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Introductions and Test Posts

Analysis

• Banach Spaces: Part I
• Hilbert Spaces: Part I, Part II, PartIII, PartIV
• Introduction to Measure Theory
• Differentiation of Measures: The Radon–Nikodym theorem, Part I
• Differentiation of Measures: The Radon–Nikodym theorem, Part II
• Invariant Subspace Problem and Lomonosov’s Theorem: Part I, Part II, Part III

Combinatorics

• Algorithms
  • Intro to Randomized Algorithms:  Part I, Part I.V; Probability Paradox
• Ramsey Theory
  • Part 1: Intro to Ramsey Theory
  • Part 2: RT on Infinite, Colorful Graphs
  • Part 3: Hypergraphs and other generalizations
  • Part 4: The Happy Ending Theorem
  • Part 5: Intro to RT on the Naturals
  • Part 6: The Technique of Focusing
  • Part 7: Van Der Waerden’s Theorem
  • Part 8; Hales-Jewett and Tic-Tac-Toe
  • Part 9; Sparse Ramsey Theory

Linear Algebra

• Determinants: Part I, Part II, Part III, Part IV
• The Riesz Representation Theorem: Part I, Part II

Logic (and set theory)

• Axiom of Choice: Part I, Part II, Part III
• Miscellaneous: Well-ordering the reals

Math in the “Real World”

• Grad School Survival Tip #1 – Exam Sorting
• “Math” in advertising – Getting Attention with Trivial Statements
• Math in Elections
  • Part 1: Every Voting System is Flawed.
  • Part 2: A Primary Example.
  • Part 3: Delegates, Conventions and Kings.
  • Part 4: Democracy and The Electoral College?
  • Part 5: There are Alternatives!
  • Part 6: Does Your Vote Matter?
  • Part 7: The Complexity of Declaring a Victor.

Physics

• Some Physics, Part I

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Asides/Uncategorized:

• p-adic integers (2012/11/12)
• Analysis exercise (2012/3/3)
• Difficult undergrad proofs (2011/11/24)
• Rings from Sets (2011/11/18)
• Some excellent texts in analysis (2011/10/31)
• Two neat things (2011/10/26)
• ZN’s website (2011/10/19)
• HMS Badger (2011/10/12)