Making Transcendence Transparent

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Making Transcendence Transparent

Edward B. Burger,Robert Tubbs
Making Transcendence Transparent Book PDF

Author : Edward B. Burger,Robert Tubbs
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 50,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741148

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Making Transcendence Transparent by Edward B. Burger,Robert Tubbs Pdf

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.

Periods And Special Functions In Transcendence

Tretkoff Paula B
Periods And Special Functions In Transcendence Book PDF

Author : Tretkoff Paula B
Publisher : World Scientific
Page : 228 pages
File Size : 45,6 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9781786342966

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Periods And Special Functions In Transcendence by Tretkoff Paula B Pdf

This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Surveys in Number Theory

Krishnaswami Alladi
Surveys in Number Theory Book PDF

Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 54,9 Mb
Release : 2009-03-02
Category : Mathematics
ISBN : 9780387785103

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Surveys in Number Theory by Krishnaswami Alladi Pdf

Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).

Mathematical Writing

Franco Vivaldi
Mathematical Writing Book PDF

Author : Franco Vivaldi
Publisher : Springer
Page : 213 pages
File Size : 54,5 Mb
Release : 2014-11-04
Category : Mathematics
ISBN : 9781447165279

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Mathematical Writing by Franco Vivaldi Pdf

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150 of them have complete solutions, to facilitate self-study. Mathematical Writing will be of interest to all mathematics students who want to raise the quality of their coursework, reports, exams, and dissertations.

Diophantine Analysis

Jörn Steuding
Diophantine Analysis Book PDF

Author : Jörn Steuding
Publisher : Birkhäuser
Page : 232 pages
File Size : 47,7 Mb
Release : 2016-12-21
Category : Mathematics
ISBN : 9783319488172

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Diophantine Analysis by Jörn Steuding Pdf

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.

All the Math You Missed

Thomas A. Garrity
All the Math You Missed Book PDF

Author : Thomas A. Garrity
Publisher : Cambridge University Press
Page : 417 pages
File Size : 49,9 Mb
Release : 2021-07
Category : Business & Economics
ISBN : 9781009009195

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All the Math You Missed by Thomas A. Garrity Pdf

Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

Early Fourier Analysis

Hugh L. Montgomery
Early Fourier Analysis Book PDF

Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 41,8 Mb
Release : 2014-12-10
Category : Mathematics
ISBN : 9781470415600

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Early Fourier Analysis by Hugh L. Montgomery Pdf

Fourier Analysis is an important area of mathematics, especially in light of its importance in physics, chemistry, and engineering. Yet it seems that this subject is rarely offered to undergraduates. This book introduces Fourier Analysis in its three most classical settings: The Discrete Fourier Transform for periodic sequences, Fourier Series for periodic functions, and the Fourier Transform for functions on the real line. The presentation is accessible for students with just three or four terms of calculus, but the book is also intended to be suitable for a junior-senior course, for a capstone undergraduate course, or for beginning graduate students. Material needed from real analysis is quoted without proof, and issues of Lebesgue measure theory are treated rather informally. Included are a number of applications of Fourier Series, and Fourier Analysis in higher dimensions is briefly sketched. A student may eventually want to move on to Fourier Analysis discussed in a more advanced way, either by way of more general orthogonal systems, or in the language of Banach spaces, or of locally compact commutative groups, but the experience of the classical setting provides a mental image of what is going on in an abstract setting.

