Math 171 - Fundamental Concepts of Analysis - Spring 2013

Homepage http://math.stanford.edu/~galatius/171F13/

Classes TTh 9:30 - 10:45 in Littlefield 107
Instructor Soren Galatius
Office 383-DD
e-mail galatius@stanford.edu
Office hours Wednesday 9:30--11
Course Assistant Shotaro Makisumi
Office 380-U1
e-mail makisumi@math.stanford.edu
Office hours Mo 2:30-4PM, 5-6:30PM

Textbook Foundations of Mathematical Analysis, by Johnsonbaugh and Pfaffenberger.

About the class. Math 171 is Stanford's honors analysis class and will have a strong emphasis on rigor and proofs. The class will take an abstract approach, especially around metric spaces and related concepts.

For some students, Math 115 will be a suitable alternative to 171. The two classes cover similar material, but 171 will be more fast-paced and have a more abstract and proof-based flavor. If you are in doubt which of the two classes is more appropriate for you, you should come and talk to me as early as possible (and certainly before the drop deadline, which is April 19th). Math 171 is required for honors majors, and satisfies the WIM requirement.

Topics. The class will cover approximately chapters I-X of the book. A more detailed lecture plan (updated after each lecture) is here. The topics will fall under the following three headlines.

Writing in the Major. Writing is an important part of mathematics, and the WIM assignment is an important part of this class. A draft of your text will be due May 17th, the final text will be due May 30th. More information here.

Exams
Midterm In-class 5/2. Open book, open notes.
Final6/11, 12:15PM - 3:15PM in 380-380X (note: this is in the math department, not the same room as the lectures.) Open book, open notes.

Grades Homework 25%, WIM assignment 15%, Midterm 25%, Final exam 35%.

Homework is due each week. You may discuss the problems with each other, but you must work alone when you write up your solutions. Late homework will not be accepted, but the lowest scoring problem set will be dropped. JB refers to problems in the book.
Due date Problems
4/11JP 5.4, 5.5, 9.11, 16.8 (bonus question: explain why any proof of this must use the supremum property), 18.1, 18.4, 20.12, and these exercises. Solutions.
4/18JP 20.10, 23.1, 23.4, 24.5, 26.9 (bonus question: discuss what happens if an = 9 for all n), 27.1 ((a)+(d)), and these exercises. Solutions.
4/25JP 35.1, 35.2, 35.5, 35.6, 35.9, 37.2, 37.3, 40.11 and these exercises. Solutions.
5/2In-class midterm. No homework due, but here are some practice problems. Solutions to the midterm.
5/934.4, 34.6, 40.12, 40.17, 41.3, 41.5, 42.1, 42.2, and these exercises. Solutions.
5/16 (Half weight, due to WIM draft) 37.11, 43.4, 43.6, this exercise. Solutions.
5/23 42.12, 44.7, 46.1, 46.5, 46.10, 46.11, these exercises. Solutions.
5/30 these exercises. Solutions.
not due some practice problems. (Updated 6/6 9:30pm. Might be further updated.)