Math 301: Real Analysis

Spring 2003

General Information

Instructor: Margaret Robinson

• Office: Clapp 402A
• Telephone x2394 (with answering machine)
• email: robinson (This is the fastest way to get in touch with me.)
• Office hours: MWF 1-2

Class Meetings: MWF 9-9:50, Clapp 401; TH 10-10:50 Clapp 422.

Text: Elementary Analysis: The Theory of Calculus, Kenneth Ross

Topics covered in this course: The real number system, convergence of sequences and series, power series, uniform convergence, compactness and connectedness, continuity, abstract treatment of differential and integral calculus, and metric spaces. We will go through the whole of Ross' book and also cover additional material on metric spaces and topology.

Homework: Homework will be assigned weekly to be due the following week. Graded homework can be picked up from the envelope outside my office or in class. Homework can be redone and handed in again, if done promptly (i.e. within a week of getting it back). I reserve the right not to accept redone homework that is too late. You may want to set up a weekly homework session to work on the problem sets in the evening as a group. I will try to come to some of them.

Homework is extremely important in this class. One of the most important things you can learn in mathematics is how to tell when you understand and when you do not. Homework, discussing mathematics with others, and the quizzes are your only way of telling if you understand the material before the exams. I want you to work together on the homework; when you explain your ideas to one another you will learn the mathematics well. BUT if you COPY the solutions from others you will not learn the material. You must write up the problems on your own. I will be reading/grading all the homework assignments and I will speak to you if your write ups are not independently done. Copying is of course a breach of the honor code.

Tests and Quizzes: On most Thursdays, we will have book work quizzes on the most important theorems and definitions of the last week. There will be two tests, and a self-scheduled or take-home final examination. If you are unable to take a test for any reason, you should contact me well before the test. (You can email me at robinson any time of the day or night.)

Grading: The homework and class participation make up 20%, Quizzes make up 25% of your grade, each test is 15%, and the final examination is 25%.

I expect everyone to present homework problems to the class. Everyone will also present a theorem to me and to the class if there is time. By the end of class everyone should know the statements and proofs of the following theorems:

• Bounded monotone sequences converge.
• Convergent sequences are Cauchy sequences.
• The Bolzano-Weierstrass theorem.
• Absolutely convergent series converge conditionally.
• The Heine-Borel theorem.
• Continuous functions on a closed interval attain their maximum.
• The intermediate value theorem.
• The uniform limit of continuous functions is continuous.
• Rolle's theorem and the mean value theorem.
• A monotone function on the interval [a,b] is Riemann integrable on [a,b].
• The fundamental theorem of Calculus.

Web sites to become familiar with:

• Women in Mathematics
  • Women in Mathematics
    • Women in Mathematics
    • History of Mathematics