© Maintained by George Voutsadakis

Intermediate Algebra The Real Numbers Linear Equations and Inequalities in One Variable Linear Equations and Inequalities in Two Variables Systems of Linear Equations Exponents and Polynomials Rational Expressions and Functions Radicals and Rational Exponents Quadratic Equations, Functions and Inequalities Exponential and Logarithmic Functions	Intermediate Algebra (New! openstaxTM) Rational Expressions and Functions Roots and Radicals Quadratic Equations and Functions Exponential and Logarithmic Functions
College Algebra Functions, Graphs and Models Linear Models, Equations and Inequalities Quadratic, Piecewise-Defined and Power Functions Additional Topics with Functions Exponential and Logarithmic Functions Higher-Degree Polynomial and Rational Functions	College Algebra (New! openstaxTM) Functions Linear Functions Polynomial and Rational Functions Exponential and Logarithmic Functions Systems of Equations and Inequalities
Trigonometry Functions and Graphs Trigonometric Functions Identities and Equations Applications Complex Numbers Analytic Geometry Exponentials and Logarithms	Trigonometry (New! openstaxTM) The Unit Circle: Sine and Cosine Functions Periodic Functions Trigonometric Identities and Equations Further Applications of Trigonometry Analytic Geometry
Calculus I Review of Precalculus Limits Differentiation Applications of the Derivative The Integral	Calculus for Business & Biology Functions Derivatives and Their Uses Further Applications of Derivatives Exponential and Logarithmic Functions Integration and Its Applications Integration Techniques and Differential Equations Calculus of Several Variables
Calculus II Applications of the Integral Techniques of Integration Further Applications and Taylor Polynomials Introduction to Differential Equations Infinite Series	Differential Equations Introduction First-Order Differential Equations Second-Order Linear Equations Higher-Order Linear Equations Series Solutions of Second-Order Linear Equations The Laplace Transform Systems of First-Order Linear Equations
Calculus III Parametric Equations, Polar Coordinates, Conic Sections Vector Geometry Calculus of Vector-Valued Functions Differentiation in Several Variables Multiple Integration	Advanced Calculus Line and Surface Integrals Fundamental Theorems of Vector Analysis Fourier Series and Orthogonal Functions
Fundamental Concepts of Mathematics Definitions and Proofs Collections Counting and Relations More on Proofs Functions	Topics in Discrete Mathematics Probability Number Theory Algebra Public Key Cryptography Graphs Partially Ordered Sets
Discrete Structures for Computer Science Proofs, Sets and Structures Functions Construction Techniques and Induction Analysis Tools and Techniques Finite Automata and Regular Languages Pushdown Automata and Context-Free Languages Turing Machines, Computability and Complexity
Combinatorial Mathematics Permutations and Combinations Generating Functions Recurrence Relations The Principle of Inclusion and Exclusion Pólya's Theory of Counting	Graph Theory Definitions and Examples Paths and Cycles Trees Planarity Coloring Graphs Digraphs Matching, Marriage and Menger's Theorem Matroids
Euclidean Geometry The Basics Triangles Circles and Lines Ceva's Theorem and its Relatives Vector Methods of Proof	Projective Geometry Introduction Triangles and Quadrangles The Principle of Duality The Fundamental Theorem and Pappus' Theorem One- and Two-Dimensional Projectivities Polarities The Conic A Finite Projective Plane Parallelism Coordinates
Linear Algebra Linear Equations Matrix Algebra Determinants Vector Spaces Eigenvalues and Eigenvectors Orthogonality
Abstract Algebra I Preliminaries Introduction to Groups Subgroups Quotient Groups and Homomorphisms Group Actions Direct Products and Abelian Groups	Abstract Algebra II Introduction to Rings Euclidean, Principal Ideal and Unique Factorization Domains Polynomial Rings Introduction to Module Theory Vector Spaces Modules over Principal Ideal Domains
