MTH 265H "Functions of a Real Variable (Honors)"

Syllabus: The real and complex number systems. Basic topology. Numerical sequences and series. Continuity. Differentiation. Riemann-Stieltjes integral. Sequences and series of functions. (These are Chapters 1-7 of the textbook.)

Prerequisites: MTH163 or MTH164 or MTH200 or MTH174.

Textbook: Walter Rudin, Principles of Mathematical Analysis (3rd Edition), McGraw-Hill, 1976.

Course philosophy:

Apart from being a course in real analysis, this is one of the classes where you will be asked to write an argument in order to solve a problem. Some of you may have experience with this, but we will make sure everyone is comfortable with it by the end of this course. It is not as easy as it sounds.

We will also work on developing your independent reading skills in Mathematics. I certainly won't be able to cover in class all the material you will be required to learn. As a result, you will be expected to do some independent reading. The reading assignments will be on topics to be discussed in the following lecture. This will enable you to ask focused questions in class and to better understand the material.

This course is very challenging and requires a lot of time commitment. Proficiency will be achieved only by hard work and MASSIVE PROBLEM SOLVING. Please take full advantage of my office hours and of the seminar coordinated by Christopher Kauffman, one of the TA's for this class.

Grading: HOMEWORK 30%, MIDTERM 30%, FINAL 40%.

There are NO MAKE-UP EXAMS. If you miss the Midterm, your Final will count as 70% of your grade. If you miss the Final, you are in trouble.

The final grade will not be based on a curve, nor on previously fixed scales for certain grades. It will reflect how well the class is doing, and it will be high if everyone is working hard at the homework and is doing well on the exams. Almost all the questions in the midterm/final will be in the same spirit with the ones discussed/assigned in class.

Incomplete grades:

Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or a genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

Seminar:

There will be a weekly seminar, which is designed to answer questions that you might have regarding applications or theoretical concepts discussed in class. Please come prepared and do not expect that Christopher will solve the problems for you. I will drop by from time to time to see how everybody is doing.

Hours and location: Wednesdays, 6-8pm, Hylan 1104.

Exams:

The MIDTERM EXAM is in class on Wednesday, 10/22, with a review session scheduled for 10/20, also in class. Sample midterms: 1, 2.

The FINAL EXAM is on 12/18, 7:15-10:15pm. There will be two review sessions scheduled for the last lectures in the course, 12/8 and 12/10. It will be mostly on the material covered after the midterm, though there will be some problems on earlier material. Practice problems and sample final.

Homework:

Homework is due on Friday, one week after it was assigned, with two exceptions: the one assigned on 11/21 is due on 12/5, while the last homework, assigned on 12/5, is due on 12/10. There are 11 assignments, from which the best 10 will be counted toward your final grade. Late homework is not accepted.

There will be about 7-8 problems per homework from which 3, arbitrarily chosen, will be graded. Each of these problems is worth 3 points and, for a maximum grade of 10, 1 point will be awarded for substantial efforts on all of the problems from the homework.

Weekly schedule: