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Teaching
I have been awarded a 2013-2014 Certificate of Recognition for
Contribution to Students by the UNL Teaching Council and
UNL Parents Association.
Lecture notes from recent graduate courses:
·
Math
817-818 lecture notes
·
Math
901 lecture notes
·
Math
902 lecture notes
·
Math
918 Lefschetz Properties lecture notes
·
Math
981 Computational Algebra lecture notes
Courses taught at UNL:
·
Math 189H - The Joy of Numbers (freshman honors seminar) A guided exploration into number theory from Euclid’s proof of the
infinitude of primes to applications in public key cryptography. ·
Math 208 – Calculus III Calculus of several variables including vectors and surfaces, parametric
equations and motion, functions of several variables, partial
differentiation, maximum-minimum, Lagrange multipliers, multiple integration,
vector fields, path integrals, Green's Theorem, and applications. ·
Math 310
- Introduction to Modern Algebra An introduction to proofs course designed for mathematics majors and
pre-service secondary education majors, covering mathematical induction,
elementary number theory, the Fundamental Theorem of Arithmetic, modular
arithmetic and elementary notions in abstract ring theory. ·
Math 314 - Applied Linear Algebra (Matrix Theory) Fundamental concepts of linear algebra from the point of view of matrix
manipulation, with emphasis on concepts that are most important in
applications. Includes solving systems of linear equations, vector spaces,
determinants, eigenvalues, orthogonality. ·
Math 325 – Elementary Analysis An introduction to mathematical reasoning, construction of proofs, and
careful mathematical writing in the context of continuous mathematics and
calculus. · Math 407 – Math for High School Teaching I An abstract reasoning course, highlighting the connections between
college mathematics and high school algebra and precalculus. ·
Math 417 - Introduction to Modern Algebra I An introduction to abstract group theory and some of its applications. · Math 435 – Math in the City. See also previous topics (2006-2012) of
this class. A capstone course in mathematical modeling for issues of current
interest. Run in collaboration with the Nebraska Natural Resources
Districts. Below are the slides from two presentation I gave
regarding my experience with the course:
·
Math 817 – Introduction to Modern Algebra I Topics from elementary group theory and ring theory, including
fundamental isomorphism theorems, ideals, quotient rings, domains. Euclidean
or principal ideal rings, unique factorization. ·
Math 818 - Introduction to Modern Algebra II Modules, vector space, and topics from field theory including Galois
theory and finite fields and from linear transformations including
characteristic roots, matrices, canonical forms. · Math 901 – Algebra I An introduction to category theory, representation theory of groups, and
homological algebra. · Math 902 – Algebra II An introduction to commutative ring theory and basic notions of algebraic
geometry. · Math 905 – Commutative Algebra Fundamental concepts of commutative ring theory: primary decomposition,
filtrations and completions, dimension theory, integral extensions,
homological methods, regular rings. · Math 918 - Topics in Algebra: The Lefschetz properties An introduction to the algebraic Lefschetz
properties, following the book by the same title by Harima, Maeno, Morita, Numata, Wachi, and Watanabe. ·
Math 918 - Topics in Algebra: The Geometry of Syzygies An introduction to graded free resolutions viewed from a geometric
perspective, following the book by the same title by David Eisenbud. ·
Math 918 - Topics in Algebra: Computational Algebra An introduction to Gröbner bases and their many
applications in algebra and geometry, with several homological and
combinatorial detours.
·
Putnam
Training Seminar
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