**UNDERGRADUATE COURSES
**

I have taught **undergraduate courses** regularly since 2001. I started as a Teaching Assistant at the University of Warwick (England), and then went on to teach as a Graduate Student Instructor at the University of Michigan, till 2007.

I have taught 18 different undergraduate courses, a total of 40 times, mainly in the areas of abstract algebra, topology, calculus and computational geometry. The following is a complete list of these courses, arranged according to the institution where they were taught, the academic year and the corresponding semester or quarter.

**Universidad Complutense de Madrid**

**Academic year 2023-24
**Basic Mathematics/Matemáticas Básicas (Year 1º. Semester 1)

Algebraic Structures/Estructuras Algebraicas (Year 2º. Semester 1)

**Academic year 2022-23
**Basic Mathematics/Matemáticas Básicas (Year 1º. Semester 1)

Algebraic Structures/Estructuras Algebraicas (Year 2º. Semester 1)

**Academic year 2021-22
**Basic Mathematics/Matemáticas Básicas (Year 1º. Semester 1)

Algebraic Structures/Estructuras Algebraicas (Year 2º. Semester 1)

**Academic year 2020-21
**Computational Geometry/Geometría Computacional (Year 4º of the Mathematics Major and Year 5º of the Computer Science – Mathematics Double Major. Semester 2, starting February 15, 2021)

**University of California San Diego**

**Academic year 2019-20**

Modern Algebra I Math 103A (Winter 2020)

Modern Algebra I Math 103A (Fall 2019)

Foundations of Topology I Math 190A (Winter 2019)

**Summer 2019**

Mathematical Reasoning Math 109 (Session 2)

Modern Algebra II Math 103B (Session 2)

Mathematical Reasoning Math 109 (Session 1)

Modern Algebra I Math 103A (Session 1)

**Academic year 2018-19**

Mathematical Reasoning Math 109 (Winter 2019)

Mathematical Reasoning Math 109 (Fall 2018)

Modern Algebra I Math 103A (Fall 2018)

**Academic year 2017-2018**

Modern Algebra I Math 103A (Winter 2018)

**Academic year 2016-17**

Modern Algebra I Math 103A (Winter 2017)

Introduction to Topology Math 190 (Winter 2017)

Modern Algebra I Math 103A (Fall 2016)

**Academic year 2015-16**

Mathematical Reasoning Math 109 (Spring 2016)

Modern Algebra I Math 103A (Winter 2016)

**Academic year 2014-15**

Mathematical Reasoning Math 109 (Winter 2015)

Mathematical Reasoning Math 109 (Fall 2014)

**Washington University in St Louis**

**Academic year** **2013-14**

Abstract Algebra Math 430 (Spring 2014)

**Academic year** **2012-13**

Calculus of Several Variables Math 318 (Fall 2012)

**Academic year** **2010-11**

Calculus for the Social and Life Sciences Math 128 (Fall 2010)

Calculus of Several Variables Math 318 (Fall 2010)

**University of California Berkeley**

**Academic year** **2009-10**

Introduction to Abstract Algebra Math 113 (Fall 2009, two sections)

**Academic year** **2008-09**

Introduction to Abstract Algebra Math 113 (Fall 2008, two sections)

Morse Theory Math 190 (Fall 2008)

**Academic year** **2005-06**

Calculus of One Variable, Calculus I Math 115 (Fall 2005)

**Academic year** **2004-05**

Multivariable Calculus Lab, Calculus III Math 215 (Fall 2004)

Multivariable Calculus Lab, Calculus III Math 215 (Winter 2004)

**Academic year** **2003-04
**Multivariable Calculus Lab, Calculus III Math 215 (Fall 2003)

**Academic year** **2002-03**

Multivariable Calculus Lab, Calculus III Math 215 (Winter 2003)

Precalculus Math 105 (Fall 2002)

**Academic year 2001-02**

Geometry Laboratory (Fall 2001)

Analysis of several variables Laboratory (Fall 2001)

Geometry of curves and surfaces Laboratory (Fall 2001)

**GRADUATE COURSES**

I have taught 9 different **PhD doctoral level** courses, a total of 13 times, mainly in the areas of symplectic geometry and topology and occasionally on mathematical analysis, particularly spectral theory and applications of PDE to geometry.

Most of these courses are second year graduate courses, meaning they are more specialized and require first year graduate courses (for example, a course on symplectic geometry requires a good knowledge of smooth manifolds, which is often taught as a first year graduate course). The following is a complete list of these courses, arranged according to the institution where they were taught, the academic year and the corresponding semester or quarter.

**University of California San Diego**

**Academic year 2019-20**

Topics in Differential Geometry Math 257A – Symplectic Geometry (Winter 2020)

**Academic year 2018-19**

Topics in Differential Geometry Math 257A – Symplectic Geometry (Winter 2019)

**Academic year 2017-18**

Topics in Topology Math 291A – Symplectic Geometry and Topology (Winter 2018)

Symplectic Geometry Math 258 (Winter 2018)

**Academic year 2016-17**

Symplectic Geometry Math 258 (Winter 2017)

Topics in Topology Math 291A – Symplectic Geometry and Topology (Fall 2016)

**Academic year 2015-16**

Topics in Differential Geometry Math 257A – Symmetries and Invariants (Spring 2016)

**Academic year 2014-15**

Topics in Differential Geometry Math 257A – Symplectic and Spectral Geometry (Fall 2014)

**Washington University in St Louis**

**Academic year 2012-13
**Topics in Analysis Math 523 – Microlocal Analysis and Spectral Theory (Fall 2012)

**University of California Berkeley**

**Academic year 2009-10**

Symplectic and Spectral Geometry Math 299 (Winter 2010)

Differential Topology Math 290 (Fall 2009)

Differentiable Manifolds Math 214 (Fall 2009)

**Academic year 2008-09**

Geometry of Singular Spaces Math 299 (Fall 2008)

A professor is one who can speak on any subject – for precisely ﬁfty minutes.

N. Wiener