# Teaching

My yearly teaching load is 3-2, which means three courses one semester, and then two courses the other semester.

**2019-2020 ** (Sabbatical year)

**Spring 2019**

Math 264: Differential Equations (two sections)

Math 312: Partial Differential Equations

**Fall 2018**

Math 141: Differential Calculus with Economic Modeling (two sections).

Math 323: Geometry.

**Spring 2018**

Math 376: Set Theory

Math 400: Senior Seminar

**Fall 2017**

Math 141: Differential Calculus with Economic Modeling (two sections).

Math 264: Differential Equations.

**Spring 2017**

Math 312: Partial Differential Equations

**Fall 2016**

Math 264: Differential Equations (two sections).

Math 357: Real Analysis II.

**Spring 2016**

Math 264: Differential Equations (two sections).

Math 310: Ordinary Differential Equations.

**Fall 2015**

Math 264: Differential Equations (two sections).

Math 290: Transition to Theoretical Mathematics.

**Spring 2015**

Math 264: Differential Equations (two sections).

Math 312: Partial Differential Equations.

**Fall 2014**

Math 162: Calculus II.

Math 351: Abstract Algebra.

**2013-2014 ** (Sabbatical year)

Even while on sabbatical, I did a non-trivial amount of teaching, most recently in the summer of 2014, where I am delivering an invited five-hour lecture mini-course on the Einstein Constraint Equations at the ESI-EMP-IAMP Summer School on Mathematical Relativity at the Erwin Schrodinger Institute in Vienna, Austria, July 28-August 1, 2014. Here are Beamer slides from the first three lectures. (Last update: July 30) A fourth lecture should be added soon! Here is the problem set I cobbled together, and a bibilography is forthcoming.

In the summer of 2013, I served as the Undergraduate Faculty Program Lecturer at the Summer Program on Geometric Analysis at the IAS/Park City Math Institute , and as co-organizer and lecturer at the Clay-MSRI-INdAM Summer School on Mathematical Relativity in Cortona, Italy.

I also gave an invited mini-course *Scalar Curvature and the Einstein Constraint Equations*, together with Pengzi Miao (University of Miami) at the National Taiwan University in Taipei. Here are some exercises that were handed out there, along with a revised (from the summer schools) version of introductory notes on general relativity, and (coming soon!) a slightly revised version of a published article with Daniel Pollack on the Einstein Constraint Equations (in the near future a revision will be posted as a second version on arXiv).

**Spring 2013**

Math 141: Differential Calculus & Economic Modeling.

Math 290: Transition to Theoretical Mathematics.

**Fall 2012**

Math 264: Differential Equations (two sections).

Math 358: Topology.

**Spring 2012**

Math 162: Calculus II.

Math 264: Differential Equations (two sections).

I was invited to teach a graduate topics course at Lehigh University in the Fall of 2011 on Geometric Analysis and General Relativity. Here is the Course Description:

Math 450: Topics in Geometric Analysis & General Relativity

TR: 10:45-12:00, Fall 2011

Pre-requisite: Riemannian Geometry (Math 424)

**Course Description**: General relativity is a theory of gravity that has fascinated physicists and mathematicians since its formulation by Einstein in 1915. The theory is stated in the language of differential geometry, and the notion of curvature is at the very heart of the theory. Dating from the proof of the Positive Mass Theorem by Schoen and Yau in the late 70’s, the past several decades have seen a tremendous amount of activity in differential geometry and differential equations related to questions about general relativity. Interestingly enough, such geometric results have not only given us information about physics, but have also led to new results in geometry. In this course, we will discuss the foundations of the theory of general relativity and derive the Einstein equation, emphasizing the mathematical structure. We will then introduce the initial-value problem, and study solutions of the constraint equations which govern the geometry of spacelike hypersurfaces in spacetimes satisfying the Einstein equation.

**Fall 2011. **

Math 141: Differential Calculus and Economic Modeling.

Math 386: Advanced Analysis.

I also taught a graduate course at Lehigh University:

Math 450: Geometric Analysis and General Relativity.

**AY 2010-2011.**

*Fall. * Math 264: Differential Equations (two sections). Math 389: Advanced Analysis 2.

* Spring.* Math 162: Calculus 2. Math 312: Partial Differential Equations (two sections). Syllabus (PDF)

**AY 2009-2010.** * *

*Fall.* Math 264: Differential Equations (two sections). Math 343: Advanced Multivariable Calculus.

*Spring* Math 264: Differential Equations. Math 381: Differential Geometry.

**AY 2008-2009.** * *

*Spring* Math 264: Differential Equations (two sections). Math 300: Vector Spaces.

* Fall.* On leave.* *

* *

**AY 2007-2008. **

*Fall*. Math 161: Calculus I (two sections). Math 343: Advanced Multivariable Calculus.

* Spring. * Math 264: Differential Equations. Math 386: Advanced Analysis.

**AY 2006-2007. **

*Fall*. Math 161: Calculus I (two sections). Math 335: Probability. *Spring*. Math 336: Mathematical Statistics.

**AY 2005-2006.**

*Fall.* Math 162: Calculus II (two sections). Math 343: Advanced Multivariable Calculus.

*Spring*. Math 263: Calculus III (two sections). Math 381: Differential Geometry.

**AY 2004-2005.**

*Fall.* Math 162: Calculus II (two sections).

*Spring* Math 162: Calculus II (two sections). Math 312: Partial Differential Equations.