01Probability and Statistics
- Counting (Permutations and Combinations)
- Probability Axioms
- Sample Space, Events
- Independent Events, Mutually Exclusive Events
- Marginal, Conditional, and Joint Probability
- Bayes' Theorem
- Conditional Expectation and Variance
- Mean, Median, Mode, and Standard Deviation
- Correlation and Covariance
- Random Variables
- Discrete Random Variables and Probability Mass Functions
- Uniform, Bernoulli, Binomial Distribution
- Continuous Random Variables and Probability Distribution Functions
- Uniform, Exponential, Poisson, Normal, Standard Normal Distributions
- t-Distribution, Chi-Squared Distributions
- Cumulative Distribution Function
- Conditional Probability Density Function
- Central Limit Theorem
- Confidence Interval
- z-Test, t-Test, Chi-Squared Test
02Linear Algebra
- Vector Space
- Subspaces
- Linear Dependence and Independence of Vectors
- Matrices
- Projection Matrix
- Orthogonal Matrix
- Idempotent Matrix
- Partition Matrix and their Properties
- Quadratic Forms
- Systems of Linear Equations and Solutions
- Gaussian Elimination
- Eigenvalues and Eigenvectors
- Determinant
- Rank
- Nullity
- Projections
- LU Decomposition
- Singular Value Decomposition
03Calculus and Optimization
- Functions of a Single Variable
- Limit
- Continuity
- Differentiability
- Taylor Series
- Maxima and Minima
- Optimization Involving a Single Variable
04Programming, Data Structures, and Algorithms
- Programming in Python
- Basic Data Structures
- Stacks
- Queues
- Linked Lists
- Trees
- Hash Tables
- Search Algorithms
- Linear Search
- Binary Search
- Basic Sorting Algorithms
- Selection Sort
- Bubble Sort
- Insertion Sort
- Divide and Conquer
- Introduction to Graph Theory
- Basic Graph Algorithms
- Traversals
- Shortest Path