 2010 -- one of the biggest classes ever, and the 2nd largest major (behind Biology) in 2010. Congratulations to the students, parents, and faculty who helped this happen!
Goodbyes: At graduation we say goodbye not only to 79 mathematics majors, but also to Professors Delia Letang and Mike Weimerskirch. Delia will begin a tenure-track position at Century College (part of the MNSCU system) in the fall, and Mike will be working closer to home at Macalester College. Thanks to both of them for their excellent service to St. Olaf.
See you laters: Professors Olaf Hall-Holt, Bruce Hanson, and Kay Smith will be on sabbatical next academic year. Olaf and Kay will be gone the entire year and Bruce will be gone during spring.
Award winners:
Nathan Clement '10, Mat Deram '11, and Vladimir Sotirov '12 took first place in the 18th Annual Konhauser Problemfest, held February 27th at the University of St. Thomas; they scored 85 points of 100. Better still, the trophy for the competition returns to St. Olaf for the second straight year. The Konhauser contest, named for the late Macalester mathematics professor Joe Konhauser, pits 3-person teams against challenging problems. No fewer than 18 Ole mathematics majors participated this year, including Mckenzie West, Amelia Stonesifer, Cathryn Holm, Bjorn Wastvedt, Thu Tran, Cameron Marcott, Trevor Knapp, Thomas Hegland, Benjamin Simmons, Daniel Bryant, Warren Shull, Joshua Wilson, Ling Gu, Yan Jing, and Yujie Li. Congratulations to all. |
More About
This Textbook
Overview
Mathematical reform is the driving force behind the organization and development of this new precalculus text. The use of technology,primarily graphing utilities,is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology,wherever appropriate. The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically,as well as algebraically. Proceeding in this way,students gain a broader,deeper,and more useful understanding of a concept or process. Even though concept development and technology are emphasized,manipulative skills are not ignored,and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme.
The second major objective of this book is the development of a library of elementary functions,including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes,students will be able to move into calculus with greater confidence and understanding. In addition,a concise review of basic algebraic concepts is included in Appendix A for easy reference,or systematic review.
The third major objective of this book is to give the student substantialexperience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journalsandprofessional books. No specialized experience is required to solve any of the |
Description:
This page, by historians Tracy Lai and Ileana Leavans and mathematician Lawrence Morales at Seattle Central Community College, presents a course which incorporates anthropology, history, and art into math education. This course "provides a transcultural approach towards the understanding of the existing relationships between visual images, mathematics, and the written/spoken word." Here, visitors will find a course description, outcomes, activities and assignments, as well as some sample projects and reflections from instructors. It is an excellent starting point for educators looking to design a course which incorporates math across the curriculum. |
Full description for Introduction to Graph Theory
A stimulating excursion into pure mathematics aimed at the mathematically traumatized, but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Eul |
Core Courses
Pre-Core and Core Math/Stat Courses
Notes:
Students need to meet only one of the prerequisites for a course.
Accuplacer EA = Accuplacer Elementary Algebra Test
Accuplacer CLM = Accuplacer College Level Math Test
When students take Accuplacer at UNR they are given the Elementary Algebra test first; if they do well enough (score 80 or higher), Accuplacer will automatically lead them into the College Level Math test.
Math 095 Elementary Algebra
PREREQUISITE:
ACT: less than 19
SAT: less than 470
Accuplacer: less than EA 76
Preparation for Intermediate Algebra. Topics include the fundamental operations on real numbers, inequalities in one variable, polynomials, integer exponents, and solving quadratic equations by factoring.
An S, or C or better, in MATH 095, taken anywhere in NSHE, will allow a student to enroll in MATH 096.
Students do not receive college credit for MATH 095 toward their degree, nor does it satisfy the core mathematics requirement. However, the three credits do count towards scholarship eligibility and enrollment.
Math 096 Intermediate Algebra
PREREQUISITE:
ACT 19
SAT 470
Accuplacer: EA 76
Math 095 Course Grade C/S
This is a non-college-credit developmental algebra course which covers topics from Algebra 1 (Algebra 1-2 in WCSD) available at middle school and high school levels. These topics include: exponents, factoring, fraction, radicals, linear and quadratic equations and graphs.
An S, or C or better, in MATH 096, taken anywhere in NSHE, will allow a student to enroll in MATH 120 or MATH 126.
Students do not receive college credit for MATH 096 toward their degree, nor does it satisfy the core mathematics requirement. However, the three credits do count towards scholarship eligibility and enrollment.
Math 120 Fundamentals of College Mathematics(3cr)
PREREQUISITE:
ACT 22
SAT 500
Math 096 Course Grade C/S
Accuplacer: EA 80 and CLM 55
This is a Core mathematics course intended for students who wish to major in a non-quantitative discipline. MATH 120 is not a preparatory course for MATH 126 or for any other mathematics or statistics course on UNR campus.
Students will see a brief overview of basic set operations, probability, statistics, consumer mathematics, variation, geometry and trigonometry for measurement, linear, quadratic, exponential and logarithmic functions with emphasis on problem solving and applications. (MATH 019-119 is a one year alternative to 120 for students with disabilities.)
Any UNR course that lists MATH 120 as a prerequisite accepts a higher level Mathematics or Statistics course in its place.
Credit may not be received for MATH 120 if credit has already been awarded for MATH 127 or above.
-----------------------------------------------------------------
"Stretch" Math 120 Fundamentals of College Mathematics (4cr*)
PREREQUISITE:
ACT 19
SAT 470
Math 095 Course Grade C/S
Accuplacer: EA at least 76
This version of MATH 120 covers all of the material from MATH 120 as well as material from the first part of MATH 096. This course requires students to "co-enroll" in the 1 credit course MATH 096a.
Math 126 Pre-calculus I (3cr)
PREREQUISITE:
ACT 22
SAT 500
Math 096 Course Grade C/S
Accuplacer: EA 80 and CLM 55
As of Spring 2012, Math 126 satisfies UNR's core mathematics requirement. Fundamentals of algebra; polynomial, rational, exponential, and logarithmic functions, their graphs, and applications; complex numbers; absolute value and quadratic inequalities; systems of equations, matrices, determinants. Credit may not be received for MATH 126 if credit has already been awarded for MATH 128 or above.
A course grade of C- or better in MATH 126 will allow a student to enroll in MATH 127, 176 OR STAT 152.
MATH 126-127 is a two-semester, six-credit alternative to the five-credit one-semester course MATH 128. Credit cannot be received for both MATH 126 and MATH 128.
-----------------------------------------------------------------
"Stretch" Math 126 Pre-calculus I (5cr*)
PREREQUISITE:
ACT 20
SAT 480
Accuplacer: EA 80 and CLM 30
This version of MATH 126 covers all of the material from MATH 126 as well as material from the last part of MATH 096. This course requires students to "co-enroll" in the 2 credit course MATH 096d.
Math 127 Pre-calculus II (3cr)
This Core math course includes the study of trigonometric functions, identities and equations; conic sections; complex numbers, and vectors.
A course grade of C- or better in MATH 127 will allow a student to enroll in MATH181, CALCULUS I.
In order to receive Core mathematics credit for MATH 127 students must demonstrate algebra proficiency by meeting the prerequisites listed above.
MATH 126-127 is a two-semester, six-credit alternative to the one-semester five-credit MATH 128. Credit cannot be received for both MATH 127 and MATH 128.
Math 128 Pre-calculus and Trigonometry (5cr)
PREREQUISITE:
ACT 27
SAT 610
Accuplacer: EA 80 and CLM 70
This is a Core math course which includes study of polynomial, rational, exponential, logarithmic, and trigonometric functions with graphs and applications, complex numbers, coordinate geometry in the plane, trigonometric identities, matrices, determinants, and the binomial theorem.
A course grade of C- or better in MATH 128 will allow a student to enroll in MATH 181, Calculus I.
Credit may not be received for both MATH 126 and 128, or for both MATH 127 and 128.
Credit may not be received for MATH 128 if credit has already been awarded for MATH 181 or above.
Stat 152 Introduction to Statistics (3cr)
PREREQUISITE:
ACT 27
SAT 610
Math126 Course Grade C-
Accuplacer: EA 80 and CLM 84
This Core math course is taken by many Biology majors and by students who desire a statistics course without a calculus prerequisite. It covers descriptive statistics, probability models, normal and binomial distributions, statistical estimation and hypothesis testing, and linear regression.
In order to receive Core Mathematics credit for STAT 152, students must demonstrate algebra proficiency by one of the following:
1. Earning a C- or better in Math 126 (or an equivalent course).
2. Meeting the ACT/SAT/Accuplacer prerequisite scores for Stat 152.
Math 176 Calculus for Business and Social Sciences (3cr)
PREREQUISITE:
ACT 27
SAT 610
Math126 Course Grade C-
Accuplacer: EA 80 and CLM 84
This is a Core math course primarily intended for business majors. It is an algebra-based differential and integral calculus course including functions, graphs, limits, derivatives, integrals, the fundamental theorem of calculus, rates of change and extrema with applications to Business.
Credit may not be received for MATH 176 if credit has already been awarded for MATH 181 or above.
Math 181 Calculus I (4cr)
PREREQUISITE:
ACT 28
SAT 630
Math127 / Math 128 Course Grade C-
Accuplacer: EA 80 and CLM 101
This is a Core math course intended for science and engineering majors. It is primarily a differential calculus course. Topics include limits, derivatives and integrals of algebraic and trigonometric functions, the fundamental theorem of calculus, and applications to Science and Engineering. It may include techniques of integration such as integration by substitution.
