100 Years Of Math Milestones The Pi Mu Epsilon Centennial Collection

Author : Stephan Ramon Garcia,Steven J. Miller
Publisher : American Mathematical Soc.
Page : 581 pages
File Size : 54,9 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9781470436520

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100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection by Stephan Ramon Garcia,Steven J. Miller Pdf

This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes. Stephan Ramon Garcia is WM Keck Distinguished Service Professor and professor of mathematics at Pomona College. He is the author of four books and over eighty research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He has coauthored dozens of articles with students, including one that appeared in The Best Writing on Mathematics: 2015. He is on the editorial boards of Notices of the AMS, Proceedings of the AMS, American Mathematical Monthly, Involve, and Annals of Functional Analysis. He received four NSF research grants as principal investigator and five teaching awards from three different institutions. He is a fellow of the American Mathematical Society and was the inaugural recipient of the Society's Dolciani Prize for Excellence in Research. Steven J. Miller is professor of mathematics at Williams College and a visiting assistant professor at Carnegie Mellon University. He has published five books and over one hundred research papers, most with students, in accounting, computer science, economics, geophysics, marketing, mathematics, operations research, physics, sabermetrics, and statistics. He has served on numerous editorial boards, including the Journal of Number Theory, Notices of the AMS, and the Pi Mu Epsilon Journal. He is active in enrichment and supplemental curricular initiatives for elementary and secondary mathematics, from the Teachers as Scholars Program and VCTAL (Value of Computational Thinking Across Grade Levels), to numerous math camps (the Eureka Program, HCSSiM, the Mathematics League International Summer Program, PROMYS, and the Ross Program). He is a fellow of the American Mathematical Society, an at-large senator for Phi Beta Kappa, and a member of the Mount Greylock Regional School Committee, where he sees firsthand the challenges of applying mathematics.

Author : Sidney A. Morris,Arthur Jones,Kenneth R. Pearson
Publisher : Springer Nature
Page : 233 pages
File Size : 44,7 Mb
Release : 2022-11-26
Category : Mathematics
ISBN : 9783031056987

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Abstract Algebra and Famous Impossibilities by Sidney A. Morris,Arthur Jones,Kenneth R. Pearson Pdf

This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 288 pages
File Size : 47,8 Mb
Release : 2019-11-05
Category : Crafts & Hobbies
ISBN : 9780691198354

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The Best Writing on Mathematics 2019 by Mircea Pitici Pdf

An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Author : Pi Mu Epsilon
Publisher : Unknown
Page : 710 pages
File Size : 51,5 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015046583194

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Pi Mu Epsilon Journal by Pi Mu Epsilon Pdf

Author : Donald Albers,Gerald L. Alexanderson
Publisher : CRC Press
Page : 416 pages
File Size : 52,6 Mb
Release : 2008-09-18
Category : Mathematics
ISBN : 9781439865170

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Mathematical People by Donald Albers,Gerald L. Alexanderson Pdf

This unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introdu

Author : Anonim
Publisher : Unknown
Page : 2966 pages
File Size : 40,8 Mb
Release : 2003
Category : Biography
ISBN : 0837969751

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Who's who in America by Anonim Pdf

Author : Peter J. Floriani,Stanley R. Church
Publisher : Unknown
Page : 548 pages
File Size : 50,6 Mb
Release : 1989
Category : Greek letter societies
ISBN : OCLC:21076972

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The Faithful Home of the Three Stars by Peter J. Floriani,Stanley R. Church Pdf

Author : Margaret Cozzens, Steven J. Miller
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 50,6 Mb
Release : 2013-09-05
Category : Business & Economics
ISBN : 9780821883211

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The Mathematics of Encryption by Margaret Cozzens, Steven J. Miller Pdf

How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

Author : Steven J. Miller,Ramin Takloo-Bighash
Publisher : Princeton University Press
Page : 532 pages
File Size : 52,9 Mb
Release : 2006-03-26
Category : Mathematics
ISBN : 0691120609

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An Invitation to Modern Number Theory by Steven J. Miller,Ramin Takloo-Bighash Pdf

