Real Variables I
UBC Math 320, Autumn 2025 — Philip D. Loewen
MWF 12:00–12:50, room BUCH A203

The official course site is served to registered students only, through UBC's Canvas Learning Management System. Please use the MATH 320 Canvas Page if you can.

The table below provides an informal mirror of some of the resources served through Canvas. The newest additions are at the top.

Code	Due	Details	Updated on ...
RR		Construction of the Real Numbers Here are the Prof's lecture notes for the classroom sessions about Constructing the Reals from Cauchy Sequences.	29 Sep 2025
HW	29 Sep 2025, 03:00	Assignment 3 Solve the problems in the attached PDF. Submissions should come through canvas, in the form of an 8-page PDF document where, for each k, page k contains nothing but the solution to problem number k. Update [2025-09-29]: Here are some Solutions.	29 Sep 2025
RR		Sequences Here are the Prof's lecture notes for the classroom sessions about Sequences.	23 Sep 2025
HW	22 Sep 2025, 03:00	Assignment 2 Solve the problems in the attached PDF. Submissions should come through canvas, in the form of an 8-page PDF document where, for each k, page k contains nothing but the solution to problem number k. Update [2025-09-23]: Here are some Solutions.	23 Sep 2025
HW	15 Sep 2025, 03:00	Assignment 1 Solve the problems in the attached PDF. Submissions should come through canvas, in the form of an 8-page PDF document where, for each k, page k contains nothing but the solution to problem number k. Update [2025-09-18]: Here are some Solutions.	18 Sep 2025
RR		Cardinal Numbers Here are the Prof's lecture notes for sessions 1-6, on Cardinal Numbers.	12 Sep 2025
HW	08 Sep 2025, 03:00	Assignment 0 Our first assignment is optional, easy, and instructive. However, the deadline is short. All the details are in the attached PDF. Professor Loewen endorses the LaTeX system for producing mathematical documents. Here are the Professor's solutions, and a link to the main source file that produces them: m320hw00-sol.tex. One way to finish this assignment and set up for the future would be to get yourself a free account at overleaf.com, figure out how to import a copy of the Prof's source file, make some minor edits to personalize it, and then figure out how to acquire a local copy of the PDF and upload it to Canvas. Good luck! The Prof's solutions show how to embed a graphic file. To use them as provided, you will need to make a copy of the file LoremIpsum.jpg available to the LaTeX system. To do this, download a copy and put it in the same directory (file folder) that contains your copy of m320hw00-sol.tex.	04 Sep 2025
RR		Prerequisites Here's a 3.5-page review of the ideas and notation we will use to describe Sets and Logic.	04 Sep 2025
RR		Syllabus Here's a PDF snapshot of the main MATH 320 page on Canvas.	04 Sep 2025
RR		Past Final Exams The Math Department's collection of past final exams includes a few classics from MATH 320.	29 Aug 2025
LINK		Registration Problems MATH 320 is popular, and full. The instructor is forbidden by Math Department Policy from intervening in any student's registration. On the other hand, the Department has a page called Registration Issues describing what you can do to optimize your chances to secure a place before registration is locked down later this month. Please look there. Make your best case on the Advising Contact Form linked from that page, and submit it.	29 Aug 2025

Codes: RR = reading/reference; PP = practice problems (not to hand in); HW = homework problems (to be submitted); EXAM = midterm or final exam materials.

Details--Autumn 2025

Recommended Texts:

Rudin, Walter, Principles of Mathematical Analysis (Third Edition). Toronto: McGraw-Hill, 1976.
Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner, Elementary Real Analysis (second edition). Online: ClassicalRealAnalysis.com, 2008. Free PDF available.

Other Books:

Irving Kaplansky, Set theory and metric spaces, Boston: Allyn and Bacon, 1972. UBC library call number QA248.K36 1972.
George F. Simmons, Introduction to Topology and Modern Analysis, New York: McGraw-Hill, 1963. UBC library call number QA611.S49 1963.
Michael Spivak, Calculus. Houston: Publish or Perish Press, 1994.

Online Resources:

Andrew Rechnitzer, Notes for MATH 319. (UBC MATH 319 is a majors-level course treating many of the topic we consider in MATH 320. These notes offer a different, sometimes more approachable, perspective that students may find helpful.)
Wikipedia. Honestly!
Philip D. Loewen, MATH 101 Enrichment Videos. This collection of videos intended for MATH 101 students provides a glimpse of the style of reasoning that is typical in MATH 320. The archive lists the most recent item first. Work up from the bottom of the list to view them in chronological order.

Calendar (Autumn 2025):

03 September (Wed)–First class of the term.
15 September (Mon)–UBC's deadline for registration changes.
29 September (Tue)–Indigenous Reconciliation Day, UBC Closed.
13 October (Mon)–Thanksgiving Day, UBC Closed.
17 October (Fri)–Midterm test in class.
10-12 November (Mon-Wed)–Autumn Break, no lectures.
05 December (Wed)–Last class of the term.
09-20 December inclusive–Formal examination period.

Grading Formula:

Term scores will count for 50% of the final grade; the final exam will count for the other 50%. Term scores will be the average of the score on the midterm and the average homework grade. The final exam will last 2.5 hours, and be held at some time during UBC's formal examination period. The homework will be challenging and essential. Grades may be scaled due to the challenging nature of the course material.

Policies:

All tests, including the final examination, will be strictly closed book: no formula sheets or electronic resources will be allowed.
Students are encouraged to discuss the material in person and on Piazza. However, each individual should ultimately hand in a document that expresses their own thoughts and their own words.
The goal of this course is to train human thinkers. If you must use Artificial Intelligence, please make sure that your interactions are strengthening your personal problem-solving and reasoning skills. Expect this to involve confusion, struggle, even frustration, at times. Prioritize building up your own brain over getting the right answer.

Last update: 29 Sep 2025 (Mon), 16:06:15. (Click a graphic to recheck.)

Real Variables I UBC Math 320, Autumn 2025 — Philip D. Loewen MWF 12:00–12:50, room BUCH A203