Advanced Calculus I
- Course description
This three-credit 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.
- Course objective
A main goal 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.
The required textbook is Elementary Real Analysis, Second Edition (2008), Volume One, by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner. The course material is contained in Chapters 1, 2, 4, 5, 7, and 8.
The authors have kindly made the book available for free download. You can buy a paperback hard copy if you prefer to read on paper. There are links at the authors' website to purchase the book from either Amazon or CreateSpace.
The list price for Volume One is $17.95.
- The authors maintain an online list of errata for the second edition.
- (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.”)
The prerequisites for this 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).
- Meeting time and place
The course meets in room
163 111 of the Blocker building on Tuesdays and Thursdays from 11:10 to 12:25.
The first class meeting is on Tuesday, January 19. The
last class meeting is on
Thursday, April 28, because the final class day of the semester
(Tuesday, May 3) is a redefined day on which students attend their Friday classes.
- Exams and grades
There will be examinations in class on February 23 (Tuesday) and April 12 (Tuesday). The final examination takes place on Thursday, May 5, from 3:00 to 5:00 in the afternoon.
Each of these three exams counts for 25% of the course grade. Homework/classwork counts for the remaining 25% of the course grade.
Course letter grades are based on the standard scale (60% is passing, 70% or higher earns a C, 80% or higher earns a B, 90% or higher earns an A).
- Course website
- Office hours
During the Spring 2016 semester, my office hour in Blocker 601L
is on Monday and Wednesday afternoons from 2:00 to 3:00; I am
available also by appointment.
The best way to contact me is via email to firstname.lastname@example.org. Telephone messages can be left at the Department of Mathematics, 979-845-7554.
- Help sessions
For Section 200 (the honors section of Math 409), there is a dedicated Honors Mentor who will hold walk-in help sessions in Blocker 602 on Monday and Wednesday afternoons from 3:00 to 5:30, starting on January 20.
- Additionally, there is a general Math 409 help session starting the second week of classes.
Check http://www.math.tamu.edu/courses/helpsessions.html for the schedule and room.