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Choose a Section: Logic, Calculus, H.S. Math, Number Theory,

Logic and Model Theory

  • Topological Transfer Theorems — Topological transfer theorems, Pacific Journal of Mathematics, 61 (1975), No. 2, 427-440. A compact structure is almost a homomorphic image of a dense substructure
  • Bi-Model Complete Theories — Unified proof of Craig interpolation, Robinson consistency, Svenonius’ theorems and characterization of Cantor-Bernstein theories
  • Distributive Normal Form — A strong normal form for Boolean expressions

    • Calculus

  • Complex derivatives made easy — Using the multivariable chain rule, American Mathematical Monthly,92 (1985), No. 2, 144-145.
  • Dn F(x,x,...,x) — Extends D F(x,x,…,x) to higher order derivatives
  • Integration by Guessing — Easy calculation of some complex integrals
  • Integration by Linear Combination — New integration technique
  • Pease's Theorem — Resurecting a useful formula
  • From Discrete to Analytic Inequality — Easy derivation of Classic Analytic Inequalities
  • Fundamental Theorem of calculus — Integrated exposition of all aspects of the theorem
  • Non-Standard Analysis — Write up for students , omitting the Transfer Principle

    • High School Math

  • Math Basics — List basic topics with pithy advice
  • Factoring — Factoring Polynomials
  • Asymptotes — Asymptotes, Absolute value, and solving inequalities. Quick facts
  • The four-fold way — Permutations and Combinations organized
  • The spreadsheet Metaphor for Word problems — Classic word problems

    • Number Theory

  • Irrational Roots of Integers — In depth look at classic proof of irrationality of root 2. Rational root theorem rocks.

    • Combinatorics (Papers not available, yet)

  • Traveling Salesman Problems — Classic Supnick results obtained with added detail. Almost Convex Points
  • Rearrangeability Revisited — Neglected concept applies to most optimization and extremal graph theory problems
  • Traveling Salesman Problems on graphs — Some useful theorems
  • Multi-transversal Existence — Cases with criteria
  • Symmetric Polynomial p-Congruences — Wilson’s theorem and much more using High school algebra. Lagrange's original proof
  • Extensions of Z/p with a new n-th root — One new n-th root produces all n-th roots
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