Instructor: Igor Kortchemski.

Tutorial Assistants:
Luca Calatroni, Mathieu Kohli, Benoit Tran.

Discrete Mathematics MAA 103 (Year 1) has two main objectives: (i) teach fundamental concepts in discrete mathematics, which are the building blocks of many different areas of science and of advanced mathematics (ii) teach how to write proofs. The course starts with elementary logic (e.g. quantifiers, different methods of proof), sets, and functions. The second part of the course introduces students to combinatorics and probability (on finite sets).

The lectures will closely follow the textbook Mathematics: A Discrete Introduction (3rd Edition) by Scheinerman. For a different presentation and broader applications concerning computer science, one may have a look at Discrete Mathematics with Applications by Epp.

Each tutorial sheet contains homework assignments, which have to be handed the next week to your TA (tutorial assistant). You **ARE** are allowed and encouraged to discuss the homework problems with other students. However, all written solutions must be individually submitted and must not be copied from somewhere else. A solution that is blatantly copied from another source will receive zero credit.

The goal of the homework assignments is to train you to write proofs on your own. The corrections of your TA are there to show you how you can improve, and the marks are there to help you see to what extent your work meets the requirement of the course.

- Tutorial sheet 1 (September 24)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises
- Tutorial sheet 2 (October 1)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises
- Tutorial sheet 3 (October 8)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises
- Tutorial sheet 4 (October 15)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises

- Tutorial sheet 5 (October 22)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises

- Tutorial sheet 6 (November 5)
- Solutions of the important exercises which have not been solved in some group.
- Solutions of the optional exercises

- Tutorial sheet 7 (November 12)
- Solutions of the important exercises which have not been solved in some group.

Midterm exam 2017-2018: exercises - solutions.

Final exam 2017-2018: exercises - solutions.

Past weeks (the numbering refers to sections in the textbook Mathematics: A Discrete Introduction by Scheinerman):

- Week 1 (September 20): Sets. (Section "To the student", Section 10: Sets I, Section 12: Sets II)
- Slides of the first part (PDF format without animations)
- Proof template 1.

- Week 2 (September 25): Functions, logical symbols, truth tables. (Section 7: Boolean algebra, Section 5: Proof).
- Truth tables (for the proof of the Very Important Theorem).

- Week 3 (October 2): Quantifiers and examples. (Section 11: Quantifiers).
- Week 4 (October 9): Functions: injectivity, surjectivity. (Section 24: Functions)
- Week 5 (October 16): Functions (images and pre-images). (Section 24: Functions)
- Week 6 (October 23): Induction. (Section 22: Induction)
*Holidays*- Week 7 (November 6): no course.
- Week 8 (November 13): Cardinality and bijective combinatorics. (Several parts of Section 12: Sets II)

Next weeks:

- Week 9 (November 20): Binomial coefficients.
- Week 10 (November 27): Permutations
- Week 11 (December 4): Midterm exam (8am-10am)
- Week 12 (December 11): Modeling (graphs, trees).
- Week 13 (December 18): Introduction to finite probability spaces.
*Holidays*- Week 14 (January 8): Independence and conditional probabilities.
- Week 15 (January 15): Random variables.
- Week 16 (January 22): Examples and applications in probability.
- Week 17 (week of January 28): Final exam

- Lectures on Tuesday 8:30-10 am (Amphi Cauchy) (but first lecture on
**Thursdsay**, September 20 8:30-10 am) - Tutorials on Monday 10:15-11:45 or 12:45-14:15.

Grading:

- Homework assignments: 50 % (your lowest two homework scores will be dropped)
- Exam grade: 50 %. If M is your grade on the midterm exam and F is your grade on the final exam, your exam grade will be max(F,(F+M)/2).

*No books, notes, calculators or collaboration are permitted at any exam.*