Discrete Mathematics

Class Information

  • Instructor: Edgar SIMO-SERRA
  • Dates: Oct, 2021〜Jan, 2022
  • Lectures: Thursday, 4th Period (15:05〜16:45)
  • Room: Online and 53-303
  • E-mail: ess@waseda.jp
The class is planned to be held dominantly online with on-demand. Some classes will be taught optionally offline. There will be no requirement to come to campus and no final exam!
Depending on the evolution of the corona virus, details are subject to change.

Overview

This course covers elementary discrete mathematics for computer science and engineering. An emphasis is given on mathematical definitions and proof with topics covering proof methods, induction, graph theory, counting and discrete probability. The course will be given in English.

The course will be evaluated fundamentally with a midterm examination on the 8th week and a final examination on the 15th week. In the case that the midterm evaluation goes poorly, it will not be used in the evaluation, which will then be based on fundamentally the final examination. Small in-class quizzes and attendance will also be considered in the final grade.

Objectives

  1. Learn to think logical and analytically
  2. Be able to do simple proofs
  3. Ability to understand and manipulate graphs
  4. Notions of discrete probability

Schedule

  1. Introduction and Proofs slides MCS Chapters 1+2 DM Chapter 1
  2. Induction I slides MCS Chapter 2+5 DM Chapter 5
  3. Induction II slides MCS Chapter 5 DM Chapter 5
  4. Number Theory I slides MCS Chapter 9 DM Chapter 4
  5. Number Theory II slides MCS Chapter 9 DM Chapter 4
  6. Graph Theory I slides MCS Chapter 10+11 DM Chapter 10
  7. Graph Theory II slides MCS Chapter 12+13 DM Chapter 10
  8. Graph Theory III slides MCS Chapter 13 DM Chapter 10
  9. Probability slides MCS Chapter 17 DM Chapter 7
  10. Conditional Probability slides MCS Chapter 18
  11. Independence slides MCS Chapter 18
  12. Expectation I slides MCS Chapter 19
  13. Expectation II slides MCS Chapter 20
  14. Recurrences and Random Walks slides MCS Chapter 21

Textbook

  • MCS Main Textbook Eric Lehman, F. Thomson Leighton, Albert R. Meyer, Mathematics for Computer Science, 2017. PDF
  • DM Kenneth Rosen, Discrete Mathematics and Its Applications, McGraw-Hill Education, 2018.