Ramble Contents

[stoutfellow]

Since the Ramble has gotten so long, I've decided to put together a table of contents, with links to the individual posts. I'm adding a link to this post to each Ramble post as well, and will update this post as the Ramble extends. Finally, I'm introducing a "ramble" tag, so that anyone interested can pull them out as a whole. The table of contents is under the cut.

0. Prologue
1. The Pythagorean Project: Pythagorean Geometry
2. Eudoxus Explains: The Eudoxian Theory of Proportion
3. What Euclid Did: The Historical Importance of Euclid's Elements
4. What Euclid Didn't Do: Problems with the Elements
5. Exhausting!: Eudoxus and the Method of Exhaustion
6. Give Me a Lever: Archimedes' Method
7. Uncertainties: Problems of Historiography
8. What's Gray and Has Integer Solutions?: Diophantus and Syncopated Algebra
9. A Matter of Magnitude: The Homogeneity Problem
10. A Crash of Symbols: Systems of Numeration
11. Paperwait: The Adoption of Hindu-Arabic Numerals
12. Italian Interlude: The Cardano-Tartaglia Brouhaha
13. Completing the Cube: The Solution of Cubic Equations
14. Even Stevin: Simon Stevin and the Decimal Point
15. Deep Water: Galileo and the Problem of Infinity
16. "Slowly I Turn": Viète, Algebraic Symbolism, and Recursive Approximation
17. A New Perspective: Girard Desargues and Projective Geometry
18. Polymath: Pascal and Mathematical Induction
19. Going Down...: Fermat's Method of Infinite Descent
20. Powers to the People!: Exponents
21. Autonomy: Descartes and Analytic Geometry
22. One Graph Is Worth...: Fermat and Analytic Geometry
23. Breaking the Bounds: Descartes and the Elaboration of Curves
24. Let's Be Rational: Geometry and Number Theory
25. The Coming of Calculus: Developments Before Newton
26. As Above, So Below: Newtonian Gravitation
27. All Is Flux: Newton and the Calculus
28. Symbols of Change: The Notation of Calculus
29. My Friend Barbara: Ancient and Medieval Syllogistic
30. A Logic of Nouns: Leibniz and the Mathematization of Logic
31. The Need for Narrowing: The Future of the Ramble
32. What Do You Expect?: Mathematical and Moral Expectation
33. Function-al Notation: Euler and the Notion of a Function
34. Dysfunctional Notation: Problems with Functional Notation
35. But Seriesly, Folks...: Infinite Series
36. Closer and Closer: Series and the Limit Concept
37. A Different Distance: p-adic Series
38. The Sum of Things: Other Notions of Summability
39. The Complexity of Numbers: The Complex Plane
40. Meanwhile, Off the Coast...: The Euclid of Algebra
41. Interlude, with Philosophers: Kant and Mathematics
42. Comes the Revolution: Rigorization and Abstraction
43. Non-Euclidean Prehistory: Early Work on the Parallel Postulate
44. A Little Hyperbolic: The Discovery of Non-Euclidean Geometry
45. Making Models: The Problem of Consistency
46. Hydra: The New Geometries and Their Consequences
47. The Fourfold Way: Quaternions
48. Going Modular: Gauss and Modular Arithmetic
49. Fighting for Fermat: The Gaussian Integers
50. Idealism: Lamé, Kummer, and the Concept of an Ideal
51. Up the Ladder: Algebraic Structures
52. Beyond Barbara: Extending Medieval Syllogistic
53. An Algebra of Logic: George Boole and The Laws of Thought
54. "Or...?": Inclusive versus Exclusive "Or"
55. Imply or Implicate?: Linguistics and "Or"
56. If...: Material and Strict Implication
57. Digging Deeper: Pierce and Predicate Logic
58. Predicate Games: The Subtleties of Quantification
59. The Power of Series: From Taylor to Weierstrass
60. Good Vibrations: The Work of Fourier
61. Take It to the Limit: Rigorizing the Limit Concept
62. The Real and the Rational: Cauchy Sequences
63. Incisive Thinking: Dedekind Cuts
64. One, Two, Three,... Infinity, Infinity Plus One...: Cantor and Transfinite Ordinals
65. The Whole and the Part: Cantor Diagonalization
66. No Ceiling: The Infinitude of Infinities
67. Refoundation: Frege and the Beginnings of Logicism
68. Stumble: Russell's Paradox
69. Escape?: Resolutions of Russell's Paradox
70. Function Follows Form: Hilbert and Formalism
71. Where Do We Begin?: Peano's Axioms

Comments

[dan-ad-nauseam.livejournal.com]

Hm. "Ramblin' Math"?

[stoutfellow.livejournal.com]

"Tryin' to prove a lemma and phrase it the best I can..."

[filkferengi]

To the tune of "Ramblin' Rose"?

[stoutfellow.livejournal.com]

I'm assuming he's referring to "Ramblin' Man", by Hank Williams; the Allman Brothers did a cover later. Here (http://www.lyricsfreak.com/a/allman+brothers+band/ramblin+man_20006516.html) are the lyrics.

[filkferengi]

Dude, filk a little; write both. :)

rambling rose

[(Anonymous)]

There is also a rambling rose song also too.

ramblin rose

[(Anonymous)]

by nat king cole.