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Math for CS

CS

Math for Computer Science

Logic, algorithms, complexity — the math every CS student needs

181Modules

9Units

Being rebuilt

This course is still in our original format. All the content is here and free to use, but it has not yet been through the rebuild that gives our newer courses their interactive animations and cleaner visuals — so you may hit some rough edges. Spot an error? Send us a note and we will fix it.

Recommended preparation

Algebra 2 and a first taste of proofs (Intro to Proofs) are helpful — this course gathers the math computer science relies on.

Algebra 2 Intro to Proofs

Welcome to Math for CSINTRO

Diagnostic AssessmentASSESSMENT

Why Math for Computer Science?LESSON

Proof Techniques OverviewLESSON

Direct ProofLESSON

Proof by ContrapositiveLESSON

Proof Examples & TechniquesEXAMPLE

Proof by ContradictionLESSON

Mathematical InductionLESSON

Mathematical Notation & SymbolsLESSON

Foundation Practice ProblemsPRACTICE

Unit 1 SummarySUMMARY

Proof Techniques Formula SheetFORMULA SHEET

Unit 1 QuizQUIZ

Introduction to LogicINTRO

Propositions and Propositional VariablesLESSON

Logical Connectives (AND, OR, NOT)LESSON

Truth TablesLESSON

Truth Table Builder ActivityACTIVITY

Logical Equivalences & LawsLESSON

Normal Forms (DNF, CNF)LESSON

Real World: Circuit DesignREAL WORLD

Predicates and QuantifiersLESSON

Universal Quantifier (∀)LESSON

Existential Quantifier (∃)LESSON

Nested QuantifiersLESSON

Real World: SQL Queries & LogicREAL WORLD

Logical Arguments & ValidityLESSON

Proof by Contradiction in LogicLESSON

Logic Examples & Case StudiesEXAMPLE

Logic Practice ProblemsPRACTICE

Unit 2 SummarySUMMARY

Logic Formula SheetFORMULA SHEET

Unit 2 QuizQUIZ

Introduction to Set TheoryINTRO

Sets and Set NotationLESSON

Set Operations (Union, Intersection, Complement)LESSON

Venn DiagramsLESSON

Venn Diagram ActivityACTIVITY

Power SetsLESSON

Cartesian ProductsLESSON

Set Theory Examples & ApplicationsEXAMPLE

Set Theory Practice ProblemsPRACTICE

RelationsLESSON

Relation Properties (Reflexive, Symmetric, Transitive)LESSON

Equivalence RelationsLESSON

Real World: Database Schemas & RelationsREAL WORLD

Partial Orders & Total OrdersLESSON

FunctionsLESSON

Real World: Type Systems & FunctionsREAL WORLD

Injective, Surjective, and Bijective FunctionsLESSON

Inverse FunctionsLESSON

Function CompositionLESSON

Unit 3 SummarySUMMARY

Set Theory Formula SheetFORMULA SHEET

Unit 3 QuizQUIZ

Introduction to Number TheoryINTRO

Divisibility and Prime NumbersLESSON

Greatest Common Divisor & Least Common MultipleLESSON

Euclidean AlgorithmLESSON

Fundamental Theorem of ArithmeticLESSON

Modular ArithmeticLESSON

Real World: Hashing AlgorithmsREAL WORLD

Modular ExponentiationLESSON

Fermat's Little TheoremLESSON

Euler's TheoremLESSON

RSA CryptosystemLESSON

RSA Encryption ActivityACTIVITY

Linear Congruences & SolutionsLESSON

Chinese Remainder TheoremLESSON

Diffie-Hellman Key ExchangeLESSON

Real World: Encryption & SecurityREAL WORLD

Cryptography ExamplesEXAMPLE

Number Theory Practice ProblemsPRACTICE

Unit 4 SummarySUMMARY

Number Theory Formula SheetFORMULA SHEET

Unit 4 QuizQUIZ

Introduction to Counting & CombinatoricsINTRO

Basic Counting PrinciplesLESSON

