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Exploring Discrete Geometry Thomas Q. Sibley Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society,, NML, 56.E, 2024

Together with its clear mathematical exposition, the problems in this book take the reader from an introduction to discrete geometry all the way to its frontiers. Investigations start with easily drawn figures, such as dividing a polygon into triangles or finding the minimum number of “guards” for a polygon (“art gallery” problem). These early explorations build intuition and set the stage. Variations on the initial problems stretch this intuition in new directions. These variations on problems together with growing intuition and understanding illustrate the theme of this book: “When you have answered the question, it is time to question the answer.” Numerous drawings, informal explanations, and careful reasoning build on high school algebra and geometry.

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lgli/Hahn - Complex Numbers and Geometry.pdf

Complex Numbers and Geometry Liang-Shin Hahn MAA Press, an imprint of the American Mathematical Society, AMS/MAA Textbooks; 52, Reprint, 2019

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more. -- Provided by publisher.

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lgli/O. A. Ivanov [Ivanov, O. A.] - Portal Through Mathematics: Journey to Advanced Thinking (2019, American Mathematical Soc.).pdf

Portal through Mathematics: Journey to Advanced Thinking (Anneli Lax New Mathematical Library) O. A. Ivanov [Ivanov, O. A.] MAA Press, an imprint of the American Mathematical Society, 2019

"A Portal Through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer. The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone. A Portal Through Mathematics will be useful for prospective secondary teachers of mathematics and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it." -- Publisher's description

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ia/graphtheory0000dani.pdf

Graph Theory : A Problem Oriented Approach Marcus, Daniel A.; Mathematical Association of America MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Washington, D.C., 2020

"Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in that it combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems. This problem-oriented format is intended to promote active involvement by the reader while always providing clear direction. This approach figures prominently on the presentation of proofs, which become more frequent and elaborate as the book progresses. Arguments are arranged in digestible chunks and always appear along with concrete examples to keep the readers firmly grounded in their motivation. Spanning tree algorithms, Euler paths, Hamilton paths and cycles, planar graphs, independence and covering, connections and obstructions, and vertex and edge colorings make up the core of the book. Hall's Theorem, the Konig-Egervary Theorem, Dilworth's Theorem and the Hungarian algorithm to the optional assignment problem, matrices, and Latin squares are also explored."--Page 4 of cover

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TASTY JAPANESE MORSELS IN RECREATIONAL MATHEMATICS. Kotani, Yoshiyuki Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society,, AMS / MAA, 105, 2024

This book is a charming collection of puzzles created by Yoshiyuki Kotani, one of the founding members of the Academy of Recreational Mathematics, Japan. Kotani has selected some of his favorite puzzles from over 40 years of puzzle setting, most of which have never appeared in western literature. The distinctive culture of Japanese recreational mathematics is encapsulated in this volume from one of its leading architects.Beginning with a sampler of problems to whet the appetite, the reader is led through a three-course menu of combinatorial, arithmetic, and geometrical problems. Highlights include the Wagashi Combo, a puzzle devised during Kotani's youth, where the reader has to combine two plane figures to construct a new shape in two distinct ways. Everything is tied together with a playful narrative of a Japanese restaurant, adding fun and humor to the challenge. The book ends with a miscellany of problems that expand on the ideas from earlier chapters.Suitable for anyone with an interest in recreational mathematics, the puzzles in this book require no formal mathematical training. Novice and experienced solvers alike will delight in this original and delicious offering of Japanese puzzles.

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ia/opendoortonumber0000camp.pdf

An Open Door to Number Theory (MAA Textbooks) (AMS / MAA Textbooks) Duff Campbell Providence, Rhode Island: MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Providence, Rhode Island, 2018

A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the $p$-adic numbers, quadratic extensions of the integers, and arithmetic generating functions.

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Mathematical Interest Theory: Third Edition (AMS/MAA Textbooks) Leslie Jane Federer Vaaler, Shinko Kojima Harper, James W. Daniel MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Providence, 2019

Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. The text has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam. To that end, Mathematical Interest Theory includes more than 260 carefully worked examples. There are over 475 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to use the Texas Instruments BA II Plus and BA II Plus Professional calculators to efficiently solve the problems. This Third Edition updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17. Online assignments for this title are available in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.

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nexusstc/Portal through Mathematics: Journey to Advanced Thinking (Anneli Lax New Mathematical Library)/5746ec00e526683859f8fe24645aec67.pdf

Portal through Mathematics: Journey to Advanced Thinking (Anneli Lax New Mathematical Library) Oleg A. Ivanov MAA Press, an imprint of the American Mathematical Society, Anneli Lax New Mathematical Library, 52, 02, 2018

"A Portal Through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer. The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone. A Portal Through Mathematics will be useful for prospective secondary teachers of mathematics and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it." -- Publisher's description

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lgli/Kennedy B.B. Welcome to real analysis.. continuity and calculus, distance and dynamics (text70, AMS, 2022)(ISBN 9781470464547)(O)(375s)_MCet_.pdf

Welcome to Real Analysis: Continuity and Calculus, Distance and Dynamics (Ams/Maa Textbooks, 70) Benjamin B. Kennedy MAA Press, an imprint of the American Mathematical Society, AMS/MAA textbooks, Providence, Rhode Island, 2022

