Josh's Math Stuff

Ph.D. Thesis

Completed and filed May 23rd, 2003. There are several files:

PDF 2-sided,
zipped PS also 2-sided,
zipped LaTeX source and figures, (coming soon)
zipped contouring code, and
zipped natural neighbor interpolation code (coming soon).

Feb 2003 Talks

I gave 3 talks starting Feb 13, 2003 on contouring (my thesis). LaTeX for first set of notes; LaTeX for second set of notes; PDF for second set of notes.

October 2002 Talk

Here are my notes on the talk I gave on October 2, 2002 entitled "Three methods of computing the distance and closest point functions on grids" in LaTeX format.

Counting Pandiagonal Magic Squares

Here is my undergraduate thesis in Gzipped PostScript format. I researched and wrote this at Reed College during 1993-4.

December 2000 Talk

Here are my notes on the talk I gave on December 5, 2000 entitled "Intersecting subgroups of a free group" in Gzipped PostScript format and Adobe PDF format.

November 1999 Talk

This has some materials related to my talk on November 23, 1999 entitled "Graphs with a common finite cover."

The abstract
My notes (Gzipped Postscript)
Some (Gzipped PostScript) pictures of graphs and the corresponding covers:
- The cover over Lips and Tetra: Lips, Tetra
- The cover over Barbell and Tetra: Barbell, Tetra
- The cover over HexBox and OX: HexBox, OX
C++ source to find a common finite cover (zip) - Currently compiles under recent version of g++ and MSVC++
- Valence 3 graphs: Barbell, Lips, Tetra
- Graphs with 2 valence 2 vertices, and 4 valence 3 vertices: OX, HexBox
C++ source to draw a graph with a cover (zip) - Currently compiles under recent version of g++ and MSVC++
- The cover over Lips and Tetra: Lips, Tetra
- The cover over Barbell and Tetra: Barbell, Tetra
- The cover over HexBox and OX: HexBox, OX
Required include files for the above (zip) - these abstract out the differences between G++ STL and MSVC++ with STLPort
People trying to compile the above in the Berkeley Math department should try logging into yuban and compile with /local/sol/2.6/depot/gcc-2.95.1/bin/g++

Qual Study Materials

Algebraic Topology / Math 215A - A Gzipped Postscript transcription of my notes from Justin Robert's lectures. Includes sections on:
- the fundamental group
- covering spaces
  - free groups
  - CW-complexes
- simplicial/singular/cellular homology
  - exact sequences
  - the Mayer-Vietoris sequence
  - reduced and relative homology
  - homology with coefficients
  - Euler characteristic
- cohomology
  - cup/cap product
  - orientation and Poincare duality for manifolds
  - representations by submanifolds
Algebraic Topology / Math 215B - A Gzipped Postscript study guide on material from Hatcher, and Justin Robert's lectures. Much less complete than the above. Includes sections on:
- higher homotopy groups
  - long exact sequence
  - Whitehead's theorem
  - cellular approximation
  - cellular models
  - Hurewicz theorem
- fibrations
- fiber bundles
- obstruction theory
Differential Topology / Math 214 - A Gzipped Postscript transcription of some of my notes from Andrew Casson's lectures and the material in Differentiable Manifolds by Spivak. Includes sections on:
- manifolds
- differentiable structures
- the tangent bundle
- orientation
- tensors
- vector fields and differential equations
- lie brackets
- distributions and Frobenius theorem
- tranversality
Combinatorics - A Gzipped Postscript transcription of some of my notes from Enumerative Combinatorics I by Richard Stanley. Includes sections on:
- counting
  - sets, multisets
  - permutations
  - the twelvefold way
- inclusion-exclusion
- partially ordered sets
  - lattices
  - distributive lattices
  - incidence algebra
  - Mobius inversion
  - lattice Mobius algebras
  - zeta polynomials
  - rank-selection
  - Eulerian posets
  - binomial posets and generating functions
- Rational Generating Functions
  - Rational Power Series in One Variable
  - Corollary: Polynomials
My syllabus (LaTeX) - NOT a model syllabus, oh well.
Qual questions - those that were actually asked. These should have been incorporated into the MGSA's archives

T-Shirt Images

The last T-Shirt image - Reeb foliation
The current project - Mobius+Mobius=Klein

Back to Josh's home page, Technomagi.com