Introduction to Advanced Mathematics, MATH 215, Fall 2018


Instructor: Daniel Groves, 727 SEO e.mail

Course webpage: http://www.math.uic.edu/~groves/teaching/2018-19/215/

Syllabus: Download here.

Course hours:

MWF, 12:00-12:50PM, Room 304, Taft Hall.

Office hours:

Mondays 10am, Fridays 2pm.

(Or, you can make an apointment by e.mail or try stopping past my office.)

Text: "An Introduction to Mathematical Reasoning", by P. Eccles, Cambridge University Press. ISBN:9780521597180


Course description:
The goal of this course is to learn how to create and write mathematical proofs, and to learn why one might want to do such a thing. We will introduce and study some important mathematical concepts used in advanced mathematics courses, particularly equivalence relations.

Assessment:
There will be homework for most classes, two in class midterm exams and a final exam. Since there will be a lot of writing, explaining and critiquing in class, there will also be a class participation component of the grade. The relative weighting of these components will be:
  • Homework: 20%
  • Class participation: 10%
  • Midterm exams: 20% each
  • Final exam: 30%

    Exams:

  • The first midterm will be on Wednesday, September 26, during the regular class period.

    Two midterms, and one final, dates and times to be announced.



    Daily Homework:

  • Due, Wednesday September 5, at the beginning of class. Do this homework.

  • Due, Friday September 7, at the beginning of class. Do the first homework again. (Note: Part 1b has now been corrected. Everyone except Phillip should give a different example than the one we did in class.)

  • Due, Monday September 10, at the beginning of class. Do this homework.

  • Due, Wednesday September 12, at the beginning of class. Do this homework.

  • Due, Monday September 17, at the beginning of class. Do this homework.

  • Due, Friday September 21, at the beginning of class. Graded homework 1.

  • On Monday, September 17 we will start working on this worksheet. (On the graded homework, this is the worksheet that is referred to.)

  • For Wednesday, September 19, come to class prepared to present proofs of Propositions 7 and 8 from the worksheet above.

  • Here is the second worksheet, for when we are ready for it.

  • For Monday, September 24, come to class prepared to present proofs of Propostions 10, 11, 12 and 13.

  • Here is a list of definitions and statements of results that we covered about functions and sets.