Welcome to Real Analysis is designed for use in an introductory undergraduate course in real analysis. Much of the development is in the setting of the general metric space. The book makes substantial use not only of the real line and $n$-dimensional Euclidean space, but also sequence and function spaces. Proving and extending results from single-variable calculus provides motivation throughout. The more abstract ideas come to life in meaningful and accessible applications. For example, the contraction mapping principle is used to prove an existence and uniqueness theorem for solutions of ordinary differential equations and the existence of certain fractals; the continuity of the integration operator on the space of continuous functions on a compact interval paves the way for some results about power series. The exposition is exceedingly clear and well-motivated. There are a wide variety of exercises and many pedagogical innovations. For example, each chapter includes Reading Questions so that students can check their understanding. In addition to the standard material in a first real analysis course, the book contains two concluding chapters on dynamical systems and fractals as an illustration of the power of the theory developed.

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lgli/P:\kat_magz\Assorted Books Collection - November 11 2020 Part-2/Bicycle or Unicycle - A Collection of Intriguing Mathematical Puzzles.pdf

Bicycle or Unicycle?\_A Collection of Intriguing Mathematical Puzzles Velleman, Daniel J.;Wagon, Stan MAA Press, an imprint of the American Mathematical Society, AMS/MAA problem books vol 36, 2020

Bicycle or Unicycle? is a collection of 105 mathematical puzzles whose defining characteristic is the surprise encountered in their solutions. Solvers will be surprised, even occasionally shocked, at those solutions. The problems unfold into levels of depth and generality very unusual in the types of problems seen in contests. In contrast to contest problems, these are problems meant to be savored; many solutions, all beautifully explained, lead to unanswered research questions. At the same time, the mathematics necessary to understand the problems and their solutions is all at the undergraduate level. The puzzles will, nonetheless, appeal to professionals as well as to students and, in fact, to anyone who finds delight in an unexpected discovery. These problems were selected from the Macalester College Problem of the Week archive. The Macalester tradition of a weekly problem was started by Joseph Konhauser in 1968. In 1993 Stan Wagon assumed problem-generating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twenty-five years of the archive. The title problem in that collection was inspired by an error in logic made by Sherlock Holmes, who attempted to determine the direction of a bicycle from the tracks of its wheels. Here the title problem asks whether a bicycle track can always be distinguished from a unicycle track. You'll be surprised by the answer.

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nexusstc/A History of Mathematics in the United States and Canada: Volume 1: 1492–1900/9af7a099b7133aa96d4d48333321eeb3.pdf

A history of mathematics in the United States and Canada. volume 1 : 1492-1900 David E. Zitarelli, American Mathematical Society Staff MAA Press, an imprint of the American Mathematical Society, MAA spectrum (Print), volume 94, Providence, RI, 2019

This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli is emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he is one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this is his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.

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nexusstc/Mathematical interest theory/b40d79b3b0aac5d3751f65d0eb2ce91c.pdf

Mathematical Interest Theory: Third Edition (AMS/MAA Textbooks) Leslie Jane Federer Vaaler, Shinko Kojima Harper, James W. Daniel MAA Press, an imprint of the American Mathematical Society, AMS/MAA textbooks, vol. 57, Third edition, Providence, Rhode Island, 2019

Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course.The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. The text has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam. To that end, Mathematical Interest Theory includes more than 260 carefully worked examples. There are over 475 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to use the Texas Instruments BA II Plus and BA II Plus Professional calculators to efficiently solve the problems. This Third Edition updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17.Online assignments for this title are available in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.ReadershipUndergraduate and graduate students interested in preparing for the Society of Actuaries (SOA) Financial Mathematics (FM) exam.

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lgli/Arithmetical, Geometrical, and Combinatorial Puzzles from Japan (2021) [AMS_MAA Spectrum] by Tadao Kitazawa, Andy Liu, George Sicherman.pdf

Arithmetical, Geometrical and Combinatorial Puzzles from Japan (Spectrum, 102) Tadao Kitazawa; Andy Chiang-Fung Liu; George Sicherman MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Providence, Rhode Island, 2021

"The vibrant recreational mathematics culture of Japan presents puzzles that are often quite different from the classics of western literature. This book is the first collection of original puzzles by Tadao Kitazawa, a prominent Japanese puzzle-maker. These puzzles, which feature arithmetic, geometry, and combinatorics, are novel, creative, and require almost no formal mathematical knowledge. Kitazawa is particularly skillful in subtly modifying existing ideas to explore their potential to the full. For one example, a Tower Square is a Sudoku-like grid, but each row and column contains one 1, two 2s, three 3s, etc. The resulting transformation of the familiar problem is magical, and it is one of a variety of gems in this book. The common denominator is fun!" -- Provided by publisher

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nexusstc/Never a Dull Moment: Hassler Whitney, Mathematics Pioneer/8ec3fbb535d3a5b870dd418615f4876d.pdf

Never a Dull Moment: Hassler Whitney, Mathematics Pioneer (Spectrum) Keith Kendig MAA Press, an imprint of the American Mathematical Society, AMS/MAA spectrum, vol. 93, Providence, Rhode Island, 2018

