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Essential Math for Computer Science: A Comprehensive Approach to Discrete Mathematics

This course offers an in-depth exploration of the mathematical foundations crucial for Computer Science students, focusing on discrete mathematics topics not typically covered in standard math classes. Students will learn formal logic, graph theory, probability, counting, and number theory, along with essential proof techniques such as contradiction and induction. The course emphasizes active learning through collaborative problem-solving, mini-lectures, and consistent assessments. Attendance is mandatory, and a structured grading mix ensures comprehensive evaluation. Resources include web materials and office hours for support.

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Essential Math for Computer Science: A Comprehensive Approach to Discrete Mathematics

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  1. Computer Science 20 All the Math you need for your Computer Science courses that you won’t learn in your Math Courses Discrete Mathematics for Computer Science

  2. Some Topics b a c d f Formal logic (p∨q) ∧¬(p∧q) Graphs and digraphs Probability Counting Number theory p ≡ qr (mod m) … see the “placement test” on the web site

  3. Skills!!! • How to do proofs • By contradiction • By induction • … • How to read and write mathematics • And typeset! • How to collaborate • How to present clearly and persuasively

  4. 3 Principles of Course Philosophy Learning, not competing Learn by doing, not by listening Many small bites

  5. Typical Class Day • Before class: • Reading and check-in problems (30-60 mins) • In class • Mini-lecture (10-20 mins) • Collaborative problem solving in groups of 4 (30-40 mins) • After class and before next class • Homework (60-90 mins) • So class week = • 3 hours class time • ≤ 7.5 hours out-of-class time • Most readings from MIT course notes

  6. Requirements • Attendance is mandatory! • See “Course policies” for details • Official/emergency absences ⇒ email cs20@seas.harvard.edu • Class begins at 10:10 sharp • Homework boxes removed at 10:15, no late submissions • 2 hour exams • 3-hour final during exam period

  7. Tentative Grading Mix Homework 35% Midterms (2) 30% Final exam 25% Check-in questions 10% (Poor attendance: Exclusion or failure)

  8. Support and Resources • Web site • Where schedule, HWs, slides, etc. are posted • TFs • See calendar on web site for office hours • Volunteers • Piazza (after study card day) • Tool for answering check-in questions (see course home page and get an account!) • Reading assignments and check-in questions are on the check-in tool

  9. And now – the course in action!

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