Contemporary Mathematics, Volume: 613
2014; 176 pp; softcover
ISBN-13: 978-1-4704-1015-5
Expected publication date is April 14, 2014.
This book is a collection of expository articles based on four lecture series presented during the 2012 Notre Dame Summer School in Topology and Field Theories.
The four topics covered in this volume are: Construction of a local conformal field theory associated to a compact Lie group, a level and a Frobenius object in the corresponding fusion category; Field theory interpretation of certain polynomial invariants associated to knots and links; Homotopy theoretic construction of far-reaching generalizations of the topological field theories that Dijkgraf and Witten associated to finite groups; and a discussion of the action of the orthogonal group O(n) on the full subcategory of an n-category consisting of the fully dualizable objects.
The expository style of the articles enables non-experts to understand the basic ideas of this wide range of important topics.
Graduate students and research mathematicians interested in field theories from an algebraic topology and higher category perspective.
*A. Henriques -- Three-tier CFTs from Frobenius algebras
*S. Gukov and I. Saberi -- Lectures on knot homology and quantum curves
*G. Heuts and J. Lurie -- Ambidexterity
*C. J. Schommer-Pries -- Dualizability in low-dimensional higher category theory
2014; 192 pp; softcover
ISBN-13: 978-1-4704-1425-2
Expected publication date is May 12, 2014.
A superb, beautifully illustrated book for kids -- and those of us still children at heart -- that takes you up (and up, and up,and up, and up, and ...) through the counting numbers, illustrating the power of the different notations mathematicians have invented to talk about VERY BIG NUMBERS. Many of us use words to try to describe the beauty and the power of mathematics. Schwartz does it with captivating, full-color drawings.
--Keith Devlin, NPR Math Guy and author of "The Math Instinct" and "The Math Gene"
Large numbers may seem like a banal subject, but Richard Evan Schwartz goes way, way beyond the banal, presenting the concept of big numbers with a freshness and originality rarely seen elsewhere. Using beautiful and imaginative illustrations to build from single digit numbers to sextillions, googols and beyond, his evocative drawings will give the readers, not only children, a true feeling for the vastness of numbers, nearly to infinity. I am anxiously waiting for my granddaughter to become old enough, just so I can give her this book.
--George Szpiro, Neue Zurcher Zeitung (Switzerland) and author of "Secret Life of Numbers" and "Mathematical Medley"
Open this book and embark on an accelerated tour through the number system, starting with small numbers and building up to really gigantic ones, like a trillion, an octillion, a googol, and even ones too huge for names! Along the way, you'll become familiar with the sizes of big numbers in terms of everyday objects, such as the number of basketballs needed to cover New York City or the number of trampolines needed to cover the earth's surface. Take an unforgettable journey part of the way to infinity!
Appropriate for ages 6 and up, their parents and teachers, and anyone curious about Big Numbers.
Graduate Studies in Mathematics, Volume: 151
2014; approx. 293 pp; hardcover
ISBN-13: 978-1-4704-1020-9
Expected publication date is June 16, 2014.
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology.
The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex.
With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Graduate students and research mathematicians interested in low-dimensional topology.
*Perspectives on manifolds
*Surfaces
*3-manifolds
*Knots and links in 3-manifolds
*Triangulated 3-manifolds
*Heegaard splittings
*Further topics
*General position
*Morse functions
*Bibliography
*Index
Publication planned for: March 2014
available from March 2014
format: Paperback
isbn: 9781107603455
Cryptography has been employed in war and diplomacy from the time of Julius Caesar. In our Internet age, cryptography's most widespread application may be for commerce, from protecting the security of electronic transfers to guarding communication from industrial espionage. This accessible introduction for undergraduates explains the cryptographic protocols for achieving privacy of communication and the use of digital signatures for certifying the validity, integrity, and origin of a message, document, or program. Rather than offering a how-to on configuring web browsers and e-mail programs, the author provides a guide to the principles and elementary mathematics underlying modern cryptography, giving readers a look under the hood for security techniques and the reasons they are thought to be secure.
1. Introduction
2. Modular arithmetic
3. The addition cypher, an insecure block cypher
4. Functions
5. Probability theory
6. Perfect secrecy and perfectly secure cryptosystems
7. Number theory
8. Euclid's algorithm
9. Some uses of perfect secrecy
10. Computational problems, easy and hard
11. Modular exponentiation, modular logarithm, and one-way functions
12. Diffie and Hellman's exponential-key-agreement protocol
13. Computationally secure single-key cryptosystems
14. Public-key cryptosystems and digital signatures.
Part of Cambridge Companions to Philosophy
Publication planned for: May 2014
available from May 2014
format: Hardback
isbn: 9780521828345
This volume is the first systematic presentation of the work of Albert Einstein, comprised of fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's gmiracle year,h 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to his light quantum hypothesis. Further essays relate Einstein's path to the general theory of relativity (1915) and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings
Introduction Michel Janssen and Christoph Lehner
1. Einstein's Copernican revolution Jurgen Renn and Robert Rynasiewicz
2. Einstein's special theory of relativity and the problems in the electrodynamics of moving bodies that led him to it John D. Norton
3. Einstein on statistical physics: fluctuations and atomism A. J. Kox
4. The quantum enigma Olivier Darrigol
5. The experimental challenge of light quanta Roger H. Stuewer
6. 'No success like failure c': Einstein's quest for general relativity, 1907*20 Michel Janssen
7. Einstein's role in the creation of relativistic cosmology Christopher Smeenk
8. Einstein, gravitational waves, and the theoretician's regress Daniel J. Kennefick
9. Einstein's unified field theory program Tilman Sauer
10. Einstein's realism and his critique of quantum mechanics Christoph Lehner
11. Einstein and the development of twentieth-century philosophy of science Don Howard
12. 'A believing rationalist': Einstein and 'the truly valuable' in Kant Thomas Ryckman
13. Space, time, and geometry Michael Friedman
14. Einstein's politics Robert Schulmann
Appendix. Special relativity Michel Janssen.
Part of London Mathematical Society Student Texts
Publication planned for: July 2014
available from July 2014
format: Hardback
isbn: 9781107044036
The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma*Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.
Part I. Elementary Number Theory:
1. Prelude
2. Arithmetic functions and integer points
3. Congruences
4. Quadratic reciprocity and Fourier series
5. Sums of squares
Part II. Fourier Analysis and Geometric Discrepancy:
6. Uniform distribution and completeness of the trigonometric system
7. Discrepancy and trigonometric approximation
8. Integer points and Poisson summation formula
9. Integer points and exponential sums
10. Geometric discrepancy and decay of Fourier transforms
11. Discrepancy in high dimension and Bessel functions
References
Index.