Introduction to Mathematical Thinking

The Formation of Concepts in Modern Mathematics

Nonfiction, Science & Nature, Mathematics, Logic
Cover of the book Introduction to Mathematical Thinking by Friedrich Waismann, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Friedrich Waismann ISBN: 9780486167428
Publisher: Dover Publications Publication: August 7, 2012
Imprint: Dover Publications Language: English
Author: Friedrich Waismann
ISBN: 9780486167428
Publisher: Dover Publications
Publication: August 7, 2012
Imprint: Dover Publications
Language: English

This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.
Contents include examinations of the various types of numbers and a criticism of the extension of numbers; arithmetic, geometry, and the rigorous construction of the theory of integers; the rational numbers, the foundation of the arithmetic of natural numbers, and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.
In issues of mathematical philosophy, the author explores basic theoretical differences that have been a source of debate among the most prominent scholars and on which contemporary mathematicians remain divided. "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics." — Carl B. Boyer, Brooklyn College. 27 figures. Index.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.
Contents include examinations of the various types of numbers and a criticism of the extension of numbers; arithmetic, geometry, and the rigorous construction of the theory of integers; the rational numbers, the foundation of the arithmetic of natural numbers, and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.
In issues of mathematical philosophy, the author explores basic theoretical differences that have been a source of debate among the most prominent scholars and on which contemporary mathematicians remain divided. "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics." — Carl B. Boyer, Brooklyn College. 27 figures. Index.

More books from Dover Publications

Cover of the book Wit and Wisdom from Poor Richard's Almanack by Friedrich Waismann
Cover of the book Easy Italian Phrase Book by Friedrich Waismann
Cover of the book An Introduction to Finite Projective Planes by Friedrich Waismann
Cover of the book Big Book of Indian Beadwork Designs by Friedrich Waismann
Cover of the book Some Thoughts Concerning Education by Friedrich Waismann
Cover of the book Patents and How to Get One by Friedrich Waismann
Cover of the book Othello by Friedrich Waismann
Cover of the book The Importance of Being Earnest by Friedrich Waismann
Cover of the book Early Domestic Architecture of Connecticut by Friedrich Waismann
Cover of the book The Brothers Karamazov by Friedrich Waismann
Cover of the book The Tatter's Treasure Chest by Friedrich Waismann
Cover of the book Short-Cut Math by Friedrich Waismann
Cover of the book Selected Poems by Friedrich Waismann
Cover of the book Practical and Ornamental Knots by Friedrich Waismann
Cover of the book Egg Decoration by Friedrich Waismann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy