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

Syllabus: the real and complex number systems, basic topology, numerical sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, sequences and series of functions.

Prerequisites: MTH 172 or MTH 200.

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

Apart from the textbook, the following problem books will be on reserve at the Carlson Library reserve collection:

• "Problems in mathematical analysis" (vol. 1-3) by Kaczor and Nowak.

Course philosophy: This course serves an introduction to real analysis, which is nothing but the theory of calculus. It will contain all the information, pertinent to the subject, that is considered to be essential for the education of an honor math major. Moreover, this is a class which is heavily based on writing proofs. If you do not have familiarity with this, then you will have a hard time in this course. We will also work on developing independent reading skills, as reading assignments will be assigned weekly.

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 Evan Witz (ewitz@ur.rochester.edu), the teaching assistant for this class.

Grading: Homework 30%, Midterm 30%, Final 40%.

Homework

There will be about 10 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 homework problems.

Exams

The Final is scheduled for Monday, 12/17, 19:15-22:15, in 2110D Dewey Hall. It will be mostly on the material covered after the midterm, though there may be some problems on material pertinent to the midterm. Sample finals: Fall 2007, Fall 2008, Fall 2012. Here is also a list of practice problems for the final: Practice.

Seminar

There will be a weekly seminar which is designed to answer questions that you might have regarding the problems in the homework and/or the concepts discussed in class. The first meeting is on 9/11.

Hours and location TBA.

Course policies

1. The course average is not based on a curve, nor on previously fixed scales. It will reflect how well the class is doing, and it will be high if everyone is working hard for the homework and is performing well on the exams.

2. 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.

3. If you miss a midterm exam with a valid excuse (e.g., illness or emergency), you must notify the instructor and provide supporting documentation verifying your excuse as soon as possible. For a valid excuse with supporting documentation, the Final will count as your make-up test. If you miss the Final, you are in trouble. No make-up exams will be given for any reason. If you miss an exam without a valid excuse (and supporting documentation), you will receive a score of 0 on that test.

4. You are responsible for knowing and abiding by the University of Rochester's academic honesty policy. Any violation of academic honesty will be pursued according to the specified procedures.

Weekly schedule:

Please check the website frequently for updates.