Courses Taught:

Michigan State University:

[Students, see D2L or Math Department Class Pages for course webpages]

MTH 103 -- College Algebra -- Sample syllabus.

This algebra course covers functions, graphing, and modeling, with a focus on linear, exponential, logarithmic, polynomial, and rational functions. I have led a team redesigning the course and taught large (220 person) lectures.

MTH 124 -- Survey of Calculus I -- Sample syllabus.

This first semester applied calculus course covers the basics of differentiation and integration as well as applications to the life sciences or economics (depending on the section). I have redesigned the structure and curriculum of the course and taught several 300-person lectures.

LB 118 -- Calculus I-- Sample syllabus.

This course is the first in the Lyman Briggs calculus series, covering limits, differentiation, integration, and applications.

LB 220 -- Calculus III-- Sample syllabus.

This course is the third in the Lyman Briggs calculus series, covering multivariable calculus.

MTH 301 -- Foundations of Higher Math-- Sample syllabus.

This transition to proofs course covers material in logic, set theory, and functions, in addition to proof techniques.

MTH 310 -- Abstract Algebra I and Number Theory-- Sample syllabus.

This is a first course in abstract algebra. Students learn about the structure of the integers, congruences, rings, ring homomorphisms, polynomial rings, ideals, and quotient rings. Students learn to write clear, concise, and rigorous proofs of mathematical statements.

MTH 317H -- Honors Linear Algebra-- Sample syllabus.

This advanced track course teaches proof-writing skills along with linear algebra content including vector spaces, linear transformations, determinants, spectral theory, inner product spaces..

MTH 327H -- Introduction to Advanced Anaylsis-- Sample syllabus.

This advanced track real analysis course covers topics including real and complex numbers, topology, sequences and series, continuity, differentiation, and integration.

MTH 490 -- Directed Studies - Algebraic Topology

This directed studies course covers an introduction to algebraic topology at a level appropriate for an undergraduate student.

                     

MTH 490 -- Directed Studies - Differential Topology

This directed studies course covers an introduction to differential topology at a level appropriate for an undergraduate student.

                     

MTH 869 -- Graduate Geometry and Topology II-- Sample syllabus.

This one semester qualifying exam course gives an introduction to algebraic topology. Topics covered include covering spaces, fundamental group, homology, and cohomology.

                     

MTH 960 -- Algebraic Topology I-- Sample syllabus.

This is a second course in Algebraic Topology. The course starts with a study of cohomology, covering topics including universal coefficients, the cup product, the Kunneth Theorem, and Poincaré Duality. The second unit of the course is on homotopy theory, covering Whitehead’s Theorem, the Hurewicz Theorem, Eilenberg-MacLane spaces, stable homotopy groups, spectra, and representability.

                     

MTH 961 -- Algebraic Topology II-- Sample syllabus.

This is a third course in Algebraic Topology. The course covers topics including stable homotopy groups, spectra, representability, spectral sequences, and cohomology operations.

                     

Indiana University:

[Students, see Oncourse for course webpages]

M 119 -- Brief Survey of Calculus I

This application focused introduction to calculus course is aimed at students in business and social sciences. I have taught sections of this course with up to 250 students.

M522 -- Topology II

This is a graduate level course on algebraic topology, covering homology and cohomology.

M 211 -- Calculus I

This first semester calculus course covers limits, differentiation, integration, and applications

M 212 -- Calculus II

This second semester calculus course covers integration techniques, applications of integration, and infinite series.

MIT:

18.03 -- Differential Equations

Recitation Leader

This course covers ordinary differential equations, including modeling physical systems.

18.06 -- Linear Algebra

Recitation Leader

This is a first course in matrix theory and linear algebra.

Stanford University:

CS106A -- Programming Methodology

Recitation Leader

This is an introduction to programming course emphasizing modern software engineering principles: object-oriented design, decomposition, encapsulation, abstraction, and testing.