Math 508: Advanced Analysis I | Fall 2014 |
---|
Faculty: Jerry L. Kazdan
Telephone: (215) 898-5109
email: kazdan AT math.upenn.edu
Office Hours: Wed. 10:30-11:30 (and by appointment) in DRL 4E15TA: Spencer Tofts, DRL 3E2
Telephone: (215) 898-8175
email: spencertofts AT gmail.com
Office Hours: Mon. and Wed. 4:30-5:30 (and by appointment) in DRL 3E2Text: Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976 (3rd Edition, ISBN:9780070542358.
An electronic version seems to be available online for free.The course will mainly follow the order of topics in the Rudin text.
Solutions to problems in Rudin: In a simple search, I located two sources of solutions to the problems in the Rudin text
Rudin Solutions (Cooke) and Rudin Solutions (Bergman)
Also: (Bergman) Remarks and Errata on Rudin, Rudin: Answers to questions asked by studentsIn Fall 2006, 2008 and 2010 I taught a similar course. See the web pages:
Math 508: Fall 2006, Math 508: Fall 2008, Math 508: Fall 2010,Prerequisites & Review Material
Exams: There will be two in-class exams, from 9:00-10:20 on
You may always use one 3"x5" card with notes on both sides
- Exam 1, Tues. Oct. 14: PDF condensed Solutions
- Exam 2, Tues. Dec. 9: PDF condensed Solutions
- No Final Exam
- Exam Scores
Some References: books, articles, web pages
Note that a Canvas site has been arranged for the course. You may find it useful for communication. Step one is to sign-up.
Notes:
LaTeX: If you will be writing many documents that contain equations, it is wise to learn (and use) LaTeX. It is available on Windows, Macs, and Linux -- and is free. See TeX Stuff. For some students, this might be the most useful item you learn in this course.
Aug 28
Field Axioms
Reals: Archimedean property [LaTeX source]
Notes for Sept. 4, 2014 [LaTeX source]
Some Basic Definitions [LaTeX source] [large]
Some Basic Examples [ LaTeX source] [large]
Relative Topology
Compactness [LaTeX source] [large]
Logic notation: Convergence and Continuity [LaTeX source]
Mobius Strip (Maple 15)
Completeness of l_1
Cobweb Model
Dirichlet's Principle [LaTeX Source] [large]
Compactness and Uniform Continuity [ LaTeX Source]
Taylor's Theorem: Integral Remainder [LaTeX Source] [large]
Differentiation of a limit
Contracting Mappings (K-F) Existence: u'=Au + f ODE Systems Existence: Marsden-Hoffman
Notes on Convolution [large]
Some Puzzles
Homework Assignments: Remark: The difficulty of an exercise is not at all the same as the amount of work it involves. A long series of straightforward manipulations can have a low level of difficulty, but involve a lot of work. In this course the majority of problems will have short solutions -- although it may take real time to think them through.
- Set 0 Due: Thurs., Sept. 4 (Rust Remover. These problems mainly involve only High School mathematics. They will not be collected.)
- Set 1 Due: Tues., Sept. 9. Late papers: accepted until 1:00 PM Wednesday [LaTeX source]
- Set 2 Due: hurss., Sept. 11. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 3 Due: Thurs., Sept. 18. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 4 Due: Thurs., Sept. 25. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 5 Due: Thurs., Oct. 2. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 6 Due: Thurs., Oct. 23. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 7 Due: Thurs., Oct. 30. Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 8 Due: Thurs., Nov. 6 Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 9 Due: Thurs., Nov. 13 Late papers: accepted until 1:00 PM Friday [LaTeX source]
- Set 10 Due: Thurs., Nov. 20 Late papers: accepted until 1:00 PM Friday [LaTeX source]
Solution of Maximal Ideals Bonus Problem- Set 11 Due: Tues., Dec. 2 (lLate papers: accepted until 1:00 PM Wednesday) [LaTeX source]
Solution of hw 11 Bonus #1
Old Exams:
Fall 2010 Exam 1 Fall 2010 Exam 2 [Exam 2 solutions]
Fall 2008 Exam 1   Fall 2008 Exam 2 [solutions]
Fall 2006 Exam 1 [solutions] Fall 2006 Exam 2 [solutions].