Author Archive
Math 311 Introduction to Algebra
by pinarongan on Feb.28, 2011, under Assistantship
Comments Off on Math 311 Introduction to Algebra more...Math 636 Algebraic Function Fields
by pinarongan on Oct.17, 2010, under Taken Course History
Places,valuation rings and discrete valuations of a function field; the rational function field; divisors, Weil different adeles, genus; Riemann-Roch Theorem and its consequences; extensions of function fields, ramification, Hurwitz genus formula; constant field extensions, Galois extensions, Kummer and Artin-Schreier extensions.
Math 514 Finite Fields and Its Applications I
by pinarongan on Oct.17, 2010, under Taken Course History
Characterization of finite fields, roots of irreducible polynomials, traces, norms, and bases, representation of elements of finite fields. Order of polynomials, irreducible polynomials and their construction. Factorization of polynomials. Linear recurring sequences. Introduction to applications of finite fields; algebraic coding theory and cryptology.
Math 201 Linear Algebra
by pinarongan on Oct.17, 2010, under Assistantship
some warnings after quiz 1 (to see the questions and solutions of quiz 1: )
MATH 203 Introduction to Probability
by pinarongan on Jul.16, 2010, under Assistantship
Comments Off on MATH 203 Introduction to Probability more...MATH 581 Special Topics in Advanced Linear Algebra
by pinarongan on Jun.15, 2010, under Taken Course History
Euclidean and unitary vector spaces, normal forms for endomorphisms of Euclidean and unitary spaces (e.g., orthogonal, self-adjoint, normal endomorphisms), linear optimization, simplex algorithm, introduction to coding theory.
MATH 512 Algebra II
by pinarongan on Jun.15, 2010, under Taken Course History
Modules. Fields, extension fields, Galois theory. Categories and functors.
MATH 511 Algebra I
by pinarongan on Jun.15, 2010, under Taken Course History
Introduction to group theory. Isomorphism theorems. Permutation groups and Cayley’s theorem. Conjugacy classes. Lagrange’s theorem and the Sylow theorems. principle ideal domains. Polynomial ring.
MATH 520 Calculus on Manifolds
by pinarongan on Jun.14, 2010, under Taken Course History
Differentiable manifolds. Smooth mappings; differential of a map. Implicit and inverse function theorems. Submanifolds. Vector fields. Differential forms. Orientation on manifolds. Integration on manifolds. Stokes’ theorem.
MATH 204 Discrete Mathmematics
by pinarongan on Jun.14, 2010, under Assistantship
some warnings after quiz 1 (For questions see the followings: 1st quiz A & 1st quiz B)
some warnings after quiz 2 (For questions see the followings: 2nd quiz A & 2nd quiz B)
some warnings after quiz 4 (For questions see the followings: 4th quiz A & 4th quiz B)
some warnings after quiz 5 (For questions see the followings: 5th quiz A & 5th quiz B)
some warnings after quiz 6 (For questions see the followings: 6th quiz A & 6th quiz B)