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II. The Human Significance of Mathematics
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Cassius J. Keyser
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Chapters in this book
- Frontmatter I
- Preface V
- Preface to the Second Edition VII
- Contents IX
- I. The Human Worth of Rigorous Thinking 1
- II. The Human Significance of Mathematics 25
- III. The Humanization of the Teaching of Mathematics 60
- IV. The Walls of the World; or Concerning the Figure and the Dimensions of the Universe of Space 80
- V. Mathematical Emancipations: Dimensionality and Hyperspace 100
- VI. The Universe and Beyond: The Existence of the Hypercosmic 120
- VII. The Axiom of Infinity: A New Presupposition of Thought 137
- VIII. The Permanent Basis of a Liberal Education 161
- IX. Graduate Mathematical Instruction for Graduate Students Not Intending to Become Mathematicians 173
- X. The Source and Functions of a University 197
- XI. Research in American Universities 204
- XII. Principia Mathematica 215
- XIII. Concerning Multiple Interpretations of Postulate Systems and the " Existence" of Hyperspace 228
- XIV. Mathematical Productivity in the United States 251
- XV. Mathematics 265
- XVI. Man and Men 308
- XVII. Educational Ideals That Are Most Worthy of Loyalty 315
- Index of Authors 321
Chapters in this book
- Frontmatter I
- Preface V
- Preface to the Second Edition VII
- Contents IX
- I. The Human Worth of Rigorous Thinking 1
- II. The Human Significance of Mathematics 25
- III. The Humanization of the Teaching of Mathematics 60
- IV. The Walls of the World; or Concerning the Figure and the Dimensions of the Universe of Space 80
- V. Mathematical Emancipations: Dimensionality and Hyperspace 100
- VI. The Universe and Beyond: The Existence of the Hypercosmic 120
- VII. The Axiom of Infinity: A New Presupposition of Thought 137
- VIII. The Permanent Basis of a Liberal Education 161
- IX. Graduate Mathematical Instruction for Graduate Students Not Intending to Become Mathematicians 173
- X. The Source and Functions of a University 197
- XI. Research in American Universities 204
- XII. Principia Mathematica 215
- XIII. Concerning Multiple Interpretations of Postulate Systems and the " Existence" of Hyperspace 228
- XIV. Mathematical Productivity in the United States 251
- XV. Mathematics 265
- XVI. Man and Men 308
- XVII. Educational Ideals That Are Most Worthy of Loyalty 315
- Index of Authors 321