Math 318

Instructor: Clay Shonkwiler
Time: Monday, Wednesday and Friday, 11:30–12:30
Location: KINSC H011 (MQC room)
Office: KINSC H210
Office Hours:
Texts: Understanding Analysis, by Stephen Abbott (textbook web page) and An Introduction to Lebesgue Integration and Fourier Series, by Howard J. Wilcox and David L. Myers
Syllabus

Homework
Final project topics

Take-Home part of Exam #1
Solutions to self-scheduled part of Exam #1
Solutions to take-home part of Exam #1

Take-Home part of Exam #2
Solutions to self-scheduled part of Exam #2
Solutions to take-home part of Exam #2

Course Description

The goal of this course is to deepen our understanding of real-valued functions, to deal with some of the unresolved problems with the Riemann integral, and to develop the theory that underpins much of the modern study of differential equations, harmonic analysis, and quantum mechanics.

We will try to make sense of the following questions, among others:

• How can we make sense of infinite series of functions? Why is this a useful thing to attempt?
• What can be done to correct the shortcomings of the Riemann integral? Can we find a sense in which the Dirichlet function is integrable?
• In solving differential equations, it's often essential to relax our notions of what a function is---how can these “generalized functions” be made rigorous, and what does this have to do with signal processing?

Homework

There will be weekly homework assignments, typically due Thursday at 5:00. Homework is an important part of any math class, as it is impossible to learn mathematics without actually doing mathematics. The goal of the assignments is to deepen your understanding of the concepts, tools and techniques discussed in class, as well as to give you the opportunity to practice explaining your mathematical thinking. The importance of effective communication is vital: knowledge without the ability to communicate that knowledge is of limited value. As such, to get full credit on a problem your solution must be clear and well-written.

Each homework problem is worth 5 points, with the points divided between content (4 points) and exposition (1 point). Any problem with a score of 3 or below may be re-written and re-submitted with your original solution within one week of the original due date. The average score will be recorded. The grading scale for content points is:

4 points: A completely correct solution.

3 points: A solution demonstrating a good understanding of the problem, but with some minor mistakes or omissions.

2 points: An attempted solution which is incorrect due to a significant error, but which employs a reasonable strategy.

1 point: An attempted solution which contains the beginnings of some good ideas.

0 points: Not a serious attempt at a solution.

The point for exposition will be awarded for solutions which exhibit both clear writing and clear organization. You should write each solution so that a fellow-student can understand it.

Unless you have received pre-approval from me, late homework will be subject to a 50% penalty and must be turned in no more than 1 week after the original due date. Solutions to homework problems will be posted to Blackboard; it is your responsibility not to consult those solutions until after you have submitted a late assignment.

Collaboration on homework is not only allowed, it is highly encouraged. The process of doing mathematics is a strange mixture of the social and the antisocial: it is often the case that you will understand a problem and its solution better when you discuss it with someone else, but it is also essential that you work through the details on your own so that you don’t use another’s understanding as a crutch. As such, you should follow these guidelines when collaborating:

• You must work on each problem on your own before discussing it with your collaborators.
• When discussing a problem with your collaborators, you should work on a white board, a blackboard, or a colored sheet of paper. You should work in groups of no more than 4 at a time; in larger groups it is virtually impossible for everybody to contribute to the discussion and develop their own understanding of the problem.
• You should write up your solution separately from your collaborators and without reference to the white board, blackboard, or colored sheets of paper containing your joint work so as to communicate your own understanding of the problem. If you cannot write up your solution without referring to your collaboration materials, then you probably have not understood the problem and should throw away your solution, work further on your own, and re-start the collaborative process.
• You must indicate with whom you collaborated on your homework. Who you work with may change from problem to problem, so please note your collaborators separately for each problem.

Online or other outside resources are not allowed unless you have received my permission ahead of time.

Please contact me if you have any questions; you may also want to refer to the math department’s guidelines on collaboration.

Exams

There will be two midterm exams. Each midterm will take the place of a homework assignment and will consist of two parts:

Part I: Self-scheduled, closed-book, 90 minutes. Covers basic definitions, true/false, short answer, etc.

Part II: Take-home, open-book. Longer examples and proofs.

Collaboration is not allowed on any of the exams.

Final Project

In lieu of a final exam, you will do a final project. I will provide a list of possible project topics, or you may design your own in consultation with me. Each project will have analysis as its core, but this theory may also be combined with an application or computation, depending on your interest.

You may have noticed that Curtis Greene is listed as a second instructor for this course; he will be providing assistance with the final projects. You will meet regularly with Curtis as you work on formulating your project, and he will provide help with TeX, literature searches, and mathematical writing.

You will submit a project proposal the week after spring break. A draft of the project report (roughly 8–12 pages) will be due on the last day of class, with the final version due by the end of the finals period.

• Homework: 25%
• Midterms: 25% each
• Final Project: 25%

Accommodations

If you think you may need accommodations in this course due to the impact of a disability please meet with me privately as soon as possible. You should also contact Rick Webb, Coordinator, Office of Disabilities Services (rwebb@haverford.edu, 610-896-1290) to confirm your eligibility for appropriate accommodations. Doing so early in the semester will help prevent unnecessary inconvenience.