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.

  • The second midterm will be on Wednesday, November 7, during the regular class period.

  • The final exam will be on Tuesday, December 11, 8am-10am, in Taft Hall 304.





    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.

  • Here is the third worksheet on number theory.

  • For class on Wednesday, October 3: Come to class prepared to present proofs of Propositions 22, 23, 24 and 25 on the third number theory worksheet.

  • For class on Friday, October 5: Come to class prepared to present a proof of Proposition 25. Also, look at the rest of the worksheet, and be ready to work on Lemma 27, Theorem 30 and Theorem 31.

  • For class on Monday, October 8: Come to class prepared to present proofs of Lemma 27 and Theorem 30.

  • For when we need it, here is the next number theory worksheet.

  • For class on Wednesday, October 10: Come to class prepared to present proofs of Theorems 30 and 31.

  • Due, Monday, October 15, at the beginning of class. Here is the second homework to be graded for points.

  • For class on Friday, October 12: Come to class prepared to present proofs of Proposition 33 and statement 1 from Theorem 35 from the fourth number theory worksheet.

  • For class on Monday, October 15: Come to class prepared to present proofs of statements 1,2,3 and 4 from Theorem 35.

  • For when we need it, here is the fifth number theory worksheet.

  • For Monday, October 22, at the beginning of class. Turn in a complete proof of Theorem 35.

  • In class, on Monday October 22 we will work on this worksheet on equivalence relations.

  • For Wednesday, October 24, at the beginning of class. Turn in solutions to Exercises 1 and 2 on the worksheet on equivalence relations.

  • For Friday, November 2, at the beginning of class Graded Homework 3

  • Here are the first five number theory worksheets in one pdf file, for ease of use. We will start working on Worksheet 5 on 10/31.

  • For Monday, November 5. Come to class prepared to present proofs of Theorem 42, Proposition 43 and Theorem 46.

  • On Friday, November 9, we will start working on the following two worksheets (in parallel, or series, as you decide): Number Theory 6 and Rings and Fields.

  • On Monday, November 19, we will start on this worksheet.

  • There will be no class on Wednesday, November 21

  • Due Monday, December 3, at the beginning of class. Do this homework.

  • NO CLASS ON Monday, November 26. For complaints, talk to the weather, and/or southwest airlines.

  • EXTRA Office Hours: Monday, December 10, 9am-10am and 11am-2pm.

  • You may turn in Graded HW 4 at the beginning of the final exam on Tuesday, December 11 (at 8am). You will receive the better of the two scores. This will be calculated on a question-by-question basis. Therefore, you can turn in only some of the questions if you are already happy with your score on the others.