Multiplication PrincipleLESSON

Addition PrincipleLESSON

PermutationsLESSON

Real World: Password ComplexityREAL WORLD

CombinationsLESSON

Binomial TheoremLESSON

Pascal's TriangleLESSON

Real World: Network Routing & PathsREAL WORLD

Inclusion-Exclusion PrincipleLESSON

Pigeonhole PrincipleLESSON

Stars and BarsLESSON

Combinatorial Counting ActivityACTIVITY

Combinatorics ExamplesEXAMPLE

Recurrence RelationsLESSON

Generating Functions IntroductionLESSON

Combinatorics Practice ProblemsPRACTICE

Unit 5 SummarySUMMARY

Combinatorics Formula SheetFORMULA SHEET

Unit 5 QuizQUIZ

Introduction to Graph TheoryLESSON

Graphs and TerminologyINTRO

Types of Graphs (Directed, Undirected, Weighted)LESSON

Graph Representation: Adjacency MatrixLESSON

Graph Representation: Adjacency ListLESSON

Graph Visualizer ActivityACTIVITY

Graph Traversal OverviewLESSON

Breadth-First Search (BFS)LESSON

Depth-First Search (DFS)LESSON

Real World: Routing AlgorithmsREAL WORLD

Trees and Tree PropertiesLESSON

Spanning TreesLESSON

Minimum Spanning Trees (Kruskal, Prim)LESSON

Euler Paths and CircuitsLESSON

Graph Theory ExamplesEXAMPLE

Hamiltonian Paths and CyclesLESSON

Planar GraphsLESSON

Graph ColoringLESSON

Real World: Social NetworksREAL WORLD

Matching in GraphsLESSON

Bipartite GraphsLESSON

Network Flow BasicsLESSON

Graph Theory Practice ProblemsPRACTICE

Unit 6 SummarySUMMARY

Graph Theory Formula SheetFORMULA SHEET

Unit 6 QuizQUIZ

Introduction to ProbabilityINTRO

Sample Spaces and EventsLESSON

Probability BasicsLESSON

Probability Simulation ActivityACTIVITY

Conditional ProbabilityLESSON

Bayes' TheoremLESSON

Independence and Conditional IndependenceLESSON

Random VariablesLESSON

Real World: Spam Filters & Machine LearningREAL WORLD

Probability DistributionsLESSON

Expectation (Expected Value)LESSON

Variance and Standard DeviationLESSON

Normal DistributionLESSON

Real World: Randomized AlgorithmsREAL WORLD

Binomial DistributionLESSON

Poisson DistributionLESSON

Markov's InequalityLESSON

Chebyshev's InequalityLESSON

Probability ExamplesEXAMPLE

Probability Practice ProblemsPRACTICE

Unit 7 SummarySUMMARY

Probability Formula SheetFORMULA SHEET

Unit 7 QuizQUIZ

Introduction to Algorithm ComplexityINTRO

Big-O NotationLESSON

Big-Omega NotationLESSON

Big-Theta NotationLESSON

Analyzing Loop ComplexityLESSON

Complexity Analysis ActivityACTIVITY

Little-o and Little-omega NotationLESSON

Solving Recurrence RelationsLESSON

Master TheoremLESSON

Real World: Sorting AlgorithmsREAL WORLD

Amortized AnalysisLESSON

Space ComplexityLESSON

Common Complexity ClassesLESSON

Complexity Analysis ExamplesEXAMPLE

P vs NP OverviewLESSON

NP-CompletenessLESSON

Real World: Database Query OptimizationREAL WORLD

Complexity Practice ProblemsPRACTICE

Unit 8 SummarySUMMARY

Complexity Analysis Formula SheetFORMULA SHEET

Unit 8 QuizQUIZ

Introduction to Automata & Formal LanguagesINTRO

Finite Automata (DFA and NFA)LESSON

Converting between DFA and NFALESSON

Regular ExpressionsLESSON

Automata ExamplesEXAMPLE

Context-Free GrammarsLESSON

Pushdown AutomataLESSON

Turing Machines OverviewLESSON

Decidability and ComputabilityLESSON

Automata Practice ProblemsPRACTICE

Unit 9 SummarySUMMARY

Automata & Formal Languages Formula SheetFORMULA SHEET

Unit 9 QuizQUIZ