News

1. There *will* be tutorials on Sep 6,7,8 (first week of classes).
2. Welcome to Math/EECS 1028!

General Information

Grades

1. Tests (35%)
   Three in-class tests (15% each): [Note that the test in which a student gets her/his minimum mark will be weighted down to 5%]
   1. Test 1 (Sep 29). Syllabus: Sets, functions, simple proofs, relations. That is everything covered before sequences and series. A sample test is on eClass (note that the syllabus included sequences and series, which we have not yet covered this year).
   2. Test 2 (Oct 27): Syllabus: Sequences and sums, propositional logic. A more detailed syllabus, practice questions and a sample test is on eClass.
   3. Test 3 (Nov 24): Syllabus: Predicate logic, Proofs, Induction and Recursion, Pigeonhole Principle, Counting (6.1 only) A more detailed syllabus, practice questions and a sample test is on eClass.
2. Tutorials (12%): Every second tutorial will have a short quiz making a total of 6 quizzes). These will carry a weight of 2% each. You will also get 0.5% for each tutorial you attend, to a maximum of 6 marks. These get added to your quiz marks, to a maximum of 12%.
   If you do not attend the quiz you get no marks, except if you have a medical reason.
3. Homework (8%):
4. Final (45%):  date/time TBA by the registrar's office. Syllabus: everything covered.

Lectures

• Lecture 1 (Sep 6): Intro to Discrete Math. Slides
• Lecture 2 (Sep 8): Intro to Discrete Math - contd.
• Lecture 3 (Sep 11): Intro to Discrete Math - contd.
• Lecture 4 (Sep 13): Intro to Functions Slides
• Lecture 5 (Sep 15): Intro to Functions - contd.
• Lecture 6 (Sep 18): Intro to Relations Slides
• Lecture 7 (Sep 20): Intro to Relations - contd.
• Lecture 8 (Sep 22): Sequences and Series Slides
• Lecture 9 (Sep 25): Sequences and Series
• Lecture 10 (Sep 27): Sequences and Series
• Sep 29: Test 1
• Lecture 11 (Oct 2): Propositional Logic Slides
• Lecture 12 (Oct 4): Propositional Logic
• Lecture 13 (Oct 16): Propositional Logic
• Lecture 14 (Oct 18): Inference in Propositional Logic Slides
• Lecture 15 (Oct 20): Predicate Logic Slides
• Lecture 16 (Oct 23): Predicate Logic - covered upto slide 13.
• Lecture 17 (Oct 25): Predicate Logic - contd. Nested quantifiers; Inference.
• Lecture 18 (Oct 30): Proofs Slides.
• Lecture 19 (Nov 1): Proofs
• Lecture 20 (Nov 3): Proofs
• Lecture 21 (Nov 6): Pigeonhole Principle Slides
• Lecture 22 (Nov 8): Pigeonhole Principle
• Lecture 23 (Nov 10): Recursive Definitions Slides
• Lecture 24 (Nov 13): Counting Slides
• Lecture 25 (Nov 15): Counting
• Lecture 26 (Nov 17): Counting
• Lecture 27 (Nov 20): Counting
• Lecture 28 (Nov 22): Counting
• Lecture 29 (Nov 27): Graphs Slides

Assignments

1. Assignment 1 (2%): Released Sep 18 on eClass, due 11 pm Sep 25.
2. Assignment 2 (3%): Released Nov 13 on eClass, due 11 pm Nov 20.
3. Assignment 3 (3%): TBA

Learning objectives and list of topics

• Basic tools and techniques in discrete mathematics
  • Set Theory, Functions and Relations
  • Propositional and Predicate logic
  • Induction, recursion
  • Series and series sums
  • Introductory Graph Theory
• Precise and rigorous mathematical reasoning -- Writing proofs

We will cover the following topics.

• Ch 1: Logic and Proofs. (Omit the subsection on page 51 called "Logic programming".
• Ch 2: Sets, functions, sequences, sums. (Omit 2.6: Matrices)
• Ch 5: Induction and recursion. (Omit 5.4, 5.5)
• Ch 6: Counting
• Ch 8: Advanced counting techniques (8.1 - 8.3)
• Ch 9: Relations
• Ch 10: Graphs (10.1-10.5).
• Ch 11: Trees (11.1, 11.2)

Resources

Required Textbook

Kenneth H. Rosen. Discrete Mathematics and Its Applications, Eighth Edition. McGraw Hill, 2019. Textbook web site.

Other References

• Norman L. Biggs. Discrete Mathematics. Oxford University Press, 2002.
• Bernard Kolman, Robert C. Busby and Sharon Cutler Ross. Discrete Mathematical Structures. Pearson, 2004.
• Daniel Solow. How to Read and Do Proofs: An Introduction to Mathematical Thought Processes. Wiley, 2002.

Academic Honesty

Although you may discuss the general approach to solving a problem with other people, you should not discuss the solution in detail. You must not take any written notes away from such a discussion. Also, you must list on the cover page of your solutions any people with whom you have discussed the problems. The solutions you hand in should be your own work. While writing them, you may look at the course textbook and your own lecture notes but no other outside sources.

Important Dates (from here)

• Sep 6: First day of class
• Oct 7-13: Reading week (no classes or tests)
• Nov 8: Drop deadline
• Dec 4: Classes end
• Dec 6: Study day
• Oct 9: Thanksgiving
• Dec 7-20: Exam period

Missed test/exam

If you miss an assignment or test for valid reasons, the weight will be transferred to the final. If you miss the final, you have to get the instructor to sign a deferred standing agreement within 7 days of the scheduled exam (the instructor has the right to refuse to agree, and in that case the student can petition to take the deferred examination). The department will arrange for a deferred examination at the beginning of the following term. If you miss a test or final for some non-medical reasons, please contact the instructor. These will be dealt with a case-by-case basis.