Fields and Galois Theory Rings and Fields Integral Domains and Polynomials Field Extensions Applications to Geometry Splitting Fields Finite Fields The Galois Group Equations and Groups Some Group Theory Groups and Equations Regular Polygons	Algebraic Geometry Introduction Affine Varieties Projective Varieties Smooth Points and Dimension Plane Cubic Curves Cubic Surfaces Introduction to the Theory of Curves
Number Theory Divisibility Arithmetical Functions Congruences Quadratic Residues Quadratic Forms Diophantine Approximation Quadratic Fields
Analytic Number Theory The Fundamental Theorem of Arithmetic Arithmetical Functions and Dirichlet Multiplication More on Dirichlet Multiplication Averages of Arithmetical Functions Elementary Theorems on the Distribution of Prime Numbers Congruences Finite Abelian Groups and Their Characters Dirichlet's Theorem on Primes in Arithmetic Progressions Periodic Arithmetical Functions and Gauss Sums Quadratic Residues and the Quadratic Reciprocity Law Primitive Roots	Algebraic Number Theory Unique Factorization in the Natural Numbers Number Fields Fields, Discriminants and Integral Bases Ideals Prime Ideals and Unique Factorization Imaginary Quadratic Fields Lattices and Geometrical Methods Other Fields of Small Degree Cyclotomic Fields and Fermat Equation Analytic Methods
Topology Theory of Sets Metric Spaces Topological Spaces Connectedness Compactness	Algebraic Topology Geometric Complexes and Polyhedra Simplicial Homology Groups Simplicial Approximation The Fundamental Group Covering Spaces The Higher Homotopy Groups Further Developments in Homology
Knot Theory Introduction Tabulating Knots Invariants of Knots Surfaces and Knots Types of Knots Polynomials
Real Analysis Axioms for the Real Field Basic Properties of Reals Sequences and Convergence Special Subsets Continuity Continuity on an Interval Limits Derivatives Riemann Integral	Complex Analysis Complex Numbers and Plane Complex Functions and Mappings Limits and Continuity Analytic Functions Elementary Functions Integration in the Complex Plane Series and Residues Consequences and Applications of the Residue Theorem Conformal Mappings
Measure Theory Sets and Classes Measures and Outer Measures Extension of Measures Measurable Functions Integration General Set Functions Product Spaces	Fractal Geometry Mathematical Background Hausdorff Measure and Dimension Alternative Definitions of Dimension Techniques for Calculating Dimensions Local Structure of Fractals Projections, Products and Intersections Applications and Examples
Dynamical Systems Basic Notions and Examples Topological Dynamics Low-Dimensional Dynamics Hyperbolic Dynamics Symbolic Dynamics Ergodic Theory	Differential Geometry Introduction to Manifolds Functions of Several Variables and Mappings Differentiable Manifolds and Submanifolds Vector Fields of a Manifold Tensors and Tensor Fields on Manifolds Integration on Manifolds Differentiation on Riemannian Manifolds Curvature
Probability Combinatorial Analysis Axioms of Probability Conditional Probability and Independence Random Variables Continuous Random Variables Jointly Distributed Random Variables Properties of Expectation Limit Theorems	Markov Chains Discrete Time Markov Chains Continuous Time Markov Chains I Continuous Time Markov Chains II Further Theory Applications
Functional Analysis: General Theory Metric Spaces Normed Spaces. Banach Spaces Inner Product Spaces. Hilbert Spaces Fundamental Theorems for Normed and Banach Spaces Banach Fixed Point Theorem Approximation Theory	Functional Analysis: Spectral Theory Spectral Theory of Linear Operators in Normed Spaces Compact Linear Operators on Normed Spaces Bounded Self-Adjoint Linear Operators Unbounded Linear Operators in Hilbert Space Unbounded Linear Operators in Quantum-Mechanics
Convexity Introduction The Euclidean Space Convex Sets Convex Polytopes Linear Programming Convex Functions Mixed Volumes and Extremum Problems	Theory of Distributions Locally Convex Spaces Test Functions and Distributions Distributions with Compact Support and Convolutions Fourier Transforms and Tempered Distributions Distributions in Hilbert Space
