Spring 2024: MATH 354, MATH 382, MATH 232
I take the LaTeX notes in real time on my Fedora Linux Thinkpad, aided by the incredible flexibility and ergonomics of Vim and Ultisnips. I remain indebted to Gilles Castel for pioneering this incredible ecosystem that makes taking math notes and diagrams faster than hand. Currently I am using a fork of the LaTeX package ahsan.sty that I have trimmed to suit my needs. I hope to upload the package texabit.sty after I have a stable code.
The first few notes are a little bit bad because I am still learning.
MATH 354: Honors Linear Algebra
Class 01: Covers the bare minimum basics of the first portion of the textbook.
Class 02: Continued up to direct sums, with an introduction to induction.
Class 03: Theorems in “Finite Dimensional Vector Spaces”. Includes my own notes.
Class 04: Dimension of Vector Spaces, related Exercises, and intro to Mapping.
Class 05: Some exercises on dimension, linear transformation, defined null space and injections.
Class 06: More exercises on dimension, linear transformations etc.
Class 07: Some more problems from the 3B. To be further edited.
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Class 09:
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Class 13:
MATH 232: Honors Multivariable Calculus
Class 01: This was on the epsilon-delta definition of limits and what it meant to be continuous.
Class 02: Further examples relating to epsilon-delta limit definition. Ended by N-Dim generalization.
Class 03: Talked about sequences, and a few examples on limits on multiple dimensions.
Class 04: Completed the proof in last class, finished with domain definition for limits.
Class 05: A proper introduction to continuity, ends with open-closed sets.
Class 06: Played with Open Sets, and a few proofs regarding that.
Class 07: Intro to Differentiation, and some shoutout to Physics!
Class 08: Derivative vectors and motivation to tangent line (showed wolfram).
Class 09: Introduction to derivative as Linear Transformation.
Class 10: More on derivative and turning it into Directional Derivative.
Class 11: If partial derivatives exist, then it’s continuous.
Class 12: Introduction to the Chain Rule.
Class 13: Proof to Chain Rule.
Class 14: Clairaut’s Theorem, and taking two partial derivatives.
Class 15: Taylors Polynomials, generalized for n dimensions.
Class 16: Primer on Quadratic Forms, and max-min for multi.
Class 17:
Class 18: Example on Max-Min.
Class 19:
Class 20:
Class 21: Implicit Functions.
Class 22: General Implicit Functions.
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Class 30: Sphere’s in N-dimension.
Class 31: Volume of the Hypersphere.
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MATH 382: Computational Complex Analysis
Class 01: The basic definition of complex numbers, with some maths on series.
Class 02: Polar definition, Hyperbolic Definition, ending with roots of complex numbers.
Class 03: Missed Class for Friday Prayer - still edited from friends notes.
Class 04: Showed Complex Logarithms, Differentiation and finally Cauchy Riemann equation.
Class 05: Derivation of Cauchy-Riemann Equation(s).
Class 06: Power series, Sequences, and their limits.
Class 07: Further discussion regarding series and sums.
Class 08: Revision on paths (multivariable calculus) and path independence.
Class 09: Green’s Theorem, Path integral being zero for z, conformal map.
Class 10: Derivation of Cauchy’s Integral Formula, Moirrer’s Theorem.
Class 11: Theorems Review, Maximum Modulus Principle and Liouville’s Theorem.
Class 12: Every Holomorphic function is Analytic and others.
Class 13: Minimum and Maximum Modulus Theorem.
Class 14: Laurent’s Theorem.
Class 15: Using Laurent’s Theorem to move to Residue and Poles.
Class 16: Some formulas for finding Residues.
Class 17: Integrals from Residue Theorem (interesting!).
Class 18: Further calculation on integrals and some key points.
Class 19: Working on a specific integral problem.
Class 20: Multiplying logarithms to find residues.
Class 21: Looking alpha over z integral.
Class 22: Rouche’s Theorem.
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Class 30: Riemann Manifold and Elliptic Functions.
Class 31: Intro to Conformal Mapping.
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