Course:

Advanced Calculus
MATH 321
Fall 2001
MT TF 2:00 Thompson 316

Instructor: Martin Jackson
Office: Thompson 325
Phone: 879-3567
E-mail: martinj@ups.edu

Course Overview and Text

Our goals for this course are

to learn the basic definitions, axioms, and theorems of calculus;
to practice careful reading of mathematics; and
to become proficient in constructing and writing proofs.

Many of the topics in this course are familiar, at least in name, from the introductory calculus sequence: real numbers, sequences, functions, limits, continuity, differentiation, integration. Advanced calculus differs from introductory calculus in the level of rigor. We will strive to prove every theorem starting from definitions and axioms.

Throughout the semester we will hone our skills in reading and writing mathematical proofs. The structure of mathematics is contained in definitions, axioms, theorems, and proofs. ``Doing mathematics'' often culminates in proving a theorem. Proofs in analysis are generally quite different in spirit compared to proofs in algebra. In particular most proofs in analysis involve some use of inequalities. Becoming proficient in analysis requires becoming proficient with inequalities.

The text for this course is Advanced Calculus, Patrick M. Fitzpatrick, (PWS, 1996). Our goal is to cover most of the material contained in the first nine chapters of the text. In pursuing this goal we will generally place the priority on depth over breadth.

Coursework, Grading, and Policies

Coursework will consist of problems, exams, and a course project.

I will assign problems from the text. Of these, you will turn in a select number, about 30 throughout the semester, to be evaluated. The majority of these problems require constructing and writing proofs. You should write a careful, complete, and neat solution for each problem that is turned in.

I will evaluate each submitted problem as acceptable or unacceptable. A problem is acceptable if the argument is valid and presented in a conventional format. If a submitted problem is deemed unacceptable it will be returned for revision and resubmission. If a submitted problem is acceptable, I will assign a score from 7 to 10 on the basis of style and argument. A concise and precise proof will garner more points than a rambling and loose proof.

In order to keep you moving through the course material at a reasonable pace, the semester will be split into three periods with an absolute deadline for problems assigned in each period. Each period will include about ten assigned problems.

For problems assigned through September 20, the last day to submit an attempt is September 28 at 5:00 pm.
For problems assigned from September 21 through October 26, the last day to submit an attempt is November 6 at 5:00 pm.
For problems assigned after October 26, the last day to submit an attempt is December 10 (the Monday of finals week) at 5:00 pm.

The best strategy is to work on problems as they are assigned and to submit attempts at a steady pace. The worst strategy is to submit nothing until the final deadline. In order to provide some pressure to maintain a steady pace, we'll operate under the following rules.

On any given day, you can submit at most three attempts.
I will evaluate and return an attempt by 5:00 pm of the second work day following the day the attempt is submitted. For example, if you submit an attempt on Tuesday, I will evaluate and return it by the 5:00 pm on Thursday.

You should think through the consequences of these rules.

I will designate some of the problems as ``open'' and others as ``individual work only.'' For ``open'' problems, you are free, and encouraged, to work with others in the class. In doing this, you should work out ideas and details together but write final proofs individually. For ``individual work only'' problems, you should consult with no one other than me. For these problems, you must include and sign the following statement: I pledge that I consulted with no living source other than the course instructor in developing and writing this proof.

We will have four exams during the semester. I think of these as ``basic competency'' exams. You will be expected to give accurate statements of important definitions and theorems and to construct straightforward proofs using basic techniques. Exact dates for exams will be announced at least one week in advance. It is possible that the last exam will be during the last week of classes.

The course project will consist of understanding the material and doing selected problems from Sections 5.1 and 5.2. We will not cover this material in class. Problems from the course project will be due Friday, December 14 at 2:00 pm (the scheduled time for the final exam).

To determine course grades, I calculate a total course score according to the following weights:

1. Problems 50%
2. Exams 40%
2. Course project 10%

I assign a preliminary course grade based on an objective standard (93.0-100% for an A, 90.0-92.9% for an A-, 87.0-89.9% for a B+, 83.0-86.9% for a B, etc.). I then look at each student's performance subjectively. Occasionally I will assign a course grade that is higher than the objective standard. For example, if a student has a grade of B according to the objective standard but has shown steady improvement, I might assign a course grade of B+.

Office Hours

I am available in my office for help several hours each day. I am usually in my office during the day in hours at which I do not have a scheduled class, meeting, or other activity. A copy of my schedule is included below. Feel free to come look for me. To be (almost) guaranteed that I will be in, come during one of the hours labeled as an ``office hour.'' You can also call, send e-mail, or stop me after class to schedule an appointment for a specific time.

Schedule

File translated from T_EX by T_TH, version 2.25.
On 6 Sep 2001, 16:38.