**
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.