Hassler Whitney was a giant of twentieth-century mathematics. This biography paints a picture of him and includes dozens of revealing anecdotes. Mathematically, he had a rare detector that went off whenever he spotted a piece of mathematical gold, and he would then draw countless pictures, gradually forging a path from hunch to proof. This geometric path is seldom reflected in the rigor of his formal papers, but thanks to a close friendship and many conversations over decades, author Kendig was able to see how he actually worked. This book shows this through accessible accounts of his major mathematical contributions, with figures copiously supplied. Whitney is probably best known for introducing the grandfather of today's innumerable embedding theorems his strong embedding theorem stating that any smooth manifold can be smoothly embedded in a Euclidean space of twice the manifold's dimension. This in turn led to several standard techniques used every day in algebraic topology. Whitney also established the fundamentals of graph theory, the four-color problem, matroids, extending smooth functions, and singularities of smooth functions. He almost never used complicated technical machinery, so most of his work is accessible to a general reader with a modest mathematical background. His math-music connection was intense: He played piano, violin, and viola and won best composition of the year while earning a Bachelor's degree in music at Yale. He was an accomplished mountain climber, and as a tinkerer, at age fourteen he built the large-format camera used to take this book's cover photograph. Whitney's family generously provided dozens of photographs appearing here for the very first time. This biography is a revealing portrait of a fascinating personality and a titan of twentieth-century mathematics.

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nexusstc/Nuggets of Number Theory: A Visual Approach/29114a4f33033b96924964919bee17e6.pdf

Nuggets of Number Theory: A Visual Approach (Classroom Resource Materials) (Classroom Resource Materials, 55) Roger B. Nelsen MAA Press, an imprint of the American Mathematical Society, Classroom resource materials, volume 55, Providence, Rhode Island, 2018

Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a long-time contributor of “Proofs Without Words” in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.

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Functions and Graphs (Problem Books) James Tanton MAA Press, an imprint of the American Mathematical Society, Study Guide, 2018-07-26

A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. Tanton provides a coherent guided tour of exploration and discovery of a rich mathematical landscape. The exploration is presented through problems selected from the history of the Mathematical Association of America's American Mathematics Competition (AMC). Secondary school teachers looking for supplementary and enrichment materials will find this a rich resource, which aligns with national curriculum standards. High school and college calculus and precalculus students will discover an approachable and thought-provoking review, preview, and overview of these central mathematical ideas. Students preparing for the AMC should find it especially helpful. Active reading, with pencil in hand, will result in a deep appreciation and understanding of the properties of functions. James Tanton is the MAA's mathematician-at-large. A research mathematician with experience teaching at both the college and high school levels, he now works to encourage and aid all mathematics instructors to teach--and all mathematics students to learn-joyously and effectively.

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nexusstc/Elementary Mathematical Models/26da14e59e32ed1a48e7e01551289469.pdf

Elementary Mathematical Models: An Accessible Development Without Calculus, Second Edition (AMS/MAA Textbooks) (AMS/MAA Textbooks, 50) Dan Kalman, Sacha Forgoston, Albert Goetz MAA Press, an imprint of the American Mathematical Society, 2, 2019-08-02

Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus. This book builds, successively, a series of growth models defi ned in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically—and scientifi cally—interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefi t from more than 1,000 carefully crafted exercises.

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Number Theory Through the Eyes of Sophie Germain (Classroom Resource Materials) David Pengelley MAA Press, an imprint of the American Mathematical Society, Classroom Resource Materials, 70, 2023

Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course. Sophie Germain (1776–1831) was largely self-taught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood this work from her unpublished letters and manuscripts. David Pengelley has been a driving force in unraveling this mystery and here he masterfully guides his readers along a path of discovery. Germain, because of her circumstances as the first woman to do important original mathematical research, was forced to learn most of what we now include in an undergraduate number theory course for herself. Pengelley has taken excerpts of her writings (and those of others) and, by asking his readers to decipher them, skillfully leads us through an inquiry-based course in elementary number theory. It is a detective story on multiple levels. What is Sophie Germain thinking? What do her mathematical writings mean? How do we understand what she knew and what she was trying to do, where she succeeded and where she didn't? Number Theory Through the Eyes of Sophie Germainis simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician. Work is required of the reader. Readers are carefully guided to discover and prove almost all results for themselves in a sequence of scaffolded exploratory tasks with hints, fully integrated with the narrative. The difficulty of the inquiry tasks varies considerably, but the author provides the reader with appropriately helpful guidance at every step. An introductory number theory course taught with this text would be a remarkable, potentially life-changing, experience.

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nexusstc/A Gateway to Number Theory - Applying the Power of Algebraic Curves/d72cde1609e3fee60a42c1f8fa30f569.pdf

A Gateway to Number Theory - Applying the Power of Algebraic Curves Keith Kendig MAA Press, an imprint of the American Mathematical Society, Dolciani Mathematical Expositions 57, 1, 2021

Challenge: Can you find all the integers a, b, c satisfying 2a^2+3b^2=5c^2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, b, c will usually be large. So the challenge remains ... Find all integers a, b, c satisfying 2a^2+3b^2=5c^2. A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables a, b, c into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to 2a^2+3b^2=5c^2 is included in the book.) In addition to equations of degree two, the book addresses degree-three equations—a branch of number theory that is today something of a cottage industry, and these problems translate into “elliptic curves”. This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp. This book will fit nicely into an introductory course on number theory. In addition, the many solved examples, illustrations, and exercises make self-studying the book an option for students, thus becoming a natural candidate for a capstone course.

