Introduction to Advanced Mathematics, MATH 215, Spring 2019
Instructor: Daniel Groves, 727 SEO e.mail
Syllabus: Download here.
MWF, 2:00-2:50PM, Room 309, Taft Hall.
Tuesdays 10am, Fridays 11am (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 Friday, February 15 during the regular class period.
The dates of the second midterm will be determined at a later date. The final exam will be as scheduled by the UIC registrar.
Here is a document containing the `moves' and other advice that I have given in class. I hope to had to it over the course of the semester, with new advice and moves as they come up. Please feel free to e.mail with questions or suggestions for new rules. (UPDATED 1/23)
On Wednesday, January 16, we will start working on this worksheet in class.
Due Friday, January 18, at the beginning of class. Proofs of Propositions 4 and 6 from Worksheet 1.
Due Wednesday, January 23, at the beginning of class. Proofs of Propositions 7,8,9 and 10 from Worksheet 1.
On Wednesday, January 23 we will probably start working on this worksheet.
Due Friday, January 25, at the beginning of class. Proofs of Propositions 11, 12 and 13 from Worksheet 2.
Due Monday, January 28, at the beginning of class Prove Proposition 14 from Worksheet 2, and also give the truth tables for (P ⇒ Q) ∧ R and P ⇒ (Q ∧ R).
On Wednesday, January 30, we will probably start working on this worksheet.
Due Wednesday, January 30, at the beginning of class, prove Propositions 17, 18 and 19 from Worksheet 2. UPDATE: Class cancelled on 1/30, so turn this in on 2/1.
Due Friday, February 1, at the beginning of class. Do this homework, which will be graded for points.
Due, Monday, February 4, at the beginning of class. Prove Propositions 23, 24, 25 and 26 from Worksheet 3.
On Monday, February 4, we will take a break from Number Theory and start working on this worksheet.
Due, Wednesday, February 6, at the beginning of class. Give three examples of relations on the integers which are not the one I gave in class (r less than s) or any of the ones on the relations worksheet).
Due, Friday 8, at the beginning of class. Give two examples of relations on the integers. The first should be reflexive and symmetric but not transitive. The second should be transitive but not reflexive and not symmetric. For each property that holds, explain why it holds. For each property that does not hold, give an example of numbers which show that it does not hold.
Due, Wednesday, February 13, at the beginning of class. Prove Lemma 28 from the worksheet 'Elementary Number Theory, III'.
Due, Wednesday, February 20, at the beginning of class. Prove Theorem 31 from the third number theory worksheet.
Here is the next worksheet, which we will probably start working on on 2/22.
Due, Friday, February 22, at the beginning of class. Prove Theorem 32 from the third number theory worksheet.