This is the first course in the 12-credit Calculus sequence 181-182-283, which is the foundation for all upper division MATH/STAT courses. |
Basic Algebra
Basic Algebra topics are the very beginning of learning Algebra. When you start on these topics, you're expected to have little more than Arithmetic knowledge (you know, those problems to do with "+", "-", "÷", and "×"). You'll also need to be familiar with Pre Algebra topics, but you don't need to worry about that now. You can easily refer back to the Pre Algebra topics later if you need to.
This section is designed specifically for those who are beginning Algebra, but will be useful for reference if you're learning Intermediate or Advanced algebra topics. You'll find a list of topics followed by a brief description.
How do you use these pages? If you're starting out, I recommend that you start with Algebraic Expressions, Algebraic Equations, Algebraic Factoring and Exponents. These will give you the foundation needed to understand the other basic algebra topics.
If you just want to find information to solve a problem, go to the topic that is most obviously relevant to your problem, and read. What if you can't solve a problem with the knowledge from one topic? Recognize that some problems might need a combination of different techniques from Pre Algebra and basic Algebra. Identify the techniques and you'll solve the problem easily.
Your topic request will appear on a Web page exactly the way you enter it here. You can wrap a word in square brackets to make it appear bold. For example [my request] would show as my request on the Web page containing your request.
TIP: Since most people scan Web pages, include your best thoughts in your first paragraph. |
A free series of textbooks on the subjects of electricity and electronics. These books DC, AC, Semiconductors, Electronics, Digital, Reference, and Experiments, and all related files are published under the terms and...
The online math center at Whatcom Community College is intended for a range of audiences, particularly students looking for additional assistance on a variety of math subjects from geometry to calculus. The materials...
Webmath, from Discovery Education, provides help for mathematics students. Categories include general mathematics, K-8 math, algebra, geometry, trigonometry and calculus. The site covers everything you need to know,...
Teaching college mathematics can be a daunting task, indeed. It's nice for seasoned professionals and others to have a solid primer on the subject and this guide from Professor Suzanne Kelton is quite useful. The |
Russell Gardens, NY MathThe laws of exponents are extended to the cases of zero, negative and fractional exponents. The idea of a function and its inverse is introduced. Extensive use is made of exponential and logarithmic functions, including graphing and solving equations. |
An interactive mathematics course offered via the Internet to students throughout the Hawaiian islands. Cathi Sanders, a teacher at Punahou School in Honolulu, teaches this course through ESchool, a pilot project of the...
Shockwave whiteboard movies on algebra, geometry, probability, statistics, the mathematics of finance, and more. A whiteboard movie (WM) is a multimedia screen recording of writing on an electronic whiteboard (real or...
A unit designed to teach metrics. It discusses what metrics are, and how and why the system came about. Arguments are presented for why it should be taught, and disadvantages are mentioned. Includes an outline of the...
This commercial website, developed by GCSE Answers Ltd., offers short tutorials on various topics in mathematics, such as algebra, trigonometry, and measurement. The tutorials include a short overview of the topic...
Beginning with the September-October 1999 issue, the electronic version of the National Institute of Standards and Technology (NIST) Journal of Research will be available in .pdf format. The journal contains current... |
WaterFlow is an application to support you in the hydraulic field. It supports you to develop flows and geometry in open channels, the energy heads in a pipe, the Reynolds number, hydraulic jump and more. This is the perfect support for engineers and
1)
Matrix Inverse Calculator
This program uses the complicated Gauss-Jordan elimination method to find the inverse of any square matrix. You simply choose your matrix's dimensions, then enter the elements of the matrix you want inverted and press Enter. License:Freeware,
0 to buy Size:
27KBMirror 1
3)
SurGe
SurGe is a computer program which enables to generate a surface as an interpolation (approximation) function of two independent variables. Implements an interpolation / approximation method called ABOS. License:Shareware,
20 to buy Size:
3100KBMirror 1
4)
Mágico Mundo de las Matemáticas entre 9 y 10 años
Joyful math leraning for ages 9-10 children in the hispanic and Latin world. Children can effectively learn math with friendly animals. The comprehensive game to rescue princess frog from witch's castle make the children excited in learning math. License:Demo,
14 to buy Size:
7 MBMirror 1
6)
WebCab Functions (J2SE Edition)
This Java class library offers refined numerical procedures to either construct a function of one or two variables from a set of points (i.e. interpolate), or solve an equation of one variable. License:Demo,
119 to buy Size:
5080KBMirror 1
9)
PDAcalc matrix
Programmable graphical matrix calculator for PDA's and windows. This program was especial designed for palm devices and the PocketPC but also runs on windows platforms. Using the windows makes writing and debugging scripts, when needed, very easy. License:Shareware,
24.95 to buy Size:
4660KBMirror 1 |
Saint
Louis University
Department
of Mathematics and Mathematical Computer
Science
Occasional
Maple Worksheets for Calc II
(For
Maple 9.5)
In trying
to appropriately incorporate technology into the teaching
of mathematics, there are a number of reasonable strategies. The best
strategy for any given school and sequence of courses will depend on
factors specific to the situation including a description of a
typical student, the technological support available, and financial
constraints.
At Saint
Louis University, we are using graphing calculators as
the primary technology incorporated into teaching our main calculus
sequence. The easy arguments for graphing calculators are that they
are relatively inexpensive (about the cost of a standard calculus
textbook), moderately easy to learn to use, and are in the students'
hands so that the students have the same set of tools available in
class, for homework, and during quizzes and tests. Hopefully they
will understand that the tools are tools for doing mathematics rather
than tools for working in mathematics classes. Quite simply, we felt
that graphing calculators made the best fit for the needs of the
calculus students we have.
Nevertheless,
as the students move through the calculus sequence
there are topics where a computer algebra system is much more
effective than a graphing calculator. These topics include symbolic
integration, power series, and numerical solutions to differential
equations. A computer algebra system like Maple can be used
effectively for these topics.
One of the
drawbacks of a program as powerful as Maple is that the
difficulties of learning Maple and learning to use a computer need to
be consciously factored in when planning the course. One pedagogical
strategy is to make using Maple a routine part of the course and
consistently teach use of the program along with the mathematics.
This strategy is not feasible if computer algebra is a secondary
technology that is used only on occasion.
A second
strategy (and the one I have used) is to introduce Maple
through carefully designed worksheets. The worksheets are set up so
that the first time through a student can get through the worksheet
by hitting enter repeatedly. The worksheets include a significant
amount of exploratory text. The exercises tend to ask to student to
repeat the examples from the worksheets with minor modification. I
use the template model because I want them to use the power of the
Maple to look at problems where I could not expect them to produce
the code, but I can expect them to copy and modify a code template,
focusing on the results.
With that
long winded introduction, here are some worksheets I
produced for topics in calculus II. I find it is best to take the
class to the lab for a worksheet, assigning the students to finish it
on their own time. A zipped
archive of all the worksheets is available.
The preliminary worksheet - Just
Enough Maple- is designed to cover the skills the students need to
run the worksheets and answer the exercises they contain. This
worksheet covers those pesky skills, like copying, pasting, saving, and
printing, that get in the way of getting started on a computer
worksheet.
The first worksheet -
Integration check - is designed to walk the students through the
process of using Maple to do symbolic integration. This worksheet is
tied to the book we use, giving exercises that refer back to specific
pages. Unless you use Ostebee and Zorn, you will want to modify this
worksheet.
The second worksheet - Numeric
Integration - explores the various ways of approximating an
integral with a Riemann sum rule. The student package with Maple
produces pretty pictures of the graph and sum.
The fourth worksheet -
Animating Taylor Series - is probably the most impressive for
using Maple as a teaching tool. It gives code to animate a series of
Taylor series wrapping down to a function. It makes it much easier to
discuss series as polynomial approximations of functions and to discuss
the interval of convergence of a series.
The fifth worksheet - Working
with Power Series as Functions - shows how to use Maple to work
with a power series that is defined with sigma notation. It is
noteworthy that Maple can produce closed form equivalents for many
power series.
The two worksheets are of a different nature. They are
intended for use by the instructor, rather than by the class. They are
intended to give templates for producing nice graphics that can be
useful for quizzes and tests. Thus although I use other software for
the introduction to differential equations that is part of calc II, I
have a Maple worksheet for producing slope field
diagrams for quizzes and tests. Similarly, there is a Maple
worksheet for producing graphs of
surfaces of revolution.
The
worksheets were originally written for Maple V R4 on the
Macintosh platform. They were updated to be compatible with Maple
9.5, but no major conceptual ravision was made.
A revision for Maple 10 is in the works. It should be more
substantial revision. |
Description: Algebra Assistant, the first module of a three-program learning system, allows introductory and intermediate-level students to work through algebra problems in detail, step-by-step.
Reviewer Comments:
The products are cumulative in nature: Calculus Assistant contains all of the materials included in both Pre-Calculus Assistant and Algebra Assistant. Pre-Calculus Assistant contains all of the problems and materials found in the initial offering, Algebra Assistant. As might be expected, Calculus Assistant is the most expensive package ($195--single user; $995--10-user network license).
The features of all three products are identical. Students can quickly check their work on problems by comparing answers with the computer. The disks include more than 6,700 problems; teachers and students can add new problems or change existing problems. All of the work can be printed for student work away from a computer, and it can be saved on a disk to be revisited later.
Algebra Assistant can offer hints so that students see only a single step of a problem, or it can work the entire problem showing each step (complete with annotation). As many as six different graphs can be produced on the screen simultaneously.
The program differs from the more powerful computer algebra systems in that it allows simple step-by-step interaction with the student.
With the straightforward menu, a student may select what he or she believes to be the next best, most plausible, step toward a solution. This simplicity frees teachers from spending additional time teaching the special codes and syntax that computer algebraic manipulators require.
The program's strength is its ability to remove the fear that some students have. It can eliminate trivial mistakes, offer hints, show what operation to perform next, perform the next step automatically, or provide a complete step-by-step solution.