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nexusstc/Calculus from Approximation to Theory/b226bb10e9f71f1d0fc0550b627c3cfa.pdf

Calculus From Approximation to Theory (Ams/Maa Textbooks) Daniel C. Sloughter MAA Press: an imprint of the American Mathematical Society, AMS/MAA Textbooks, 64, 2020

Calculus from Approximation to Theory takes a fresh and innovative look at the teaching and learning of calculus. One way to describe calculus might be to say it is a suite of techniques that approximate curved things by flat things and through a limiting process applied to those approximations arrive at an exact answer. Standard approaches to calculus focus on that limiting process as the heart of the matter. This text places its emphasis on the approximating processes and thus illuminates the motivating ideas and makes clearer the scientific usefulness, indeed centrality, of the subject while paying careful attention to the theoretical foundations. Limits are defined in terms of sequences, the derivative is defined from the best affine approximation, and greater attention than usual is paid to numerical techniques and the order of an approximation. Access to modern computational tools is presumed throughout and the use of these tools is woven seamlessly into the exposition and problems. All of the central topics of a yearlong calculus course are covered, with the addition of treatment of difference equations, a chapter on the complex plane as the arena for motion in two dimensions, and a much more thorough and modern treatment of differential equations than is standard. Dan Sloughter is Emeritus Professor of Mathematics at Furman University with interests in probability, statistics, and the philosophy of mathematics and statistics. He has been involved in efforts to reform calculus instruction for decades and has published widely on that topic. This book, one of the results of that work, is very well suited for a yearlong introduction to calculus that focuses on ideas over techniques.

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Calculus in 3D: Geometry, Vectors, and Multivariate Calculus (MAA Textbooks) (AMS/MAA Textbooks) Nitecki, Zbigniew H MAA Press : American Mathematical Society. C, AMS/MAA Textbooks, 40, 1, 2018

Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, MAA Press.

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nexusstc/Differential Equations: From Calculus to Dynamical Systems/73b8f93424a0a7d6a178a44e6c0d90be.pdf

Differential Equations: From Calculus to Dynamical Systems: Second Edition (AMS/MAA Textbooks) (AMS/MAA Textbooks, 43) Virginia Walbran Noonburg MAA Press, an imprint of the American Mathematical Society, AMS/MAA Textbooks, 43, 2, 2019

A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.ReadershipUndergraduate students interested in teaching and learning differential equations (both ordinary and PDE).

English [en] · PDF · 5.3MB · 2019 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

ia/exercisesinstyle0000john.pdf

Exercises In (mathematical) Style: Stories Of Binomial Coefficients (anneli Lax New Mathematical Library) McCleary, John MAA Press, an imprint of the Mathematical Association of America, American Mathematical Society, Providence, 2018

What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the well-known numbers, the binomial coefficients. The author follows the example of Raymond Queneau's Exercises in Style. Offering the reader 99 stories in various styles. The book celebrates the joy of mathematics and the joy of writing mathematics by exploring the rich properties of this familiar collection of numbers. For any one interested in mathematics, from high school students on up.

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nexusstc/Hex. A Playful Introduction/bf6ebe8b034632850169c33e7d0b3f5b.pdf

Hex : a playful introduction Ryan B. Hayward, Bjarne Toft MAA Press, an imprint of the American Mathematical Society, AMS / MAA ANNELI LAX NEW MATHEMATICAL LIBRARY, VOL 54

This book offers a gentle introduction to Hex, the classic board game created by Piet Hein and popularized by John Nash and Martin Gardner. The first three chapters cover rules, basic strategy, and history. The remaining eight chapters cover a variety of topics: mathematical properties (there are no draws, the first player can win, the acute corner is a losing first move), the related game of Y, winning strategies for small boards, how computers play Hex, and analysis of Random-Move Hex (where one or both players move randomly) and Dark Hex (the imperfect information version of the game, where you can't see your opponent's moves). Did we mention puzzles? There are puzzles in every chapter, with solutions. This book is intended for anyone interested in playing board games or learning some recreational mathematics. It is written for a wide audience and will be enjoyed equally by general readers and professional mathematicians. The book could be used as a textbook or companion resource for a topics course on recreational mathematics or game theory or as a source for undergraduate research questions.

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nexusstc/A History of Mathematics in the United States and Canada, Volume 2: 1900–1941/b86b2e39cf503ceecbfc926951d793cd.pdf

A History of Mathematics in the United States and Canada, Volume 2: 1900–1941 David E. Zitarelli, Della Dumbaugh, Stephen F. Kennedy MAA Press, an imprint of the American Mathematical Society, AMS/MAA Spectrum, 2022

This is the first truly comprehensive and thorough history of the development of a mathematical community in the United States and Canada. This second volume starts at the turn of the twentieth century with a mathematical community that is firmly established and traces its growth over the next forty years, at the end of which the American mathematical community is pre-eminent in the world. In the preface to the first volume of this work Zitarelli reveals his animating philosophy, “I find that the human factor lends life and vitality to any subject.” History of mathematics, in the Zitarelli conception, is not just a collection of abstract ideas and their development. It is a community of people and practices joining together to understand, perpetuate, and advance those ideas and each other. Telling the story of mathematics means telling the stories of these people: their accomplishments and triumphs; the institutions and structures they built; their interpersonal and scientific interactions; and their failures and shortcomings. One of the most hopeful developments of the period 1900–1941 in American mathematics was the opening of the community to previously excluded populations. Increasing numbers of women were welcomed into mathematics, many of whom―including Anna Pell Wheeler, Olive Hazlett, and Mayme Logsdon―are profiled in these pages. Black mathematicians were often systemically excluded during this period, but, in spite of the obstacles, Elbert Frank Cox, Dudley Woodard, David Blackwell, and others built careers of significant accomplishment that are described here. The effect on the substantial community of European immigrants is detailed through the stories of dozens of individuals. In clear and compelling prose Zitarelli, Dumbaugh, and Kennedy spin a tale accessible to experts, general readers, and anyone interested in the history of science in North America.

