Introduction to Mathematical Thinking - The Formation of Concepts in Modern Mathematics (Paperback, Dover ed)

"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College.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. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; 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. 1959 ed. 27 Figures. Index.