A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

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This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

Introduction to Real Analysis

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 9883

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This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

Elementary Point-Set Topology

A Transition to Advanced Mathematics

Author: Andre L. Yandl,Adam Bowers

Publisher: Courier Dover Publications

ISBN: 0486811018

Category: Mathematics

Page: 256

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In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

Mathematical Brain Benders

2nd Miscellany of Puzzles

Author: Stephen Barr

Publisher: Courier Corporation

ISBN: 0486242609

Category: Games

Page: 224

View: 1056

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Challenge yourself with over 100 fresh paradoxes, puzzles, riddles, conundrums, word and number games for the jaded, skeptical puzzlist. Over 100 pages of comprehensive answers. Approximately 300 illustrations. "Excellent collection of unusual, offbeat, and completely original puzzles." ? Scientific American.

Dynamical Systems

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486135144

Category: Mathematics

Page: 272

View: 8910

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A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.

Algebraic Logic

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 0486810410

Category: Mathematics

Page: 272

View: 1623

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Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index.

Interpolation and Approximation

Author: Philip J. Davis

Publisher: Courier Corporation

ISBN: 0486624951

Category: Mathematics

Page: 393

View: 7111

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Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486678709

Category: Mathematics

Page: 209

View: 9940

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A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

Advanced Calculus

Author: David Vernon Widder

Publisher: Courier Corporation

ISBN: 9780486661032

Category: Mathematics

Page: 520

View: 8337

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Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.

Adventures in Mathematical Reasoning

Author: Sherman Stein

Publisher: Courier Dover Publications

ISBN: 0486814114

Category: Mathematics

Page: 192

View: 6647

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Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.

From Geometry to Topology

Author: Graham Flegg

Publisher: Courier Corporation

ISBN: 9780486419619

Category: Mathematics

Page: 186

View: 5841

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Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.

Introduction to Nonlinear Differential and Integral Equations

Author: Harold Thayer Davis

Publisher: Courier Corporation

ISBN: 9780486609713

Category: Mathematics

Page: 566

View: 6058

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Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Mathematical Puzzles

Author: Samuel Loyd,Martin Gardner

Publisher: Courier Corporation

ISBN: 9780486204987

Category: Games

Page: 167

View: 6113

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Choice puzzles by one of America's most ingenious creators of mathematical entertainments, ranging from simple exercises in arithmetic to complex calculus problems

Mathematics for the Physical Sciences

Author: Herbert S Wilf

Publisher: Courier Corporation

ISBN: 0486153347

Category: Mathematics

Page: 304

View: 5040

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Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

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This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Algebraic Geometry

Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 0486154726

Category: Mathematics

Page: 256

View: 6407

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An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Algebras of Holomorphic Functions and Control Theory

Author: Amol Sasane

Publisher: Courier Corporation

ISBN: 0486153312

Category: Mathematics

Page: 160

View: 8255

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Accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the stabilization of a linear control system. Concise, self-contained treatment avoids advanced mathematics. 2009 edition.

Conformal Mapping

Author: Zeev Nehari

Publisher: Courier Corporation

ISBN: 0486145034

Category: Mathematics

Page: 396

View: 4845

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DIVTheoretical and practical approach covers functions of a complex variable and conformal mapping. Only prerequisite is advanced calculus. /div

Introduction to Vector and Tensor Analysis

Author: Robert C. Wrede

Publisher: Courier Corporation

ISBN: 0486137112

Category: Mathematics

Page: 418

View: 4717

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Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.