Fourier Analysis

Eric Stade
Fourier Analysis Book PDF

Author : Eric Stade
Publisher : John Wiley & Sons
Page : 519 pages
File Size : 50,5 Mb
Release : 2011-10-07
Category : Mathematics
ISBN : 9781118165515

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Fourier Analysis by Eric Stade Pdf

A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of applications of Fourier analysis in the natural sciences and the enormous impact Fourier analysis has had on the development of mathematics as a whole. Systematic and comprehensive, the book: Presents material using a cause-and-effect approach, illustrating where ideas originated and what necessitated them Includes material on wavelets, Lebesgue integration, L2 spaces, and related concepts Conveys information in a lucid, readable style, inspiring further reading and research on the subject Provides exercises at the end of each section, as well as illustrations and worked examples throughout the text Based upon the principle that theory and practice are fundamentally linked, Fourier Analysis is the ideal text and reference for students in mathematics, engineering, and physics, as well as scientists and technicians in a broad range of disciplines who use Fourier analysis in real-world situations.

Mathematical Constants II

Steven R. Finch
Mathematical Constants II Book PDF

Author : Steven R. Finch
Publisher : Cambridge University Press
Page : 783 pages
File Size : 51,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9781108470599

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Mathematical Constants II by Steven R. Finch Pdf

Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

From Arithmetic to Zeta-Functions

Jürgen Sander,Jörn Steuding,Rasa Steuding
From Arithmetic to Zeta Functions Book PDF

Author : Jürgen Sander,Jörn Steuding,Rasa Steuding
Publisher : Springer
Page : 552 pages
File Size : 45,7 Mb
Release : 2016-12-29
Category : Mathematics
ISBN : 9783319282039

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From Arithmetic to Zeta-Functions by Jürgen Sander,Jörn Steuding,Rasa Steuding Pdf

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Invitation to Real Analysis

César Ernesto Silva
Invitation to Real Analysis Book PDF

Author : César Ernesto Silva
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 54,6 Mb
Release : 2019
Category : Education
ISBN : 9781470449285

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Invitation to Real Analysis by César Ernesto Silva Pdf

Provides a careful introduction to the real numbers with an emphasis on developing proof-writing skills. The book continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.

Auxiliary Polynomials in Number Theory

David Masser
Auxiliary Polynomials in Number Theory Book PDF

Author : David Masser
Publisher : Cambridge University Press
Page : 367 pages
File Size : 55,8 Mb
Release : 2016-07-21
Category : Mathematics
ISBN : 9781107061576

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Auxiliary Polynomials in Number Theory by David Masser Pdf

A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.

An Illustrated Theory of Numbers

Martin H. Weissman
An Illustrated Theory of Numbers Book PDF

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 50,7 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.

The Palgrave Handbook of Literature and Mathematics

Robert Tubbs,Alice Jenkins,Nina Engelhardt
The Palgrave Handbook of Literature and Mathematics Book PDF

Author : Robert Tubbs,Alice Jenkins,Nina Engelhardt
Publisher : Springer Nature
Page : 628 pages
File Size : 55,8 Mb
Release : 2020-12-30
Category : Literary Criticism
ISBN : 9783030554781

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The Palgrave Handbook of Literature and Mathematics by Robert Tubbs,Alice Jenkins,Nina Engelhardt Pdf

This handbook features essays written by both literary scholars and mathematicians that examine multiple facets of the connections between literature and mathematics. These connections range from mathematics and poetic meter to mathematics and modernism to mathematics as literature. Some chapters focus on a single author, such as mathematics and Ezra Pound, Gertrude Stein, or Charles Dickens, while others consider a mathematical topic common to two or more authors, such as squaring the circle, chaos theory, Newton’s calculus, or stochastic processes. With appeal for scholars and students in literature, mathematics, cultural history, and history of mathematics, this important volume aims to introduce the range, fertility, and complexity of the connections between mathematics, literature, and literary theory. Chapter 1 is available open access under a Creative Commons Attribution 4.0 International License via [link.springer.com|http://link.springer.com/].

The Annotated Turing

Charles Petzold
The Annotated Turing Book PDF

Author : Charles Petzold
Publisher : John Wiley & Sons
Page : 391 pages
File Size : 44,8 Mb
Release : 2008-06-16
Category : Computers
ISBN : 9780470229057

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The Annotated Turing by Charles Petzold Pdf

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.