Some learners need to know that the last step they tried was correct before they can move on to the next stop in a problem. For students who fear math, fear being wrong, or fear uncertainty, Algebra Assistant can be a constant reassurance that doesn't add to the teacher's load.
My experience with the 800-phone number was terrible! It took four tries to reach someone who would answer my questions about pricing information. I left voice messages twice and never received a single response.
I did not try Internet support because the product worked the first time, and the included user's guide suggested simple solutions to the "How-to" questions.
Algebra Assistant can be used as an additional method of reaching math students who aren't responding to current approaches for any variety of reasons. It is a simple and inexpensive method to add another way to help students to understand mathematics. |
Abstract
Over 100 years ago, E. H. Moore (1903), in his presidential address to the Mathematical Association of America, called for a unified mathematics curriculum built around the notion of functions but rejecting a completely axiomatic approach at the secondary level. Moore's address followed a major move to standardize the secondary school curriculum in 1894 in the report of the "Committee of Ten." Successive other calls for change and unification came across the decades but until 1989, the United States had little national direction about what the mathematics curriculum either could or should be at the pre-collegiate level. Since 1989, there has been a growing move to establish a national curriculum for the country, but the move continues to struggle. This paper outlines some of the recent history of the movement and suggests some barriers still in the way of achieving it. |
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Mathematics in Action : Prealgebra Problem Solving - 3rd edition
Summary: The first book of the Mathematics in Action series, Prealgebra Problem Solving, Fourth Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities And The accompanying practice exercises. Along with the activities And The exercises within the text, MathXL and MyMathLab have been enhanced to create a better overall learning experience For The reader. Technology integrated throughout the text helps readers interpret ...show morereal-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops readers' mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines149.66 +$3.99 s/h
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An excellent and comprehensive article from Lillian Jones' BestHomeschooling.org site: The question of how to provide our children with a good math education often causes undue anxiety. With a clearer and more relaxed understanding of what it is that we're trying to accomplish, we can present it as just one more interesting part of... Read More »
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Lessons: "How do you really do this stuff?" — Purplemath's algebra lessons are written with the student in mind. These lessons emphasize the practicalities rather than the technicalities, demonstrating dependable techniques, warning of likely "trick" questions, and pointing out common mistakes. The lessons are cross-referenced to help you find related material, and a "search"... Read More »
Learn math at "Interactive Mathematics", where the lessons are easy to understand and easy to read. The site uses interactive documents so you can learn while playing with the concepts. Topics range from Grade 8 algebra through to Fourier series and Laplace Transform. Read More »
The New Totally Awesome Business Book for Kids by Arthur Bochner and Rose Bochner From Newmarket Press: This first-of-its-kind book for young entrepeneurs is now completely revised and updated for a new generation by one of the original authors (now an adult) and his 14-year-old sister. Synopsis Originally written by Arthur Bochner when he... Read More »
Hotmath.com provides homework help correlated with textbooks used from middle-school math through calculus. Hotmath shows step-by-step explanations to the odd-numbered problems (the ones where the numerical answer is typically in the back of the book). Students (and parents!) can see how to do the problems and then challenge themselves on the even-numbered problems. Hotmath |
Intermediate Algebra, CourseSmart eTextbook, 3rd Edition
Description
The Sullivan/Struve/Mazzarella Algebraprogram is designed to motivate students to "do the math"— at home or in the lab—and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do. |
Mathematics (Specification A) is designed for use in schools and colleges. It is part of a ... appreciate the importance of mathematics in society, employment and study. ...... Edexcel (Oxford University Press, 2007) ISBN 9780199152629 ... Turner D and Potts I – Longman Mathematics for International GCSE Practice Book 2 ...
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quickest route to learning a subject is through a solid grounding in the basics. So what you won't find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques.
This book features:
Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties
Stay-in-step panels show how to cope with variations to the core steps |
This 45-lesson series is designed to offer a comprehensive review of Calculus for students looking to test their knowledge and prepare for midterm and final exams.
Taught by Professor Edward Burger, this selection of lessons comes from a comprehensive Calculus course available from Thinkwell, Inc. The course can also be found at or all of the video portions of the course can be purchased through MindBitesLimits finally make sense to me! I was having a hard time wondering why we would want to find the limit of a function but thanks to the Doctor here, I finally understand it and appreciate it that much more.
Excellent lesson from Dr. Berger! I am returning to school after being out for 26 years and lessons like this really do improve my self-confidence level. Thank you, Dr. Berger. You are a very gifted teacher.
A clear, enjoyable presentation of examples illustrating The Fundamental Theorem of Calculus. "Painless!"
Below are the descriptions for each of the lessons included in the
series:
Calculus: Finding Limits Graphically I
In this lesson, you will learn about the limits of functions. Since limits are real numbers, you can apply many of the properties of real numbers to limits. Professor Burger walks you through many of these, including: limits of function combinations (limits of the sum of two functions, limits of the product of two functions, limits of the quotient of two functions) and limits of functions times a constant.
For Part II II
In this lesson you will look at a number of limit laws and their applications. These will include rules that govern the limit of a constant, limits of a function x, limit of a function x^n (or raised to any fixed value, n), the limit of polynomial functions (like 2x^2-4x+7), the limit of rational functions (the quotient of two polynomials), and the limit of functions expressed with radicals (e.g. the nth root of x). Additionally, this lesson will explain and demonstrate the power law for limits (for raising expressions to an exponential power) and the root law for limits.
For Part IEdward Burger, Professor of Continuity and Discontinuity Limits
The limit is the range value that a function is tending towards as you get closer to a domain value. In this lesson you will learn about evaluating limits by substituting values into the expression as well as what notation denotes a limit (and how to read and interpret the notation). If a function is well-behaved, the limit will be equal to the function at that point. Well-behaved functions include lines, parabolas and square root functions. Poorly-behaved functions, however, include piecewise-defined functions and step functions. We will also look at how to evaluate limits by canceling (which is what you should do when you get an answer of 0/0, an indeterminate form, after trying to solve for the limit using substitution). Limits that produce indeterminant forms may or may not exist. An indeterminate form is a mathematically meaningless expression and, in this case, it is just an indication that more work needs to be done to evaluate the limit. Professor Burger will walk you through how to progress once you arrive at an indeterminate Limits and Indeterminate Forms
The limit is the range value that a function is tending towards as you get closer to a domain value. In this lesson, you will learn how to evaluate a limit at a value where a function is well-behaved by substituting the value into the expression. If direct substitution produces zero divided by a non-zero number, the limit is zero. If direct substitution produces a non-zero number divided by zero, the limit does not exist. You will also cover how to handle limits that produce indeterminate forms (0/0) that may or may not exist. An indeterminate form, unfortunately, is just a sign that more work should be done and Professor Burger walks you through what should be done in what order to determine whether there is a limit (and what it is having Two Techniques for Evaluating Limits
The limit is the range value that a function is tending towards as you get closer to a domain value. This lesson will cover the cancellation technique and the rationalization technique to evaluate and solve for limits which give you an indeterminate form when evaluated with substitution. When evaluating the limit of a compound fraction, Professor Burger will teach you to simplify the fraction by using the lowest common denominator (LCD). He will also walk you through how to simplify a binomial that contains radicals by rationalizing (multiplying by the conjugate of the binomial to remove the radical). The conjugate of binomial a-b is the binomial a+b Instantaneous Velocity
This lesson will start with a recap of average and instantaneous rates as well as their relationships with secants, and tangents. A secant line is a straight line that intersects a curve at two or more points, and a tangent line is a straight line that touches but does not intersect a curve. While you can use the secant line to calculate average velocity, you will use the tangent line to evaluate instantaneous velocity. This is because the average rate of change is equal to the slope of the secant line and the instantaneouse rate of change is equal to the slope of the tangent line. To find the instantaneous rate of change, you will learn to take the limit of the average rate on the interval [t, t+delta t] as delta t approaches zero Derivative
This lesson is a review of how we arrive at the derivative. We start with secants and tangents and then move to average and instantaneous rates before we conclude with the definition of the derivative. We know that tangent lines are a graphical representation of instantaneous rates of change. To find the slope of the tangent line, we take the limit as the change in the independent variable (delta X) approaches zero. The derivative is the function that gives you the instantaneous rate and slope of the tangent line at a particular point. The derivative gets its name because it is derived from another function. The derivative of a function at x is equal to the limit as delta x approaches zero of [f(x+ delta x) - f(x)]/delta x (provided the limit exists sequences Differentiability Slope of a Tangent Line
In this lesson, we will review tangent lines, learn how to find the derivative, and learn how to use the derivative once we find it. We begin by finding the slope the tangent line f(x) = 2x^2 at x=3. We find the slope by taking the derivative of f(x). We compute this derivative by evaluating the limit as delta x approaches 0 of [f(x + delta x) - f(x)]/delta x or, in this case, the limit as delta x approaches zero of [2(x+ delta x)^2 - 2x^2]/delta Equation of a Tangent Line
In this lesson, you will cover how to find the equation of a line tangent to a curve, equations of tangent lines, how to find the derivative, and how to find the point where the tangent line is horizontal. To find the equation of the tangent line, you'll start by taking the derivative of the curve and then evaluate that derivative at the point of tangency. You'll then substitute the coordinates of the point of tangency as well as the calculated slope into the point-slope form of the line: y-y1 = m*(x-x1) to get the equation of the tangent line. To find where the tangent line is horizontal, you'll set the derivative of the function equal to zero and solve for America Uses of the Power Rule
This lesson covers the power rule, the sum rule, and the constant multiple rule (all related to differentiation). Through this video, you will learn how to evaluate derivatives without using the definition as the method. The power rule is the shortcut used for finding a derivative of any variable raised to the power of a rational exponent. The constant multiple rule asserts that the derivative of any function times a constant is the same as the derivative of that function times that exponent. The sum rule shows that the derivative of the sum of two functions is equal to the sum of the derivatives of both Product Rule