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nexusstc/Looking for Math in All the Wrong Places/eec5d37aece0548483de2422d7b10b03.pdf

Looking for math in all the wrong places : math in real life Shai Simonson MAA Press, an imprint of the American Mathematical Society, Spectrum, Spectrum, 104, 2022

The soul of mathematics is the practice of skeptical inquiry: asking how and why things work, experimenting, exploring, and discovering. Estimation, analysis, computation, conjecture, and proof are the mathematical path to uncovering truth and we can use them in nearly every human pursuit. In this thoroughly charming and beguiling book, Shai Simonson applies mathematical tools in a variety of contexts that arise in everyday life to prove his claim that math is, literally, everywhere. Simonson applies his mathematical cast of mind to hiking, birthday parties, carnival games, lock picking, and kite flying. We see unexpected depths and connections when we look in the "wrong" places in the right way. No advanced mathematical knowledge is required to travel with Simonson and share in his investigations. All a reader needs is an open and curious mind, an eagerness to ask questions, and a willingness to think deeply and carefully about seemingly mundane things. There is wonder and joy in quotidian life with Simonson as your guide -- Amazon

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lgli/N:\!genesis_files_for_add\_add\kolxo3\93\M_Mathematics\MT_Number theory\Campbell D. An open door to number theory (text-39, MAA, 2018)(ISBN 9781470443481)(O)(297s)_MT_.pdf

An Open Door to Number Theory (MAA Textbooks) (AMS / MAA Textbooks) Campbell, Duff Mathematical Association of America, AMS/MAA textbooks, volume 39, Providence, Rhode Island, 2018

A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the $p$-adic numbers, quadratic extensions of the integers, and arithmetic generating functions.

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nexusstc/The History of Mathematics: A Source-Based Approach, Volume 2 (AMS/MAA Textbooks, 61)/86d45ff9c8589c30a11200cbf3f9521a.pdf

The History of Mathematics: A Source-Based Approach, Volume 2 (AMS/MAA Textbooks, 61) June Barrow-Green, Jeremy Gray, Robin Wilson, Jeremy J. Gray, Robin J. Wilson MAA Press, an imprint of the American Mathematical Society, Providence, Rhode Island, 2022

The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

English [en] · PDF · 94.8MB · 2022 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

upload/newsarch_ebooks/2023/02/28/extracted__A_Panoply_of_Polygons.zip/A Panoply of Polygons/A Panoply of Polygons.pdf

A Panoply of Polygons Claudi Alsina, Roger B. Nelsen MAA Press, an imprint of the American Mathematical Society, AMS/MAA | Dolciani Mathematical Expositions, 58, 1, 2023

A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal numbers (figurate numbers based on polygons). Applications, real-life examples, and uses in art and architecture complement the presentation where many proofs with a visual nature are included. A Panoply of Polygons can be used as a supplement to a high school or college geometry course. It can also be used as a source for group projects or extra-credit assignments. It will appeal, and be accessible to, anyone with an interest in plane geometry. Claudi Alsina and Roger Nelsen are, jointly and individually, the authors of thirteen previous MAA/AMS books. Those books, and this one, celebrate and illuminate the power of visualization in learning, teaching, and creating mathematics.

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nexusstc/The Lebesgue Integral for Undergraduates/d9faa0999facc8283b55a27a2344d77b.pdf

The Lebesgue Integral for Undergraduates (MAA Textbooks) William Johnston MAA Press, an imprint of the American Mathematical Society, AMS/MAA Textbooks, MAA Textbooks, 2015

In 1902, modern function theory began when Henri Lebesgue described a new integral calculus. His Lebesgue integral handles more functions than the traditional integral so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.

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nexusstc/Hex: A Playful Introduction/00f5954f870f73ef3bb4b1ecf4c2f747.pdf

Hex : a playful introduction Ryan B. Hayward, Bjarne Toft MAA Press, an imprint of the American Mathematical Society, Anneli Lax New Mathematical Library, Anneli Lax New Mathematical Library, 54, 1, 2022

This book offers a gentle introduction to Hex, the classic board game created by Piet Hein and popularized by John Nash and Martin Gardner. The first three chapters cover rules, basic strategy, and history. The remaining eight chapters cover a variety of topics: mathematical properties (there are no draws, the first player can win, the acute corner is a losing first move), the related game of Y, winning strategies for small boards, how computers play Hex, and analysis of Random-Move Hex (where one or both players move randomly) and Dark Hex (the imperfect information version of the game, where you can't see your opponent's moves). Did we mention puzzles? There are puzzles in every chapter, with solutions. This book is intended for anyone interested in playing board games or learning some recreational mathematics. It is written for a wide audience and will be enjoyed equally by general readers and professional mathematicians. The book could be used as a textbook or companion resource for a topics course on recreational mathematics or game theory or as a source for undergraduate research questions.

