Math 618 (Phillips)

Course information:

• Course number: Math 618.
• Course title: Real Analysis.
• Canvas site for this course.
• CRN: 32843.
• UO class schedule page for this course.
• Instructor: N. Christopher Phillips.
• Office: 320 Fenton. Please knock. I don't leave my door open, to keep down distractions.
• Office hours: MW 1:00--1:50 pm, F 10:00--10:50, or by appointment.
• Email. All messages should have a subject starting "Math 618:". I do not accept binary files or attachments, except by prior arrangement. I do not ever accept Microsoft Word documents, html (web) files, or encoded text messages. Please send 7 bit ASCII plain text only.
• Time and place: MWF 9:00-9:50 am, room 347 McKenzie.
• Textbook: Rudin, Real and Complex Analysis, 3rd edition.
• Official prerequisites: Math 617. (In fact, measure theory can be avoided.)
• The quarter will start with Chapter 10 of Rudin's book, on the basics of complex analysis. Projected topics include:
  • Cauchy's Theorem (Chapter 10 of Rudin).
  • Cauchy's Formula (Chapter 10 of Rudin).
  • Power series (Chapter 10 of Rudin).
  • Liouville's Theorem (Chapter 10 of Rudin).
  • Maximum Modulus Theorem (Chapter 10 of Rudin).
  • Open Mapping Theorem (the one in complex analysis, not the one about linear maps between Banach spaces) (Chapter 10 of Rudin).
  • Residue Theorem (Chapter 10 of Rudin).
  • The Riemann Mapping Theorem (Chapter 14 of Rudin).
  • Weierstrass factorization and existence of holomorphic functions with prescribed zeros (Chapter 15 of Rudin).
  • A proof of the Prime Number Theorem (Newman's proof, Donald J. Newman, "Simple analytic proof of the prime number theorem," Amer. Math. Monthly 87 (1980), no. 9, 693--696.
• Finals week office hours: To be announced.
• Final Exam: Wednesday 12 June 2024, 10:15 am--12:15 pm, room 347 McKenzie.

Course files. See the comments on the different formats for more information on the formats of files posted below. One warning is important enough to give here: In the spring quarter 1998, somebody printed some of my pdf files somewhere on campus and found that certain mathematical symbols (such as minus signs in exponents) did not print, damaging the meanings.

Material on TeX coding; on readable mathematics. Both are plain text files, written to be sent in email and intended to be displayed using a fixed width font. I am happy to take comments and suggestions for either of them. In particular, what I say about TeX has been picked up from miscellaneous souces over many years, and does not come from any systematic study. For readable mathematics, as the file suggests, start with "Some Hints on Mathematical Style", by David Goss (not the origoinal location, which is gone) and "Some Remarks on Writing Mathematical Proofs" by John M. Lee. I have only a little to add to this--for now, just a few topics.

Material related to exams.

• Final exam from Math 618 in Spring 2010, as a pdf file, or as an AMSLaTeX file. Most of it is on Chapter 10 of Rudin, but there are two plus epsilon problems involving Fourier transforms (1c, 3, and 6). I don't have an old final exam covering anything beyond Chapter 10 of Rudin.
• Solutions to the final exam from Math 618 in Spring 2010, as a pdf file, or as an AMSLaTeX file.

Homework. Problems are worth 10 points each, unless otherwise specified.

• Math 618 Homework 1, due Wednesday 10 April 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 1, as a pdf file, or as an AMSLaTeX file.
• Math 618 Homework 2, due Wednesday 17 April 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 2, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Changes since the last version of the solutions to Homework 2: difference file (pdf); AMSLaTeX; reverse difference file (pdf); AMSLaTeX. The difference file has new text wavy underlined in blue and old text crossed out in red; the reverse difference file reverses the color scheme. Some marked changes only reflect improvements in the TeX code. The correction to the definition of Omega near the bottom of page 4 is not shown correctly. More information.
• Math 618 Homework 3, due Wednesday 24 April 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 3, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Changes since the last version of the solutions: difference file (pdf); AMSLaTeX; reverse difference file (pdf); AMSLaTeX. The difference file has new text wavy underlined in blue and old text crossed out in red; the reverse difference file reverses the color scheme. Some marked changes only reflect improvements in the TeX code. The correction to the definition of Z in Proposition 1 is not shown correctly. More information.
• Math 618 Homework 4, due Wednesday 1 May 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 4, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Math 618 Homework 5, due Wednesday 8 May 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 5, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Changes since the last version of the solutions: difference file (pdf); AMSLaTeX; reverse difference file (pdf); AMSLaTeX. The difference file has new text wavy underlined in blue and old text crossed out in red; the reverse difference file reverses the color scheme. More information.
• Math 618 Homework 6, due Wednesday 15 May 2024, as a pdf file. As an AMSLaTeX file. (Problem 2 has been rewritten, but its content is the same.)
• Solutions to Math 618 Homework 6, not complete and not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Math 618 Homework 7, due Wednesday 22 May 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 7, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Math 618 Homework 8, due Monday 3 June 2024, as a pdf file. As an AMSLaTeX file.
• Solutions to Math 618 Homework 8, not carefully proofread, as a pdf file, or as an AMSLaTeX file.
• Math 618 Homework 9, due Monday 10 June 2024, as a pdf file.

This page maintained by N. Christopher Phillips, email.

When emailing me, please use 7 bit ASCII plain text only. In particular:

• No binary files or attachments (except by prior arrangement).
• No Microsoft Word files. I do not accept these under any circumstances, since I don't have software that reads them. If you really want to send something in a word processor format, use TeX.
• No html encoded messages.
• No mime encoding or other encoding of ordinary text messages.

Last significant change 4 April 2024.