In this lesson, we learn about taking the derivatives of products and applying the product rule of differentiation. The derivative of the product of two differentiable functions is NOT equal to the product of the derivatives of both functions. Instead, you must learn and apply the product rule to calculate the derivative of the product of two functions. The product rule states that the derivative of f(x)*g(x) = f(x)* derivative of g(x) + g(x)* derivative of f Quotient Rule
In this lesson, we learn about taking the derivatives of quotients and applying the quotient rule of differentiation. The derivative of the quotient of two differentiable functions does not necessarily exist and is not necessarily equal to the quotient of the derivatives of both functions. Instead, you must learn and apply the quotient rule to calculate the derivative of the quotient of two functions. The quotient rule states that, when f(x) and g(x) are both differentiable and g(x) does not equal 0, the derivative of f(x)/g(x) = [g(x)* derivative of f(x) - f(x)* derivative of g(x)]/g(x)^2 Making the Chain Rule
The chain rule is a technique used for differentiating composite functions. In this lesson, you will learn the chain rule as well has how to apply it. Professor Burger will carefully walk through mistakes to avoid when using the chain rule as well as the correct way to use the chain rule in conjunction with the product rule for differentiation. The chain rule states that the derivative of g(h(x)), where g(x) and h(x) are differentiable functions, is the derivative of g(h(x)) times the derivative of h Combining Computational Techniques Trigonometric Functions
In this lesson you will learn how to calculate the derivative of different trigonometric functions. Professor Burger will teach you how to calculate the derivative of the most common trig functions (sine, cosine, and tangent). To arrive at the derivatives of cos, sin and tan, you will be walked through the derivation of these formulas given the definition of the derivative. The derivative of sin(x) = cos(x), the derivative of cos(x) is -sin(x), and the derivative of tan(x) is sec^2(x) Exponential Functions
The power rule for differentiation does not apply to exponential functions (e.g. the derivative of 2^x does NOT equal x*2^(x-1)). In this lesson, we will return to the limit definition of the derivative to discover how to differentiate exponential functions like 2^x. Professor Burger will graph the exponential function and calculate the slope of the tangent line. In the end, we will arrive at the fact that the derivative of an exponential function is the product of the function and the natural log of its base. You will also see how to arrive at e = 2.71828..., which is the only constant for which its derivative, when raised to any power is equal to the same thing. Thus, the derivative of e^x is equal to e^x and the e^(ln x) = e. The derivative of N^x is equal to N^x*ln N. The constant 'e' turns out to be very important in math, and Dr. Burger will explain some of its uses as a critical constant of the Natural Log Function
In this lesson, you will learn how to find the derivative of the natural log function. To start with, we will review exponential functions and the natural logarithmic function, and then you move on to learning about composite functions that include natural log functions. To find the derivative of one of these composite functions, like e^(3x^2), you must combine the fact that the derivative of e^x is e^x and the chain rule. You will also see how to use the natural exponential function to prove why the derivative of f(x) = ln x is equal to 1/x. Last, this lesson will cover how to use the chain rule or the properties of logs to find the derivative of the composition of a natural log function and another function, like finding the derivative of ln(x^3 Rules-Transcendental Function the Derivative Implicitly Implicit Differentiation
Here, we will use implicit differentiation (in which you find the dy/dx of things that aren't simple functions). This will include looking at lines tangent to curves of relations (like a circle equation of x^2 + y^2 = 1). Professor Burger will show you how to find the derivative of a relation by differentiating each side of its equation implicitly and solving for the derivative as an unknown. For instance, this is what you would use to differentiate a formula like x^2 + xy + y^2 = 3.75 or for x + x/y - y^3 = 4 + 3/8 to find dy/dx (the derivative of y with respect to x Solve Distance & Velocity Word Problems FenceAmerican Box Ladder Critical Maximum and Minimum referees First Derivative Test
To find the maxima and minima of a graph, you first have to find all of the critical points. Thus, you will always find the max or min at one of these points where slope is 0 or is undefined (though the function is defined). The first derivative test is a way to determine if a critical point is a max, a min, or neither. To do the test, you look at how the derivative is changing around the point. If slope is positive before and negative after, it is a max. If it is negative before and positive after, it is a min. Note that these maximums and minimums are relative maximums and relative minimums. If the derivative of the function does not change sign around the critical point, it is neither a maximum nor a minimum Concavity and Inflection Use 2nd Derivative to Examine Concavity Graphs of Polynomial Functions the of Powers of x
This lesson is a more advanced view of antidifferentiation and integration. In it, you will be introduced to the proper notation for denoting an integral or antiderivative and you will also be introduced to the power rule for integration and some properties of indefinite integrals. You will also learn several rules about antiderivatives or integrals. If a function has an antiderivative, it has an infinite number of antiderivatives, and the properties of antidifferentiation mirror those of differentiation. Professor Burger will go over some of these properties, including the constant multiple rule for integration and the sum rule for integrationrals of Trig and Exponent Functions
This lesson will teach you how to approach and solve problems involving antiderivatives and integration for trigonometric functions and exponential functions. To do this, we will review the power rule, the trig derivatives and some exponential derivatives. Professor Burger will go through integration problems involving functions such as sin, cos, tan, sec, cot, csc, e^x, a^x, ln a, etc. To attack these problems, you will break down the integration/antidifferentiation problems into component parts and apply the laws of integration to arrive at the correct solutionrating Polynomials by Substitution
This lesson will teach you how to do integration of polynomials using substitution. Before digging in on substitution in antidifferentiation, Professor Burger will review notation associated with differentiation and antidifferentation (with respect to x). Next, he will move on to teach you integration by substitution, a technique that is helpful for finding the antiderivative of a composite function. While running through the chain rule backwards, he will highlight several rules and properties of antidifferentiation; for instance, the integral of a product is not necessarily equal to the product of the integrals. He also gives us advice on what expressions to select and replace with a constant when using substitution as a method of integration. To illustrate all of this, you will find the integral of 42x(x^2+4)^20 dx as well as the integral of this expression that contains radicals 2x^2*(5+x^3)^(1/2)dx integrals Substitution to Integrate Trig Functions
In this lesson, we will work on solving antidifferentiation problems involving composite trigonometric functions using the substitution method to solve for the integral. A composite function is a function that results from applying one function first and then another (e.g. f(g(x))). When these involve trig functions, they look like: find the antiderivative (or integral) of (2x+1)*sin(x^2+x)dx. After using substitution, if you end up with the du-expression being off by a factor of a constant, remember that you can take that constant multiple out of the integral (because of the constant multiple rule of integration and antidifferentiation). Additionally, this lesson will cover the integration of composite functions that involve the trigonometric function secant (in addition to other, more basic, trig functions Comp. Exponent, Rational Funct Trig Functions - Substitution Weighty I
In this lesson, you will learn how the derivative and the integral are related. This is the first part of the fundamental theorem of calculus; it asserts that differentiation is 'undone' by integration. It also means that the rate of change of the area under the graph of a function with respect to x is equal to the value of the original function at x. In addition to explaining the theorem and the implications of it, Professor Burger will also walk you through a proof of sorts that explains why the theorem is true.
This lesson explains the first half of the Fundamental Theorem of Calculus. To see the second half of Professor Burger's explanation, check out: II
The Second part of the Fundamental Theorem of Calculus provides the link between velocity and area. It states that the sum of the area under the curve between two points (A and B) is equal to the difference of the antiderivatives of A and B. Thus, to find the area under a curve between two points, you will take the difference of the derivatives calculated at the end points, A and B. This theorem enables you to evaluate definite integrals by finding the area between the function described and the X axis. The lesson will also cover proper notation that should be used to denote what you're evaluating over which interval. You will also work problems that involve trigonometric functions (like finding the area under a portion of the sine curve or cosine curve)
This lesson explains the second half of the Fundamental Theorem of Calculus. To see the fist half of the explanation, check out: Applied journals Definite Integrals and Motion Area between Two Curves |
Every president, from Johnson to Obama, has made big promises when it comes to "fixing" education in America. And almost every parent, from then until now has asked themselves an essential question—"Is my child getting a good education?" Regardless of neighborhood or income, it's a concern that keeps parents up at night, and the answer rests at the heart of a national firestorm brewing over education.
"Waiting for Superman": What it Means for You and Your Child
ted
math
nature
The Messenger Series
Hi. This is the first lecture in MIT's course 18.06, linear algebra, and I'm Gilbert Strang. The text for the course is this book, Introduction to Linear Algebra. And the course web page, which has got a lot of exercises from the past, MatLab codes, the syllabus for the course, is web.mit.edu/18.06. And this is the first lecture, lecture one.
Mathematics | 18.06 Linear Algebra, Spring 2010 | Video Lectures | Lecture 1: The geometry of linear equations
fun
science
physics
Luminosity: Fλ is the radiative flux at the stellar surface. Energy may be lost due to neutrinos or direct mass loss. Flux: At the Earth's surface, observed flux is Stellar flux
Astrophysics I « Physics Made Easy |
Merchandising Mathematics for Retailing199.97
FREE
About the Book
Written by experienced retailers, "MECHANDISING MATH FOR RETAILING, 5/e" introduces students to the essential principles and techniques of merchandising mathematics, and explains how to apply them in solving everyday retail merchandising problems. Instructor- and student-friendly, it features clear and concise explanations of key concepts, followed by problems, case studies, spreadsheets, and summary problems using realistic industry figures. Most chapters lend themselves to spreadsheet use, and skeletal spreadsheets are provided to instructors. This edition is extensively updated to reflect current trends, and to discuss careers from the viewpoint of working professionals. It adds 20+ new case studies that encourage students to use analytic skills, and link content to realistic retail challenges. This edition also contains a focused discussion of profitability measures, and an extended discussion of assortment planning. |
Better student preparation needed for university maths: UK study
Aug 01, 2012
Moving from sixth form, or college, into higher education (HE) can be a challenge for many students, especially those who start mathematically demanding courses. Life prior to university focuses on achieving maximum examination success to be sure of a place. Faced with this pressure, school and college maths courses pay little attention to preparing students to use maths in other areas of study according to a project funded by the Economic and Social Research Council (ESRC).