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nexusstc/Optical Illusions in Rome: A Mathematical Travel Guide/2e2d3e65d078d361cbfb96b2fee72133.pdf

Optical Illusions in Rome: A Mathematical Travel Guide (Spectrum) Kirsti Andersen; Viktor Blåsjö MAA Press, an imprint of the American Mathematical Society, AMS/MAA Spectrum, #99, 2019

__Optical Illusions in Rome__ is a beautifully written and richly illustrated guide that takes the reader on a tour through ingenious uses of geometry to create illusory impressions of space and grandeur in Italian Renaissance art and architecture in the Eternal City. The book takes us to some of the most striking and historically important uses of optical illusion and includes works of Peruzzi, Borromini, and Pozzo. The artworks are analyzed geometrically and placed in their historical context. The notes on visiting the art described make the volume the perfect companion for a study trip to Rome. A chapter on the principles of perspective geometry and a collection of exercises make the book a wonderful resource for a module on perspective in a geometry or art history course. The mathematical discussion is kept at a level accessible to a reader with a familiarity with high school geometry. Kirsti Andersen is a distinguished historian of mathematics and emerita faculty at Aarhus University. Her previous book, __The Geometry of an Art__, is widely recognized as the definitive work on the history of the use of perspective in European art. Viktor Blåsjö, the translator, is a historian of mathematics on the faculty at Utrecht University. Blåsjö has won both the Ford and Pólya prizes for expository writing from the Mathematical Association of America.

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nexusstc/Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers/010554beada6601a28949819abba24b6.pdf

Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers (Spectrum) Tomas Rokicki (editor) MAA Press, an imprint of the American Mathematical Society, AMS/MAA spectrum, vol. 100, Providence, Rhode Island, 2020

The Gathering 4 Gardner is a biannual conference founded and for many years organized by Tom Rodgers to celebrate the spirit of Martin Gardner. While primarily concerned with recreational mathematics, most of Gardner's intellectual interests are featured, including magic, literature, philosophy, puzzles, art, and rationality. Gardner's writing inspired several generations of mathematicians by introducing us to the joy of discovery and exploration, and the Gathering's aim is to continue that tradition of inspiration. This volume, a tribute to Rodgers and Gardner, consists of papers originally presented at the Gathering 4 Gardner meetings. Recreational mathematics is strongly prominent with contributions from Neil Sloane, Richard Guy, Solomon Golomb, Barry Cipra, Erik Demaine, and many others. There are games and puzzles, including new Nim-like games, chess puzzles, coin weighings, coin flippings, and contributions that combine art and puzzles or magic and puzzles. Two historical articles present the stories of combinatorial game theory and the search for God's number for Rubik's Cube. Anyone who finds pleasure in clever and intriguing intellectual puzzles will find much to enjoy in Barrycades and Septoku.

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upload/newsarch_ebooks_2025_10/2021/12/27/Proofs and Ideas A Prelude to Advanced Mathematics.pdf

Proofs and ideas : a prelude to advanced mathematics B. A. Sethuraman MAA Press, an imprint of the American Mathematical Society, AMS/MAA Textbooks, 68, 1, 2021

Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts. The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine. This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India.

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Lost in the Math Museum: A Survival Story (Anneli Lax New Mathematical Library) (Anneli Lax New Mathematical Library, 55) Colin Adams MAA Press, an imprint of the American Mathematical Society, Anneli Lax new mathematical library, Providence, Rhode Island, 2022

“But when I turned the handle on the door, suddenly the buzzing went crazy. I slapped my hands over my ears, when I should have jerked the door shut. It flew open, and I was face-to-face with the Weierstrass function. It was the ugliest function I could imagine, with kinks, and kinks on kinks and kinks on those. And it was shrieking in its buzz-like way, vibrating all over like a plucked string. I stood there, frozen for just a second, and then I was sprinting after the others, with the wild frantic buzzing right behind me.” From the twisted imagination of best-selling author Colin Adams (Zombies & Calculus, The Knot Book) comes this tale of sixteen-year-old Kallie trying to escape death at the hands of the exhibits in a mathematics museum. Kallie crosses paths with Carl Gauss, Bertrand Russell, Sophie Germain, G. H. Hardy, and John von Neumann, as she tries to save herself, her dad, and his colleague Maria from the deadly Hairy Ball theorem, the harrowing Hilbert Hotel, the bisecting Ham Sandwich machine, and a variety of other mathematical menaces. It's a wild romp through a mathematical bestiary featuring the bizarre, the exotic, and the counterintuitive. You'll never think of math the same way again.

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lgli/M_Mathematics/MA_Algebra/MAl_Linear algebra/Cuoco A. Linear algebra and geometry (text-46, MAA, 2019)(ISBN 9781470443504)(O)(575s)_MAl_.pdf

Linear Algebra and Geometry (AMS/MAA Textbooks) Al Cuoco, Kevin Waterman, Bowen Kerins, Elena Kaczorowski, Michelle Manes MAA Press, an imprint of the American Mathematical Society, Ams/Maa Textbooks (Book 46), 2019

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. The materials in Linear Algebra and Geometry have been used, field tested, and refined for over two decades. It is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. Secondary teachers will find the emphasis on developing effective habits of mind especially helpful. The book is written in a friendly, approachable voice and contains nearly a thousand problems. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information.

