Journey Into Mathematics

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Journey into Mathematics

Author : Joseph J. Rotman
Publisher : Courier Corporation
ISBN 13 : 0486151689
Total Pages : 386 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Journey into Mathematics by : Joseph J. Rotman

Download or read book Journey into Mathematics written by Joseph J. Rotman and published by Courier Corporation. This book was released on 2013-01-18 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.

1089 and All that

Author : D. J. Acheson
Publisher : Oxford University Press, USA
ISBN 13 : 9780198516231
Total Pages : 200 pages
Book Rating : 4.5/5 (162 download)

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Book Synopsis 1089 and All that by : D. J. Acheson

Download or read book 1089 and All that written by D. J. Acheson and published by Oxford University Press, USA. This book was released on 2002 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.

Journey through Mathematics

Author : Enrique A. González-Velasco
Publisher : Springer Science & Business Media
ISBN 13 : 0387921540
Total Pages : 479 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Journey through Mathematics by : Enrique A. González-Velasco

Download or read book Journey through Mathematics written by Enrique A. González-Velasco and published by Springer Science & Business Media. This book was released on 2011-08-08 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

A Journey in Mathematics Education Research

Author : Erna Yackel
Publisher : Springer Science & Business Media
ISBN 13 : 9048197295
Total Pages : 248 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis A Journey in Mathematics Education Research by : Erna Yackel

Download or read book A Journey in Mathematics Education Research written by Erna Yackel and published by Springer Science & Business Media. This book was released on 2010-11-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.

Journey Through Genius

Author : William Dunham
Publisher : Penguin Books
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Journey Through Genius by : William Dunham

Download or read book Journey Through Genius written by William Dunham and published by Penguin Books. This book was released on 1991-08 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov

A Journey Into Partial Differential Equations

Author : William O. Bray
Publisher : Jones & Bartlett Publishers
ISBN 13 : 0763772569
Total Pages : 334 pages
Book Rating : 4.7/5 (637 download)

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Book Synopsis A Journey Into Partial Differential Equations by : William O. Bray

Download or read book A Journey Into Partial Differential Equations written by William O. Bray and published by Jones & Bartlett Publishers. This book was released on 2012 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the International Series in Mathematics Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.

Journey Into Discrete Mathematics

Author : Owen Byer
Publisher : MAA Press
ISBN 13 : 9781470449124
Total Pages : 388 pages
Book Rating : 4.4/5 (491 download)

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Book Synopsis Journey Into Discrete Mathematics by : Owen Byer

Download or read book Journey Into Discrete Mathematics written by Owen Byer and published by MAA Press. This book was released on 2018 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.

Discovering Mathematics

Author : A. Gardiner
Publisher : Courier Corporation
ISBN 13 : 0486452999
Total Pages : 226 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Discovering Mathematics by : A. Gardiner

Download or read book Discovering Mathematics written by A. Gardiner and published by Courier Corporation. This book was released on 2006-01-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.

Living Proof

Author : Allison K. Henrich
Publisher :
ISBN 13 : 9781470452810
Total Pages : 136 pages
Book Rating : 4.4/5 (528 download)

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Book Synopsis Living Proof by : Allison K. Henrich

Download or read book Living Proof written by Allison K. Henrich and published by . This book was released on 2019 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wow! This is a powerful book that addresses a long-standing elephant in the mathematics room. Many people learning math ask ``Why is math so hard for me while everyone else understands it?'' and ``Am I good enough to succeed in math?'' In answering these questions the book shares personal stories from many now-accomplished mathematicians affirming that ``You are not alone; math is hard for everyone'' and ``Yes; you are good enough.'' Along the way the book addresses other issues such as biases and prejudices that mathematicians encounter, and it provides inspiration and emotional support for mathematicians ranging from the experienced professor to the struggling mathematics student. --Michael Dorff, MAA President This book is a remarkable collection of personal reflections on what it means to be, and to become, a mathematician. Each story reveals a unique and refreshing understanding of the barriers erected by our cultural focus on ``math is hard.'' Indeed, mathematics is hard, and so are many other things--as Stephen Kennedy points out in his cogent introduction. This collection of essays offers inspiration to students of mathematics and to mathematicians at every career stage. --Jill Pipher, AMS President This book is published in cooperation with the Mathematical Association of America.

A Journey Through Discrete Mathematics

Author : Martin Loebl
Publisher : Springer
ISBN 13 : 3319444794
Total Pages : 810 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis A Journey Through Discrete Mathematics by : Martin Loebl

Download or read book A Journey Through Discrete Mathematics written by Martin Loebl and published by Springer. This book was released on 2017-10-11 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Charming Proofs

Author : Claudi Alsina
Publisher : MAA
ISBN 13 : 0883853485
Total Pages : 321 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Charming Proofs by : Claudi Alsina

Download or read book Charming Proofs written by Claudi Alsina and published by MAA. This book was released on 2010 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, and to develop the ability to create proofs themselves. The authors consider proofs from topics such as geometry, number theory, inequalities, plane tilings, origami and polyhedra. Secondary school and university teachers can use this book to introduce their students to mathematical elegance. More than 130 exercises for the reader (with solutions) are also included.

What's Happening in the Mathematical Sciences

Author : Barry Cipra
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890431
Total Pages : 108 pages
Book Rating : 4.8/5 (94 download)

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Book Synopsis What's Happening in the Mathematical Sciences by : Barry Cipra

Download or read book What's Happening in the Mathematical Sciences written by Barry Cipra and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

The Meaning of Proofs

Author : Gabriele Lolli
Publisher : MIT Press
ISBN 13 : 0262371049
Total Pages : 177 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis The Meaning of Proofs by : Gabriele Lolli

Download or read book The Meaning of Proofs written by Gabriele Lolli and published by MIT Press. This book was released on 2022-09-27 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

A Concise History of Mathematics

Author : Dirk Jan Struik
Publisher : Courier Corporation
ISBN 13 : 9780486602554
Total Pages : 260 pages
Book Rating : 4.6/5 (25 download)

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Book Synopsis A Concise History of Mathematics by : Dirk Jan Struik

Download or read book A Concise History of Mathematics written by Dirk Jan Struik and published by Courier Corporation. This book was released on 1967 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.

Proofs from THE BOOK

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Mathematics: Journey from Basic Mathematics through Intermediate Algebra

Author : Richard N. Aufmann
Publisher : Cengage Learning
ISBN 13 : 9780357032671
Total Pages : 50 pages
Book Rating : 4.0/5 (326 download)

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Book Synopsis Mathematics: Journey from Basic Mathematics through Intermediate Algebra by : Richard N. Aufmann

Download or read book Mathematics: Journey from Basic Mathematics through Intermediate Algebra written by Richard N. Aufmann and published by Cengage Learning. This book was released on 2020-04-28 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

How Not to Be Wrong

Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 0143127535
Total Pages : 482 pages
Book Rating : 4.1/5 (431 download)

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Book Synopsis How Not to Be Wrong by : Jordan Ellenberg

Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin. This book was released on 2015-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.