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Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability.
Study of "graph operators" or "graph-valued functions" such as the line graph, the clique graph, the complement, and powers, raises several immediate questions: Which graphs are fixed under the operator? Which graphs appear as images of graphs? What happens if the operator is iterated? Over the last 30 years these questions have been answered and methods developed for particular operators in literally hundreds of papers on the subject. Nowhere, however, could one find a comprehensive treatment-a unification of terminology, questions, and methods.G
This is the only book that deals comprehensively with fixed point theorems throughout mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers.
The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.
This advanced textbook covers the central topics in game theory and provides a strong basis from which readers can go on to more advanced topics. The subject matter is approached in a mathematically rigorous, yet lively and interesting way. New definitions and topics are motivated as thoroughly as possible. Coverage includes the idea of iterated Prisoner’s Dilemma (super games) and challenging game-playing computer programs.
Engineers around the world depend on MATLAB for its power, usability, and outstanding graphics capabilities. Yet too often, engineering students are either left on their own to acquire the background they need to use MATLAB, or they must learn the program concurrently within an advanced course. Both of these options delay students from solving realistic design problems, especially when they do not have a text focused on applications relevant to their field and written at the appropriate level of mathematics.
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing.
Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use.
"The book is filled with Mathematica programming gems and is particularly valuable for researchers using special functions in their work because of extensive coverage of these topics. … Every chapter has numerous exercises with full solutions. Every computer science, mathematics, physics, engineering library should have this … on its shelves, because this is the best source of the applications of Mathematica to numerous computational tasks." (Matti Vuorinen, Zentralblatt MATH, Vol. 1095 (21), 2006)"This guidebook has three chapters.
The Petersen graph occupies an important position in the development of several areas of modern graph theory, because it often appears as a counter-example to important conjectures. In this account, the authors examine those areas, using the prominent role of the Petersen graph as a unifying feature. Topics covered include: vertex and edge colorability (including snarks), factors, flows, projective geometry, cages, hypohamiltonian graphs, and "symmetry" properties such as distance transitivity.
From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remaining accessible to the uninitiated while retaining enough rigor for the seasoned cryptologist.
For senior/graduate-level courses in Discrete-Time Signal Processing.Discrete-Time Signal Processing, Third Edition is the definitive, authoritative text on DSP – ideal for those with introductory-level knowledge of signals and systems. Written by prominent DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field.A
This introductory textbook explains cryptography with a strongly mathematical foundation. The major book parts are mathematical background, symmetric encryption, public-key encryption and signatures, security issues, and advanced protocols. The book is suitable for undergraduate students in Computer Science, Mathematics and Engineering.
Cryptography is an outstanding book that covers all the major areas of cryptography in a readable, mathematically precise form. Several chapters deal with especially active areas of research and give the reader a quick introduction and overview of the basic results in the area.
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