Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics) free ebook download.

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Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics) free ebook download

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Mathematics

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Author(s):	Friedrich Waismann

Date:	2012	Format:	epub	Language:	English	ISBN/ASIN:	0486428044
Pages:	272	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	10/24/2024 4:56:30 AM

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0486428044 epub
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.

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Tags: Books Concepts Dover Formation Introduction Mathematical Mathematics Mathematics Modern Thinking

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