American Mathematical Textbooks

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Mathematics and Music

David Wright
Mathematics and Music Book PDF

Author : David Wright
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 45,9 Mb
Release : 2009
Category : Music theory
ISBN : 9780821848739

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Mathematics and Music by David Wright Pdf

Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text.

A TeXas Style Introduction to Proof

Ron Taylor,Patrick X. Rault
A TeXas Style Introduction to Proof Book PDF

Author : Ron Taylor,Patrick X. Rault
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 54,7 Mb
Release : 2019-07-26
Category : Proof theory
ISBN : 9781470450465

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A TeXas Style Introduction to Proof by Ron Taylor,Patrick X. Rault Pdf

A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.

Discovering Discrete Dynamical Systems

Aimee Johnson,Kathleen Madden,Ayse Sahin
Discovering Discrete Dynamical Systems Book PDF

Author : Aimee Johnson,Kathleen Madden,Ayse Sahin
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 40,9 Mb
Release : 2017-12-31
Category : Mathematics
ISBN : 9781614441243

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Discovering Discrete Dynamical Systems by Aimee Johnson,Kathleen Madden,Ayse Sahin Pdf

Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.

Creative Mathematics

H. S. Wall
Creative Mathematics Book PDF

Author : H. S. Wall
Publisher : American Mathematical Soc.
Page : 219 pages
File Size : 40,6 Mb
Release : 2006-12-31
Category : Mathematics
ISBN : 9780883857502

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Creative Mathematics by H. S. Wall Pdf

Professor H. S. Wall (1902-1971) developed Creative Mathematics over a period of many years of working with students at the University of Texas, Austin. His aim was to lead students to develop their mathematical abilities, to help them learn the art of mathematics, and to teach them to create mathematical ideas. This book, according to Wall, ``is not a compendium of mathematical facts and inventions to be read over as a connoisseur of art looks over paintings. It is, instead, a sketchbook in which readers try their hands at mathematical discovery.'' In less than two hundred pages, he takes the reader on a stimulating tour starting with numbers, and then moving on to simple graphs, the integral, simple surfaces, successive approximations, linear spaces of simple graphs, and concluding with mechanical systems. The book is self contained, and assumes little formal mathematical background on the part of the reader.

American Mathematics 1890-1913

Steve Batterson
American Mathematics 1890 1913 Book PDF

Author : Steve Batterson
Publisher : The Mathematical Association of America
Page : 244 pages
File Size : 43,5 Mb
Release : 2017-06-29
Category : Mathematics
ISBN : 9780883855904

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American Mathematics 1890-1913 by Steve Batterson Pdf

At the turn of the twentieth century, mathematical scholarship in the United States underwent a stunning transformation. In 1890 no American professor was producing mathematical research worthy of international attention. Graduate students were then advised to pursue their studies abroad. By the start of World War I the standing of American mathematics had radically changed. George David Birkhoff, Leonard Dickson, and others were turning out cutting edge investigations that attracted notice in the intellectual centers of Europe. Harvard, Chicago, and Princeton maintained graduate programs comparable to those overseas. This book explores the people, timing, and factors behind this rapid advance. Through the mid-nineteenth century most American colleges followed a classical curriculum that, in mathematics, rarely reached beyond calculus. With no doctoral programs of any sort in the United States until 1860, mathematical scholarship lagged far behind that in Europe. After the Civil War, visionary presidents at Harvard and Johns Hopkins broadened and deepened the opportunities for study. The breakthrough for mathematics began in 1890 with the hiring, in consecutive years, of William F. Osgood and Maxime Bôcher at Harvard and E. H. Moore at Chicago. Each of these young men had studied in Germany where they acquired vital mathematical knowledge and taste. Over the next few years Osgood, Bôcher, and Moore established their own research programs and introduced new graduate courses. Working with other like-minded individuals through the nascent American Mathematical Society, the infrastructure of meetings and journals were created. In the early twentieth century Princeton dramatically upgraded its faculty to give the United States the stability of a third mathematics center. The publication by Birkhoff, in 1913, of the solution to a famous conjecture served notice that American mathematics had earned consideration with the European powers of Germany, France, Italy, England, and Russia.

