Journey Into Mathematics

Author: Joseph J. Rotman
Publisher: Courier Corporation
ISBN: 0486151689
Size: 14.56 MB
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This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.

Introduction To Proof In Abstract Mathematics

Author: Andrew Wohlgemuth
Publisher: Courier Corporation
ISBN: 0486141683
Size: 10.26 MB
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This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.

An Accompaniment To Higher Mathematics

Author: George R. Exner
Publisher: Springer Science & Business Media
ISBN: 1461239982
Size: 71.94 MB
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Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.

Journey Through Genius

Author: William Dunham
Publisher: Egully.com
ISBN:
Size: 22.69 MB
Format: PDF, Docs
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A rare combination of the historical, biographical, and mathematicalgenius, this book is a fascinating introduction to a neglected field of human creativity. Dunham places mathematical theorem, along with masterpieces of art, music, and literature and gives them the attention they deserve.

Mathematics And Logic

Author: Mark Kac
Publisher: Courier Corporation
ISBN: 0486670856
Size: 26.57 MB
Format: PDF, Mobi
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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Introduction To Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Size: 10.89 MB
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

An Introduction To The Philosophy Of Mathematics

Author: Mark Colyvan
Publisher: Cambridge University Press
ISBN: 0521826020
Size: 56.57 MB
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This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Zermelo S Axiom Of Choice

Author: G.H. Moore
Publisher: Springer Science & Business Media
ISBN: 1461394783
Size: 19.80 MB
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This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

Introduction To Projective Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486141705
Size: 45.75 MB
Format: PDF
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This introductory volume offers strong reinforcement for its teachings, with detailed examples and numerous theorems, proofs, and exercises, plus complete answers to all odd-numbered end-of-chapter problems. 1970 edition.

Number Theory

Author: George E. Andrews
Publisher: Courier Corporation
ISBN: 0486135101
Size: 59.14 MB
Format: PDF, ePub, Mobi
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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more