Math 618 (Phillips)

Course information:

• Course number: Math 618.
• Course title: Real Analysis.
• Canvas site for this course.
• CRN: 33122.
• UO class schedule page for this course.
• Instructor: N. Christopher Phillips.
• Office: 320 Fenton. Please knock. I sometimes don't leave my door open, to keep down distractions.
• Office hours: M 10--10:50 am, Tu 9--9:50 am, W 1--1:50 pm, 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 193 Anstett.
• Textbook: Rudin, Real and Complex Analysis, 3rd edition.
• Official prerequisites: Math 617. (For the complex analysis part, in fact, measure theory can be avoided.)
• The quarter will start with Chapter 9 of Rudin's book, on the Fourier Transform. Then it will go on to Chapter 10 of Rudin's book, on the basics of complex analysis. It will continue with other topics from complex analysis, to be decided. The ones included below are a tentative choice. Projected topics include:
  • Fourier Transform (Chapter 9 of Rudin).
  • 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).
  • 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: Thursday 12 June 2025, 10:15 am--12:15 pm, room 193 Anstett.

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. Just this last quarter, a student printed a homework assignment and all the math symbols came out strangely.

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). It has no problems 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.
• Final exam from Math 618 in Spring 2024, as a pdf file, or as an AMSLaTeX file. This covered only complex analysis. Beyond Chapter 10 in Rudin, it in principle covered the Riemann Mapping Theorem (Chapter 14 of Rudin), Weierstrass factorization and existence of holomorphic functions with prescribed zeros (Chapter 15 of Rudin), some earlier material needed for these, and the proof of the Prime Number Theorem.
• 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 Monday 6 April 2025, as a pdf file.
• Math 618 Homework 2, due Monday 13 April 2025, as a pdf file.
• Math 618 Homework 3, due Monday 20 April 2025, as a pdf file.
• Math 618 Homework 4, due Monday 27 April 2025, as a pdf file.
• Math 618 Homework 5, due Monday 5 May 2025, as a pdf file. (Not yet posted.)
• Math 618 Homework 6, due Monday 12 May 2025, as a pdf file. (Not yet posted.)
• Math 618 Homework 7, due Monday 19 May 2025, as a pdf file. (Not yet posted.)
• Math 618 Homework 8, due Wednesday 29 May 2025, as a pdf file. (Not yet posted.)
• Math 618 Homework 9, due Wednesday 4 June 2025, as a pdf file. (Not yet posted.)

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 30 March 2025. (Addition of homework assignments and solutions is not considered "significant".)