Set Theory Sets Relations, Functions and Orderings Natural Numbers Finite, Countable and Uncountable Sets Cardinal Numbers Ordinal Numbers Alephs The Axiom of Choice Arithmetic of the Cardinal Numbers	Mathematical Logic Introduction and Primer on Sets Sophistry, Aristotle and Boole Propositional Logic Terms, Interpretations and Term Functions First-Order Languages
Model Theory Structures and Formulas Classifying Structures Structures that Look Alike Automorphisms and Interpretations The First-Order Case: Compactness The Countable Case The Existential Case Saturation	Finite Model Theory Preliminaries The Ehrenfeucht-Fraïssé Method More on Games 0-1 Laws Satisfiability in the Finite Finite Automata and Logic Descriptive Complexity Theory
Lattice Theory Ordered Sets Lattices and Complete Lattices Modular, Distributive and Boolean Lattices Representation Theory: The Finite Case Congruences Complete Lattices and Galois Connections Maximality Principles A Brief Topological Detour Representation Theory: The General Case
Universal Algebra Lattices Algebras, Subalgebras, Homomorphisms & Direct Products Varieties Selected Topics	Category Theory Categories, Functors and Natural Transformations Adjoints Interlude on Sets Representables Limits Adjoints, Representables and Limits
Game Theory Introduction Strategic Games: Nash Equilibrium Strategic Games: Mixed Equilibrium Rationalizability and Iterated Elimination of Dominated Actions Extensive Games: Perfect Information Extensive Games: Imperfect Information Sequential Equilibrium Coalitional Games: The Core Stable Sets, the Bargaining Set and the Shapley Value	Information Theory Entropy, Relative Entropy and Mutual Information Asymptotic Equipartition Property Entropy Rates of a Stochastic Process Data Compression Channel Capacity Differential Entropy Gaussian Channel Rate Distortion Theory Information Theory and Statistics Kolmogorov Complexity
Mathematical Finance Probability Normal Random Variables Brownian Motion Interest Rates and Present Value Analysis Pricing Contracts via Arbitrage The Arbitrage Theorem The Black-Scholes Formula Valuing by Expected Utility Stochastic Order Relations Optimization Models Stochastic Dynamic Programming	Evolutionary Dynamics Evolution Fitness Landscapes and Sequence Spaces Evolutionary Games Prisoners of the Dilemma Finite Populations Games in Finite Populations Evolutionary Graph Theory Spatial Games Evolutionary Dynamics of Cancer Language Evolution
Algorithms Sorting Insertion Sort Merge Sort Heap Sort Quick Sort Sorting in Linear Time Data Structures Elementary Data Structures Hash Tables Binary Search Trees Design and Analysis Techniques Dynamic Programming Greedy Algorithms Amortized Analysis Graph Algorithms Elementary Graph Algorithms Minimum Spanning Trees Single Source Shortest Paths All-Pairs Shortest Paths Maximum Flow
Languages and Computation Introduction Regular Languages Context-Free Languages The Church-Turing Thesis Decidability Reducibility	Computational Complexity Time Complexity Space Complexity Intractability Advanced Topics in Complexity
Quantum Computing Single-Qubit Quantum Systems Multiple-Qubit Systems Measurement of Multiple-Qubit States Quantum State Transformations Quantum Versions of Classical Computations Introduction to Quantum Algorithms Shor's Algorithm Grover's Algorithm and Generalizations	Descriptive Complexity Background in Logic Background in Complexity First-Order Reductions Inductive Definitions Parallelism Ehrenfeucht-Fraïssé Games Second-Order Logic and Fagin's Theorem Second-Order Lower Bounds Complementation and Transitive Closure Polynomial Space
Artificial Intelligence Introduction Propositional Logic First-Order Predicate Logic Search, Games and Problem Solving Reasoning With Uncertainty Machine Learning and Data Mining Neural Networks Reinforcement Learning Support Vector Machines