Propositional Logic, Truth Tables, and Equivalence | Stanford CS103 Lecture 3
Propositional logic abstracts English statements into Boolean variables, then uses truth tables to check connectives, translation direction, and equivalences.
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345 postsObjects, Quantifiers, and Types in First-Order Logic | Stanford CS103 Lecture 4
This lecture extends propositional logic into a language about objects: distinguish constants, predicates, functions, and propositions, then express some and every with existential and universal quantifiers.
First-Order Logic II—Nested Quantifiers, Negation, and Uniqueness | Stanford CS103 Lecture 5
Translate natural language one layer at a time: identify universal and existential forms, then handle quantifier order, negation, restricted quantifiers, and uniqueness.
Functions I, from Definitions to Injection and Surjection Proofs | Stanford CS103 Lecture 6
A function is more than a formula: domain, codomain, totality, and determinism are essential, while the quantifiers defining involutions, injections, and surjections dictate their proofs.
Functions II—Surjections, Assumptions, and Composition | Stanford CS103 Lecture 7
This lecture uses surjections and a proof about birds to separate assuming from proving, then shows that involutions are injective and surjective and carries those ideas into function composition.
Cardinality by Bijections and Cantor's Diagonal Argument | Stanford CS103 Lecture 8
Two sets have equal cardinality when a bijection pairs their elements; Cantor's diagonal set defeats every function from S to its power set by constructing a value it misses.
Graphs, Part I | Stanford CS103 Lecture 9
This lecture moves from the formal definitions of graphs and digraphs to independent sets, vertex covers, and their complement relationship.
Walks, Graph Complements, and the Pigeonhole Principle | Stanford CS103 Lecture 10
Starting with walks, paths, cycles, and components, this lecture proves that a graph or its complement is connected and develops the pigeonhole principle through degrees and monochromatic triangles.
Generalized Pigeonhole, Ramsey Theory, and Average Load | Stanford CS103 Lecture 11
Use the generalized pigeonhole principle to force a monochromatic triangle at a six-person party, then solve a movie-preference puzzle through average load and contradiction.
Induction, Counterfeit Coins, and Invariants | Stanford CS103 Lecture 12
Induction is not a list of checked examples: establish a true starting point, prove that an arbitrary true case transmits truth to the next case, and invoke the induction principle.
Mathematical Induction, Part II | Stanford CS103 Lecture 13
This lecture connects starting from ordinary induction to induction may start later, following the official examples and proof obligations.
Finite Automata, Part I | Stanford CS103 Lecture 14
This lecture connects why begin with a weak computer to from device behavior to a state machine, following the official examples and proof obligations.
Finite Automata, Part II | Stanford CS103 Lecture 15
This lecture connects the dfa definition connects the first half of cs103 to regular means that some dfa exists, following the official examples and proof obligations.
Finite Automata, Part III | Stanford CS103 Lecture 16
This lecture connects the automata ladder measures power with languages to dfa transition tables, following the official examples and proof obligations.
Regular Expressions | Stanford CS103 Lecture 17
This lecture connects from closure properties to a language syntax to regex is mathematics, not one library, following the official examples and proof obligations.
Nonregular Languages | Stanford CS103 Lecture 18
This lecture connects four equivalent descriptions of regularity to the precise finite-memory intuition, following the official examples and proof obligations.
Context-Free Languages | Stanford CS103 Lecture 19
This lecture connects from finite-state limits to recursion to the arithmetic grammar, following the official examples and proof obligations.
Turing Machines, Part I | Stanford CS103 Lecture 20
This lecture connects why the model changes after cfgs to long addition and local access, following the official examples and proof obligations.
Turing Machines, Part II | Stanford CS103 Lecture 21
This lecture connects the sample tm looks back from the end to beyond pairwise marking, following the official examples and proof obligations.
Turing Machines, Part III | Stanford CS103 Lecture 22
This lecture connects a quick quantifier audit for recognizers and deciders to why every decision problem can be represented as a language, following the official examples and proof obligations.