100 Years Of Math Milestones The Pi Mu Epsilon Centennial Collection

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100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection

Author : Stephan Ramon Garcia
Publisher : American Mathematical Soc.
ISBN 13 : 1470436523
Total Pages : 581 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection by : Stephan Ramon Garcia

Download or read book 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection written by Stephan Ramon Garcia and published by American Mathematical Soc.. This book was released on 2019-06-13 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Algebra and Famous Impossibilities

Author : Sidney A. Morris
Publisher : Springer Nature
ISBN 13 : 3031056981
Total Pages : 233 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Abstract Algebra and Famous Impossibilities by : Sidney A. Morris

Download or read book Abstract Algebra and Famous Impossibilities written by Sidney A. Morris and published by Springer Nature. This book was released on 2022-11-26 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Best Writing on Mathematics 2019

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 0691198357
Total Pages : 288 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Best Writing on Mathematics 2019 by : Mircea Pitici

Download or read book The Best Writing on Mathematics 2019 written by Mircea Pitici and published by Princeton University Press. This book was released on 2019-11-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pi Mu Epsilon Journal

Author : Pi Mu Epsilon
Publisher :
ISBN 13 :
Total Pages : 762 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Pi Mu Epsilon Journal by : Pi Mu Epsilon

Download or read book Pi Mu Epsilon Journal written by Pi Mu Epsilon and published by . This book was released on 1984 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Concepts and Principles of Pharmacology

Author : James E. Barrett
Publisher : Springer Nature
ISBN 13 : 3030353621
Total Pages : 466 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Concepts and Principles of Pharmacology by : James E. Barrett

Download or read book Concepts and Principles of Pharmacology written by James E. Barrett and published by Springer Nature. This book was released on 2019-12-24 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical People

Author : Donald Albers
Publisher : CRC Press
ISBN 13 : 1439865175
Total Pages : 416 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Mathematical People by : Donald Albers

Download or read book Mathematical People written by Donald Albers and published by CRC Press. This book was released on 2008-09-18 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Model Spaces and their Operators

Author : Stephan Ramon Garcia
Publisher : Cambridge University Press
ISBN 13 : 1316390438
Total Pages : 339 pages
Book Rating : 4.3/5 (163 download)

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Book Synopsis Introduction to Model Spaces and their Operators by : Stephan Ramon Garcia

Download or read book Introduction to Model Spaces and their Operators written by Stephan Ramon Garcia and published by Cambridge University Press. This book was released on 2016-05-17 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

The Faithful Home of the Three Stars

Author : Peter J. Floriani
Publisher :
ISBN 13 :
Total Pages : 548 pages
Book Rating : 4.:/5 (21 download)

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Book Synopsis The Faithful Home of the Three Stars by : Peter J. Floriani

Download or read book The Faithful Home of the Three Stars written by Peter J. Floriani and published by . This book was released on 1989 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mathematics of Encryption

Author : Margaret Cozzens
Publisher : American Mathematical Soc.
ISBN 13 : 0821883216
Total Pages : 355 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mathematics of Encryption by : Margaret Cozzens

Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Invitation to Modern Number Theory

Author : Steven J. Miller
Publisher : Princeton University Press
ISBN 13 : 9780691120607
Total Pages : 532 pages
Book Rating : 4.1/5 (26 download)

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Book Synopsis An Invitation to Modern Number Theory by : Steven J. Miller

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2006-03-26 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Riemann Hypothesis

Author : Roland van der Veen
Publisher : The Mathematical Association of America
ISBN 13 : 0883856506
Total Pages : 157 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis The Riemann Hypothesis by : Roland van der Veen

Download or read book The Riemann Hypothesis written by Roland van der Veen and published by The Mathematical Association of America. This book was released on 2016-01-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Invariant Theory of Matrices

Author : Corrado De Concini
Publisher : American Mathematical Soc.
ISBN 13 : 147044187X
Total Pages : 153 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Invariant Theory of Matrices by : Corrado De Concini

Download or read book The Invariant Theory of Matrices written by Corrado De Concini and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

Benford's Law

Author : Steven J. Miller
Publisher : Princeton University Press
ISBN 13 : 1400866596
Total Pages : 465 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Benford's Law by : Steven J. Miller

Download or read book Benford's Law written by Steven J. Miller and published by Princeton University Press. This book was released on 2015-06-09 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Illustrated Theory of Numbers

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
ISBN 13 : 1470463717
Total Pages : 341 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Illustrated Theory of Numbers by : Martin H. Weissman

Download or read book An Illustrated Theory of Numbers written by Martin H. Weissman and published by American Mathematical Soc.. This book was released on 2020-09-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Culver-Stockton College Academic Catalog

Author : Culver-Stockton College
Publisher :
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Culver-Stockton College Academic Catalog by : Culver-Stockton College

Download or read book Culver-Stockton College Academic Catalog written by Culver-Stockton College and published by . This book was released on 1919 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Impactful Times

Author : James R. Asay
Publisher : Springer
ISBN 13 : 331933347X
Total Pages : 668 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Impactful Times by : James R. Asay

Download or read book Impactful Times written by James R. Asay and published by Springer. This book was released on 2017-05-02 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a history of shock compression science, including development of experimental, material modeling, and hydrodynamics code technologies over the past six decades at Sandia National Laboratories. The book is organized into a discussion of major accomplishments by decade with over 900 references, followed by a unique collection of 45 personal recollections detailing the trials, tribulations, and successes of building a world-class organization in the field. It explains some of the challenges researchers faced and the gratification they experienced when a discovery was made. Several visionary researchers made pioneering advances that integrated these three technologies into a cohesive capability to solve complex scientific and engineering problems. What approaches worked, which ones did not, and the applications of the research are described. Notable applications include the turret explosion aboard the USS Iowa and the Shoemaker-Levy comet impact on Jupiter. The personal anecdotes and recollections make for a fascinating account of building a world-renowned capability from meager beginnings. This book will be inspiring to the expert, the non expert, and the early-career scientist. Undergraduate and graduate students in science and engineering who are contemplating different fields of study should find it especially compelling.

99 Variations on a Proof

Author : Philip Ording
Publisher : Princeton University Press
ISBN 13 : 0691218978
Total Pages : 272 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis 99 Variations on a Proof by : Philip Ording

Download or read book 99 Variations on a Proof written by Philip Ording and published by Princeton University Press. This book was released on 2021-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.