25 episodes

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

    • 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.

    • 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.

    • 1 hr 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.

    • 1 hr 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.

    • 1 hr 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.

    • 1 hr 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.

    • 1 hr 22 min

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