Mathematics
Core mathematics underpinning computer science and research work.
Mathematical foundations — algebra, analysis, probability, and beyond. Browse the subtopics below.
Subtopics
Documents
- Algorithmic game theory My annotations of the book "Algorithmic game theory" 24 notes in reading order Open ↗
- Elements of Information Theory My annotations of the book "Elements of Information Theory" (Cover & Thomas). 16 notes in reading order Open ↗
- Optimization for data analysis My annotations of the book "Optimization for data analysis" 8 notes in reading order Open ↗
Notes
- Measure Theory
- Balanced Networks, Chaos, and Input-Driven Dynamics
- BCH and Reed-Solomon Codes
- Bifurcations in One Dimension, and Flows on the Circle
- Bra-Ket Notation and a Quantum Linear Algebra Review
- Composite Quantum Systems and Entanglement
- First-Order Methods for Constrained Optimization
- Controllability, Observability, and Canonical Forms
- Deletion-Correcting Codes and Trace Reconstruction
- Descent Methods and Momentum
- Differentiation, Adjoints, and Automatic Differentiation
- Distributed Storage Codes
- Duality and Lagrangian Methods
- Entanglement Measures and Distillation
- Estimation and the Kalman Filter
- Expander Codes, LDPC Codes, and Fountain Codes
- Finite Fields and Algebraic Preliminaries
- Forced Linear Systems and State-Space Realizations
- Foundations of Smooth Optimization
- Fractals and Strange Attractors
- Group Testing
- Introduction and Autonomous Linear Dynamical Systems
- Introduction to Nonlinear Dynamics, and Flows on the Line
- Introduction to Optimization for Data Analysis
- Learning as a Dynamical System
- Limit Cycles and Bifurcations in Two Dimensions
- Linear Codes, Bounds on Code Size, and the MacWilliams Identities
- Two-Dimensional Linear Systems and the Phase Plane
- LOCC, Quantum Teleportation, and Repeaters
- The Lorenz Equations and One-Dimensional Maps
- Molecular and DNA Storage Coding
- Nonsmooth Optimization — Subgradients and Proximal Methods
- Partial Trace and Purification
- Phase-Space Geometry, Fixed Points, and Linearization
- The Postulates of Quantum Mechanics and the Qubit
- Quantum Channels — CP Maps and Their Representations
- Quantum Entropy, Fidelity, and Hypothesis Testing
- Quantum Error Correction and Generalized Measurements (POVMs)
- Quantum Measurement and Steering
- Random Recurrent Networks and Dynamic Mean-Field Theory
- Reed-Muller Codes and Polar Codes
- Sphere Packings, Kissing Numbers, and Lattices
- Spiking Neuron and Network Dynamics
- State Feedback and Linear Quadratic Regulation
- Stochastic Gradient and Coordinate Descent
- Tangent Dynamics, Chaos, and Lyapunov Exponents
- Tangent Dynamics Through Spikes, Structure, and Advanced Topics
- The Separability Problem and Entanglement Witnesses
- Typicality and Quantum Source Compression
- Unitary Dynamics and Quantum Circuits
- Information Theory and Portfolio Theory
- Kolmogorov Complexity
- Network Information Theory
- Gambling and Data Compression
- Universal Source Coding
- ECE 313 Course Notes
- A First Course in Probability
- Canonical Forms
- Concentration Inequalities, the Law of Large Numbers, and the Central Limit Theorem
- Conditional Probability, Independence, and Bayes' Formula
- Continuous-Type Random Variables and Their Distributions
- Determinants and Multilinear Forms
- Diagonalization
- Discrete Random Variables and Their Distributions
- Eigenvalue Problems and Sturm–Liouville Theory
- Parameter Estimation and Binary Hypothesis Testing
- Correlation, Covariance, MMSE Estimation, and the Joint Gaussian Distribution
- First-Order Differential Equations
- Fourier Series
- Inner Product Spaces
- Jointly Distributed Random Variables
- Linear Transformations and Matrices
- Mechanical Vibrations, Forced Oscillations, and Resonance
- Operators on Inner Product Spaces
- Partial Differential Equations — Heat, Wave, and Laplace
- Polynomials, Invariant Subspaces, and Eigenvalues
- Foundations of Probability
- Second-Order Linear Differential Equations
- Vector Spaces and Subspaces
- Cascading Behavior In Networks
- Computational Evolutionary Game Theory
- Cost Sharing
- Distributed Algorithmic Mechanism Design
- Incentives And Information Security
- Incentives In Peer-To-Peer Systems
- Incentives And Pricing In Communication Networks
- The Inefficiency Of Equilibria
- Network Formation Games And The Potential Function Method
- Online Mechanisms
- Computational Aspects Of Prediction Markets
- The Price Of Anarchy And Scalable Resource Allocation Mechanisms
- Manipulation-Resistant Reputation Systems
- Routing Games
- Selfish Load Balancing
- Sponsored Search Auctions
- Basic Solution Concepts and the Complexity of Nash Equilibria
- Combinatorial Auctions and Approximation Mechanisms
- Computing Market Equilibria
- Cryptography and Game Theory
- Graphical Games
- Introduction to Mechanism Design
- Learning, Regret Minimization, and Equilibria
- Profit Maximization in Mechanism Design
- Maximum Entropy
- Information Theory and Statistics
- Rate Distortion Theory
- The Gaussian Channel
- Differential Entropy
- Channel Capacity
- Entropy Rates of a Stochastic Process
- The Asymptotic Equipartition Property
- Information Theory Inequalities
- Data Compression and Source Coding
- Information, Entropy, Relative Entropy, and Mutual Information