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This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic problems, and their connections with problems in number theory such as Fermatās Last Theorem, the Congruent...
Author
Description
Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields. The book contains most of the fundamental classical facts about the theory, such as knot diagrams,...
4) Groups
Author
Description
"This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying...
Author
Description
This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variable-length codes that culminates...
Author
Description
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new.
Author
Description
"This unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics cofounded and popularized by Paul Erdos. Janos...
Author
Description
"In this lively and accessible book Lorraine Code addresses one of the most controversial questions in contemporary theory of knowledge, a question of fundamental concern for feminist theory as well: Is the sex of the knower epistemologically significant? Responding in the affirmative, Code offers a radical alterantive to mainstream philosophy's terms for what counts as knowledge and how it is to be evaluated. Code first reviews the literature of...
15) Knots and links
Author
Description
Together with standard topics related to knots & links, this book covers polygonal & smooth presentations, the surgery equivalence of surfaces, the behaviour of invariants under factorisation & the satellite construction, the arithmetic of Conway's rational tangles, & arc presentations.
Author
Description
Just as physics made sense out of the mysteries of earth, air, fire, and water, it can be said that the science of information enriches and unifies an amazing diversity of modern sciences, from physics and mathematics to biology and linguistics. Because symbols, messages, and codes are the stuff not only of computers and telecommunications, but also of living organisms and the forms of human knowledge, information, and thus information theory, is...
Author
Description
"This book can be described as a student's edition of the author's Dynamical Theory of Gases. It is written, however, with the needs of the student of physics and physical chemistry in mind, and those parts of which the interest was mainly mathematical have been discarded. This does not mean that the book contains no serious mathematical discussion; the discussion in particular of the distribution law is quite detailed; but in the main the mathematics...
Author
Description
This book provides the mathematics necessary for the study of fractal geometry. It includes background material on metric topology and measure theory and also covers topological and fractal dimension, including the Hausdorff dimension. Furthermore, the book contains a complete discussion of self-similarity as well as the more general "graph self-similarity."
Author
Description
As this Preface is being written, the twentieth century is coming to an end. Historians may perhaps come to refer to it as the century of information, just as its predecessor is associated with the process of industrialisation. Successive technological developments such as the telephone, radio, television, computers and the Internet have had profound effects on the way we live. We can see pic tures of the surface of Mars or the early shape of the...
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