GEORGETOWN COLLEGE

MAT 431A Real Analysis I(3 hours)

Fall 2009

Dr. Christine Leverenz

Science Center 102A, Phone: 8097

Catalog Description: A theoretical development of the elements of calculus. Topics include sequences, continuity, derivatives and integrals of single-variable functions. Corequisite: MAT 325; Prerequisite: MAT301

COURSE
MATERIALS: Gordon, Russell A. __Real Analysis, A First Course, 2 ^{nd}
ed__., Addison-Wesley, Boston, MA, 2002. Class notes available from Scholar/Moodle
(or distributed in class.)

COURSE OBJECTIVES:

To deductively examine and prove the theory of single variable calculus. To become better theorem provers and thus to become better mathematical communicators. To learn to read mathematics from a textbook.

REQUIREMENTS:

**Daily
work: **Homework and text reading will
be assigned for each class period and posted on Moodle. Most homework will be
due the next class period. Required corrections
must be resubmitted, along with the original paper, before the grade for the
entire paper is recorded. Corrections are due on the class period after the
paper is returned.

Collected homework is due at the beginning of class and must be submitted by the author; late homework is not accepted. Use of any sources other than the text, your class notes, your class group work, and yourself is illegal. Students may work together as long as it is true collaboration and not copying. Students should do all of their own writing. All help must be acknowledged, eg: I received help from (Source Name) on this problem. Acknowledging help will not count against the paper. Allowing people to copy your work and/or copying someone else’s work is not ethical behavior and will be penalized when discovered. Penalties are described in the Student Handbook under “Honor Code”.

A list of “A” problems is available on Moodle; one problem will be assigned each week and will be due in one week. “A” problems must be worked completely by each individual using only class notes, the textbook, and the mental work of the author; no collaboration is allowed. A student must work correctly, with corrections, at least 80% of the problems to earn an A in the course. Most “A” problems will be proofs and are intended for the student to demonstrate theorem proving abilities.

Short quizzes covering definitions and theorem statements will also be given weekly, generally on __________.

**Testing**: There will be approximately 2 tests and a
comprehensive take-home final. Make-ups will be given only if you let me know
of your absence BEFORE a test is given. The tests are tentatively scheduled
for Oct. 2 and Nov. 23.

COURSE OUTLINE: We will cover most of chapters 1 – 4, 5.1 – 5.3, and 8.1.

EVALUATION: The grading scale for everything is 92 – 100% A, 87 – 92% A-/B+, 82 – 87% B, 77 – 82% B-/C+, 70 – 77% C, 60 – 70% D. Your overall average is determined by counting the final exam 25%, the hourly tests 40%, and the daily work 35%. In addition, to receive the A grade, a student must demonstrate proficiency in proving theorems by individually proving 80% of the “A” problems. Any borderline student with a history of absences will receive the lower grade.

ATTENDANCE: You are required to attend every class. If illness or some other legitimate reason prevents you from being in class, it is your responsibility to inform me of such. Allowances in grades will be made for work missed due to illness or some other legitimate reason; no allowance will be made for cuts. I expect you to be prepared for class on the day that you return. Remember that you must be present in class to submit homework.

OFFICE HOURS: I have regularly scheduled office hours posted on Moodle dedicated to helping students with math problems. If you call my office and I don’t answer please leave a message; when speaking with someone in my office I don’t answer the phone. I will also be happy to meet at other times if we arrange it ahead of time. If you have cut class for an unexcused reason, do not come to my office for help on that material since it is not fair to the rest of the class to give one-on-one special teaching to those who do not see fit to attend class.

__Real Analysis Homework__

__ __

1. Almost all homework will be collected daily. Late homework is not accepted. Quizzes will be given on Mondays at the start of class.

2. You are expected to read the text and make sense of the proofs and examples given there. To this end, some homework problems will be based on material from the textbook that is not explicitly covered in class.

3. Homework assignments will be posted on Moodle.

4. ** Homework OK’s** **Homework
No-no’s**

Any paper including straggly edges. Multiple columns on one page.

Pen or pencil No work or reasoning.

Problems out of order. Cramped papers – leave space between problems.

Continued problems with note of where to look.

Cross outs.

5. If you want my feedback on homework you must leave me room to write – about 5 lines for a longer problem. If I don’t have room to write I won’t make comments on how to correct a problem or on how well you did.

6. It is fine for students to collaborate on all homework (except for “A” problems) as long as it is true collaboration – that is everyone is contributing equally to the solution. All such collaboration on homework must be acknowledged, eg: I worked with or received help from (Source Name) on this problem. Such acknowledgments will not count against the paper. Allowing people to copy your work and/or copying someone else's work is not ethical behavior and will be penalized when discovered. See the Student Handbook for the penalties associated with cheating. Use of any sources other than the text, your class notes, your class group work, and yourself is illegal.

7. I will grade almost every proof and a selection of the problems. Proofs are generally worth 5 points and problems are worth 3 points. I will grade as much as I have time to grade; thus the point totals for a week’s homework will vary from week to week.

8. You will do corrections on problems that I indicate. Corrections must be written on separate paper and submitted with the original paper. Corrections are due the class period after the paper is returned. I add at least 0.5 x correction points to the paper’s grade.