Common Sense Mathematics: Second Edition

Ethan D. Bolker,Maura B. Mast
Common Sense Mathematics Second Edition Book PDF

Author : Ethan D. Bolker,Maura B. Mast
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 42,7 Mb
Release : 2021-01-21
Category : Education
ISBN : 9781470461348

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Common Sense Mathematics: Second Edition by Ethan D. Bolker,Maura B. Mast Pdf

Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them—common sense and common knowledge—not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world—this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully—and critically—about numerical information in everyday contexts.

Exercises in (Mathematical) Style

John McCleary
Exercises in Mathematical Style Book PDF

Author : John McCleary
Publisher : The Mathematical Association of America
Page : 289 pages
File Size : 40,7 Mb
Release : 2017-05-17
Category : Mathematics
ISBN : 9780883856529

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Exercises in (Mathematical) Style by John McCleary Pdf

Hover over the image to zoom. Click the image for a popup.Email a Friend About This ItemLogin to Submit a Review inShare John McCleary In Exercises in (Mathematical) Style, the author investigates the world of that familiar set of numbers, the binomial coefficients. While the reader learns some of the properties, relations, and generalizations of the numbers of Pascal's triangle, each story explores a different mode of discourse - from arguing algebraically, combinatorially, geometrically, or by induction, contradiction, or recursion to discovering mathematical facts in poems, music, letters, and various styles of stories. The author follows the example of Raymond Queneau's Exercises in Style, giving the reader 99 stories in various styles. The ubiquitous nature of binomial coefficients leads the tour through combinatorics, number theory, algebra, analysis, and even topology. The book celebrates the joy of writing and the joy of mathematics, found by engaging the rich properties of this simple set of numbers.

The Knot Book

Colin Conrad Adams
The Knot Book Book PDF

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 51,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Bridge to Abstract Mathematics

Ralph W. Oberste-Vorth,Bonita A. Lawrence
Bridge to Abstract Mathematics Book PDF

Author : Ralph W. Oberste-Vorth,Bonita A. Lawrence
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 52,7 Mb
Release : 2012
Category : Education
ISBN : 9780883857793

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Bridge to Abstract Mathematics by Ralph W. Oberste-Vorth,Bonita A. Lawrence Pdf

A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.

Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning

Wendy M. Smith,Matthew Voigt,April Ström,David C. Webb,W. Gary Martin
Transformational Change Efforts Student Engagement in Mathematics through an Institutional Network for Active Learning Book PDF

Author : Wendy M. Smith,Matthew Voigt,April Ström,David C. Webb,W. Gary Martin
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 47,6 Mb
Release : 2021-05-05
Category : Education
ISBN : 9781470463779

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Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning by Wendy M. Smith,Matthew Voigt,April Ström,David C. Webb,W. Gary Martin Pdf

The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. We report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study. SEMINAL's purpose is to help change agents, those looking to (or currently attempting to) enact change within mathematics departments and beyond—trying to reform the instruction of their lower division mathematics courses in order to promote high achievement for all students. SEMINAL specifically studies the change mechanisms that allow postsecondary institutions to incorporate and sustain active learning in Precalculus to Calculus 2 learning environments. Out of the approximately 2.5 million students enrolled in collegiate mathematics courses each year, over 90% are enrolled in Precalculus to Calculus 2 courses. Forty-four percent of mathematics departments think active learning mathematics strategies are important for Precalculus to Calculus 2 courses, but only 15 percnt state that they are very successful at implementing them. Therefore, insights into the following research question will help with institutional transformations: What conditions, strategies, interventions and actions at the departmental and classroom levels contribute to the initiation, implementation, and institutional sustainability of active learning in the undergraduate calculus sequence (Precalculus to Calculus 2) across varied institutions?

How to Teach Mathematics, Second Edition

Steven George Krantz
How to Teach Mathematics Second Edition Book PDF

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 54,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821813980

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How to Teach Mathematics, Second Edition by Steven George Krantz Pdf

This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues. Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. He also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner. The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications.

