A repository of expository notes in pure and applied mathematics. Select a category below to expand its contents.
In 2017, I presented a poster at McGill's Undergraduate Research Conference. The poster is available here.
Real & Complex Analysis Notes
-
Notes on Single Variable Calculus 15/04/16PDF
-
Notes on Metric Spaces (MATH 255) 15/04/16PDF
-
Measure & Lebesgue Integration Theories 14/12/16PDF
-
Abstract Measure and Integration Theories 11/11/17PDF
-
Lebesgue Criterion for Riemann Integrability 24/04/16PDF
-
Selected Solutions to Problems in Complex Analysis 13/11/16PDF
-
The Identity and Holomorphic Equivalence Theorems 25/11/16PDF
-
Notes and Examples on Conformal Mappings 27/11/16PDF
-
Harmonic Functions & The Fundamental Theorem of Algebra 12/12/16PDF
-
A Useful Construction of a Holomorphic LogarithmPDF
-
A Convergence Criterion for Bounded Families in Lp-SpacesPDF
-
The Basics of Subharmonic Functions 14/09/18PDF
Functional Analysis & Operator Theory Notes
-
Functional Analysis: Hilbert Spaces, Linear Operators, and Fourier Analysis 14/05/17PDF
-
On Complex Hilbert Spaces 14/03/17PDF
-
The Spectral Theorem for Compact Hermitian Operators 26/03/17PDF
-
Fourier Analysis in Schwartz Space 30/03/17PDF
-
A Riemann Integral for Banach Space Valued FunctionsPDF
-
The Spectral Radius TheoremPDF
-
The GNS ConstructionPDF
-
The Classification of Finite Dimensional C*-AlgebrasPDF
-
A Short Proof of the Baire Category Theorem 12/01/18PDF
-
A Proof of the Uniform Boundedness Principle 30/01/18PDF
-
Honours (Real) Analysis 1 Tutorial Notes 07/02/20PDF
Differential Equations & Distributions Notes
-
A Crash Course in PDE 08/01/18PDF
-
A Global Compactness Theorem for Critical p-Laplace Equations With Weights (MSc Thesis)PDF
-
On Semiclassical Defect MeasuresPDF
-
On the Global Compactness of Positive Palais–Smale Sequences for Critical p-Laplace EquationsPDF
-
About Complex Distributions on ℝ 12/10/17PDF
-
Solving the Heat Equation in One Spatial Dimension 30/10/17PDF
-
Partial Differential Equations: Solved Exercises 31/10/17PDF
-
Distributions in Higher Dimensions 11/12/17PDF
-
MATH 475 — Solved Exercises Related to the Final Exam 11/12/17PDF
-
Some Series of Even Power 13/12/17PDF
Algebra, Topology, Number Theory & Probability Notes
-
The Elements of Group Theory 28/12/17PDF
-
The Essentials of Rings, Modules, Fields, and Galois Theory 05/01/18PDF
-
A First Course in Topology 16/08/18PDF
-
Essential Theorems in Number Theory 14/04/17PDF
-
On Dirichlet Characters Modulo n 05/04/17PDF
-
Partial Solutions to MATH 235 Practice Final 02/12/16PDF
-
Some Facts About Probability Convergence and Distributions 12/12/16PDF
-
MATH 455 Review Problems (Final Exam) 12/04/17PDF
-
Group Theory: Solved Exercises 11/12/17PDF
-
A Brief Review of Topics in Probability Theory 12/01/18PDF
-
Three Problematic Problems About Rings and Modules 23/03/18PDF
-
Selected Solutions to Problems in Abstract Algebra 27/04/18PDF
-
On p-adic Topology and Ostrowski's TheoremPDF
-
On an Uncountable Set of Lebesgue Measure Zero Dense in ℝnPDF