Mathematics for Computer Science (2010) MIT

 Technology
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.

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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.

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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.

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Lecture 3: Strong Induction
Covers strong induction as a tool for proofs. Introduction to invariants with different games, including the nblock game and grid puzzles.

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Lecture 4: Number Theory I
Explores the basics of number theory with state machines, linear combinations, and algorithms for computation with integers.

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Lecture 5: Number Theory II
Delves deeper into number theory, covering the basics of encryption and decryption using modular arithmetic.

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Lecture 6: Graph Theory and Coloring
An introduction to graph theory basics and intuition with applications to scheduling, coloring, and even sexual promiscuity.