I began typing up my notes in LaTeX during the last couple of semesters in my undergrad at SFSU. Thus, I have maintained a collection of condensed notes from those times.
These notes are specifically the theorems, remarks and corollaries used in proofs within the homework, and are written without justification.
I’ve organized my notes from these classes into four major topics:
Then you’ll see links to my Masters Thesis.
Please contact me if you find any mistakes in the notes!
|Number Theory||Dr. Matthias Beck||Divisibility|
|Modern Algebra I||Dr. Matthias Beck||Integers & the Euclidean algorithm|
Complex numbers, roots of unity & Cardano’s formula
Modular arithmetic & commutative rings
Polynomials, power series & integral domains
Permutations & groups
|Modern Algebra II||Dr. Matthias Beck||Review of basic properties of groups and rings and their quotient structures and homomorphisms, group actions, Sylow’s theorems, principal ideal domains, unique factorization, Euclidean domains, polynomial rings, modules, tensor products, field extensions, primitive roots, finite fields.|
|Graduate Algebra||Dr. Matthias Beck||Rings and modules; further material is selected from such topics as Wedderburn theory, Noetherian ring theory, field theory, and general algebraic systems.|
|Real Analysis I||Dr. Alex Schuster||In this course we will prove many of the results from|
Calculus. We will examine in detail the concepts of limits, continuity, differentiation and
|Real Analysis II||Dr. Alex Schuster||Sequences and series of functions, uniform convergence, real-analytic functions, metric spaces, open and closed sets, compact and connected sets, and continuous functions.|
|Graduate Analysis||Dr. Sheldon Axler|
|Geometry||Dr. Joseph Gubeladze||
|Mathematics of Optimization||Dr, Serkan Hosten||
|Probability and Statistics with Computing||Dr. Mohammad Kafai||
My Master’s Thesis, “Computerational Verification of the Cone Conjecture” is hosted in a few ways: