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Abstract-Algebra

• Introduction
• Isomorphism
• Binary Operations
• Groups
• More on Groups
• Subgroups
• Cyclic Subgroups
• Interlude: Magic & Math
• Symmetry Groups on N-gons
• Cayley's Theorem
• Groups of Permutation
• Coset
• Finitely Generated Abelian Groups
• Lagrange's Theorem
• Homomorphism & Normal Subgroups
• More on Normal Subgroups
• Rings and Fields
• Integral Domain and Characteristic
• Fields of Quotients
• Rings of Polynomials
• Zeros of Polynomials
• Polynomial Factorization
• Field Extension
• Algebraic Extension
• Matrix Representation of Field Extensions
• Algebraic Closures
• Finite Field
• Group Action
• More on Group Action
• Three Isomorphism Theorems
• Burnside's Lemma
• Group Structure of NH
• Normal Subgroups with Small Indexes & Normalizer
• Sylow Theorem
• Quaternion and Ring Homomorphism
• Ideals
• More on Ideals
• UFD, PID, ED
• Multiplicative Norm
• More on Automorphisms
• Galois Extensions
• Normal Extension and Separable Extension
• Galois Theory
• Trace and Norm
• Computation on Galois Groups

Concrete-Math

• Extended Euclidean Algorithm
• Relation
• Solving Recurrences I
• Master Theorem
• Number Theory I
• Stirling Numbers
• Finite Calculus
• Binomial Coefficient
• Hypergeometric Functions I
• Hypergeometric Functions II
• Bernoulli Numbers
• Eulerian Numbers
• Fibonacci Numbers
• Harmonic Numbers
• Solving Recurrences II
• Continuant
• Generating Functions

Linear-Algebra

• Introduction to Vectors
• Solving Linear Equations
• Matrix
• (LU) LDU Factorization
• Linear Independence
• Vector Spaces and Subspaces
• Basis
• Orthogonality
• Projection
• Least Square Approximation
• More on Orthogonality
• Isometry
• Four Fundamental Subspaces
• Linear Transformation

Misc

• Github Page

Probability-Theory

• Introduction
• Discrete Random Variables
• Conditioning
• Continous Random Variables
• More on Conditioning
• Derived Distribution
• Covariance & Correlation Coefficient
• Transforms
• Bayesian Inference
• Linear Model
• LMS Revisited
• Linear LMS
• Weak Law of Large Numbers
• Central Limit Theorem
• Classical Statistics
• The Bernoulli Process
• The Poisson Process
• Markov Chains

Quantum-Computation

• Introduction

Representation-Theory

• Group Represnetations

Theory-of-Computation

• Computational Complexity