25 épisodes

This course covers elementary discrete mathematics. Mathematical definitions and proofs are emphasized. Topics include formal logic, induction, graph theory, asymptotic notation and growth of functions, counting principles, and discrete probability.

Mathematics for Computer Science (2010) MIT

• Technologies

This course covers elementary discrete mathematics. Mathematical definitions and proofs are emphasized. Topics include formal logic, induction, graph theory, asymptotic notation and growth of functions, counting principles, and discrete probability.

• video
Lecture 1: Introduction and Proofs

Lecture 1: Introduction and Proofs

Introduction to mathematical proofs using axioms and propositions. Covers basics of truth tables and implications, as well as some famous hypotheses and conjectures.

• 44 min
• video
Lecture 2: Induction

Lecture 2: Induction

An introduction to proof techniques, covering proof by contradiction and induction, with an emphasis on the inductive techniques used in proof by induction.

• 1h 19 min
• video
Lecture 3: Strong Induction

Lecture 3: Strong Induction

Covers strong induction as a tool for proofs. Introduction to invariants with different games, including the n-block game and grid puzzles.

• 1h 21 min
• video
Lecture 4: Number Theory I

Lecture 4: Number Theory I

Explores the basics of number theory with state machines, linear combinations, and algorithms for computation with integers.

• 1h 20 min
• video
Lecture 5: Number Theory II

Lecture 5: Number Theory II

Delves deeper into number theory, covering the basics of encryption and decryption using modular arithmetic.

• 1h 18 min
• video
Lecture 6: Graph Theory and Coloring

Lecture 6: Graph Theory and Coloring

An introduction to graph theory basics and intuition with applications to scheduling, coloring, and even sexual promiscuity.

• 1h 22 min