A student's ability to apply mathematical reasoning is critical to their success, especially in HE courses like science, technology, engineering and medicine. The study, undertaken by Professor Julian Williams, Dr Pauline Davis, Dr Laura Black, Dr Birgit Pepin of the University of Manchester and Associate Professor Geoffrey Wake from the University of Nottingham, shows that it is important to understand how students can prepare for the 'shock to the system' they face and how they can be given support at school, college and university to help in the transition.
The researchers found that students were not fully aware of the importance of the mathematical content in the courses they had joined at university, and particularly how to apply maths in practice.
Associate Professor Geoffrey Wake states, "Different teaching styles of university lecturers and the need for autonomously-managed learning, where students need to learn some mathematical content of their courses on their own without input from lecturers, also came as a bit of a shock for many students. On the other hand, some of the lecturers had limited knowledge of the exam-driven priorities of A-level maths courses and were not aware of the techniques students had been taught prior to attending their university courses."
The researchers also found significant problems in motivating students to engage with the mathematics within their chosen university coursewhere mathematics was not their main area of study. Generally, schools and colleges were found not to be preparing students for university learning practices, and the level of learning-skills support was variable once students arrived at university.
"Many students felt that they would benefit from student-centred learning and greater opportunity for dialogue with their lecturers," says Associate Professor Wake. "Unfortunately, the efficiencies required of university teaching resulting in lecturing of large numbers of students makes developing such a learning culture unlikely."
The findings led the researchers to consider the implications for the policies and practices of schools, colleges and universities recommending a better two-way flow of information between schools and colleges and universities to address the issues of preparation and expectation.
They concluded that the sixth-form curriculum should provide 'learning to learn' skills and mathematical modelling for students following A-level maths courses.
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Listed below is a selection of problems from each section
that should provide practice on the key concepts and skills, while keeping the
redundancy to a minimum.As such, it
is important that you complete all of
these problems.Some will
(hopefully) be relatively quick and easy; others will likely take a fair amount
of time.Unfortunately, there is no
shortcut to learning mathematics– make sure you allow enough time every day to
keep up with the work.
Feel free to practice on additional problems if you think
the extra practice will help - I'll gladly help with any problems you encounter
whether or not a given question was assigned!This suggestion applies especially in Chapter 1, where I tried not to
assign too many problems that too closely resemble those that you would have
done in precalculus.
As a general rule homework will not be collected.However, I will on occasion select a couple
of questions and tell you that I will be collecting them for a grade.For these problems, you are expected to turn
in a complete solution – not just a final answer.
What is included in a
complete solution?It depends on the
problem, obviously, but will generally include such things as:
all
work leading from the original problem to the answer, shown in neat, easy
to follow steps;
tables
and/or complete graphs; and
explanations in complete English sentences.
A good rule of thumb is that someone should be able to read
your work, and know what the problem was, what your answer is, and why,
without needing to refer to the book. |
More About
This Textbook
Overview
With the advent of computers, theoretical studies and solution methods for polynomial equations have changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasizing computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Editorial Reviews
From the Publisher
"I took great pleasure in reading this book and, in my opinion, it should become the livre de chevet of people working in the part of computer algebra that deals with univariate polynomials."
Mathematical |
M Hutchings's Recommendations
I loove Hutchings! The best math teacher I have ever had in my life!! He has neat handwriting, explains complex concepts in a fun and easy to understand way, and has a geeky sense of humor. The homework load is fair, his exams are hard but fair, and he is an overall fair guy. He is really laid back and extremely helpful at office hours, too. GO TO HIS OFFICE HOURS!! Also, on the last day of lec, the entire hall (2050 vlsb) gave him a standing ovation and cheered and applauded for like, seriously, 5 minutes. He's that good.
Professor Hutchings is really enthusiastic about math, and it shows through his lectures. Furthermore, I feel that he really wants us to understand the concepts covered in multivariable calculus because he's always willing to take questions during class, and when students express confusion, he immediately reviews the confusing concepts with example problems.The professor organizes his lectures well and coherently, so that students understand how previous material relates to later material. Of course, the midterms and exams were difficult (the midterm was slightly easier) but fundamentally, they are fair because they test understanding of the concepts learned. Definitely a challenging class, but the professor is more effective and helpful than many professors I've met.
His lectures were very clear, easy to follow, and well organized. He had legible handwriting, spoke clearly and went at a good pace. He also told plenty of funny jokes and juggled the chalk board erasers. On harder concepts he would poll the large lecture hall to see how many students understood and how many wanted him to explain a concept again. The midterms were straight-forward but the final was hard. Regardless, he gave a generous curve |
Graph Theory Lessons
derek velez
(Student)
i have always had trouble with mathematics especially graphs when they became more complicated. but this was actually rather informational. i will definately be using this link further down the line of my school career if needed. It clearly explained everything was going on in the graph although i didnt know anything about some of the graphs
Time spent reviewing site:
15 min
4 years ago
Jacob Cook
(Student)
for someone who is not very good at graphs i was able to easily understand the steps and directions it takes to solving the problems.
Technical Remarks:
clear links to the problems that you have
Time spent reviewing site:
10 minutes
5 years ago
allie fiorentino
(Student)
This is awesome. For someone that was having trouble with lessons in class, they could come here and get a ton of help very quickly. This is like 10 math books in one. You have a bunch of reliable information right at your finger tips. This is extremely effective for anyone, either for review or first time learning. It is easily understood and you can keep coming back to it again and again if you need more repetition. This gives the student just one more outlet to use and go to whenever they need help or even a refresher.
Time spent reviewing site:
I spent about 20 minutes browsing around at all the different lessons and information.
5 years ago
Jennifer Brown
(Student)
I clicked through the links, read through explanations, and generally browsed the site. Content is good, very relevant, and highly useful, but could be presented better. The fact that it has a Java aspect is useful, yet not the easiest for some users as Java can cause a few problems with slower connections, or for those who are using public computers. However, explanations of the theories are well-presented and easy to understand, with plenty of information on each topic and diagrams for every concept. Students would probably find this page more useful than teachers, as the layout is simple and there are spaces for one to try out various examples. However, teachers could use these as examples in teaching, and the multiple graphs/images are useful when trying to explain concepts. This would be easy to use for an average user, as the layout is just links which lead to html content with images that explain the concepts. While not the most aesthetically pleasing site, it does provide good information, easy to use applets, and a simple layout that is useful when trying to navigate to specific topics.
Technical Remarks:
Java applets are tricky, because they are useful for the content trying to be conveyed, but they can run slow and even get caught up in firewalls, which is a hindrance, especially for slower connections (i.e. public computers). The layout of the site is good in the sense that it is simple, with links to the various topics, which is easy to navigate to, especially for an average user who is not willing to do a ton of sifting through content. Layout is simple, could benefit from a few improvements, but overall does not deter from the information conveyed.
latisha mills
(Student)
This website was very strait to the point, there was no introduction home page, it immedietly listed about 24 lessons on all types of graph theories. I felt I would reccomend this site to someone studying for a graphing test to get sample problems from and review some lessons, but not to someone like my self just learning about different types of graphs. The site was somewhat boring to me, but would be very helpful like i said to a student who wants some practice but is pretty familar with graphing, this website would definently refresh your memory!
Time spent reviewing site:
I spent about 5-10 minutes here :(
5 years ago
vishal sharda
(Student)
very interesting. talks about null graph theory. and also undergrduate graph theory.
5 years ago
Andy Luong
(Student)
i thought this was really cool section because it shows how easy to graph by plotting points and the system will automatically graph it for us. Platonic Graphs are really awesome because it shows how a cube is a non-planar depiction of a cube, which means a regular cube and a planar depiction of a cube is a cube that has vanishing points. I think this section is really cool because if a student doesn't get graph that much that can read more and go over examples in this section.
Used in course
5 years ago
Nabeel Oqbi
(Student)
This website gives a detailed beginning to graph theory. because it shows the student how to do graph step by step.
Time spent reviewing site:
20 min
Used in course
5 years ago
Thuy Nguyen
(Student)
This site includes many links for those who want to follow up on more of the math details.It's useful and easy to understand because it give you an interactive lessons with step by step instruction, and interesting example.therefore, you will get Line Graph,then answer the questions at the end of lesson if you read previous lessons (null graphs, isomorphism,complete graph,platonic graph, circuits.)moreover,i really like the Petersen program;it is fun and it can find complements of graphs, line graphs.you 'll get fun in graph, so i recommend you to enjoy it.
Technical Remarks:
This side is easy to acess, and control.
6 years ago
yonas workeneh
(Student)
This website provides a thorough introduction to graph theory. I really enjoyed because it is interactive and fun. When something is fun I learn better, quicker and also it stays in my memory for a long period of time. One of my favorite graph programs on this site is the prism. On the left side it allows you to add or delete vertices and on you can also add edge on the graph by simply dragging the point.
