**5 Mathematics eBooks**

Yearning for the Impossible: The Surprising Truths of Mathematics

Calculus of Variations

Mathematics for Economics and Business, 9th Edition

Advances in Complex Analysis and Operator Theory: Festschrift in Honor of Daniel Alpay's 60th Birthday

Number Fields, Second Edition

**Yearning for the Impossible: The Surprising Truths of Mathematics**

ISBN: 1138596213, 1138586102 | 2018 | EPUB/PDF | 328 Pages | 7 MB

Yearning for the Impossible: The Surprising Truth of Mathematics, Second Edition explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress. The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. This new edition contains many new exercises and commentaries, clearly discussing a wide range of challenging subjects

**Calculus of Variations**

English | PDF,EPUB | 2018 | 446 Pages | ISBN : 3319776363 | 16.43 MB

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether's Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and —-convergence for phase transitions and homogenization are explored.

While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

**Mathematics for Economics and Business, 9th Edition**

English | February 13th, 2018 | ISBN: 129219166X | 756 Pages | True PDF | 43.67 MB

Mathematics for Economics and Business, 9th Edition is the essential resource you need when studying mathematics as part of your economics, management or business course.

Whatever your level of prior mathematical knowledge, ability or confidence, this book will guide you step-by-step through the key mathematical concepts and techniques you need to succeed.

Starting with the basics, the book is designed to allow you to progress at your own pace, with a wealth of examples, practice exercises and self-test questions to check your understanding along the way. Worked examples throughout each chapter illustrate how mathematical concepts and techniques relate to the business world and encourage you to solve real problems yourself. Over 200 new questions have been added to this new edition, with answers provided, making it a fantastic resource for revision purposes.

**Advances in Complex Analysis and Operator Theory: Festschrift in Honor of Daniel Alpay's 60th Birthday**

English | 2017 | ISBN: 3319623613 | 398 Pages | PDF | 4.6 MB

This book gathers contributions written by Daniel Alpay's friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay's 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay's primary research interests.

The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

**Number Fields, Second Edition**

English | PDF,EPUB | 2018 | 213 Pages | ISBN : 3319902326 | 6.92 MB

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.

Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.

From the reviews:

"A thoroughly delightful introduction to algebraic number theory" - Ezra Brown in the Mathematical Reviews

"An excellent basis for an introductory graduate course in algebraic number theory" - Harold Edwards in the Bulletin of the American Mathematical Society

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