Author(s) : Timothy Gowers Publisher : Princeton Pages      : 1008 Format    : PDF ISBN-10  : 0691118809 ISBN-13  : 978-0691118802

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.

Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.

* Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
* Presents major ideas and branches of pure mathematics in a clear, accessible style
* Defines and explains important mathematical concepts, methods, theorems, and open problems
* Introduces the language of mathematics and the goals of mathematical research
* Covers number theory, algebra, analysis, geometry, logic, probability, and more
* Traces the history and development of modern mathematics
* Profiles more than ninety-five mathematicians who influenced those working today
* Explores the influence of mathematics on other disciplines
* Includes bibliographies, cross-references, and a comprehensive index

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Author(s) : Nino Boccara Publisher : Springer; 1 edition Date       : 2007 Pages      : 539 Format    : PDF ISBN       : 0387495134

Essential Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs.

The first section, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. Its aim is to provide the reader with Mathematica proficiency quickly and efficiently.

The second section covers a broad range of applications in physics, engineering and applied mathematics, including Egyptian Fractions, Happy Numbers, Mersenne Numbers, Multibases, Quantum Harmonic Oscillator, Quantum Square Potential, Van der Pol Oscillator, Electrostatics, Motion of a Charged Particle in an Electromagnetic Field, Duffing Oscillator, Negative and Complex Bases, Tautochrone Curves, Kepler's Laws, Foucault's Pendulum, Iterated Function Systems, Public-Key Encryption, and Julia and Mandelbrot Sets.

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