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Mathematics

99 VARIATIONS ON A PROOF

99 VARIATIONS ON A PROOF

By: Ording, Philip
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An exploration of mathematical style through 99 different proofs of the same theorem

This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.

Inspired by the experiments of the Paris-based writing group known as the Oulipo--whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp--Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor.

Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

ABEL'S PROOF

ABEL'S PROOF

By: Pesic, Peter
$24.95
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The intellectual and human story of a mathematical proof that transformed our ideas about mathematics.

In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé.

But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the real world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra--which even Newton resisted--and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.

ADVENTURES OF A MATHEMATICIAN

ADVENTURES OF A MATHEMATICIAN

By: Ulam, S M
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The true story that inspired the 2020 film.

The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects.

With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

ANCIENT & MEDIEVAL TRADITIONS IN THE EXACT SCIENCES

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This volume of essays is dedicated to Wilbur Knorr, an outstanding historian of science whose career was cut short much too early. Inspired by Knorr's work, this volume concentrates on the history of ancient mathematics, the associated mathematical sciences, and their medieval and modern tradition.

This volume emulates the quality and diverse interests of Knorr's innovative, exact, and far-reaching research. Topics inspired by Knorr include a study of geometric analysis and synthesis in ancient Greece and medieval Islam; examination of Eudoxus as originator for the ideas of proportionality underlying Book V of Euclid's Elements; and the extent that Renaissance theorists of linear perspective had access to ancient sources. This book considers the status of Eudoxus's theory of homocentric spheres in Greek astronomy and the examination of the status of in Greek mathematics. A detailed discussion of the geometrical chemistry of Plato's Timaeus and its interpretation in antiquity stems from Knorr's work, and a study of Plato's concept of numbers and its relation to the Theory of Forms. Knorr's varied interests motivate investigation into the representation of numbers in the Latin middle ages, or why we read Arabic numbers backwards, and the history of science in a chronology of the three dynasties in ancient China.

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ANNOTATED TURING: A GUIDED TOUR THROUGH ALAN TURING'S HISTORIC PAPER ON COMPUTABILITY AND THE TURING MACHINE

By: Petzold, Charles
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Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing

Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of present-day computer programming.

The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.

Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

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BEAUTIFUL, SIMPLE, EXACT, CRAZY: MATHEMATICS IN THE REAL WORLD

By: Lachowska, Anna
$20.00
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In this vibrant work, which is ideal for both teaching and learning, Apoorva Khare and Anna Lachowska explain the mathematics essential for understanding and appreciating our quantitative world. They show with examples that mathematics is a key tool in the creation and appreciation of art, music, and literature, not just science and technology. The book covers basic mathematical topics from logarithms to statistics, but the authors eschew mundane finance and probability problems. Instead, they explain how modular arithmetic helps keep our online transactions safe, how logarithms justify the twelve-tone scale commonly used in music, and how transmissions by deep space probes are similar to knights serving as messengers for their traveling prince. Ideal for coursework in introductory mathematics and requiring no knowledge of calculus, Khare and Lachowska's enlightening mathematics tour will appeal to a wide audience.
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BEAUTY OF NUMBERS IN NATURE: MATHEMATICAL PATTERNS AND PRINCIPLES FROM THE NATURAL WORLD

By: Stewart, Ian
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From a zebra's stripes to a spider's web: an engaging examination of patterns in nature and the mathematics that underlie them.

From a zebra's stripes to a spider's web, from sand dunes to snowflakes, nature is full of patterns underlaid by mathematical principles. In The Beauty of Numbers in Nature, Ian Stewart shows how life forms from the principles of mathematics. Each chapter in The Beauty of Numbers in Nature explores a different kind of patterning system and its mathematical underpinnings. In doing do, the book also uncovers some universal patterns--both in nature and made by humans--from the basic geometry of ancient Greece to the complexities of fractals.

Stewart draws on a wide range of sources to examine the mathematics of patterns: the Pythagoreans' obsession with numbers as the philosophical basis of the universe; a great mathematician who wondered about how a violin makes music; a clerk in a patent office who realized that space and time can get mixed together; a maverick mathematician who questioned why nature spurns such regular geometric shapes as spheres and cylinders in favor of jagged lightning bolts, asymmetrically branching trees, and the uneven terrain of mountainsides.

The book begins with a simple and often-asked question about the shape and individual uniqueness of snowflakes. How can such a strange mixture of regularity and irregularity exist in a tiny bit of frozen water? By the end of the book, readers will have learned that mathematical patterns can come in many guises, some of which don't resemble patterns at all.

