Teaching

This page lists my teaching record.

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2024

• Math 171 - Fundamental Concepts of Analysis. Stanford University, Autumn. Info
  Math171 - Syllabus

  I was the principal instructor for this 40 person class.

  Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced and general version of Math 115, introducing and using metric spaces. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology.

• Math 381C - Graduate Real Analysis Bootcamp. University of Texas - Austin, Summer. Info
  Course Webpage

  I was the principal instructor for this summer bootcamp.

  • Measure Theory and Integration
  Basic properties of Lebesgue measure and the Lebesgue integral, general measure and integration theory in an abstract measure space, Lp spaces; convergence almost everywhere, in norm and measure; approximation in Lp-norm and Lp-Lq duality; integration in product spaces and convolution; and the concept of a Banach space, Hilbert space, dual space and the Riesz representation theorem.
  
  
  • Differentiation
  The relationship between differentiation and the Lebesgue integral on a real interval, derivatives of measures, absolutely continuous functions and absolute continuity between measures, functions of bounded variation.
  
  
  • Specific Important Theorems
  Monotone and Dominated Convergence theorems, Fatou's lemma, Egorov's theorem, Lusin's theorem, Radon-Nikodym theorem, Fubini-Tonelli theorems about product measures and integration on product spaces, Fundamental Theorem of Calculus for Lebesgue Integrals, Minkowski's Inequality, Holder's Inequality, Jensen's Inequality, and Bessel's Inequality.

2022

• Math 361K - Introduction to Real Analysis. University of Texas - Austin, Spring. Info
  I was TA for this class with Prof. Mark Daniels. I received the Frank Gerth III Teaching Excellence Award for my work in this class.

  A rigorous treatment of the real number system, of real sequences, and of limits, continuity, derivatives, and integrals of real-valued functions of one real variable.