Introduction to Advanced Mathematics, MATH 215, Fall 2018
Instructor: Daniel Groves, 727 SEO e.mail
Syllabus: Download here.
MWF, 12:00-12:50PM, Room 304, Taft Hall.
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
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 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.
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.