Instructor

Will Perkins

* willp@uic.edu*

Office: SEO 626

Office Hours: Wednesdays 12:00pm-2:00pm, or by appointment

Course Information
#### Main Topics of the Course:

- The language of mathematics
- Set theory
- Proof techniques
- Functions and maps
- Number theory
- Probability theory and counting

References

- Required textbook: An Introduction to Mathematical Reasoning, P. Eccles, Cambridge University Press.

Schedule

- Aug 27 The concept of mathematical proofs
- Aug 29 Implications
- Aug 31 Direct proofs, proof by cases
- Sep 5 Backwards proofs, proof by contradiction
- Sep 7 Proof by induction
- Sep 10 Problems I
- Sep 12 Set theory
- Sep 14 Set theory
- Sep 17 Quantifiers
- Sep 19 Functions
- Sep 21 Injections, surjections, bijections
- Sep 24 Problems II
- Sep 26 Counting
- Sep 28 Pigeonhole principle
- Oct 1 Counting functions and subsets
- Oct 3 Binomial coefficients
- Oct 5 Midterm Test 1
- Oct 8 Number systems
- Oct 10 Counting infinite sets
- Oct 12 Counting infinite sets
- Oct 15 Problems III
- Oct 17 Division theorem
- Oct 19 Euclidean algorithm
- Oct 22 Euclidean algorithm
- Oct 24 Prime numbers
- Oct 26 Diophantine equations
- Oct 29 Diophantine equations
- Oct 31 Problems IV
- Nov 2 Congruences
- Nov 5 Midterm Test 2
- Nov 7 Linear congruences
- Nov 9 Arithmetic of remainders
- Nov 12 Arithmetic of remainders
- Nov 14 Equivalence relations
- Nov 16 Problems V
- Nov 19 Prime numbers II
- Nov 21 Congruence modulo a prime
- Nov 26 Number theory
- Nov 28 Problems VI
- Nov 30 Probability I
- Dec 3 Probability II
- Dec 5 Probability III
- Dec 7 Review class
- Dec 13 Final Exam, 10:30am - 12:30pm