Real Variables I
UBC Math 320, Autumn 2026 — Philip D. Loewen
MWF 12:00–12:50, room MATX 1100
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 |
|
Lecture 3
Introduction to Dedekind Cuts.
|
2026-09-15
|
| RR |
|
Lecture 2
We discussed Numbers and Mappings to conclude
Chapter I--Foundations.
|
2026-09-15
|
| HW |
2026-09-19,
19:00
|
Assignment 1
Here are the
HW01 Questions.
Please present your responses in a PDF file with
the characteristics anticipated in Assignment 0.
|
2026-09-11
|
| RR |
|
Prerequisites
Here are some notes on
Background Material.
|
2026-09-11
|
| RR |
|
Lecture 1
Here's a quick survey of the
Russell's Paradox and the ZFC Axioms.
|
2026-09-10
|
| HW |
2026-09-12,
19:00
|
Assignment 0
This is an optional calibration exercise, not for marks.
All the details are in the PDF for HW00;
supporting documents include
the LaTeX source for sample solutions,
a supporting graphic file,
and the corresponding output.
|
2026-09-10
|
| LINK |
|
Recommended Video
Where is sqrt(2)?
provides a nice warmup for our work with Dedekind cuts.
Please watch before Monday 2026-09-14.
|
2026-09-10
|
| RR |
|
Past Final Exams
The Math Department's
collection of past
final exams includes a few classics from MATH 320.
|
2026-08-18
|
| 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.
|
2026-08-18
|
Codes:
RR = reading/reference;
PP = practice problems (not to hand in);
HW = homework problems (to be submitted);
LINK = hyperlink to an online resource;
EXAM = midterm or final exam materials.
Details--Autumn 2026
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 2026):
- 09 September (Wed): First class of the term.
- 21 September (Mon): UBC's deadline for registration changes.
- 30 September (Wed): Indigenous Reconciliation Day, UBC Closed.
- 05 October (Mon): 50-minute test in class.
- 12 October (Mon): Thanksgiving Day, UBC Closed.
- 06 November (Fri): 50-minute test in class.
- 09–11 November (Mon-Wed): Autumn Break, no lectures.
- 07 December (Mon): Last class of the term.
- 11–22 December inclusive: Formal examination period.
Grading Formula:
The final exam will count for 60% of the course grade;
the other 40% will come from the in-class tests,
homework, and other activities. (Details still to come.)
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, any document intended for assessment should be formulated and written entirely by the individual submitting it.
In particular,
submissions produced or substantially influenced by Artificial Intelligence tools are not acceptable.
-
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.
-
Please consult the page of
General Syllabus Information
for notes that apply to all MATH_V courses:
essential topics covered include Academic Integrity, Attendance, Deferred Standing, and more.
Last update: 15 Sep 2026 (Tue), 10:27:24.
(Click a graphic to recheck.)
