## teaching

**teaching-related preprints**

**some things you’ll notice in my classes**

##### critical and creative thinking

##### writing and speaking

##### specifications grading

##### technology

**courses I’ve taught**

I love all of the mathematics I’ve ever learned, but the teaching I’ve done reflects mostly my mathematical interests: geometry, analysis, and topology.

##### at UPenn

**MATH 103: Introduction to Calculus**

A first course in calculus (differentiation and integration), with a focus on interpretation and application of the computations.Techniques of integration and the excellent question:**MATH 104: Calculus part I**

*What if you added like, infinitely numbers, man?*Multivariable calculus. Vectors, vector algebra, and vector functions. Functions of several variables, partial derivatives, gradients, directional derivatives, maxima and mimima. Multiple integration. Line and surface integrals, Green’s Theorem, Divergence Theorems, Stokes’ Theorem.**MATH 114: Calculus part II**

This course shows the first inklings of differential geometry.Solving systems of linear equations and the linear algebra that allows us to do it. In the second half of the course, we switch gears to apply the linear algebra to (linear) systems of ordinary differential equations.*MATH 240: Calculus part III*

Theory and practice of solving partial differential equations, focusing on those motivated by the basic physics of waves and heat.**MATH 241: Calculus part IV**

**MATH 312: Linear Algebra**

A deeper dive into linear algebra than that in MATH 240. This is a course for Engineering students; in addition to the theory, about half the course is devoted to programming computations (via SAGEmath), which can handle them better and quicker than we can and allow us to focus on the applications of linear algebra to all sorts of stuff.**MATH 360: Advanced Calculus**

Proving all of the familiar theorems of single-variable calculus.The smooth manifold is the basic object of differential geometry. This course develops smooth manifolds, vector bundles, tensors, and exterior calculus. We get a few glimpses of the differential-geometric ways to measure topological quantities: Stokes’ and de Rham’s Theorems.**MATH 600: Geometric Analysis and Topology I**

** **at NCSU

*MA 132: Computational Mathematics for Life and Management Sciences*

This is a one-hour course in using Excel and Maple to do the “grunt work”, so we can focus on applying calculus to real-world phenomena that range from a market becoming saturated to bacterial growth.

Starting Fall 2018, this course is offered online.**MA 141: Calculus for Scientists and Engineers, I**

Functions, graphs, limits, derivatives, rules of differentiation, definite integrals, fundamental theorem of calculus, applications of derivatives and integrals.**MA 225: Foundations of Advanced Mathematics**

An introduction to proofs for mathematics majors (and anyone else who wants to be introduced to proofs). This course is so much fun to teach!

A set of notes (the core of which was produced with the assistance of the NCSU Libraries’ Alt-Textbook Project) is here. (As of Fall 2018, the WordPressification of these notes is ongoing.)**MA 242: Calculus for Scientists and Engineers, III**

Same syllabus as MATH 114**MA 408: Foundations of Euclidean Geometry**

An axiomatic approach to geometry. We explore the geometry of the plane (“Euclidean geometry”) as well as the hyperbolic and spherical geometries which arise by tweaking what one means by “parallel”.**MA 425: Mathematical Analysis I**

MA 141, but we prove everything!**MA 508: Geometry for Secondary Teachers**

Originally developed for the*MAP:TICCS*grant from US Department of Education, this course explores the connections between school algebra and school geometry, picking up a lot of interesting things along the way. The glue that binds it all together is the notion of*symmetry*.

Starting Fall 2017, this course is offered online.**MA 510: Topics for Secondary Teachers**

A*MAP:TICCS*course on mathematical modeling.**MA 518: Geometry of Curves and Surfaces**

The classical geometry of Gauss: curves and surfaces in \(\mathbb{R}^3\). The major theme is*curvature*. We spend a decent amount of time on minimal and constant-mean-curvature surfaces, as well as the famous Gauss-Bonnet Theorem.**MA 555: Introduction to Manifold Theory**

Same syllabus as MATH 600

**at Michigan State**

- MTH 103: College Algebra
- MTH 110: College Algebra and Finite Mathematics
- MTH 124-126: Applied Calculus (two-course sequence covering applications of single- and multivariable calculus to business and biology)
- MTH 132: Calculus I
- MTH 234: Calculus III (multivariable calculus)