Mathematical Analysis      Last updated: 17 Aug 2026

These notes cover standard undergraduate topics for a two-semester course on analysis of real functions, including multivariable functions. Also, here, integration over surfaces and higher dimensional rectifiable sets is developed in an elementary way, with the help of sets with Hausdorff measure zero. And a conceptually simpler proof of divergence theorem is presented, which avoids the intricacies of the differential forms' machinery.

Foundations of Math       Last updated: 16 Aug 2026

These notes cover basic logic, set theory, and construction of numbers. Here a novel approach for developing basic tools of mathematical logic without using the theory of sets, or natural numbers, is introduced.

Linear Algebra      Last updated: 15 Aug 2026

These notes cover standard undergraduate topics for a proof-based course on linear algebra.

Statistical Learning, A Mathematical Introduction      Last updated: 31 Aug 2026

 

Theoretical Physics, A Mathematical Introduction      Last updated: 20 Aug 2026

 

Teaching

 

Spring 2023	Analysis II  Partial Differential Equations (Graduate)
Spring 2022	Foundations of Mathematics
Fall 2021	Calculus I  Introduction to Mathematics  Advanced Theory of Statistics (Graduate)
Spring 2021	Calculus I  Partial Differential Equations (Graduate)
Fall 2020	Analysis II  Real Analysis (Graduate)
Spring 2020	Introduction to Statistical Learning   Foundations of Mathematics
Fall 2019	Calculus I  Ordinary Differential Equations (Graduate)
Spring 2019	Analysis I  Differential Equations
Fall 2018	Introduction to Linear Algebra
Spring 2018	Partial Differential Equations (Graduate)
Fall 2017	Linear Algebra  Real Analysis (Graduate)
Spring 2017	Differential Equations  Analysis II
Fall 2016	Analysis I
Spring 2016	Geometric Measure Theory (Graduate)
Spring 2015	Partial Differential Equations (Graduate)