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upload/newsarch_ebooks/2019/12/25/1470452766.pdf

Topology Through Inquiry (AMS/MAA Textbooks) Starbird, Michael; Su, Francis Edward MAA Press : An imprint of the American Mathematical Society, AMS/MAA Textbooks, 58, 1, 2019

Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning--of mathematics and beyond--joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure;Cardinality: to infinity and beyond -- Topological spaces: fundamentals -- Bases, subspaces, products: creating new spaces -- Separation properties: separating this from that -- Countable features of spaces: size restrictions -- Compactness: the next best thing to being finite -- Continuity: when nearby points stay together -- Connectedness: when things don't fall into pieces -- Metric spaces: getting some distance -- Transition from point-set topology to algebraic and geometric topology: similar strategies, different domains -- Classification of 2-manifolds: organizing surfaces -- Fundamental group: capturing holes -- Covering spaces: layering it on -- Manifolds, simplices, complexes, and triangulability: building blocks -- Simplicial Z2-homology: physical algebra -- Applications of Z2-homology: a topological superhero -- Simplicial Z-homology: getting oriented -- Singular homology: abstracting objects to maps -- The end: a beginning-reflections on topology and learning

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nexusstc/The History of Mathematics: A Source-Based Approach, Volume 2 (AMS/MAA Textbooks, 61)/3f2350277814375973d1ad596bf40120.pdf

The History of Mathematics: A Source-Based Approach, Volume 2 (AMS/MAA Textbooks, 61) June Barrow-Green, Jeremy Gray, Robin Wilson, Jeremy J. Gray, Robin J. Wilson MAA Press, an imprint of the American Mathematical Society, 2018

The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

English [en] · PDF · 7.1MB · 2018 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

nexusstc/The impact and legacy of The ladies' diary (1704-1840) : a women's declaration/9222d3f6d2716922a3b7603879f3cb5d.pdf

The impact and legacy of The ladies' diary (1704-1840) : a women's declaration Frank J. Swetz MAA Press, an imprint of the American Mathematical Society, Spectrum, 101, 2021

It was in this period of concern and inquiry in 1977 that I first came acrossmention of The Ladies’ Diary: or The Woman’s Almanack, a British eighteenth-and nineteenth-century journal that encouraged and promoted mathematics forwomen. This periodical was the subject of an article by Teri Perl in the Math-ematics Teacher, a journal dedicated to mathematics teaching, published by theNational Council of Teachers of Mathematics.3 The concept of proper Englishladies, in the mold of Jane Austen’s or the Brontë sisters’ heroines, doing mathe-matics and revealing it for the public review in this period of history was fascinat-ing. I knew that British society of the eighteenth and nineteenth centuries hadstrict codes of conduct and expectations for their young ladies that distinctivelydid not include involvement in mathematics and science.

English [en] · PDF · 10.7MB · 2021 · 📘 Book (non-fiction) · 🚀/nexusstc/zlib · Save

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ia/thinkingalgebrai0000sibl.pdf

Thinking Algebraically: An Introduction to Abstract Algebra (Ams/Maa Textbooks) Thomas Q Sibley; American Mathematical Society MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Providence, Rhode Island, 2021

Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.

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upload/newsarch_ebooks_2025_10/2023/09/04/1470460319.pdf

The Finite Field Distance Problem (Carus Mathematical Monographs) (The Carus Mathematical Monographs, 37) David J. Covert (author) MAA Press, an imprint of the American Mathematical Society, The Carus mathematical monographs, 37, Providence, Rhode Island, 2021

Erdős asked how many distinct distances must there be in a set of $n$ points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in $R$. The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results. The tools used range over combinatorics, number theory, analysis, and algebra. The intended audience is graduate students and advanced undergraduates interested in investigating the unknown dimensions of the problem. Results available until now only in the research literature are clearly explained and beautifully motivated. A concluding chapter opens up connections to related topics in combinatorics and number theory: incidence theory, sum-product phenomena, Waring's problem, and the Kakeya conjecture.

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lgli/Alsina C., Nelsen R.B. A panoply of polygons (dol58, AMS, 2023)(ISBN 9781470471842)(400dpi)(T)(281s)_MSch_.djvu

A Panoply of Polygons (Dolciani Mathematical Expositions, 58) Claudi Alsina, Roger B. Nelsen MAA Press, an imprint of the American Mathematical Society, Dolciani mathematical expositions, volume 58, Providence, Rhode Island, 2023

A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal numbers (figurate numbers based on polygons). Applications, real-life examples, and uses in art and architecture complement the presentation where many proofs with a visual nature are included. A Panoply of Polygons can be used as a supplement to a high school or college geometry course. It can also be used as a source for group projects or extra-credit assignments. It will appeal, and be accessible to, anyone with an interest in plane geometry. Claudi Alsina and Roger Nelsen are, jointly and individually, the authors of thirteen previous MAA/AMS books. Those books, and this one, celebrate and illuminate the power of visualization in learning, teaching, and creating mathematics.