6 years ago
manvigas singh
(Student)
this site is great because it has Graph Theory Lessons. it has step by step information on graphs and how they work. it also tells you how the information is used in the graph. this website is very interative and has a lot of fun programs that allow you to play with the graphs. i recommend this site to anyone who is haveing problem understanding graphs and how they display writen information. |
textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site. less |
Homer, GA Ge algebra deals mostly with linear functions. Algebra 2 is a more advanced, more complex version of algebra 1. Here we get more involved with non-linear functions as well as imaginary and complex numbers |
Summary
This book provides guidance for elementary teachers who are looking to learn the basics of the varying levels of elementary math. Sonnabend provides an active, engaging approach to get students into the underlying concepts of elementary education mathematics. The book includes coverage of problem-solving, reasoning, sets, arithmetic, geometry, measurements, algebra, computers, statistics, and probability. Sonnabend's well-organized lesson format encourages students to participate in the development and explanation of concepts, establishing a solid understanding of mathematics. |
MCP Mathematics: Level A
Book Description: MCP Mathematics promotes mathematical success for all students, especially those who struggle with their core math program. This trusted, targeted program uses a traditional drill and practice format with a predictable, easy-to-use lesson format. MCP Math is flexible and adaptable to fit a variety of intervention settings including after school, summer school, and additional math instruction during the regular school day.By teaching with MCP Math, you can: Provide targeted intervention through a complete alternative program to core math textbooks. Help students learn and retain new concepts and skills with extensive practice. Prepare students at a wide range of ability levels for success on standardized tests of math proficiency |
This work is an introduction to mathematical analysis at an elementary level. Emphasis is given to the construction of national and then real numbers, using the method of equivalence classes and of Cauchy sequences. The text includes the presentation of: sequences of real numbers, infinite numerical series, continuous functions, deriviatives and Ramon-Darboux integration. There are also sections on convex functions and on metric spaces, as well as an elementary appendix on logic, set theory and functions. |
New Signpost Maths for Victoria
Student Book 5
New Signpost Maths for Victoria by Alan McSeveny
Book Description
The title of this book is New Signpost Maths for Victoria and is written by author Alan McSeveny. The book New Signpost Maths for Victoria is published by Pearson Education Australia. The ISBN of this book is 9780733983443 and the format is Paperback. The publisher has not provided a book description for New Signpost Maths for Victoria by Alan McSeveny.
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Perhaps the book's greatest strength is the author's zeal and skill for helping students write mathematics better. Careful guidance is given throughout the book. Basic issues like not abusing equal signs are treated explicitly. Attention is given to even relatively small issues, like not placing a mathematical symbol directly after a punctuation mark. Throughout the book, theorems are often followed first by informative 'scratch work' and only then by proofs. Thus students can see many examples of what they should think, what they should write, and how these are usually not the same."
–MAA Online
"This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course." ---Zentralblatt Math
From the Back Cover
This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis.
This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations.
A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised.
Reviews of the first edition:
This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. —Zentralblatt Math
'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book's greatest strength is the author's zeal and skill for helping students write mathematics better. —MAA Online
"Proofs and Fundamentals" by Ethan Bloch is undoubtly one of the few books I'd say would be required when beginning (and a light refrence as you progress) the undergraduate mathematics curriculum in most US schools.
There is some bit of controversay about "Foundations" courses in general. It use to be the case that there was no 'bridge' course that linked the more applied Calculus classes (something like your average 'multi-variable calculus' withi something more theory based such as Abtract Algebra)
The basics of proof writing were usually taught in your first theory course. In some institutions (I hear Cornell as one of them) still teach your basic proof writing in their first theory course. However, much of the large research state flagship schools in the country and even some of the older ivies such as Princeton (which I hear offers 2 - 3 foundations courses depending on your mathematical taste) now have come around to the concept of a bridge course in mathematics.
To be sure, the refinement of the curriculum to include some kind of bridge course in most departments in the US has led (in my opinion) to the ability for more students to study mathematics.
With that in mind, this book is wonderful for that purpose for the following reasons:
1. Its very readable 2. It gives an introduction to propositional logic and naive set theory. 3. It covers numerous fundemental topics that is the start to some very interesting mathematics.
To comment on the first point briefly, the author does utilize the standard definiton-theorem-proof-excercise template, however he addds alot of motivating exposition in between. What is motivating exposition? Well, Bloch writes (throughout the text) why we (the student) are learnign these concepts and how they fit into the various structures in mathematics.
He dosn't only talk about how concepts/theorems are relevent to theory, but mentions why a certain style maybe relevent to communication. One of Bloch's emphasis is the "communication" aspect of mathematics. That is, it is good to get good notation and adequate writing habits in the beginning (the later is something I have sort slagged on, as I'm more of a concise symbol man myself).
On reason 2, he gives a very good introduction to propositional logic. He even lists most of the rules of inferences early on. This section helped me tremendously. I was always curious on what was the final justification of many mathematical statements (which of course in the naive sense is just proof table verification). Learning this fact allowed me to enjoy mathematics more as it wasn't so much hand waving as a system of verifable statements (which makes math unique of all the subjects you could study).
After this chapter Bloch has a section for "strategy" in proofs. This section is more useful for the basic courses you will take immediatly after you take your foundations, but I honestly don't remember getting much of an impression while I was reading it. Stick to learning the naive foundational material and to doing lots of problems and you'll learn your own strategies. If you want a more concrete book on problem solving a good introduction to that is the "The Art and Craft to Problem Solving."
Of course the next section is naive set theory. Bloch does alot of work for you (and rightly so) in proving most of the results he mentions. Thus it makes this section very smooth reading. In fact, I do not think I did more then a handful of excercises and yet was able to grasp and use the material taught in the book (for most mathematics textbooks this is not possible).
Finally, the author provides the basics of topics that can lead to interesting studies into various differnt mathematics. A chapter of counting principles is included (Combinatorics), Number Systems (Real Analysis), Groups and Lattices (Algebra) and some small filler chapters in between like a chapter on binary operations, Recursion, Cardinality, Induction, and Fuzzy logic to name some.
I got a very good apprecaition for the Foundations from this book and I blame it for giving me my enthusiasm for Mathematical Logic. There are others which are better or worst on some topics, for instance, those who are interested mostly in Analysis may not find this book appealing (A good pure Analysis undergraduate handbook is 'Fundamentals of Analysis') but on balance, this book is good (I'd say excellent). I'd think the best way to utilize it would be to read it the summer before you start rigorious mathematics. Try some of the excercises and then attempt to correct your excercises (determine if they are right or wrong yourself). Then when you take your foundations course (or your first theory course), consult your instructor on your questions. I feel if one sticks to this regiment, they will be well on their way to a succesful curriculum in mathematics.Read more ›
This book is an excellent and thorough intorduction to the world of formal mathematics. Typically, a new mathematics student finds himself or herself picking up random mathematical concepts and techniques of proof along the way, without ever having the chance to sit down and go through the fundamentals of formal mathematics and proof. This book covers a little of everything, and has a thorough introduction to sets, functions, inverses, equivalence and order relations. There are also sections on introductory number theory, algebra, combinatorics, logic, and much more. It provides an excellent overview for the student who will be using these tools on a daily basis, for the layman who is interested in finding out what mathematics is really about, or for the seasoned mathematician who needs a good general reference book. There are also extensive and thorough sections on the construction and writing of mathematical proofs -- somthing on which many new and not-so-new mathematicians could use some improvement.
This book offers brief coverage of an impressive array of "fundamental" topics that are likely to come up in various later courses. The value here is that in most later (upper division) math classes there is a major benefit to knowing even a little of the material from some of the other upper division classes. On the other hand, this book simply will not help you learn how to do proofs. After going about half way through the book and working on the exercises, I realized that I was no better at doing proofs than when I began. The "hints" to the exercises in the back of the book are really no help at all for self study. I usually know the right strategy, what I really need to learn is the correct way to express my ideas as a proof, and this book does not provide very much guidance on how to do that.
I own a few proofs/transitions books. I have worked through Bloch's Proofs and Fundamentals (the first edition) and the book by Daniel Solow. Bloch has written the best and clearest book for self-study of proofs. The back of the book has over 20 useful pages of Hints for Selected Exercises. For those reviewers who think Bloch is too wordy, perhaps he is if you already have an instructor in a class explaining everything to you. But if you are on your own, trying to learn by working through a book, Bloch's explanations are just right.
I picked this book up one day in the bookstore, started reading and left with it. I was a math major at one point in college, but I moved on for other reasons. These days most math programs offer courses such as "Introduction to Proofs." This book serves that purpose. Now that I am back in college taking math courses again, I feel well prepared in my proof-oriented classes after going through about half of this book. The author does an excellent job of stressing the importance of proofs through language that is easy to understand. There is also a lot to read in the sense that concepts are explained and discussed in English. The exercises are adequate, although it would be better if more solutions were offered in the book (only select ones are). I did most of the exercises and that is where the real learning took place.
This book would not be useful for someone who has any kind of a background in proofs/fundamentals. It's for those who have only taken computation-oriented classes who want to learn how to do basic proofs. I would recommend finding a copy and opening it up to see if it fits your style. Anyone could learn from the beginning of this text, but it takes some mathematical sophistication to get through more advanced parts. The text seems technically precise (clarity on the difference between range and codomain for instance) and remains reader-friendly throughout. The author also does not hesitate on giving his opinions on how math proofs should be written. I liked the way that he emphasized writing proofs in complete sentences, and in keeping the scratch work and attempts at a proof separate from the proof itself. Also, despite the language, rigor and mathematical symbolism are not sacrificed.
*In response to critical reviews about exercises: At first glance I did not always see how the exercises related to the examples. After rereading the chapter, or trying out some different strategies, I usually was able to make sense of them. The exercises can sometimes be challenging in this manner, but that is not necessarily a bad thing. They emphasize understanding rather than modeling. I found some satisfaction in struggling through some of the exercises upon figuring them out on my own.
