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Course6.042J / 18.062J25 lectures33 h 13 min

Mathematics for Computer Science

Prof. Tom Leighton and Dr. Marten van Dijk · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Lectures

Video Lectures

  1. Lecture 1: Introduction and Proofs 45 min · Video
  2. Lecture 2: Induction 1 h 20 min · Video
  3. Lecture 3: Strong Induction 1 h 22 min · Video
  4. Lecture 4: Number Theory I 1 h 21 min · Video
  5. Lecture 5: Number Theory II 1 h 19 min · Video
  6. Lecture 6: Graph Theory and Coloring 1 h 23 min · Video
  7. Lecture 7: Matching Problems 1 h 23 min · Video
  8. Lecture 8: Graph Theory II: Minimum Spanning Trees 1 h 24 min · Video
  9. Lecture 9: Communication Networks 1 h 24 min · Video
  10. Lecture 10: Graph Theory III 1 h 23 min · Video
  11. Lecture 11: Relations, Partial Orders, and Scheduling 1 h 4 min · Video
  12. Lecture 12: Sums 1 h 19 min · Video
  13. Lecture 13: Sums and Asymptotics 1 h 24 min · Video
  14. Lecture 14: Divide and Conquer Recurrences 1 h 23 min · Video
  15. Lecture 15: Linear Recurrences 1 h 19 min · Video
  16. Lecture 16: Counting Rules I 1 h 21 min · Video
  17. Lecture 17: Counting Rules II 1 h 26 min · Video
  18. Lecture 18: Probability Introduction 1 h 24 min · Video
  19. Lecture 19: Conditional Probability 1 h 22 min · Video
  20. Lecture 20: Independence 1 h 23 min · Video
  21. Lecture 21: Random Variables 1 h 23 min · Video
  22. Lecture 22: Expectation I 1 h 24 min · Video
  23. Lecture 23: Expectation II 1 h 24 min · Video
  24. Lecture 24: Large Deviations 1 h 24 min · Video
  25. Lecture 25: Random Walks 1 h 18 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Electrical Engineering and Computer Science; Mathematics
Taught by
Prof. Tom Leighton, Dr. Marten van Dijk
Term
Fall 2010
Level
Undergraduate
Language
English
Subjects
Mathematics, Computer science, Engineering
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Tom Leighton, Dr. Marten van Dijk. Mathematics for Computer Science. Fall 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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