**My Teaching Philosophy:**

Math is a *skill*, not a *trait*, and like any skill, you can improve with practice. But just like sports, musical instruments, and strategic games, improvement requires pushing yourself beyond your comfort zone. Struggling with a problem simply means there’s a concept that you don’t understand yet, but you will. So the struggle and mistakes that come with learning are normalized in my classes, and even celebrated!

Most of the mistakes I see happen when students attempt to memorize different procedures and formulas, and try to use these procedures in a problem where the procedure doesn’t apply. Rather than focusing on what to memorize, I encourage my students to *engage with their uncertainty*: you won’t know how to solve a problem at first, but if you think about mathematics analytically rather than procedurally, you can work out creative and beautiful solutions to seemingly complex problems—and you’ll have more fun! I treat mathematics as a puzzle to be explored and played with. My goal is to break down the math anxiety some students feel by transforming mathematics into an engrossing exploratory process, and even a playful challenge to solve.

**For a detailed description of my teaching philosophy, please see my teaching statement.**

**Current courses:**

#### Modules delivered at Coventry University:

*Mathematical Skills for Computing Professionals*(Fall 2023)- Symbolic logic; axiomatic proof; set theory; number theory; RSA cryptography; algorithms; graph theory and applications; Huffman encoding; error correction; bin packing.

*Calculus*(Fall 2023)- Techniques and applications of differentiation and integration; first- and second-order differential equations; series solutions to linear ODEs; Laplace transforms; partial derivatives; multiple integrals.

*Real and Complex Analysis*(Fall 2023)- Differentiation; the implicit function theorem; the inverse function theorem; complex differentiability and analyticity; conformal maps; complex integration; Taylor and Laurent series; residues.

**Past courses:**

#### Modules delivered at Coventry University:

*Mathematics for Computer Science*(Summer 2023)- Symbolic logic; axiomatic proof; set theory; number theory; RSA cryptography; algorithms; graph theory and applications; Huffman encoding; error correction; bin packing.

#### Courses taught with International Mathematics Master:

*Complex Analysis*(Fall 2021)- Complex numbers; holomorphic functions; complex integration; Cauchy’s Theorem and its consequences; singularities and residues; power series and Laurent series; contour integrals.

#### Courses taught at Penn State:

- MATH 141:
*Calculus with Analytic Geometry II.*(Fall 2020)- Techniques of integration; volumes of rotation; applications of integration to physics; improper integrals; infinite series and Taylor series; elementary ordinary differential equations.

- MATH 111:
*Techniques of Calculus II*. (Spring 2020)- Multivariable functions; partial differentiation; multiple integrals; first-order linear and separable differential equations; applications.

- MATH 220:
*Matrices*. (Fall 2019)- Matrix algebra; linear transformations; subspaces; orthogonality; diagonalizability; characteristic polynomials; applications.

- MATH 231:
*Calculus of Several Variables*. (Spring 2019, Summer 2018*)- Three-dimensional analytic geometry; calculus of parametric curves; partial differentiation; applications.

- MATH 230:
*Calculus and Vector Analysis*. (Summer 2019*, 2018*; Spring 2018; Fall 2018, 2017)- Calculus of parametric curves, multivariable functions, and vector fields; multiple integrals; line and surface integrals; Green’s theorem, Stokes’ theorem, and the divergence theorem; applications.

- MATH 251:
*Ordinary and Partial Differential Equations.*(Spring 2017, Fall 2016)- First- and second-order equations; higher-order linear equations; Laplace transforms; systems of equations; Fourier series; partial differential equations.

- MATH 110:
*Techniques of Calculus I.*(Summer 2016)- Functions and graphs; techniques of differentiation and integration; improper integrals; applications.

- MATH 021:
*College Algebra I.*(Spring 2016)- Linear equations and inequalities; quadratic expressions; algebraic fractions; negative and rational exponents; radicals.

*These courses were taught online through Penn State World Campus.

**Other educational experience:**

**International Center for Theoretical Physics Diploma Program**,*Dynamical Systems Tutor*(Spring 2022)- Assisted student teams working on problems in flipped-classroom course on discrete dynamical systems.

**Penn State University Department of Mathematics**,*Math 429*(Spring 2021)- Graded homework in undergraduate course in point-set topology.

**Penn State University Department of Mathematics**,*MATH 141 Digital Teaching Assistant*(Summer 2017)- Facilitated online discussion board and recitation sessions for online course in Calculus II.

**Penn State University Department of Mathematics**,*MATH 022 Digital Teaching Assistant*(Fall 2015)- Led online recitation sessions and graded assignments for online course in College Algebra II.

**Hamilton College Department of Mathematics**,*MATH 337 Grader*(Spring 2015)- Graded problem sets for upper-level undergraduate course in Partial Differential Equations.

**Hamilton College Quantitative and Symbolic Reasoning Center**,*Peer Tutor*(Fall 2012 – Spring 2015)- Tutored eight to twelve drop-in students a week in calculus, linear algebra, differential equations, general and organic chemistry, and biology.

**Private tutoring:**

In addition to teaching, I also privately tutor. While privately tutoring, I focus on developing a student’s independence in mathematical thinking. Just as when I teach classes, I believe critical thinking should take precedence over knowing facts. If you are interested in private tutoring, you can email me at ae2050@coventry.ac.uk.