Mathematics and plausible reasoning

Cover
Title Page
Preface
Hints to the Reader
Table of Contents
Chapter I Induction
	1. Experience and Belief
	2. Suggestive Contacs
	3. Supporting Contacts
	4. The Inductive Attitude
Chapter II Generalization Specialization, Analogy
	1. Generalization, Specialization, Analogy, and Induction
	2. Generalization
	3. Specialization
	4. Analogy
	5. Generalizations, Specializations, and Analogy
	6. Discovery by Analogy
	7. Analogy and Induction
	Examples and Comments on Chapter II
		First Part
		Second Part
Chapter III Induction in Solid Geometry
	1. Polyhedra
	2. First Supporting Contacts
	3. More Supporting Contacts
	4. A Severe Test
	5. Verifications and Verifications
	6. A Very different case
	7. Analogy
	8. The Partition of Space
	9. Modifying the Problem
	10. Generalization, Specialization and Analogy
	11. An Analogous Problem
	12. An Array of Analogous Problems
	13. Many Problems may be easier than just one
	14. A Conjecture
	15. Prediction and Verification
	16. Again and Better
	17. Induction Suggests deduction; the particular case suggestions the general proof
	18. More Conjectures
	Examples and Comments on Chapter III
Chapter IV Induction in the Theory of Numbers
	1. Right triangles in integers
	2. Sum of Squares
	3. On the Sum of four odd squares
	4. Examining the Example
	5. Tabulating the Observations
	6. What is the rule
	7. On the nature of inductive discovery
	8. On the nature of inductive evidence
	Examples and Comments on Chapter IV
Chapter V Miscellneous Examples of Induction
	1. Expansions
	2. Approximations
	3. Limits
	4. Trying to Disprove it
	5. Trying to Prove it
	6. The role of inductive phase
	Examples and Comments on Chapter V
Chapter VI A More General Statement
	1. Euler
	2. Eulers memoir
	3. Transition to a more general viewpoint
	4. Schematic outline of Eulers Memoir
	Examples and Comments on Chapter VI
Chapter VII Mathematical Induction
	1. The Inductive Phase
	2. The Demonstrative Phase
	3. Examining Transitions
	4. The Technique of Mathematical Induction
	Examples and Comments on Chapter VII
Chapter VIII Maxima and Minima
	1. Patterns
	2. Example
	3. The Pattern of the tangent level line
	4. Examples
	5. The Pattern of Partial Variation
	6. The Theorem of the Arithmetic and Geometric Means and its first Consequences
	Examples and Comments on Chapter VIII
		First Part
		Second Part
Chapter IX Physical Mathematics
	1. Optical Interpretation
	2. Mechanicl Interpretation
	3. Reinterpretation
	4. Jean Bernoullis discovery of the Brachistochrone
	5. Archimedes Discovery of Integral Calculus
	Examples and Comments on Chapter IX
Chapter X The Isoperimetric Problem
	1. Descartes inductive reasons
	2. Latent Reasons
	3. Physical Reasons
	4. Lord Rayleighs Inductive reasons
	5. Deriving Consequences
	6. Verifying Consequences
	7. Very Close
	8. Three forms of the Isoperimetric Theorem
	9. Applications and Questions
	Examples and Comments on Chapter X
		First Part
		Second Part
Chapter XI Further Kinds of Plausible Reasons
	1. Conjecture and Conjectures
	2. Judging by a Related Case
	3. Judging by the General Case
	4. Prefering the Simpler Case
	5. Background
	6. Inexhaustible
	7. Usual Heuristic Assumptions
	Examples and Comments on Chapter XI
Final Remark
Solutions
	Chapter I
	Chapter II
	Chapter III
	Chapter IV
	Chapter V
	Chapter VI
	Chapter VII
	Chapter VIII
	Chapter IX
	Chapter X
	Chapter XI
Bibliography