Journey into Mathematics

An Introduction to Proofs

Author: Joseph J. Rotman

Publisher: Courier Corporation

ISBN: 0486151689

Category: Mathematics

Page: 256

View: 431

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.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 1839

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 Projective Geometry

Author: C. R. Wylie

Publisher: Courier Corporation

ISBN: 0486141705

Category: Mathematics

Page: 576

View: 1501

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.

Fundamentals of Mathematics

An Introduction to Proofs, Logic, Sets, and Numbers

Author: Bernd S. W. Schröder

Publisher: Wiley

ISBN: 9780470551387

Category: Mathematics

Page: 338

View: 2745

An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built.

Discourses on Algebra

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 3642563252

Category: Mathematics

Page: 279

View: 3456

Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.

Roads to Infinity

The Mathematics of Truth and Proof

Author: John C. Stillwell

Publisher: CRC Press

ISBN: 1439865507

Category: Mathematics

Page: 250

View: 6325

Winner of a CHOICE Outstanding Academic Title Award for 2011! This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel.

Excursions in Number Theory

Author: Charles Stanley Ogilvy,John Timothy Anderson

Publisher: Courier Corporation

ISBN: 9780486257785

Category: Mathematics

Page: 168

View: 9121

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

An Introduction to the Mathematical Theory of Waves

Author: Roger Knobel

Publisher: American Mathematical Soc.

ISBN: 0821820397

Category: Mathematics

Page: 196

View: 1971

Linear and nonlinear waves are a central part of the theory of PDEs. This book begins with a description of one-dimensional waves and their visualization through computer-aided techniques. Next, traveling waves are covered, such as solitary waves for the Klein-Gordon and KdV equations. Finally, the author gives a lucid discussion of waves arising from conservation laws, including shock and rarefaction waves. As an application, interesting models of traffic flow are used to illustrate conservation laws and wave phenomena. This book is based on a course given by the author at the IAS/Park City Mathematics Institute. It is suitable for independent study by undergraduate students in mathematics, engineering, and science programs.

Number Theory

Author: George E. Andrews

Publisher: Courier Corporation

ISBN: 0486135101

Category: Mathematics

Page: 288

View: 1513

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

Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 9430

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Journey through genius

the great theorems of mathematics

Author: William Dunham



Category: Mathematics

Page: 300

View: 5398

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.

Introduction to Artificial Intelligence

Second, Enlarged Edition

Author: Philip C. Jackson

Publisher: Courier Corporation

ISBN: 0486152723

Category: Science

Page: 512

View: 2668

Comprehensive survey of artificial intelligence — the study of how computers can be made to act intelligently. Includes introductory and advanced material. Extensive notes updating the main text. 132 illustrations.

Introduction to Mathematical Proofs, Second Edition

A Transition to Advanced Mathematics, Second Edition

Author: Charles Roberts

Publisher: CRC Press

ISBN: 1482246880

Category: Mathematics

Page: 414

View: 8475

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs. This new edition includes more than 125 new exercises in sections titled More Challenging Exercises. Also, numerous examples illustrate in detail how to write proofs and show how to solve problems. These examples can serve as models for students to emulate when solving exercises. Several biographical sketches and historical comments have been included to enrich and enliven the text. Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It prepares them to succeed in more advanced mathematics courses, such as abstract algebra and analysis.

Introduction to Analysis

Author: Maxwell Rosenlicht

Publisher: Courier Corporation

ISBN: 0486134687

Category: Mathematics

Page: 272

View: 3040

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.

A History of Mathematics

Author: Carl B. Boyer,Uta C. Merzbach

Publisher: John Wiley & Sons

ISBN: 0470630566

Category: Mathematics

Page: 688

View: 5678

The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Charming Proofs

A Journey Into Elegant Mathematics

Author: Claudi Alsina,Roger B. Nelsen

Publisher: MAA

ISBN: 0883853485

Category: Mathematics

Page: 295

View: 2490

A collection of remarkable proofs that are exceptionally elegant, and thus invite the reader to enjoy the beauty of mathematics.

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

View: 8640

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Foundations and Fundamental Concepts of Mathematics

Author: Howard Eves

Publisher: Courier Corporation

ISBN: 048613220X

Category: Mathematics

Page: 368

View: 8917

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

The Magic of Numbers

Author: Eric Temple Bell

Publisher: Courier Corporation

ISBN: 0486167402

Category: Mathematics

Page: 432

View: 8880

Superb, stimulating account of origins of mathematical thought and development of numerical theory. Probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring influence of "number magic" on religion, philosophy, science, mathematics.