Series: Progress in Mathematical Physics , Vol. 54
2009, Approx. 440 p., Hardcover
ISBN: 978-3-7643-8794-5
This is an introductory textbook on spectral theory of (unbounded) self-adjoint operators and quantum dynamics. It is written in an understandable, but still strongly formal style, intended for graduate (or advanced undergraduate) students and researchers interested in mathematical physics.
The book starts with linear operator theory, spectral questions and self-adjointness, and ends with the effect of spectral type on the large time behaviour of quantum systems. Many examples and exercises are included that usually are guided by quantum
Series: Oberwolfach Seminars , Vol. 40
2009, Approx. 250 p., Softcover
ISBN: 978-3-7643-8904-8
Due: January 2009
Exercises and Open Problems complement the material and stimulate further research
Introduces to the rather new field of Algebraic Statistics
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
Preface.- 1. Markov Bases.- 2. Likelihood Inference.- 3. Bayesian Inference.- 4. Conditional Independence.- 5. Hidden Variables.- 6. Exercises.- 7. Open Problems
Originally published by Center of Excellence, 1994
2009, Approx. 400 p. 140 illus., Softcover
ISBN: 978-0-387-75471-0
Due: July 2009
This second edition, originally titled The Colorado Mathematical Olympiad: the First Ten Years and Further Explorations, gives the interesting history of the competition as well as an outline of all the problems and solutions that have been created for the contest over the years. Many of the essay problems were inspired by Russian mathematical folklore and written to suit the young audience; for example, the 1989 Sugar problem was written in a pleasant Lewis Carroll-like story. Some other entertaining problems involve old Victorian map colorings, King Arthur and the knights of the round table, rooks in space, Santa Claus and his elves painting planes, football for 23, and even the Colorado Springs subway system.
Copmared to the first edition, this new book offers a 100% increase in problems, solutions, history, and 20 "further explorations," the bridges from the Olympiad to mathematical research problems. But this book is more than just problems, their solutions, and event statistics. It tells a compelling story of those who have contributed to the competition's success as well as the Colorado Springs mathematical community.
Preface.- Olympiad History: What it is and How it Started.- Three Celebrated Ideas.- Year 1.- Year 2.- Year 3.- Year4.- Year 5.- Year 6.- Year 7.- Year 8.- Year 9.- Year 10.- Year 11.- Year 12.- Year 13.- Year 14.- Year 15.- Year 16.- Year 17.- Year 18.- Year 19.- Year 20.- Introduction to Part II.- Rooks in Space.- Chromatic Number of the Plane.- Polygons in a Colored Circle, Polyhedra in a colored Sphere.- How Does one Cut a Triangle?.- Points in Convex Figures.- Triangles in a Colored Plane.- Rectangles in a Colored Plane.- Colored Polygons.- Infinite-Finite.- Schur Theorem.- Bibliography.- Chromatic Number of a Grid.- Stone Age Entertainment.- The Erdos Problem.- Squares in a Square.- Washington recTangles.- Olde Victorian Map Colouring.- More Stone Age Entertainment.- The 1-10-100 Problem.- King Arthur and the Knights of the Round Table.- A Map Coloring "Game".- Bibliography.- Index.
ISBN: 9781420061604
Publication Date: 10/2/2008
Number of Pages: 424
Explains cryptographic algorithms and their implementation, targeting various types of systems along with the tradeoffs between implementations methods
Provides real-world implementation problems
Focuses on implementations Ehardware, software, firmware Ein terms of size (gates and code) and speed (throughput and maximum frequencies)
Provides C and VHDL frameworks for implementation of problems
While cryptography books abound, this is very first to focus on teaching fundamental methods. Written from a mathematical perspective, rather than from engineering or computer science, it includes real implementation problems. Demonstrating how to select and implement proper algorithms, it relies on approaches coded in C or VHDL. The examples examine hardware, software, and embedded implementations to give readers a feel for what they will encounter in actual job situations. It encourages them to examine tradeoffs that must be made regarding code and hardware logic size, speed/throughput, and power. It covers basic ciphers, various algorithms, key exchange, signatures, and security services.
INTRODUCTION. PRIVATE-KEY CRYPTOGRAPHY. Substitutions Ciphers. Stream Ciphers. Encryption Approaches. Block Ciphers. PUBLIC-KEY CRYPTOGRAPHY. Underlying Mathematics. RSA. The Discrete Logarithm Problem. Efficient Implementation. PROTOCOLS. Digital Signatures. Message Authentication Codes. Security Services. Key Establishment.