Introduction to Advanced Mathematics, MATH 215, Fall 2019
Instructor: Daniel Groves, 727 SEO e.mail
Syllabus: Download here.
MWF, 12:00-12:50PM, Room 309, Taft Hall.
Mondays 11am, Friday 2pm (in SEO 727).
(Or, you can make an apointment by e.mail or try stopping past my office.)
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.
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:
Class participation: 10%
Midterm exams: 20% each
Final exam: 30%
The first midterm will be on Wednesday, September 25 during the regular class period.
The second midterm will be on Wednesday, November 6 during the regular class period.
The final exam will be as scheduled by the UIC registrar.
On Wednesday, August 28, we will start working on this worksheet. (Updated 9/4/19 to correct Proposition 9.)
Due Friday, August 30, at the beginning of class. Prove Proposition 4 and Proposition 6 from Worksheet 1.
Due Wednesday, September 4, at the beginning of class. Prove Propositions 7,8 and 9 and Corollary 10 from the first worksheet.
In class on Wednesday, September 4, we will probably start working on this worksheet.
Due Friday, September 6, at the beginning of class. Prove Propositions 11, 12 and 13 from the second number theory worksheet.
Due Monday, September 9, at the beginning of class. Prove Propositions 14, 17, 18 and 19 from the second number theory worksheet.
For class on Wednesday, Septmber 11, come to class ready to prove of present counterexamples to Conjectures 20 and 21. We will start working on this worksheet in class on Wednesday.
Here are the first three number worksheets in one file, for your convenience.
Due Monday, September 16, at the beginning of class. Prove Proposition 26, Lemma 28 and Theorem 29 from the third number theory worksheet.
In class on Monday, September 16, we will probably start working on this worksheet (on Induction).
Due Friday, September 20, at the beginning of class. Do this, which will be graded for points.