Notes Repository


This is intended to be a repository of notes for pure and applied sciences (mostly mathematics). I shall post my own notes as well as the notes of willing participants. In general, these notes have not been entirely proof-read.

In 2017, I took part in McGill's undergraduate research conference. My poster may be found here.

Mathematics Lecture Notes


I have written lecture notes for several mathematics courses (both analytic and algebraic in nature). These are linked below.
  1. Notes on Single Variable Calculus -- [.pdf] -- 15/04/16
  2. Notes on Metric Spaces (255) -- [.pdf] -- 15/04/16
  3. Measure & Lebesgue Integration Theories -- [.pdf] -- 14/12/16
  4. Functional Analysis: Hilbert Spaces, Linear Operators and Fourier Analysis -- [.pdf] -- 14/05/17
  5. Abstract Measure and Integration Theories -- [.pdf] -- 11/11/17
  6. The Elements of Group Theory -- [.pdf] -- 12/28/17
  7. The Essentials of Rings, Modules, Fields, and Galois Theory -- [.pdf] -- 01/05/18
  8. A First Course in Topology -- [.pdf] -- 16/08/18
  9. Honours (Real) Analysis 1 Tutorial Notes -- [.pdf] -- 07/02/20

Articles, Surveys, and Topics

  1. A Global Compactness Theorem for Critical p-Laplace Equations With Weights (MSc Thesis).
  2. On Semiclassical Defect Measures.
  3. On the Global Compactness of Positive Palais-Smale Sequences for Critical p-Laplace equations.
  4. A Convergence Criterion for Bounded Families in Lp-spaces.
  5. A Riemann Integral for Banach Space Valued Functions.
  6. The Spectral Radius Theorem.
  7. The GNS Construction.
  8. The Classification of Finite Dimensional C*-algebras.
  9. On p-adic Topology and Ostrowski's Theorem.
  10. On an Uncountable Set of Lebesgue Measure Zero Dense in R^n.

Miscellaneous

  1. Lebesgue Criterion for Riemann Integrability -- [.pdf] -- 24/04/16
  2. Selected Solutions to Problems in Complex Analysis -- [.pdf] -- 13/11/16
  3. The Identity and Holomorphic Equivalence Theorems -- [.pdf] -- 25/11/16
  4. Notes and Examples on Conformal Mappings -- [.pdf] -- 27/11/16
  5. Partial Solutions to 235 Practice Final -- [.pdf] -- 02/12/16
  6. Some Facts about Probability Convergence and Distributions -- [.pdf] -- 12/12/16
  7. Harmonic Functions & The Fundamental Theorem of Algebra -- [.pdf] -- 12/12/16
  8. On Complex Hilbert Spaces -- [.pdf] -- 14/03/17
  9. The Spectral Theorem for Compact Hermitian Operators -- [.pdf] -- 26/03/17
  10. Fourier Analysis in Schwartz Space -- [.pdf] -- 30/03/17
  11. Essential Theorems in Number Theory -- [.pdf] -- 14/04/17
  12. On Dirichlet Characters Modulo n -- [.pdf] -- 05/04/17
  13. Math 455 Review Problems (Final Exam) -- [.pdf] -- 12/04/17
  14. A Useful Contruction of a Holomorphic Logarithm
  15. About Complex Distributions on R -- [.pdf] -- 12/10/17
  16. Solving the Heat Equation in One Spatial Dimension -- [.pdf] -- 30/10/17
  17. Parial Differential Equations: Solved Exercises -- [.pdf] -- 31/10/17
  18. Group Theory: Solved Exercises -- [.pdf] -- 11/12/17
  19. Distributions in Higher Dimensions -- [.pdf] -- 11/12/17
  20. Math 475 -- Solved Exercises Related to the Final Exam -- [.pdf] -- 11/12/17
  21. Some Series of Even Power -- [.pdf] -- 13/12/17
  22. A Crash Course in PDE -- [.pdf] -- 08/01/18
  23. A Brief Review of Topics in Probability Theory -- [.pdf] -- 12/01/18
  24. A Short Proof of the Baire Category Theorem -- [.pdf] -- 12/01/18
  25. A Proof of the Uniform Boundedness Principle -- [.pdf] -- 30/01/18
  26. Three Problematic Problems About Rings and Modules -- [.pdf] -- 23/03/18
  27. Selected Solutions to Problems in Abstract Algebra -- [.pdf] -- 27/04/18
  28. The Basics of Subharmonic Functions -- [.pdf] -- 14/09/18