Real Analysis

Math 441 - Fall 2015

Announcements

The final exam will have two parts: four take-home problems (tex, pdf) and an in-class exam. The in-class portion of the final will be on Tuesday, December 15 at 2pm. It will cover this material.
Quiz 4 will be on Monday, Nov. 16. It will cover this material.
Quiz 3 will be on Monday, Oct. 26. It will cover sequences.
Quiz 2 will be on Friday, Oct. 9. It will cover this material.

Basic Info

Instructor: Brian Lins
Class Times & Location: MWF 1:30 - 2:20 Bagby 111
Office Hours: See my weekly schedule, and by appointment.
Textbook: Analysis with an Introduction to Proof, 4th Edition, by Stephen R. Lay

Course Description

Math 441 will begin with a review of logic, proof techniques and elementary set theory. From there we will study the properties of real numbers and functions use them to derive many of the most important theorems in calculus.

Tentative Schedule

The schedule above is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.

Attendance Policy

Attendance in this class is required. Repeated absences may result in a forced withdrawal from the course. You are responsible for any material you miss due to absence. Please let me know ahead of time if you know that you will not be able to attend class.

Grading Policy

The term grade will be based on the following factors.

Component	Proportion
Homework	60%
Quizzes	20%
Final Exam	20%

Homework

There will be written homework assignments due almost every week. Most of the problems will be proofs. You will use LaTeX to write your proofs. LaTeX is available on the computers in the computer labs, but I recommend downloading it on your own computer. It is free and I also recommend using a LaTeX editor to help make the transition easier. I like Texmaker.

In order to receive full credit, your homework must satisfy the following criteria:

It must be typed (in LaTeX, not a word processor).
The original LaTeX source should be submitted online and it must compile.
LaTeX files should be saved with names in the following format: <yourlastname>HW<number>. For example if I were submitting homework 1, I would save it as LinsHW1.tex. For resubmits, use an underscore, like LinsHW1_2.
Individual problems must be clearly labeled and separated from other problems by at least a full line.
Each exercise should include the statement of the problem to be solved (this can be copied from the homework template).
For proofs, all explanations must be written in complete sentences. It is okay to use symbols as long as they make sense when you read them out loud.
The end of any proof should be indicated with a Q.E.D. or a small square.

You are permitted, and in fact encouraged to work together, but all homework assignments you submit must ultimately be your own work written in your own words.

Proofs will be graded on a 4 point scale.

Missing (0 points) I have no basis on which to judge the proof.
Flawed (1 point) The attempted proof is fundamentally flawed.
Beginning (2 points) The proof includes some valid steps, but still has serious logical or factual flaws.
Partially Correct (3 points) The proof is almost correct, but has one or two important mistakes. The difference between a 2 and a 3 is that a 3 usually includes the core idea of the proof, while a 2 is still missing that insight.
Correct (4 points) This proof is either completely correct, or is essentially valid with only minor quibbles.

If you receive less than a 4 on any proof, you will have at least one opportunity to resubmit your solution for a higher score. You keep the best score on each problem you complete. Here are the requirements in order to achieve each of the final letter grades on the homework portion of the final grade.

To get an A You must complete 80% of the assigned homework problems with a score of 4.
To get a B You must complete 50% of the problems with a score of 4 and 80% with a 3 or higher.
To get a C You must complete 50% of the problems with at least a 3.

Quizzes

There will be several quizzes that will test your knowledge of real analysis concepts. These quizzes will be announced in advance, and you will know exactly what concepts will be covered on each quiz. You will not be asked to write proofs during the quizzes. Each quiz will take about 20 minutes. The chart below gives a rough correspondence between quiz score and letter grade:

Letter Grade	F	D	C	B	A
Score	0 - 39%	40 - 54%	55 - 69%	70 - 84%	85 - 100%

Final Exam

There will be a cumulative final exam. It will include questions similar to the ones on the quizzes, as well as proofs similar to the ones on the homework. A list of potential proof questions will be provided before the exam.

Special Accommodations

In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations. How does this look?