INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: 624-0355
E-MAIL ADDRESS: voronov@umn.edu. You are welcome to use e-mail to send questions to me.
INTERNET: All class announcements and assignments will be posted on the class homepage http://www.math.umn.edu/~voronov/5615f04/index.html and NOT handed out in class.
OFFICE HOURS: Wed 11-noon, Thu 1:25-2:15 p.m., Fri 1:30-2:25 p.m., and by appointment.
TEXT: The Way of Analysis by Robert S. Strichartz, revised edition, 2000. You may also find useful to use Walter Rudin's text Principles of Mathematical Analysis. Both texts are on two-hour reserve in the Math Library on third floor of Vincent Hall.
GOALS AND PREREQUISITES: This is the first course of "analysis with proofs." The goal of the course is to learn real mathematics by providing rigorous foundation to topics most of which you have seen in freshman Calculus. You have to have passed Math 5615H or a similar class before taking 5616H.
CONTENT: In the Fall semester, we have studied countability, the real number system, the topology of the real line, continuity, derivatives, the intermediate value theorem, the Riemann integral, sequences and series of functions, term-by-term differentiation and integration, power series, uniform convergence. This basically covered Chapters 1-7 of the textbook.
In the Spring semester we will finish Chapter 7 (approximation and equicontinuity), cover Chapters 8-10 (transcendental functions, euclidean and metric spaces, differentiation in R^n), selections from Chapters 12 (Fourier series) and 13 (implicit functions, curves and surfaces), and then Chapters 14 (the Lebesgue integral) and 15 (integration in R^n).
GETTING HELP:
HOUR TESTS: There will be two one-hour tests: Friday, February 25, and Friday, April 8. If you miss an hour test, your grade on it will be determined by the final exam, prorated to 100 points.
FINAL EXAM: The final exam will be given in our regular classroom VinH 113 at 1:30pm - 3:30pm Thursday, May 12.
HOMEWORK: There will be weekly problem sets assigned to be turned in. A few problems from each set will be selected at random and graded. You are expected to do your homework regularly during the week (I recommend at least three times a week) and hand it in in the beginning of each Friday class, except the first week of classes and the test weeks. The test weeks' homework will be assigned, but not collected. Getting together with other students (that is, in study groups) is a very efficient way to do homework and get ready for the tests (and also have fun and pizza).
Assignments handed in late will get a 10% penalty per any fraction of a day after 1:30 p.m. on the due day. The maximum penalty is limited to 50%.
GRADING: Based on two hour tests (100 points each), problem sets (100 points total), and final exam (200 points). Grades will be assigned on curve.
IMPORTANT DATES:
January 18 - Spring semester classes begin.
January 25 - Last day to drop a course and receive a 100% refund.
January 31 - Last day to drop a course with no grade reported.
February 25 - First midterm exam.
March 14-18 - Spring break.
April 8 - Second midterm exam.
May 6 - Last day of instruction.
May 12 - Final exam.