Final Exam Date: Thursday, December 7, 9 am until noon.

Course Description

This course is an introduction to the field of real analysis. Real analysis deals with the fundamental properties of the real number system, functions defined on the real numbers, and, perhaps most fundamentally, the notion of a limiting process (e.g. the limit of a sequence). In this course, we will focus on a rigorous development of the basic ideas of single-variable calculus.

Course Structure

The course content is a combination of in-class lectures, in-class assignments, and out-of-class assignments. Your grade in the course will be based on four components:

Graded homework: 50%

In-class quizzes: 10%

Midterm exam: 20%

Final exam: 20%

Homework

Graded homework assignments will be due on a weekly basis. Most of the problems will be proofs. You are required to use LaTeX to write up your homework. LaTeX is already installed in our computer lab, but I recommend that you go ahead and install it on your own computer. It is freely available on the web.

Homework submissions must meet the following requirements:

It must be typed in LaTeX.

Your LaTeX file must be submitted online, and it must compile.

LaTeX files should be named in this format: <lastName>HW<number>.tex. (For instance, if I were submitting Homework 1, it would be in a file named PendergrassHW1.tex. For resubmits, use an underscore; e.g. PendergrassHW1_2.tex.

Individual problems must be clearly labeled and separated from other problems by at least one blank line.

For proofs, all explanations must be written in complete sentences. Mathematical symbols can be used, as long as they make sense when read out loud.

The end of any proof should be indicated with a black square.

Homework assignments are pledged. You may ask me questions about the assignments, and you may use the text when doing homework assignments, but no other resources.

Homework problems will be graded on a 4-point scale:

Missing (0 points): Solution missing or not attempted.

No Progress (1 point): The attempted solution is fundamentally flawed.

Some Progress (2 points): The solution has some valid steps, but still has serious flaws.

Partially Correct (3 points): The solution incorporates a fundamentally correct approach, but nevertheless contains one or two serious flaws.

Correct (4 points): The solution is completely correct, modulo one or two minor quibbles.

If you receive less than a 4 on any problem, you will have an opportunity to resubmit that problem. Your final grade on the problem will be the maximum of the original and revised submissions.

At the end of the semester, the Homework portion of your course grade will be calculated as follows:

A (4 points): At least 80% of the assigned problems were completed with a score of 4.

B (3 points): At least 80% of the assigned problems were completed with a score of 3 or higher, and at least 50% of the assigned problems were completed with a score of 4.

C (2 points): At least 50% of the assigned problems were completed with a score of 3 or higher.

Quizzes

In-class quizzes will be given on a weekly basis. Quiz problems will be graded in the same way as homework problems.

Midterm Exam

An in-class midterm will be given on Wednesday, October 18.

Final Exam

The final exam will have two components:

A set of take-home problems, subject to the same rules and requirements as homework problems. The take-home problems will be due at the beginning of the final exam period for this class (see below).

An in-class component, to be given on Thursday, December 7, from 9 am until noon.