BEST OF ALL POSSIBLE WORLDS: Mathematics and Destiny

BEST OF ALL POSSIBLE WORLDS: Mathematics and Destiny

By: Ekeland, Ivar
$14.00
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Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.

This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.

Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition--one that will be essential reading for popular-science buffs and historians of science alike.

BEST WRITING ON MATHEMATICS 2013

BEST WRITING ON MATHEMATICS 2013

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The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize-winning physicist Roger Penrose

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

BEST WRITING ON MATHEMATICS 2014

BEST WRITING ON MATHEMATICS 2014

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The year's finest writing on mathematics from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2014 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here John Conway presents examples of arithmetical statements that are almost certainly true but likely unprovable; Carlo Séquin explores, compares, and illustrates distinct types of one-sided surfaces known as Klein bottles; Keith Devlin asks what makes a video game good for learning mathematics and shows why many games fall short of that goal; Jordan Ellenberg reports on a recent breakthrough in the study of prime numbers; Stephen Pollard argues that mathematical practice, thinking, and experience transcend the utilitarian value of mathematics; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes an introduction by editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

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BEST WRITING ON MATHEMATICS 2015

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The year's finest writing on mathematics from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.

Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it's worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

-- "Publishers Weekly"
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BEST WRITING ON MATHEMATICS 2016

$32.95
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The year's finest mathematics writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.

Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

-- "Math Tango"
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BEST WRITING ON MATHEMATICS 2017

$24.95
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The year's finest mathematics writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates.

Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math's highest prize--the Fields Medal--in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children's receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there's much, much more.

In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

BEST WRITING ON MATHEMATICS 2018

$24.95
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The year's finest mathematical writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice--and taking readers behind the scenes of today's hottest mathematical debates.

James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world--with glimpses at science, philosophy, music, art, and even crocheting. And there's much, much more.

In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics.

This is a must-read for anyone interested in where math has taken us--and where it is headed.

BEST WRITING ON MATHEMATICS 2019

BEST WRITING ON MATHEMATICS 2019

$24.95
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The year's finest mathematical writing from around the world

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2019 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice--and taking readers behind the scenes of today's hottest mathematical debates.

In this volume, Moon Duchin explains how geometric-statistical methods can be used to combat gerrymandering, Jeremy Avigad illustrates the growing use of computation in making and verifying mathematical hypotheses, and Kokichi Sugihara describes how to construct geometrical objects with unusual visual properties. In other essays, Neil Sloane presents some recent additions to the vast database of integer sequences he has catalogued, and Alessandro Di Bucchianico and his colleagues highlight how mathematical methods have been successfully applied to big-data problems. And there's much, much more.

In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable writings on mathematics.

This is a must-read for anyone interested in where math has taken us--and where it is headed.

BEYOND GEOMETRY: Classic Papers from Riemann to Einstein

BEYOND GEOMETRY: Classic Papers from Riemann to Einstein

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Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This original Dover publication is the only English-language collection of these important papers, some of which are extremely hard to find.
Contents include "On the Hypotheses which Lie at the Foundations of Geometry" by Georg Friedrich Riemann; "On the Facts which Lie at the Foundations of Geometry" and "On the Origin and Significance of Geometrical Axioms" by Hermann von Helmholtz; "A Comparative Review of Recent Researches in Geometry" by Felix Klein; "On the Space Theory of Matter" by William Kingdon Clifford; "On the Foundations of Geometry" by Henri Poincaré; "Euclidean Geometry and Riemannian Geometry" by Elie Cartan; and "The Problem of Space, Ether, and the Field in Physics" by Albert Einstein.
These remarkably accessible papers will appeal to students of modern physics and mathematics, as well as anyone interested in the origins and sources of Einstein's most profound work. Peter Pesic of St. John's College in Santa Fe, New Mexico, provides an introduction, as well as notes that offer insights into each paper.
BIBLICAL GAMES: Game Theory and the Hebrew Bible

BIBLICAL GAMES: Game Theory and the Hebrew Bible

By: Brams, Steven J
$30.00
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BACK IN PRINT with a new preface and a new chapter

