Discrete Math for Computer Science

Syllabus

Announcements

  • The room for MAT 304 has been changed to HI 103!!!

Calendar

The syllabus has a calendar of what is planned for each day; below we record what we actually cover each day.

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  • 10/27/2026: We went over the structured proofs handouts and then had our quiz. The exam on proofs is next week on 11/3/2026. I will put material from 5.9 on structural induction on there as extra credit for those that want to look over the material on your own.
  • 10/20/2026: We discussed the Principle of Mathematical Induction and used it to prove two summation formulas. Then we looked at two examples were we could use erroneous reasoning by induction to conclude false results; this underscores the need for both the Base Case and Induction Step in the P.M.I. Finally, I handed out scaffolded examples of direct, indirect, and induction proofs. Please look over the handouts before next time. The quiz next class will focus on proof by induction. also, the Unit 2 Proofs exam has been moved to Tuesday 11/3/2026.
  • 10/13/2026: We did additional examples of proof by contradiction and some examples of proof using the contrapositive. We also touched on when we would use proof by induction which we will introduce formally next class. At this point you should be able to read and write basic direct proofs, proofs by contradiction, and proofs using the contrapositive. You should also be able to say in loose terms when we might use a proof by induction.
  • 10/6/2026: Today we looked at the proof of the Quotient-Remainder Theorem (a.k.a. Division Algorithm) and we looked at some examples of proof by contradiction. This material covers some of the content from sections 4.3, 4.4, 4.6, and 4.7 in your text.
  • 9/29/2026: Today we had a quiz on proof types, definitions, and direct proof. Then you got your exams back; redos are due next week. Then we spent a bunch of time talking about divisibility, modular congruence, and equivalence relations. At the end of class we were playing around with the Well Ordering Principle in order to prove the Quotient-Remainder Theorem. The material we are looking at is roughly sections 4.1, 4.4, and 4.5 in the text.
  • 9/22/2026: Exam 1
  • 9/15/2026: Today we started looking at proof techniques. We went through an overview of all the types of proofs and when we might use them; you will be quizzed on this material on the October 1st. Your Unit 1 Exam is next week on the 22nd; it covers all the material we looked at from chapters 2 and 3.
  • 9/8/2026: We discussed circuits and their relation to logical statements and arguments. Then we spent some time discussing predicates. Please be sure to review this material ahead of next weeks quiz.
  • 9/1/2026: We reviewed material about statements and logical operations that is from chapter 2 in the text. Review your notes for the quiz next week.
  • 8/25/2026: We went over the syllabus and reviewed misc. material from chapters 1 and 2 on sets including Set Roaster and Builder Notation, Intersections, Unions, Set Differences, Cartesian Products, Power Sets, and Venn Diagrams.

Exams

  • Review Exam (All of chapter 1, sections 2.1-2.4 and sections 3.1-3.4) on 9/22
  • Proofs Exam (Sections 4.1, 4.4, 4.5, 4.7, 4.8, 5.2-5.4, 5.7, and 5.9) on 10/27
  • Graphs+ Exam (Previous material from Units 1 and 2 (25% of the exam) and Sections 1.4, 4.9, 10.1-10.6 (75% of the exam)) on 12/10 at 11am

Links and Handouts