A Bridge to Advanced Mathematics

Author: Dennis Sentilles
Publisher: Courier Corporation
ISBN: 9780486277585
Release Date: 2013-05-20
Genre: Mathematics

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.

Elementary Point Set Topology

Author: Andre L. Yandl
Publisher: Courier Dover Publications
ISBN: 9780486811017
Release Date: 2016-04-10
Genre: Mathematics

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

Linear Algebra and Matrix Theory

Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 9780486623184
Release Date: 2012-10-17
Genre: Mathematics

Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.

A Treatise on Advanced Calculus

Author: Philip Franklin
Publisher: Courier Dover Publications
ISBN: 9780486807072
Release Date: 2016-08-17
Genre: Mathematics

This classic offers a comprehensive logical treatment that concentrates on theory rather than on techniques and applications, providing students with a substantial base for graduate work in physics. 1940 edition.

Introduction to Real Analysis

Author: Michael J. Schramm
Publisher: Courier Corporation
ISBN: 9780486131924
Release Date: 2012-05-11
Genre: Mathematics

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.

Adventures in Mathematical Reasoning

Author: Sherman Stein
Publisher: Courier Dover Publications
ISBN: 9780486814117
Release Date: 2016-07-19
Genre: Mathematics

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.

Introduction to Graph Theory

Author: Richard J. Trudeau
Publisher: Courier Corporation
ISBN: 9780486678702
Release Date: 1993
Genre: Mathematics

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.

Mathematical Brain Benders

Author: Stephen Barr
Publisher: Courier Corporation
ISBN: 9780486242606
Release Date: 1982-05-01
Genre: Games

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.

A Bridge to Higher Mathematics

Author: Valentin Deaconu
Publisher: CRC Press
ISBN: 9781498775267
Release Date: 2016-12-19
Genre: Mathematics

A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

From Geometry to Topology

Author: Graham Flegg
Publisher: Courier Corporation
ISBN: 0486419614
Release Date: 1974
Genre: Mathematics

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.

Conformal Mapping

Author: Zeev Nehari
Publisher: Courier Corporation
ISBN: 9780486145037
Release Date: 2012-05-23
Genre: Mathematics

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

Advanced Calculus

Author: David Vernon Widder
Publisher: Courier Corporation
ISBN: 0486661032
Release Date: 1989
Genre: Mathematics

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.

Mathematics for the Physical Sciences

Author: Herbert S Wilf
Publisher: Courier Corporation
ISBN: 9780486153346
Release Date: 2013-01-18
Genre: Mathematics

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.