**Also, I agree with the critical review that this book will not make you better at doing proofs. If you want to improve upon proof technique, I would look elsewhere. This book is definitely for those entering the world of mathematical proofs for the very first time. Unfortunately, there are not enough solutions of proofs in the back that you can compare to your own.Read more › |
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The third edition of Maths Quest for Victoria has been updated and revised to comprehensively cover the Victorian Essential Learning Standards. The series continues to provide awardwinning features carefully designed to aid student thinking and learning with more opportunities for deep learning through guided investigations, integrated technology and increased problem solving.
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Summary Of The Book
TARGET CBSE Mathematics (Class - XII) is loaded with useful features that will prove to be a great help to students. Each of the chapters feature a section called 'Take a Look' which summarizes and highlights the important parts of that chapter. There are several exercises with both short and long questions for students to test what they have studied. The book also contains HOTS-based and NCERT questions along with the answers.
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this is one of the bst buk for preparation of board exams.....i and my friends found this buk to be very helpful for our preparation of board exams....
i would like to suggest all of you to buy this book only from flipkart.com....and start preparing for your exams from now onwards with the help of this amazing book....by mc graw hill.........best of luck for your board exams :)
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This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus,...
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This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus, Calculus I - III, Linear Algebra, Number Theory, and Abstract Algebra. The last two subject areas -- referred to as "books" on the site -- are under construction. To each topic within a book (for example, Epsilon and Delta within Calculus I) there is a "module" of approximately 20 to 30 problems. Each module also includes a help page of background material. The modules are interactive to some extent and often provide suggestions when wrong answers are entered site contains a Java applet that provides information about groups of order 1-15. The user selects an order of a group...
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This site contains a Java applet that provides information about groups of order 1-15. The user selects an order of a group between 1 and 15 and then a model group is generated using letters as elements. Using buttons of the applet one can illustrate different algebraic properties of this group.
This site hosts software that allows for the visualizatoin of finite groups using Pascal's Triangle. The software is...
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The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level...
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In this two-player game, players take turns assigning a value to one of the entries in a three by three matrix. Player N can select any free entry and give it a value of 1, while Player S can assign any entry the value 0. Player S wins if the matrix becomes singular; i. e. have a zero determinant. Otherwise, Player N wins. |
Solve Math Problems Online
Solving Math problems can be interesting with online learning sessions. Students can take these sessions based on their learning requirements and most importantly, they can schedule these sessions by staying at their home. It saves their time and gives personalized attention to students. They can work with proficient subject experts and solve tough Math problems in a virtual environment. It has been observed that most students face difficulties while solving Math problems and to tackle this situation, students need to revise each Math chapter in a thorough manner. Moreover, they can solve online Math questions, as well.
The following steps are generally followed to solve Math problems:
Read it carefully – Students need to read each Math problem carefully and consequently, they can solve it by using the right formula or concept. Reading as well as understanding the problem is necessary for a student in exams.
Break the problem into parts – Read and break the Math problem into two parts. Students need to solve each Math problem in a step-by-step manner by using the appropriate concepts.
Change it into an equation - It is important to convert the problem written in words into an equation. Then, students can solve it accurately.
Always cross check - Once you get the answer of Math problem, you should go back and recheck the entire steps. Sometimes, you may miss out some information that you need to include.
Ask until it gets clear - Math is all about concepts and hence, students need to understand Math concepts properly. Students should clear their doubts in each Math concept and then only, they can apply these concepts in a right manner. Moreover, students can opt for online Math sessions to solve each tough Math problem accurately.
To solve Math problems accurately and systematically, students need clear understanding of Math concepts. Solving Math problems is not an easy task, but students can make it easier by choosing online sessions with virtual tutors. TutorVista has a team of virtual Math tutors and they help students in understanding different Math problems in an accurate manner. Moreover, online tutors go through an extensive training before starting their sessions. Hence, they understand the student's learning problems and based on that they provide assistance to students.
Solving word problems is one of the tough problems in Math. It is added in the Math syllabus designed for different classes. It can happen in any Math topic like algebra, geometry and others. Students can choose online learning help for solving different Math problems. Free demo sessions are also available for this. Follow algebra word problems page offered by TutorVista as a reference.
Help with Math Topics
Several expert Math tutors are associated with TutorVista and they guide students by providing detailed information about each Math topic. Moreover, by choosing online sessions with TutorVista, students can easily solve all math problems in an organized manner. Moreover, they can schedule as many sessions as they need to revise each topic. Apart from this, students can practice online Math questions to brush up their knowledge before tests.
Solve problems in topics like:
Algebra
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Calculus
Pre-Algebra
Pre-calculus
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Discrete Mathematics
Statistics
Students can take online learning help for solving algebra expressions, geometry problems, equations, probability, statistics, calculus and many more. TutorVista provides suitable learning sessions for various topics. It is stated that online Math help session is well-organized and hence, students can take this session and improve their performance in tests.
Get a Math Problem Solver
Most students struggle with Math and they need Math problem solver. TutorVista offers Math problem solver for the convenience of students. Moreover, online calculator and virtual tutor both are known as Math Problem Solver. Based on the learning requirements, students can either use online Math calculator or they can schedule session with virtual tutor on different Math topics. In brief, by using online Math solver, students can solve all kinds of Math problems starting from simple to complex.
TutorVista offers online Math questions for different academic standards. Our virtual tutors first understand student's learning problems and then, they guide students properly throughout the entire session. Moreover, our online tutors explain the logic and make students understand the solution of each problem in a step-by-step manner. Moreover, students can practice online Math worksheets, as well. → Read More
Word Problem Solver
Math word problem solver offered by TutorVista is beneficial for students. Moreover, students can choose this learning facility as per their convenience. Students can use online calculators or else they can choose online sessions for solving Math word problems. Get online tutoring with TutorVista and improve your score in exams.
Solving Math Problems
Solve all your complex Math problems by opting for unlimited sessions with TutorVista. These online sessions are well-geared and make students familiar with each topic. In short, these are comprehensive, informative and useful for students in all manners. Through these online tutoring programs, students can get step-by-step explanations of each Math problem. Students are suggested to solve all Math problems by taking adequate help from virtual tutors.
Solved Examples
Question 1: Solve for x: 2$x^2$ - 11 $x$ - 21 = 0 Solution:
Given equation is quadratic equation, so let us solve by factorization method
2$x^2$ - 11 $x$ - 21 = 0
2$x^2$ - 14 $x$ + 3$x$ - 21 = 0
2$x$($x$ - 7) + 3($x$ - 7) = 0
(2$x$ + 3)($x$ - 7) = 0
By Zero Product Rule
2$x$ + 3 = o or $x$ - 7 = 0
$x$ = $\frac{-3}{2}$ or $x$ = 7
Question 2: Find the value of m.
5x + 10m = 6 for x = 1 Solution:
Put x = 1 in 5x + 10m = 6
5 $\times$ 1 + 10m = 6
5 + 10m = 6
10m = 1
m = $\frac{1}{10}$
Question 3: In how many different ways can the letters of the word 'OFFICES' be arranged? Solution:
The word 'OFFICES' consists of 7 letters out of which letter 'F' comes twice. |
There are only three types of solutions: no solution, one solution, or infinitely MANY solutions. Mr. Defining Wizard will explain how to analyze and determine which type of solution you have for your problem (graphically and algebraically). Don't forget to check your answersSpanish Tutor Level 1 is a spectacular app that teaches you Spanish vocabulary. This app has great features to ensure that you know your Spanish. It has a simple flashcards feature that you can use to quiz yourself and your friends. The testing feature is there to test your knowledge of the language so far with a simple multiple choice test. Concepts are things in the language other than the vocal that are necessary for anyone trying to learn Spanish. We will be constantly adding new Concepts. The number learner is a quick game to learn the numbers in Spanish.
--PLEASE READ IF YOU DOWNLOADED VERSION 1.0 or 1.1 -- There was a major bug in the specified versions. In those versions, if you quit the current run of the game through multitasking or you shut off your phone, your progress was lost. We fixed that in this version. We are sorry to say that it will reset your progress when you update this application this time, but it will never occur again. Sorry for all of the inconvenience.
Please leave comments with your thoughts and what you would like to see in future versions. If you like the application, please leave us a nice rating. It will really help us out!
A straight forward algebraic technique to solving a system may be the only option you have. In this app, Mr. Defining Wizard prepares you to utilize this method and use it to your advantage. Don't forget to check your answers. Solutions should be the same if you use the graphing, addition, or matrices method.
How many times have you been told to "reduce or simplify fractions"? Calculating the GCF is a common routine to begin to reduce your fractions completely. Master this skill and you will not be afraid of fractions any more!
Prime Factorization is a technique used to find out what all numbers are made up of. This insight is a preliminary step for many math problems such as: add, subtract, reduce, or simplify fractions. Mastering this skill will definitely prepare you for more advanced problems. Give it a try, and have fun!
A nifty algebraic technique, so good it deserves two names. The Algebraic or Elimination method hints at both the process and result of the method. In this app, Mr. Defining Wizard explains how to take advantage of this method. Don't forget to check your answers. Solutions should be the same if you use the graphing, substitution, or matrices method.
When solving logarithm equations, we can only rely on our knowledge of the logarithm properties. Understanding what the properties mean will help you in the long run. Review with Mr. Defining Wizard all properties so you are prepared for any problem you face.
What values can x be? What values can y be? Practice with Mr. Defining Wizard and develop a good eye for determining domain and range for any equation which includes: fractions, square roots, and linear equations.
Simply put, math problems containing <, >, <=, and >= are called inequalities and math problems containing = is called an equation. Solutions to both inequalities and equalities are numbers that make the statements true. Practice these type of problems with Mr. Defining Wizard for additional tips
Did you know that all inverse equations are symmetric across the line y=x? Why is this? Mr. Defining Wizard explains the definition of inverse and reviews a simple problem for you to refer back to for future referencing. Horizontal Line Test and Vertical Line Test are not reviewed in this app.
