Invitation to the Mathematics of Fermat-Wiles

2001-09-24
Invitation to the Mathematics of Fermat-Wiles
Author: Yves Hellegouarch
Publisher: Elsevier
Total Pages: 395
Release: 2001-09-24
Genre: Mathematics
ISBN: 0080478778
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Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem

An Invitation to Abstract Mathematics

2020-10-27
An Invitation to Abstract Mathematics
Author: Béla Bajnok
Publisher: Springer Nature
Total Pages: 443
Release: 2020-10-27
Genre: Mathematics
ISBN: 3030561747
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This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

Using the Mathematics Literature

2004-05-25
Using the Mathematics Literature
Author: Kristine K. Fowler
Publisher: CRC Press
Total Pages: 412
Release: 2004-05-25
Genre: Language Arts & Disciplines
ISBN: 9780824750350
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This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Quantum Field Theory I: Basics in Mathematics and Physics

2007-04-18
Quantum Field Theory I: Basics in Mathematics and Physics
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
Total Pages: 1060
Release: 2007-04-18
Genre: Science
ISBN: 354034764X
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This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Biscuits of Number Theory

2020-07-29
Biscuits of Number Theory
Author: Arthur T. Benjamin
Publisher: American Mathematical Soc.
Total Pages: 331
Release: 2020-07-29
Genre: Mathematics
ISBN: 1470458438
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An anthology of articles designed to supplement a first course in number theory.

Fearless Symmetry

2008-08-24
Fearless Symmetry
Author: Avner Ash
Publisher: Princeton University Press
Total Pages: 308
Release: 2008-08-24
Genre: Mathematics
ISBN: 0691138710
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Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.

An Invitation to Modern Number Theory

2020-07-21
An Invitation to Modern Number Theory
Author: Steven J. Miller
Publisher: Princeton University Press
Total Pages: 526
Release: 2020-07-21
Genre: Mathematics
ISBN: 0691215979
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In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Abstract Algebra

2008-09-02
Abstract Algebra
Author: Dan Saracino
Publisher: Waveland Press
Total Pages: 320
Release: 2008-09-02
Genre: Mathematics
ISBN: 1478610131
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The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course.