This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.
The present book collects most of the courses and seminars delivered at the
meeting entitled “ Frontiers in Number Theory, Physics and Geometry”, which
took place at the Centre de Physique des Houches in the French Alps, March 9-
21, 2003. It is divided into two volumes. Volume I contains the contributions on
three broad topics: Random matrices, Zeta functions and Dynamical systems.
The present volume contains sixteen contributions on three themes: Conformal
field theories for strings and branes, Discrete groups and automorphic forms
and finally, Hopf algebras and renormalization....
Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems
The aim of this book, announced in the first edition, is to give a bird’seye
view of undergraduate mathematics and a glimpse of wider horizons.
The second edition aimed to broaden this view by including new chapters
on number theory and algebra, and to engage readers better by including
many more exercises. This third (and possibly last) edition aims to increase
breadth and depth, but also cohesion, by connecting topics that were previously
strangers to each other, such as projective geometry and finite groups,
and analysis and combinatorics....
"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries.
This book presents a complete account of the foundations of the theory of
p-adic Lie groups. It moves on to some of the important more advanced
aspects. Although most of the material is not new, it is only in recent years
that p-adic Lie groups have found important applications in number theory
and representation theory. These applications constitute, in fact, an increasingly
active area of research. The book is designed to give to the advanced,
but not necessarily graduate, student a streamlined access to the basics of
the theory. It is almost self contained.
(BQ) Ebook Project Origami activities for exploring mathematics presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages, this updated and expanded edition now includes 30 activities and offers better solutions and teaching tips for all activities.
Commutative algebra is the theory of commutative rings and their modules.
Although it is an interesting theory in itself, it is generally seen as a tool for
geometry and number theory. This is my point of view. In this book I try
to organize and present a cohesive set of methods in commutative algebra, for
use in geometry. As indicated in the title, I maintain throughout the text a
view towards complex projective geometry.
In many recent algebraic geometry books, commutative algebra is often
treated as a poor relation. One occasionally refers to it, but only reluctantly.
A First Course in Discrete Mathematics I. Anderson Analytic Methods for Partial Differential Equations G. Evans, J. Blackledge, P. Yardley Applied Geometry for Computer Graphics and CAD D. Marsh Basic Linear Algebra, Second Edition T.S. Blyth and E.F. Robertson Basic Stochastic Processes Z. Brze´ niak and T. Zastawniak z Elementary Differential Geometry A. Pressley Elementary Number Theory G.A. Jones and J.M. Jones Elements of Abstract Analysis M. Ó Searcóid Elements of Logic via Numbers and Sets D.L. Johnson...
The discovery of infinite products byWallis and infinite series by Newton marked the
beginning of the modern mathematical era. The use of series allowed Newton to find
the area under a curve defined by any algebraic equation, an achievement completely
beyond the earlier methods ofTorricelli, Fermat, and Pascal. The work of Newton and
his contemporaries, including Leibniz and the Bernoullis, was concentrated in mathematical
analysis and physics.
Mathematics has its own language with numbers as the alphabet. The language is given structure
with the aid of connective symbols, rules of operation, and a rigorous mode of thought (logic). These
concepts, which previously were explored in elementary mathematics courses such as geometry, algebra,
and calculus, are reviewed in the following paragraphs
The prerequisites for this book are the “standard” first-semester course
in number theory (with incidental elementary algebra) and elementary
calculus. There is no lack of suitable texts for these prerequisites (for
example, An Introduction to the Theory of Numbers, by 1. Niven and H. S.
Zuckerman, John Wiley and Sons, 1960, cari be cited ...
This chapter is a collection of basic material on probability theory, information theory,
complexity theory, number theory, abstract algebra, and finite fields that will be used
throughout this book. Further background and proofs of the facts presented here can be
found in the references given in x2.7. The following standard notation will be used throughout:
Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and ﬁelds. ...
Knowledge of number theory and abstract algebra are pre–requisites for any engineer designing a secure internet–based system. However, most of the books currently available on the subject are aimed at practitioners who just want to know how the various tools available on the market work and what level of security they impart. These books traditionally deal with the science and mathematics only in so far as they are necessary to understand how the tools work. I
Israel Moiseevich Gelfand is one of the greatest mathematicians of the 20th century.
His insights and ideas have helped to develop new areas in mathematics and to
reshape many classical ones.
The influence of Gelfand can be found everywhere in mathematics and mathematical
physics from functional analysis to geometry, algebra, and number theory. His
seminar (one of the most influential in the history of mathematics) helped to create
a very diverse and productive Gelfand school; indeed, many outstanding mathematicians
proudly call themselves Gelfand disciples....
In this report we present some noncommutative weak and strong laws of large numbers. Two case are considered: a von Neumann algebra with a normal faithful state on it and the algebra of measurable operators with normal faithful trace.
1. Introduction and notations One of the problems occurring in noncommutative probability theory concerns the extension of various results centered around limit theorems to the noncommutative context.
The theory of automorphic functions in one complex variable was created
during the second half of the nineteenth and the beginning of the twentieth
centuries. Important contributions are due to such illustrious mathematicians
as F. Klein, P. Koebe and H. Poincare. Two sources may be
traced: the uniformization theory of algebraic functions, and certain topics
in number theory. Automorphic functions with respect to groups with
compact quotient space on the one hand and elliptic modular functions on
the other are examples of these two aspects.
Combinatorics is generally concerned with counting arrangements
within a finite set. One of the basic problems is to determine the
number of possible configurations of a given kind. Even when the
rules specifying the configuration are relatively simple, the questions
of existence and enumeration often present great difficulties. Besides
counting, combinatorics is also concerned with questions involving
symmetries, regularity properties, and morphisms of these
arrangements. The theory of block designs is an important area where
these facts are very apparent.