Teaching
Philosophy of active inquiry, undergraduate course instruction at Washington State University, and downloadable student lecture notes.
💡 Teaching Statement
My teaching philosophy is centered on fostering a collaborative and inquiry-driven learning environment where students develop into confident, independent critical thinkers. My background in both pure mathematics and computer science uniquely positions me to help students build connections between abstract theory and practical application, ensuring they not only understand the material but also appreciate its relevance.
To achieve this, I structure my courses around active learning and peer collaboration. This approach encourages students to engage directly with the material and learn from one another. My classes are generally structured around a fast, focused short lecture followed by structured group work engaging in the material presented. During group work, I move from table to table asking students questions about the general material and problems presented. This adaptive approach to teaching extends across the curriculum, from foundational courses like Calculus to advanced subjects such as Abstract and Advanced Linear Algebra.
Students learn best when they are motivated by interesting material and real-world examples. My background as a Software Engineer at Google and my research in computational mathematics allow me to infuse my teaching with real-world context. My experience tutoring has given me the patience to help students through difficult concepts and build their intuition.
Ultimately, my goal is to create an inclusive classroom where students feel empowered to ask questions, learn from their mistakes, and build a lasting appreciation for the power and elegance of mathematics. I am committed to continually refining my teaching methods to meet the needs of a diverse student body and to help them connect mathematical concepts to their own academic and professional aspirations.
🎓 Courses Taught
Advanced Linear Algebra
Advanced linear algebra with an emphasis on practical matrix factorizations, spectral theory, and special matrix classes:
- Theory and applications of vector spaces & linear transformations
- Eigenvalues, eigenspaces, similarity transformations, and diagonalization
- Inner product spaces, orthogonality, and orthogonal projections
- Common decompositions: SVD, LU decomposition, and Jordan canonical form
- Special matrix types: normal, symmetric, and nonnegative matrices
Abstract Algebra
Abstract algebra with an emphasis on algebraic structures and educational applications:
- Group theory and major classifications of finite groups
- Group morphisms, kernels, and isomorphism theorems
- Operations on groups: product and quotient groups
- Counting with groups: Lagrange’s Theorem and Burnside's Lemma
- Introduction to rings, integral domains, fields, and vector spaces
Discrete Mathematics
Foundational discrete mathematics bridging mathematical logic and theoretical computer science:
- Propositional & predicate logic, conditional statements, and quantifiers
- Proof techniques introduced through elementary number theory
- Sequences, recurrence relations, and mathematical induction
- Set theory, relations, and functions
- Combinatorics, counting principles, and discrete probability
- Introduction to graph theory and tree structures
Calculus 2 (Lab)
Active problem-solving recitation and computer laboratory sessions for second-semester calculus:
- Advanced integration techniques & improper integrals
- Sequences, infinite series, and power series
- Convergence tests for series (Ratio, Root, Integral, Comparison)
- Introduction to 3D vectors, dot & cross products
Discrete Mathematics
Undergraduate instruction covering logical statements, methods of mathematical proof, combinatorial counting, and graph theory.
- Direct proofs, contradiction, and contrapositive reasoning
- Strong and structural induction
- Permutations, combinations, and the Pigeonhole Principle