PART 1. BASIC NUMBER THEORY -- 1. Mod p Arithmetic, Group Theory and Cryptography -- 2. Arithmetic Functions -- 3. Zeta and L-Functions -- 4. Solutions to Diophantine Equations -- PART 2. CONTINUED FRACTIONS AND APPROXIMATIONS -- 5. Algebraic and Transcendental Numbers -- 6. The Proof of Roth's Theorem -- 7. Introduction to Continued Fractions -- PART 3. PROBABILISTIC METHODS AND EQUIDISTRIBUTION -- 8. Introduction to Probability -- 9. Applications of Probability: Benford's Law and Hypothesis Testing -- 10. Distribution of Digits of Continued Fractions -- 11. Introduction to Fourier Analysis -- 12. f n k g and Poissonian Behavior -- PART 4. THE CIRCLE METHOD -- 13. Introduction to the Circle Method -- 14. Circle Method: Heuristics for Germain Primes -- PART 5. RANDOM MATRIX THEORY AND L-FUNCTIONS -- 15. From Nuclear Physics to L-Functions -- 16. Random Matrix Theory: Eigenvalue Densities -- 17. Random Matrix Theory: Spacings between Adjacent Eigenvalues -- 18. The Explicit Formula and Density Conjectures -- Appendix A. Analysis Review -- Appendix B. Linear Algebra Review -- Appendix C. Hints and Remarks on the Exercises -- Appendix D. Concluding Remarks.

Author : James E. Barrett,Clive P. Page,Martin C. Michel
Publisher : Springer Nature
Page : 466 pages
File Size : 49,7 Mb
Release : 2019-12-24
Category : Medical
ISBN : 9783030353629

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Concepts and Principles of Pharmacology by James E. Barrett,Clive P. Page,Martin C. Michel Pdf

Celebrating 100 years of HEP, this volume will discuss key pharmacological discoveries and concepts of the past 100 years. These discoveries have dramatically changed the medical treatment paradigms of many diseases and these concepts have and will continue to shape discovery of new medicinies. Newly evolving technologies will similarly be discussed as they will shape the future of the pharmacology and, accordingly, medical therapy.

Author : Roland van der Veen,Jan van de Craats
Publisher : The Mathematical Association of America
Page : 157 pages
File Size : 47,8 Mb
Release : 2016-01-06
Category : Mathematics
ISBN : 9780883856505

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The Riemann Hypothesis by Roland van der Veen,Jan van de Craats Pdf

This book introduces interested readers to one of the most famous and difficult open problems in mathematics: the Riemann Hypothesis. Finding a proof will not only make you famous, but also earns you a one million dollar prize. The book originated from an online internet course at the University of Amsterdam for mathematically talented secondary school students. Its aim was to bring them into contact with challenging university level mathematics and show them why the Riemann Hypothesis is such an important problem in mathematics. After taking this course, many participants decided to study in mathematics at university.

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 46,8 Mb
Release : 2020-09-15
Category : Education
ISBN : 9781470463717

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An Illustrated Theory of Numbers by Martin H. Weissman Pdf

News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

Author : Steven J. Miller
Publisher : Princeton University Press
Page : 465 pages
File Size : 45,9 Mb
Release : 2015-06-09
Category : Mathematics
ISBN : 9781400866595

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Benford's Law by Steven J. Miller Pdf

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world’s leading experts on Benford’s law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration. Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford’s law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford’s law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford’s law can serve as a productive meeting ground for researchers and practitioners in diverse fields.

Author : Philip Ording
Publisher : Princeton University Press
Page : 272 pages
File Size : 53,9 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691218977

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99 Variations on a Proof by Philip Ording Pdf

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.

Author : Jukka Paakki
Publisher : Springer Nature
Page : 303 pages
File Size : 41,9 Mb
Release : 2019-10-08
Category : Computers
ISBN : 9783030160494

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Arto Salomaa: Mathematician, Computer Scientist, and Teacher by Jukka Paakki Pdf

This book outlines the scientific career of Arto Salomaa, a pioneer in theoretical computer science and mathematics. The author first interviewed the subject and his family and collaborators, and he then researched this fascinating biography of an intellectual who was key in the development of these fields. Early chapters progress chronologically from Academician Salomaa's origins, childhood, and education to his professional successes in science, teaching, and publishing. His most impactful direct research efforts have been in the areas of automata and formal languages. Beyond that he has influenced many more scientists and professionals through collaborations, teaching, and books on topics such as biocomputing and cryptography. The author offers insights into Finnish history, culture, and academia, while historians of computer science will appreciate the vignettes describing some of the people who have shaped the field from the 1950s to today. The author and his subject return throughout to underlying themes such as the importance of family and the value of longstanding collegial relationships, while the work and achievements are leavened with humor and references to interests such as music, sport, and the sauna.