24本のエピソード

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

• テクノロジー

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.

• 2秒
• 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.

• 4秒
• 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.

• 4秒
• 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.

• 4秒
• 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.

• 4秒
• video
Lecture 7: Matching Problems

## Lecture 7: Matching Problems

Introduces the concept of matching. Discusses the mating algorithm, its fairness, and relation to practical applications.

• 4秒