Abramowitz and Stegun: Handbook of Mathematical Functions

EBook Description: The present volume is an outgrowth of a Conference on Mathematical Tables held at Cambridge, Mass., on September 15-16, 1954, under the auspices of the National Science Foundation and the Massachusetts Institute of Technology. The purpose of the meeting was to evaluate the need for mathematical tables in the light of the availability of large scale computing machines. It was the consensus of opinion that in spite of the increasing use of the new machines the basic need for tables would continue to exist. Numerical tables of mathematical functions are in continual demand by scientists and engineers. A greater variety of functions and higher accuracy of tabulation are now required as a result of scientific advances and, especially, of the increasing use of automatic computers. In the latter connection, the tables serve mainly for preliminary surveys of problems before programming for machine operation. For those without easy access to machines, such tables are, of course, indispensable.

its book of mathematics on numerical analysis.

The Structure of Finite Algebras (Contemporary Mathematics)

The utility of congruence lattices in revealing the structure of general algebras has been recognized since Garrett Birkhoff's pioneering work in the 1930s and 1940s. However, the results presented in this book are of very recent origin: most of them were developed in 1983. The main discovery presented here is that the lattice of congruences of a finite algebra is deeply connected to the structure of that algebra. The theory reveals a sharp division of locally finite varieties of algebras into six interesting new families, each of which is characterized by the behavior of congruences in the algebras. The authors use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well. The authors begin with a straightforward and complete development of basic tame congruence theory, a topic that offers great promise for a wide variety of investigations. They then move beyond the consideration of individual algebras to a study of locally finite varieties. A list of open problems closes the work.

A Cook-Book Of Mathematics

This textbook is based on an extended collection of handouts distributed to the graduate students in economics attending summer mathematics class at the Center for Economic Research and Graduate Education (CERGE) at Charles University in Prague. There are two considerations needed to be taken in reading this book. First, this is a short textbook, which could be covered in the course of two months and which, in turn, covers the most significant issues of mathematical economics. This book attempts to maintain a balance between being overly detailed and overly schematic. Therefore this text should resemble (in the 'ideological' sense) a 'hybrid' of Chiang's classic textbook Fundamental Methods of Mathematical Economics and the comprehensive reference manual by Berck and Sydsaeter.

Elementary Mathematics

These are the first of two lecture notes used for Math130 - Mathematics IE course at the Department of Mathematics, Macquarie University. Mathematics IE is the standard entry-level mathematics unit for students who have not had the benefit of a detailed introduction to the calculus that is equivalent to a reasonably high level of the NSW HSC Mathematics course. This unit then serves as a prerequisite for further study in mathematics. Taken by itself, it provides the basic mathematical knowledge required by students in other disciplines.

A Problem Course in Mathematical Logic

This book is a free text intended to be the basis for a problem-oriented course(s) in mathematical logic and computability for students with some degree of mathematical sophistication. Parts I and II cover the basics of propositional and first-order logic respectively, Part III covers the basics of computability using Turing machines and recursive functions, and Part IV covers Godel's Incompleteness Theorems. They can be used in various ways for courses of various lengths and mixes of material. The author typically uses Parts I and II for a one-term course on mathematical logic, Part III for a one-term course on computability, and/or much of Part III together with Part IV for a one-term course on computability and incompleteness. In keeping with the modified Moore-method, this book supplies definitions, problems, and statements of results, along with some explanations, examples, and hints. The intent is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. Besides constructive criticism, it will probably be necessary for the instructor to supply further hints or direct the students to other sources from time to time. Just how this text is used will, of course, depend on the instructor and students in question. However, it is probably not appropriate for a conventional lecture-based course nor for a really large class.

Mathematics for Algorithm and Systems Analysis

Discrete mathematics is fundamental to computer science, and this up-to-date text assists undergraduates in mastering the ideas and mathematical language to address problems that arise in the field's many applications. It consists of four units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory. Discrete mathematics is an essential tool in almost all subareas of computer science. Interesting and challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, AI, theoretical computer science, and other areas.

A Short Course in Discrete Mathematics

This publication was originally made in response to the students' need for a mathematics text related tot he study of computer science. This book does assume some familiarity of calculus. Discrete mathematics is an essential tool in almost all subareas of computer science. Interesting and challenging problems in discrete mathematics arise in programming languages, computer architecture, networking, distributed systems, database systems, AI, theoretical computer science, and other areas.

The Unknowable (Discrete Mathematics and Theoretical Computer Science)

This essential companion volume to Chaitin's highly successful 'The Limits of Mathematics', also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant. The Unknowable is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for The Unknowable can be downloaded from the author's Web site.

Mathematical Analysis I

This text covers the basic topics of undergraduate real analysis including metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. The text also contains background material on set theory, the real numbers (including consequences of the completeness axiom), and Euclidean and vector spaces,taken from the author's Basic Concepts of Mathematics. This text is designed to be used as early as possible in the undergraduate curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

: Mathematical Foundations of Computer Science

: Mathematical Foundations of Computer Science

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