Dealing with a system that involves 3 or more variables and/or 3 or more equations are best solved using matrices. Learn the rules to solving a system of equations using matrices as an alternate method to the substitution and elimination methods.
A graphical representation of a system may lead to your solution. In this app, Mr. Defining Wizard explains how to take advantage of this method. Don't forget to check your answers. Solutions should be the same if you use the substitution, addition, or matrices method.
Mr. Defining Wizard keeps it real brief and simple in this app. When solving a system of equations, what method should you use? This app will help you become familiar with your options when solving a system of equations: graphing, substitution, addition, and matrices method |
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College Algebra
Our popular College Algebra course provides a working knowledge of college-level algebra and its applications. Emphasis is placed upon the solution and the application of linear and quadratic equations, word problems, polynomials, and rational and radical equations. Students perform operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions. |
Summary: - By Judith A. Penna - Contains keystroke level instruction for the Texas Instruments TI-83 Plus, TI-84 Plus, and TI-89 - Teaches students how to use a graphing calculator using actual examples and exercises from the main text - Mirrors the topic order to the main text to provide a just-in-time mode of instruction - Automatically ships with each new copy of the text |
Product description
Pre-Algebra (2nd edition) eases the transition from arithmetic to algebra. Algebraic expressions and linear equations are applied throughout a thorough review of operations on integers, fractions, decimals, percents, and radicals. Students explore relations and functions using equations, tables, and graphs. Chapters on statistics and geometry extend foundational concepts in preparation for high school courses. Problem-solving and real-life uses of math are featured in each chapter. Dominion through Math exercises regularly illustrate how mathematics can be used to manage God's creation to His glory.
Type: Boxed Set ()Category: > Home SchoolingISBN / UPC: 9780012516829/0012516821Publish Date: 1/1/2000Item No: 22440Vendor: Send The Light Distribution |
The text has been developed by the Secondary Component of the project, and constitutes the core of the sixth year in a seven-year middle and high school mathematics curriculum. All lessons have been reviewed and examined afresh for this edition but the overall content and mathematical prerequisites are the same as in previous editions. New instructional features for this edition include: a Big Idea, Mental Math questions, Activities, Guided Examples, and Quiz Yourself (QY |
20th & H: GW Law Dean's Blog
Webmath
Algebra. WebMath WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by.
Math.com Homework help
Department of Mathematics, IIT Kharagpur - ERNET Free student resources from Discovery Education. Find homework help, games and interactives, and step-by-step webmath help to help students learn and have fun. WebMath - Solve Your Math Problem Solve a Linear Equation Involving One Unknown - powered by WebMath
Solve a Linear Equation Involving One Unknown. WebMath Plot an Inequality - powered by WebMath. This page will show you how to plot an inequality. Plotting inequalities can be a bit difficult because entire portions of.
Free Student Resources | Digital textbooks and standards. Department of Theoretical and Applied Mathematics. (Akron, OH, USA)
The University of Akron : Department of Mathematics Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math. |
down to Mathematics: v. 1
Countdown to Mathematics has been written to help self-study students to revise and practise basic skills in arithmetic, algebra, geometry, graphs ...Show synopsisCountdown to Mathematics has been written to help self-study students to revise and practise basic skills in arithmetic, algebra, geometry, graphs and trigonometry. The nine teaching modules in Countdown to Mathematics have been split into two separate books. Volume 1 consists of Modules 1-4 and concentrates on basic mathematical skills. It deals with arithmetic, simple algebra, how to plot and read graphs, and the representation of data. Where possible, the techniques are illustrated with real-world applications. Volume 2 consists of Modules 5-9 and covers geometry, graphs, trigonometry and algebra.. The emphasis here is on the manipulative skills which are necessary for most mathematical courses beyond GCSE standard 256 p. Illustrations |
Differential Geometry
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.
This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.
Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.
A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
This original text for courses in differential geometry is geared toward advanced undergraduate and graduate majors in math and physics. Based on an advanced class taught by a world-renowned mathematician for more than fifty years, the treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Starting with an introduction to the various curvatures associated to a hypersurface embedded in Euclidean space, the text advances to a brief review of the differential and integral calculus on manifolds. A discussion of the fundamental notions of linear connections and their curvatures follows, along with considerations of Levi-Civita's theorem, bi-invariant metrics on a Lie group, Cartan calculations, Gauss's lemma, and variational formulas. Additional topics include the Hopf-Rinow, Myer's, and Frobenius theorems; special and general relativity; connections on principal and associated bundles; the star operator; superconnections; semi-Riemannian submersions; and Petrov types. Prerequisites include linear algebra and advanced calculus, preferably in the language of differential forms
New features of this revised and expanded second edition include:
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
Around 200 additional exercises, and a full solutions manual for instructors, available via
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.
Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations.
The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author's skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject.
The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem. |
Friendswood Precalculus
All individuals have an innate understanding of mathematics. We constantly use math concepts in our everyday lives. The successful math student understands the relationship between our intuitive understanding of math and the concepts presented in a formal class. |
College-Algebra.Com
College-Algebra.Com is affiliated with DrDelMath.Com.
Both are written, owned, and copyrighted by Delano P. Wegener, Ph.D. (DrDel)
This website and all content contained herein is for those students who are truly interested
in learning Algebra in College.College-Algebra.Com will be clearly different than most of the very many web sites which present
algebra topics. This website will be based on correct mathematics and well established principles of
learning and teaching.
Mathematics is an intellectual activity and is therefore learned by exercising
the intellect. Once the mathematics has been learned, it may be used to answer questions from virtually
every discipline or activity.
The content, presentation style, explanations, as well as frequent study advice will be designed
to emphasize conceptual understanding of the relevant mathematics principles. A solid understanding
of relevant mathematics is a necessary and sufficient condition to successfully use mathematics to
answer questions and solve problems in other areas.
In the last 25 - 30 years the United States has gone from Number 1 to Number 25
(link)
in a ranking of countries according to student's performance in mathematics.
In the last 25 - 30 years mathematics education in the United States has become a motor skill
type training activity based upon working thousands of insipid problems.
IS THERE A CORRELATION?
COGNITIVE SCIENCE EXPERTS
The teaching and learning theories employed on this website, and practiced for a lifetime by DrDel, are those well established and proven theories developed primarily by the the following cognitive scientists.
MATHEMATICS CONSIDERATIONS
Advice To The Student
Finding the answer is not your goal. Learning concepts, principles, and deductive reasoning
is your primary goal. A secondary goal is to improve your ability to use concepts, principles,
and deductive reasoning to answer a wide variety of questions both mathematical and non-mathematical.
My Pledge To The Student
I will do my utmost to assist your learning by presenting good mathematics, to present it
according to the best principles of teaching and learning as established by cognitive scientists, and to
use the computer and internet to the best of my ability to facilitate learning.
The mathematics will be correct.
There will be no "gimmicks" or "one-off" methods or procedures.
Every concept will be presented so that it is extensible.
Only noteworthy mathematics will be presented.
Reoccurring themes will be pointed out and will be clearly traceable through their various
contexts.
When a concept is an extension or abstraction of a previously learned concept that connection will be utilized to facilitate understanding.
Emphasis will be on concepts, generalizations, structure, abstraction, and algebra vs numbers.
ESSAYS
The essay section of the website is a collection of essays (past, present, and future)
about teaching and learning in general and in particular teaching and learning mathematics.
CONTENT TYPES AND PURPOSES
All the different instructional devices and their purpose.
TECHNICAL CONSIDERATIONS
I will strive to make College-Algebra.Com a state-of-the-art, standards compliant website, which passes all
relevant W3C validation tests. Accessibility issues will be addressed to the best of my abilities.
College-Algebra.Com will be a dynamic mathematics education website, with interactive content designed to facilitate learning. To accomplish these goals the
following languages, tools, and techniques will be used during development of College-Algebra.Com:
TIMELINE
Because the goals set forth above are ambitious and will be developed by one man in his spare time it will undoubtedly take years to complete.
Material will be added to the site when it is ready. That implies that during development some sections will contain more components than others. I will also use the index pages as planning documents. Therefore this site will usually have menu items that lead nowhere. I will do my best to mark them.
College-Algebra.Com will probably always be a work in progress.
CONTACT
Copyright 2007 by Delano P. Wegener, Ph.D.
All Rights Reserved. Use of text, images and other content on this website are subject to the terms and conditions specified on our Copyright and Fair Use page. |
9780387907ometry: A High School Course
At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course, naturally backed by numerous examples and exercises.
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How can I help a student whose quantitative skills are weak?
Books These books are designed specifically for self-instruction and are available for on-site use in the Quantitative Skills Center resource library. Most are also available in either the Reed library or through Summit.
Forgotten Algebra by Barbara Lee Bleau. Great self-guided course for students who either have forgotten their algebra or never really got it the first time around. Chapters are arranged by topic.
Mathematics: A Second Chance. This book was published in Britain so has some slightly unfamiliar vocabulary in places, but is otherwise excellent in taking the student from arithmetic to calculus in a straightforward way with plenty of practice problems.
Quick Calculus by Daniel Kleppner and Norman Ramsey. Co-authored by a Nobel-prizewinner in physics, this is a quick review or first run- through of integral and differential calculus. While not a replacement for a true first course in calculus, it may be a helpful refresher for students taking classes in other subjects where calculus is used.
Calculus Made Easy by Silvanus Thompson. A classic text that uses an intuitive approach to the explanation of calculus concepts. Recommended to me by a recent Reed econ alumnus who claims that for the first time he feels he can actually grasp calculus. |
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