English [en] · DJVU · 6.2MB · 2023 · 📘 Book (non-fiction) · 🚀/lgli/lgrs · Save

nexusstc/Diophantus and Diophantine Equations (Dolciani Mathematical Expositions, 54)/5248740f20680f5f79e049320210c91d.pdf

Diophantus and Diophantine Equations (Dolciani Mathematical Expositions, 54) Isabella Grigoryevna Bashmakova MAA Press, an imprint of the American Mathematical Society, American Mathematical Society, Providence, 2019

This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus a person whose very existence has long been doubted by most historians of mathematics will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem.

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nexusstc/The Hitchhiker's Guide to Calculus/8dbe5c7501039b8bfaa866dec20b7194.pdf

The Hitchhiker's Guide to Calculus (Classroom Resource Materials) Michael Spivak MAA Press, an imprint of the American Mathematical Society, Classroom Resource Materials 57, 1995

"The Hitchhiker's Guide to Calculus begins with a rapid view of lines and slope. Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapter he tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, "Watching Experts at Play." The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral"--Amazon.com

English [en] · PDF · 14.5MB · 1995 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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lgli/N:\!genesis_files_for_add\_add\kolxo3\93\M_Mathematics\MC_Calculus\MCc_Complex variable/Daepp U., et al. Finding ellipses.. what Blaschke products, Poncelet's theorem, and the numerical range know (AMS, 2018)(ISBN 9781470443832)(O)(282s)_MCc_.pdf

Finding Ellipses (Carus Mathematical Monographs) (Carus Mathematical Monographs, 34) Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss MAA Press, an imprint of the American Mathematical Society, The Carus mathematical monographs, 34, Providence, Rhode Island, 2018

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

English [en] · PDF · 1.5MB · 2018 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

nexusstc/Geometry: The Line and the Circle/3abfea1d02ce57d574dfd450fbc8409b.pdf

Geometry: The Line and the Circle (AMS/MAA Textbooks) Maureen T. Carroll, Elyn Rykken MAA Press, an imprint of the American Mathematical Society, AMS/MAA Textbooks, AMS/MAA Textbooks 44, 2018

Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.

English [en] · PDF · 6.9MB · 2018 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

lgli/N:\!genesis_files_for_add\_add\kolxo3\94\M_Mathematics\MD_Geometry and topology\Starbird M., Su F. Topology through inquiry (text-58, AMS, 2019)(ISBN 9781470452766)(O)(330s)_MD_.pdf

Topology Through Inquiry (AMS/MAA Textbooks) Starbird, Michael; Su, Francis Edward MAA Press : An imprint of the American Mathematical Society, AMS/MAA textbooks 58, 58, 1, 2019

Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning--of mathematics and beyond--joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure;Cardinality: to infinity and beyond -- Topological spaces: fundamentals -- Bases, subspaces, products: creating new spaces -- Separation properties: separating this from that -- Countable features of spaces: size restrictions -- Compactness: the next best thing to being finite -- Continuity: when nearby points stay together -- Connectedness: when things don't fall into pieces -- Metric spaces: getting some distance -- Transition from point-set topology to algebraic and geometric topology: similar strategies, different domains -- Classification of 2-manifolds: organizing surfaces -- Fundamental group: capturing holes -- Covering spaces: layering it on -- Manifolds, simplices, complexes, and triangulability: building blocks -- Simplicial Z2-homology: physical algebra -- Applications of Z2-homology: a topological superhero -- Simplicial Z-homology: getting oriented -- Singular homology: abstracting objects to maps -- The end: a beginning-reflections on topology and learning

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nexusstc/The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary/268fef63f68fbc1fdc52b1eb59e2132a.pdf

The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary (Problem Books) Kiran Sridhara Kedlaya; Daniel M Kane; Jonathan Michael Kane; Evan M O'Dorney American Mathematical Monthly, MAA problem books series, vol. 37, Providence, Rhode Island, 2020

The William Lowell Putnam Mathematics Competition is the most prestigious undergraduate mathematics problem-solving contest in North America, with thousands of students taking part every year. This volume presents the contest problems for the years 2001—2016. The heart of the book is the solutions; these include multiple approaches, drawn from many sources, plus insights into navigating from the problem statement to a solution. There is also a section of hints, to encourage readers to engage deeply with the problems before consulting the solutions. The authors have a distinguished history of engagement with, and preparation of students for, the Putnam and other mathematical competitions. Collectively they have been named Putnam Fellow (top five finisher) ten times. Kiran Kedlaya also maintains the online Putnam Archive.

English [en] · PDF · 1.5MB · 2020 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

nexusstc/The Unity of Combinatorics/7f1c1f812de0b50538c20062625dc9e8.pdf

The Unity of Combinatorics (Carus Mathematical Monographs) (AMS/MAA Carus Mathematical Monographs) Ezra A. Brown, Richard K. Guy MAA Press, an imprint of the American Mathematical Society, Carus Mathematical Monographs, Carus Mathematical Monographs, 2020

Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

English [en] · PDF · 18.3MB · 2020 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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nexusstc/φ, π, e & i/4d5f8bbb75c15f996f70de6f0d5a7873.pdf

φ, π, e & i (Phi, Pi, e, and i) David Perkins The Mathematical Association of America, Spectrum Ser., Paperback, 2018

Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (φ, π, e, and i), each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus. This material offers an excellent excuse to display the power of calculus to reveal elegant truths tha. Read more...

English [en] · PDF · 1.8MB · 2018 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save