Duarte's Web Page

Some things I wrote

Warning: Some of these have barely been reviewed. In decreasing order of refinement:

• Harmonic Analysis Project: The Uncertainty Principle on Rn and The Torus (A Review)
• Calculus of Variations Project: Holonomic and Non-Holonomic constraints, with Lagrange Multipliers
• Research Project with Jorge Silva (under review): On Optimal Bounds for Comparing Dyadic (and B-ary) Net Measures with the Hausdorff Measure on R
• On Nice Enough ODEs and Dependency on Initial Conditions (Alternate Title: In which I prove that solutions to ODEs are smooth)
• Research Project with João Rasga: SAT, Multigraphs, and CNF
• A Small Study on Lim Sup and Lim Inf
• An Alternate Definition of Conditional Probability

Here are some notes I wrote for some of my classes. They are in portuguese.

• Introduction to Optimization (The Simplex Algorithm)
• First Order Logic (Gödel's Completeness Theorem)

See also a math blog I've been working on. Its articles are mostly unfinished as yet, but they represent some of the things I've been thinking about. My Blog