Testimonios: Stories of Latinx and Hispanic Mathematicians

Pamela E. Harris
Testimonios Stories of Latinx and Hispanic Mathematicians Book PDF

Author : Pamela E. Harris
Publisher : American Mathematical Soc.
Page : 286 pages
File Size : 40,5 Mb
Release : 2021-08-16
Category : Education
ISBN : 9781470466572

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Testimonios: Stories of Latinx and Hispanic Mathematicians by Pamela E. Harris Pdf

Testimonios brings together first-person narratives from the vibrant, diverse, and complex Latinx and Hispanic mathematical community. Starting with childhood and family, the authors recount their own individual stories, highlighting their upbringing, education, and career paths. Their particular stories, told in their own voices, from their own perspectives, give visibility to some of the experiences of Latinx/Hispanic mathematicians. Testimonios seeks to inspire the next generation of Latinx and Hispanic mathematicians by featuring the stories of people like them, holding a mirror up to our own community. It also aims to provide a window for mathematicians (and aspiring mathematicians) from all ethnicities, with the hope of inspiring a better understanding of the diversity of the mathematical community.

Pre-Calculus, Calculus, and Beyond

Hung-Hsi Wu
Pre Calculus Calculus and Beyond Book PDF

Author : Hung-Hsi Wu
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 55,8 Mb
Release : 2020-10-26
Category : Education
ISBN : 9781470456771

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Pre-Calculus, Calculus, and Beyond by Hung-Hsi Wu Pdf

This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. This volume distinguishes itself from others of the same genre in getting the mathematics right. In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles. It also provides details for extending the domain of definition of sine and cosine to all real numbers. It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians. In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs. An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator. This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.

A Gentle Introduction to the American Invitational Mathematics Exam

Scott A. Annin
A Gentle Introduction to the American Invitational Mathematics Exam Book PDF

Author : Scott A. Annin
Publisher : The Mathematical Association of America
Page : 399 pages
File Size : 42,5 Mb
Release : 2015-11-16
Category : Mathematics
ISBN : 9780883858356

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A Gentle Introduction to the American Invitational Mathematics Exam by Scott A. Annin Pdf

This book is a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. There is no other book on the market focused on the AIME. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. After all, serious AIME contenders and competitors should seek a lot of practice in order to succeed. However, this book is also intended for anyone who enjoys solving problems as a recreational pursuit. The AIME contains many problems that have the power to foster enthusiasm for mathematics – the problems are fun, engaging, and addictive. The problems found within these pages can be used by teachers who wish to challenge their students, and they can be used to foster a community of lovers of mathematical problem solving! There are more than 250 fully-solved problems in the book, containing examples from AIME competitions of the 1980’s, 1990’s, 2000’s, and 2010’s. In some cases, multiple solutions are presented to highlight variable approaches. To help problem-solvers with the exercises, the author provides two levels of hints to each exercise in the book, one to help stuck starters get an idea how to begin, and another to provide more guidance in navigating an approach to the solution.

Mathematics for Social Justice: Resources for the College Classroom

Gizem Karaali,Lily S. Khadjavi
Mathematics for Social Justice Resources for the College Classroom Book PDF

Author : Gizem Karaali,Lily S. Khadjavi
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 46,6 Mb
Release : 2019-07-09
Category : Mathematics
ISBN : 9781470449261

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Mathematics for Social Justice: Resources for the College Classroom by Gizem Karaali,Lily S. Khadjavi Pdf

Mathematics for Social Justice offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book begins with a series of essays from instructors experienced in integrating social justice themes into their pedagogy; these essays contain political and pedagogical motivations as well as nuts-and-bolts teaching advice. The heart of the book is a collection of fourteen classroom-tested modules featuring ready-to-use activities and investigations for the college mathematics classroom. The mathematical tools and techniques used are relevant to a wide variety of courses including college algebra, math for the liberal arts, calculus, differential equations, discrete mathematics, geometry, financial mathematics, and combinatorics. The social justice themes include human trafficking, income inequality, environmental justice, gerrymandering, voting methods, and access to education. The volume editors are leaders of the national movement to include social justice material into mathematics teaching. Gizem Karaali is Associate Professor of Mathematics at Pomona College. She is one of the founding editors of The Journal of Humanistic Mathematics, and an associate editor for The Mathematical Intelligencer and Numeracy ; she also serves on the editorial board of the MAA's Carus Mathematical Monographs. Lily Khadjavi is Associate Professor of Mathematics at Loyola Marymount University and is a past co-chair of the Infinite Possibilities Conference. She has served on the boards of Building Diversity in Science, the Barbara Jordan-Bayard Rustin Coalition, and the Harvard Gender and Sexuality Caucus.