In this unusual book, first published by The MIT Press in 1980 and now updated with a new chapter, Steven Brams applies the mathematical theory of games to the Hebrew Bible. Brams's thesis is that God and the human biblical characters acted rationally--that is, given their preferences and their knowledge of other players' preferences, they made strategy choices that led to the best attainable outcomes. Beginning with the Creation and focusing on those stories richest in conflict and intrigue, Brams uses elementary game-theoretic tools to elucidate the rational calculations of biblical players and to show precisely the manner in which they sought to achieve their goals. He relies almost exclusively on noncooperative theory, making use of both game tree and matrix forms of games. Brams uses his strategic analyses to build a detailed assessment of God's character and motivations, including the reasons for His frequently wrathful behavior. Brams's insights have application to biblical studies, the philosophy of religion, political theory, and game theory and methodology.In the new chapter, Brams surveys the literature of the past twenty years on political-strategic interpretations of the Hebrew Bible. He also extends the game-theoretic analysis, using the theory of moves, to study a counterfactual situation--what if Abraham had refused God's command to sacrifice Isaac?--and to examine the rationality of believing in a superior being.

BOOLEAN ALGEBRA

BOOLEAN ALGEBRA

By: Goodstein, R L
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This elementary treatment by a distinguished mathematician begins with the algebra of classes and proceeds to discussions of several different axiomatizations and Boolean algebra in the setting of the theory of partial order. Numerous examples appear throughout the text, plus full solutions. 1963 edition.
CALCULUS GALLERY: Masterpieces from Newton to Lebesgue

CALCULUS GALLERY: Masterpieces from Newton to Lebesgue

By: Dunham, William
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More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.


Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.


Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

CALCULUS OF FRIENDSHIP: What a Teacher and a Student Learned about Life While Corresponding about Math

CALCULUS OF FRIENDSHIP: What a Teacher and a Student Learned about Life While Corresponding about Math

By: Strogatz, Steven
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The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough.

Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters.

For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

CALCULUS SIMPLIFIED

CALCULUS SIMPLIFIED

By: Fernandez, Oscar
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An accessible, streamlined, and user-friendly approach to calculus

Calculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a "Goldilocks approach" to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure.

Fernandez begins by offering an intuitive introduction to the three key ideas in calculus--limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources--including video tutorials and interactive graphs--are available on the book's website.

Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions--these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics--chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus.

Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.

- An accessible, intuitive introduction to first-semester calculus

- Nearly 200 solved problems and more than 300 exercises (all with answers)

- No prior knowledge of exponential, logarithmic, or trigonometric functions required

- Additional online resources--video tutorials and supplementary exercises--provided

CALCULUS: A Genetic Approach

CALCULUS: A Genetic Approach

By: Toeplitz, Otto
$37.00
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When first published posthumously in 1963, this bookpresented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus.

Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.

CALL OF THE PRIMES: SURPRISING PATTERNS, PECULIAR PUZZLES, AND OTHER MARVELS OF MATHEMATICS

CALL OF THE PRIMES: SURPRISING PATTERNS, PECULIAR PUZZLES, AND OTHER MARVELS OF MATHEMATICS

By: O'Shea, Owen
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This sampler of entertaining mathematical diversions reveals the elegance and extraordinary usefulness of mathematics for readers who think they have no aptitude for the subject. If you like any kind of game at all, you'll enjoy the amazing mathematical puzzles and patterns presented here in straightforward terms that any layperson can understand. From magic squares and the mysterious qualities of prime numbers to Pythagorean triples, probability theory, the Fibonacci sequence, and more, the author shows that math can be fun while having some profound implications.

Such ubiquitous mathematical entities as pi and the Fibonacci numbers are found throughout the natural world and are also the foundation of our technological civilization. By exploring the intriguing games presented here, you'll come away with a greater appreciation for the beauty and importance of these and many more math concepts.

This is the perfect book for people who were turned off by math in school but now as adults wonder what they may have missed.

CARTOON INTRODUCTION TO CALCULUS

CARTOON INTRODUCTION TO CALCULUS

By: Bauman, Yoram
$18.95
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The internationally bestselling authors of The Cartoon Introduction to Economics return to make calculus fun

The award-winning illustrator Grady Klein has teamed up once again with the world's only stand-up economist, Yoram Bauman, Ph.D., to take on the daunting subject of calculus. A supplement to traditional textbooks, The Cartoon Introduction to Calculus focuses on the big ideas rather than all the formulas you have to memorize.

