This course covers the axioms and the properties of the real number system; sequences of real numbers; sets of real numbers; continuity and uniform continuity of real functions; properties of derivatives of real functions; and the theory of integration on the real line developed by Cauchy and Riemann.
A main objective of the course, essential to mastering the indicated material, is to learn how to apply precise mathematical reasoning in reading, understanding, and writing proofs of theorems in analysis.
Below is some important information about the operation of the course. Also check the tabs at the top of the page for links to other items, such as a course schedule and a list of homework assignments.
The required textbook is Elementary Real Analysis, Second Edition, Part One, by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner, ISBN 978-1434-84161-2. (Math 409 Section 502, taught by another instructor, is using a different book.) The course material is contained in Chapters 1, 2, 4, 5, 7, and 8.
You should be aware that the textbook exists in multiple versions. The two parts are available either combined in a single paperback book or as two separate paperback books. You need only the first part, which is identified on the web either as “Part One” or as “Volume One”. Volume One lists at amazon.com for $17.95 (as of December 2010).
You might happen across a used copy of the hardcover first edition, published in 2001 by Prentice-Hall. Although not preferred, that edition will do, for the authors say that the second edition “differs from the original 2001 version only in that we corrected a number of misprints and other errors.”
You can download Part One for free from the authors' website. (But the pdf version, optimized for a computer screen, is not suitable for printing.)
- The official prerequisites for the course are Math 220 (Foundations of Mathematics) and Math 221 (Several Variable Calculus). The essential background is some prior exposure to writing mathematical proofs (which Math 220 provides).
- The course meets 12:45–2:00 p.m. on Tuesday and Thursday in ZACH 119A.
- Exams and grades
- There will be exams in class on February 22 (Tuesday) and April 12 (Tuesday). The final exam is scheduled for 8:00–10:00 a.m. on May 11 (Wednesday). Each of these three exams counts for 25% of the course grade. Homework counts for the remaining 25% of the course grade.
- Office hours
- During the Spring 2011 semester, my office hour in Milner 202 is 3:00–4:00 p.m. on Monday and Wednesday; I am available also by appointment.
- Help session
- Check /courses/helpsessions.html for information about help sessions operated by the Department of Mathematics.
- Update as of January 25: There is an additional help session for Math 409 meeting Tuesday and Thursday, 2:00–4:00 p.m. in ENPH 201; and Wednesday, 7:00–8:00 p.m. in Blocker 627.