Math 294 - Introduction to Advanced Mathematics ESP - Fall 2018
Sections: 23407, 25803
Time/location: Tuesdays 12:00 PM - 1:50 PM (23407) & Thursdays 12:00 PM - 1:50 PM (25803), Stevenson Hall 120
Instructor: Jānis Lazovskis (website, email)
Hours in MSLC: Tuesdays & Thursdays 2:00 PM - 3:00 PM
Class description: Syllabus
Course descriptions: UIC catalog entries for Math 215 and Math 294
Worksheets
Worksheets of (some, not all of) the problems given in class.
- 28 August: basic ideas about logic, word problems
- 3 September: logical connectives, truth tables, introduction to functions
- 10 September: sets, set operations, functions, injectivity and surjectivity, induction
- 17 September: set sizes, logical implications, proofs by computation, proofs by induction
- 24 September: basic proofs using algebra, in the context of field and ring extensions
- 1 October: different types of proofs, function composition, integer factorization, defintion of a limit
- 8 October: binary relations, equivalence relations, modular arithmetic
- 15 October: cardinality, functions, polynomials, divisibility, binomials
- 22 October: introduction to graph theory, proof by picture
- 29 October: more graph theory, Euler characteristic of a graph, countable sets, countable unions of countable sets
- 5 November: working with the Euclidean algorithm, gcd, lcm, diophantine equations
- 12 November: primes, divisors, applications of modular arithmetic
- 19 November: no class due to Thanksgiving holidays
- 26 November: working with proofs, examples of good proofs, examples of bad proofs
- 3 December: review of semester's main topics