With Klein and Bauman as our guides, we scale the dual peaks of Mount Derivative and Mount Integral, and from their summits, we see how calculus relates to the rest of mathematics. Beginning with the problems of speed and area, Klein and Bauman show how the discipline is unified by a fundamental theorem. We meet geniuses like Archimedes, Liu Hui, and Bonaventura Cavalieri, who survived the slopes on intuition but prepared us for the avalanche-like dangers posed by mathematical rigor. Then we trek onward and scramble through limits and extreme values, optimization and integration, and learn how calculus can be applied to economics, physics, and so much more. We discover that calculus isn't the pinnacle of mathematics after all, but its tools are foundational to everything that follows. Klein and Bauman round out the book with a handy glossary of symbols and terms, so you don't have to worry about mixing up constants and constraints. With a witty and engaging narrative full of jokes and insights, The Cartoon Introduction to Calculus is an essential primer for students or for anyone who is curious about math.

CHASES AND ESCAPES: The Mathematics of Pursuit and Evasion

CHASES AND ESCAPES: The Mathematics of Pursuit and Evasion

By: Nahin, Paul J
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We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day.


Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an array of challenging puzzles with their historical background and broader applications. Chases and Escapes includes solutions to all problems and provides computer programs that readers can use for their own cutting-edge analysis.


Now with a gripping new preface on how the Enola Gay escaped the shock wave from the atomic bomb dropped on Hiroshima, this book will appeal to anyone interested in the mathematics that underlie pursuit and evasion.

CHINESE MATHEMATICS IN THE 13TH CENTURY

CHINESE MATHEMATICS IN THE 13TH CENTURY

By: Libbrecht, Ulrich
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An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book.
The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China.
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CONCISE OXFORD DICTIONARY OF MATHEMATICS

By: Nicholson, James
$18.95
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Authoritative and reliable, this A-Z guide provides jargon-free definitions for even the most technical mathematical terms. With over 3,000 entries ranging from Achilles paradox to zero matrix, it covers all commonly encountered terms and concepts from pure and applied mathematics and statistics, for example, linear algebra, optimisation, nonlinear equations, and differential equations. In addition, there are entries on major mathematicians and on topics of more general interest, such as fractals, game theory, and chaos.

Using graphs, diagrams, and charts to render definitions as comprehensible as possible, entries are clear and accessible. Almost 200 new entries have been added to this edition, including terms such as arrow paradox, nested set, and symbolic logic. Useful appendices follow the A-Z dictionary and include lists of Nobel Prize winners and Fields' medallists, Greek letters, formulae, and tables of inequalities, moments of inertia, Roman numerals, a geometry summary, additional trigonometric values of special angles, and much more. This edition contains recommended web links, which are accessible and kept up to date via the Dictionary of Mathematics companion website.

COURSE IN PURE MATHEMATICS CENTENARY EDITION 10TH EDITION

COURSE IN PURE MATHEMATICS CENTENARY EDITION 10TH EDITION

By: Hardy, G H
$62.00
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Celebrating 100 years in print with Cambridge, this newly updated edition includes a foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. There are few textbooks in mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.
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COURSE OF PURE MATHEMATICS: THIRD EDITION

By: Hardy, G H
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Originally published in 1908, this classic calculus text transformed university teaching and remains a must-read for all students of introductory mathematical analysis. Clear, rigorous explanations of the mathematics of analytical number theory and calculus cover single-variable calculus, sequences, number series, and properties of cos, sin, and log. Meticulous expositions detail the fundamental ideas underlying differential and integral calculus, the properties of infinite series, and the notion of limit.
An expert in the fields of analysis and number theory, author G. H. Hardy taught for decades at both Cambridge and Oxford. A Course of Pure Mathematics is suitable for college and high school students and teachers of calculus as well as fans of pure math. Each chapter includes demanding problem sets that allow students to apply the principles directly, and four helpful Appendixes supplement the text.
CREST OF THE PEACOCK: Non-European Roots of Mathematics 3RD. ED.

CREST OF THE PEACOCK: Non-European Roots of Mathematics 3RD. ED.

By: Joseph, George Gheverghese
$45.00
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From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China.

The third edition emphasizes the dialogue between civilizations, and further explores how mathematical ideas were transmitted from East to West. The book's scope is now even wider, incorporating recent findings on the history of mathematics in China, India, and early Islamic civilizations as well as Egypt and Mesopotamia. With more detailed coverage of proto-mathematics and the origins of trigonometry and infinity in the East, The Crest of the Peacock further illuminates the global history of mathematics.