Introduction to Mathematical Thinking: The Formation of Concepts in Modern MathematicsThis 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
Authors Preface 1 The Various Types of Numbers 2 Criticism of the Extension of Numbers 3 Arithmetic and Geometry 4 The Rigorous Construction... | |
The Rational Numbers | |
Foundation of the Arithmetic of Natural Numbers | |
Rigorous Construction of Elementary Arithmetic 8 The Principle of Complete Induction | |
Present Status of the Investigation of the Foundations | |
Limit and Point of Accumulation | |
Operating with Sequences Differential Quotient | |
Remarkable Curves | |
The Real Numbers | |
Ultrareal Numbers | |
Complex and Hypercomplex Numbers | |
Inventing or Discovering? | |
Epilogue | |