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6.1200J

Mathematics for Computer Science

Prof. Erik Demaine, Dr. Zachary Abel, Dr. Brynmor Chapman | Spring 2024

Data Science, Analytics & Computer Technology Algorithms and Data Structures Computer Science Science & Math Mathematics Engineering Computation

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CC BY-NC-SA 4.0

Course introduction

This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.

Course Information

Source	MIT 開放式課程
Department	Electrical Engineering and Computer Science
Language	English
Number of videos	24

Course videos (24)

Lecture 1: Predicates, Sets, and Proofs

Lecture 1: Predicates, Sets, and Proofs

Lecture 2: Contradiction and Induction

Lecture 2: Contradiction and Induction

Lecture 3: Casework and Strong Induction

Lecture 3: Casework and Strong Induction

Lecture 4: State Machines

Lecture 4: State Machines

Lecture 5: Sums

Lecture 5: Sums

Lecture 6: Asymptotics

Lecture 6: Asymptotics

Lecture 7: Recurrences

Lecture 7: Recurrences

Lecture 8: Divisibility

Lecture 8: Divisibility

Lecture 9: Modular Arithmetic

Lecture 9: Modular Arithmetic

Lecture 10: Cryptography

Lecture 10: Cryptography

Lecture 11: Graphs and Coloring

Lecture 11: Graphs and Coloring

Lecture 12: Matching

Lecture 12: Matching

Lecture 13: Connectivity and Trees

Lecture 13: Connectivity and Trees

Lecture 14: Digraphs and DAGs

Lecture 14: Digraphs and DAGs

Lecture 15: Relations and Counting

Lecture 15: Relations and Counting

Lecture 16: Counting Techniques

Lecture 16: Counting Techniques

Lecture 17: More Counting Techniques

Lecture 17: More Counting Techniques

Lecture 18: Probability

Lecture 18: Probability

Lecture 19: Conditional Probability

Lecture 19: Conditional Probability

Lecture 20: Independence

Lecture 20: Independence

Lecture 21: Random Variables

Lecture 21: Random Variables

Lecture 22: Expectation

Lecture 22: Expectation

Lecture 23: Expectation and Variance

Lecture 23: Expectation and Variance

Lecture 24: Large Deviations: Chebyshev and Chernov Bound, Wrap Up

Lecture 24: Large Deviations: Chebyshev and Chernov Bound, Wrap Up