Introduction to Mathematical Thinking

The Formation of Concepts in Modern Mathematics

Author: Friedrich Waismann

Publisher: Courier Corporation

ISBN: 0486167429

Category: Mathematics

Page: 272

View: 1301

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Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.
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A First Course in Topology

An Introduction to Mathematical Thinking

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486791726

Category: Mathematics

Page: 272

View: 334

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Students must prove all of the theorems in this undergraduate-level text, which focuses on point-set topology and emphasizes continuity. The final chapter explores homotopy and the fundamental group. 1975 edition.
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An Introduction to Mathematical Thinking

Algebra and Number Systems

Author: William J. Gilbert,Scott A. Vanstone

Publisher: Prentice Hall

ISBN: 9780131848689

Category: Mathematics

Page: 300

View: 1864

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Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.
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Distilling Ideas

An Introduction to Mathematical Thinking

Author: Brian P. Katz,Michael Starbird,Michael P. Starbird

Publisher: MAA

ISBN: 1939512034

Category: Mathematics

Page: 171

View: 2097

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Designed for undergraduate students and lecturers, this text guides its users to develop the skills, attitudes, and habits of mind of a mathematician. It presents a carefully designed sequence of exercises and theorems so that its readers will be directed to discover mathematical ideas, strategies of proof, and strategies of thinking. Through the exploration of interesting mathematical content including graphs, groups, and calculus, this book helps to foster habits of inquiry. This book can be used by instructors as a text for an inquiry-based introduction to proof course, or as an independent study guide for mathematics students. The three core mathematical topics are presented separately, and each helps students develop theorem-proving skills and strategies of thinking whilst also providing an organised set of challenges that lead students to understand the process of mathematical creativity and development.
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Conjecture & Proof

An Introduction to Mathematical Thinking

Author: Diane Driscoll Schwartz

Publisher: Brooks/Cole Publishing Company

ISBN: 9780030983382

Category: Mathematics

Page: 419

View: 1488

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An Interactive Introduction to Mathematical Analysis Hardback with CD-ROM

Author: Jonathan Lewin

Publisher: Cambridge University Press

ISBN: 9780521815895

Category: Mathematics

Page: 492

View: 2186

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This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school but, for those who are, this book also provides the opportunity to engage in a penetrating study of real analysis.The companion onscreen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The on-screen version also provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.
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A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary,Lars Kristiansen

Publisher: Lulu.com

ISBN: 1942341075

Category: Education

Page: 365

View: 5680

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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Godel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
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Discrete Mathematics: Introduction to Mathematical Reasoning

Author: Susanna S. Epp

Publisher: Cengage Learning

ISBN: 0495826170

Category: Mathematics

Page: 648

View: 4330

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Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING, provides the same clear introduction to discrete mathematics and mathematical reasoning as her highly acclaimed DISCRETE MATHEMATICS WITH APPLICATIONS, but in a compact form that focuses on core topics and omits certain applications usually taught in other courses. The book is appropriate for use in a discrete mathematics course that emphasizes essential topics or in a mathematics major or minor course that serves as a transition to abstract mathematical thinking. The ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. This book offers a synergistic union of the major themes of discrete mathematics together with the reasoning that underlies mathematical thought. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Introduction to Crystallography

Author: Donald E. Sands

Publisher: Courier Corporation

ISBN: 0486136809

Category: Science

Page: 192

View: 6928

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Clear, concise explanation of logical development of basic crystallographic concepts. Topics include crystals and lattices, symmetry, x-ray diffraction, and more. Problems, with answers. 114 illustrations. 1969 edition.
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