## Math 115: Functions of a Real Variable

Spring 2011

**Announcements**: The course is over. Thanks to all, and have a great summer!

● ● ● ● ● ● ● ● ● ● ● ●**Time and location**: TTh 2:15-3:30, room 380-380W

**Professor**: Tai-Ping Liu, liu at math dot stanford dot edu

Office hours: M 4-6, W 3-4, room 380-382V

**Course Assistant**: Dan Jerison, jerison at stanford dot edu

Office hours: M 1:30-3:30, T 4-6, W 12-2, room 380-381A

**Textbook**: *Elementary Analysis: The Theory of Calculus*, by Kenneth Ross

**Official description**: The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Honors math majors and students who intend to do graduate work in mathematics should take 171. Prerequisite: 51.

● ● ● ● ● ● ● ● ● ● ● ●**Resources**: If you're not sure how to do a homework problem or you don't fully understand a new concept, we can help. Come to office hours or ask questions via email. In case you can't come to the scheduled office hours, email to set up an appointment at a better time. Alternatively, the Center for Teaching and Learning offers free tutoring for undergraduate Math 115 students; visit http://tutoring.stanford.edu/.

This is a proof-based course. It may take you some time to get acquainted with the style of proofs. Here are some helpful remarks on the subject written by a former CA.

**Grading policy**: Homework 35%, Midterm 25%, Final 40%.

Honor Code and Fundamental Standard

● ● ● ● ● ● ● ● ● ● ● ●**Homework**: Due in class on Thursdays unless otherwise specified.

HW #1: Due Thursday 4/7. Exercises 4.1, 4.3, 4.4 (ehkw for these), 4.9, 4.14, 8.1(a), 8.2(e), 8.3, 8.8(a). Solutions.

HW #2: Due Thursday 4/14. Exercises 9.1, 9.3, 9.11, 10.1, 10.6, 10.11, 11.3(bcd). Solutions.

HW #3: Due Thursday 4/21. Exercises 17.3(ab), 17.4, 17.9(ac), 19.1, 19.2, 19.8. Solutions.

HW #4: Due Thursday 4/28. Exercises 18.2, 18.5, 18.6, 18.7. Solutions.

HW #5: Due Thursday 5/12. Exercises 28.2, 28.4(bc), 28.9, 29.3, 29.12, 32.2, 32.8. Solutions.

HW #6: Due Thursday 5/19. Exercises 33.1, 33.3, 33.4, 33.10, 33.11. Solutions.

HW #7: Due Thursday 5/26. Exercises 23.2(ab), 24.9, 34.3, 34.5, 34.6. Solutions.

**Exams**: The midterm took place on Tuesday, May 3. The average score was 37/50. Exam. Exam with solutions.

The final took place on Tuesday, May 31. The average score was 72/90.