MATH 215: Introduction to Advanced Mathematics

MATH 215

Fall 2018

Monday, Wednesday, Friday 11:00 -11:50 am Taft Hall 219

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:

  1. The language of mathematics
  2. Set theory
  3. Proof techniques
  4. Functions and maps
  5. Number theory
  6. 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

    Homework 1

  • Aug 31 Direct proofs, proof by cases

  • Sep 5 Backwards proofs, proof by contradiction

    Homework 2

  • Sep 7 Proof by induction

  • Sep 10 Problems I

  • Sep 12 Set theory

    Homework 3

  • Sep 14 Set theory

  • Sep 17 Quantifiers

  • Sep 19 Functions

  • Sep 21 Injections, surjections, bijections

    Homework 4

  • 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