News

1. The new tutorial section (section 5) will have its first meeting on Monday Jan 21, NOT Thurs Jan 17 as some people were told.
2. There are no tutorials on Jan 4.
3. 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 (Jan 28). Syllabus: Sets, functions, simple proofs, sequences and series. Sec 2.1-2.4 in the text. Sample test is on moodle (note that the syllabus included logic, which we have not covered this year). Omit sections 2.1.7, 2.1.8, 2.2.5, 2.3.6, 2.4.4.
      Conversion between different bases is included in the test.
   2. Test 2 (Feb 25): Syllabus: Everything covered up Feb 11 that was not on the syllabus for test 1 (i.e., Propositional logic and inference. Predicate logic (no inference)). A sample test is on moodle. The sections are 1.1 (omit 1.1.6), 1.2.1, 1.2.2, 1.2.6, 1.3.1-1.3.4, 1.4.1-1.4.10, 1.5, 1.6.1-1.6.5. Proof techniques are not included in this test.
   3. Test 3 (Mar 22): The test will be in SLH B (Please note the changed room) Syllabus: Inference in predicate logic (1.6.7,1.6.8). Proofs (1.7,1.8, except, 1.8.7-1.8.10), Induction (5.1, 5.2, except 5.2.4, 5.2.5), Pigeonhole Principle (6.2, except 6.2.3), Counting (6.1, except 6.1.5, 6.1.6).
2. Tutorials (10%): Every second tutorial will have a short quiz (making a total of 5 quizzes). These will carry a weight of 2% each. You will also get 0.5% for each tutorial you attend, to a maximum of 5 marks. These get added to your quiz marks, to a maximum of 10%.
   If you do not attend the quiz you get no marks, except if you have a documented medical reason.
3. Homework (10%):
4. Final (45%):  date/time TBA by the registrar's office. Syllabus - everything covered.

Lectures

• Lecture 1 (Jan 4): Intro to Discrete Math. Slides (we covered slides 1- 11).
• Lecture 2 (Jan 7): Intro to Discrete Math continued. Same slides as before (we covered slides 12- 19).
• Lecture 3 (Jan 9): Examples of simple proofs (Slides) - updated to include the proof done on the board and the problems written on the board
• Lecture 4 (Jan 11): Functions (Slides) we covered upto slide 11.
• Lecture 5 (Jan 14): Functions continued (we covered upto slide 14).
• Lecture 6 (Jan 16): Functions continued.
• Lecture 7 (Jan 18): Start sequences and series (Slides).
• Lecture 8 (Jan 21): Finish sequences and series. Start Propositional Logic (Slides) (we reached slide 4).
• Lecture 9 (Jan 25): Propositional Logic - continued.
• Lecture 10 (Jan 30): Propositional Logic - continued. We reached slide 22.
• Lecture 11 (Feb 1): More Propositional Logic (Slides)
• Lecture 12 (Feb 4): Finish Propositional Logic
• Lecture 13 (Feb 8): Start Predicate Logic (Slides)
• Lecture 14 (Feb 11): Predicate Logic - continued (we covered upto slide 16).
• Lecture 15 (Feb 13): Guest lecture by Prof Eric Ruppert
• Lecture 16 (Feb 15): Guest lecture by Prof Eric Ruppert
• Lecture 17 (Feb 27): Proofs (Slides)
• Lecture 18 (Mar 1): Proofs
• Lecture 19 (Mar 6): Proofs
• Lecture 20 (Mar 8): Pigeonhole Principle (Slides)
• Lecture 21 (Mar 11): Counting (Slides)
• Lecture 22 (Mar 13): Counting - continued
• Lecture 23 (Mar 15): Counting - continued
• Lecture 24 (Mar 18): Counting - continued
• Lecture 25 (Mar 20): Counting - continued
• Lecture 26 (Mar 25): Counting - continued
• Lecture 27 (Mar 27): Recursive Definitions (Slides)
• Lecture 28 (Mar 29): Graphs (Slides)
• Lecture 29 (Apr 1): Graphs (Slides)

Assignments

1. Assignment 1 (2%)
2. Assignment 2 (2%)
3. Assignment 3 (3%)
4. Assignment 4 (2%)

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

Textbook

Kenneth H. Rosen. Discrete Mathematics and Its Applications, Eighth Edition. McGraw Hill, 2018.
Available from the University bookstore. 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)

• Jan 4: First day of class
• Feb 16-22: Reading week (no classes or tests)
• March 8: Drop deadline
• Apr 3: Classes end
• April 4: Study day
• April 19: Good Friday
• Apr 5-20: Exam period

Missed test/exam

If you miss an assignment or test for medical 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.