Mathematics 220 (Mathematical Proof), Fall 2013
Lecture times and locations:
Lecturer: Prof. I. Laba (Section 101)
- Section 101: Prof. I. Laba, MWF 12:00-12:50, MATX 1100
- Section 102: Prof. A. Nachmias, MWF 12:00-12:50, Buchanan B313
Lecturer: Prof. A. Nachmias (Section 102)
- Math Bldg 200, (604) 822 4457, email@example.com
- Office hours: Monday 2-3, Wednesday 1-2, Friday 11-12, in MATH 200. (This is a preliminary schedule and may change later.)
- If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance.
Drop-ins and same-day requests for appointments cannot usually be accommodated.
The best way to contact instructors is by email. Please note that email received on evenings and weekends
will be answered on the next business day.
- Math Annex 1220, (604) 822 6609, firstname.lastname@example.org
- Office hours: Monday 3-4, Wednesday 10-11, and by appointment, in MATX 1220.
Either (a) a score of 64% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001
or (b) one of MATH 121, MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.
Course web page: http://www.math.ubc.ca/~ilaba/teaching/math220_F2013
Homework assignments are posted here.
Workshop problems with solutions are posted here.
Textbook: Gary Chartrand, Albert D. Polimeni and Ping Zhang:
"Mathematical Proofs - A Transition to Advanced Mathematics",
3rd ed., Pearson / Addison Wesley, 2013. ISBN 978-0-321-79709-4.
Course goals: To learn how to construct and write mathematical proofs, with
strong emphasis on clarity and mathematical rigour. Specific topics will include:
This list is somewhat provisional and may be adjusted as needed.
- Sets: definitions, set operations (Chapter 1)
- Logic: logical connectives, quantifiers (Chapter 2)
- Proofs: direct and contrapositive (Chapters 3 and 4)
- Proofs: existence and contradiction (Chapter 5)
- Induction (Chapter 6)
- Equivalence relations (if time allows; Chapter 8)
- Functions: injective, surjective, bijective, inverses and compositions (Chapter 9)
- Cardinality of sets: finite sets and different types of infinite sets (Chapter 10)
- Elementary real analysis - limits of sequences and series, concept of supremums (if time allows; Chapter 12)
Your course mark will be based on homework (15%), workshop participation (5%),
the midterm exam (30%), and the final exam (50%). The grades may be slightly
scaled at the end of the course.
There will be one in-class 50-minute midterm scheduled on Monday, October 21,
and a 2.5 hour final exam in December.
The date of the final examination will be announced by the Registar later
in the term.
Attendance at the final examination is required, so be careful about
making other committments (such as travel) before this date is confirmed.
All examinations will be strictly closed-book:
no formula sheets, calculators, or other aids will be allowed.
Homeworks: There will be 5 homework assigmnents, due tentatively on
September 16, September 30, October 11, November 4 and November 18.
Each homework will be announced and posted here at least a week in advance.
The homeworks are to be handed in at the beginning of class.
If you cannot come to class, you may drop off your homework at your instructor's office prior to the start of class.
Late assignments will not be accepted.
Solutions will be posted on the course webpage immediately after the lecture.
To allow for minor illnesses and other emergencies, the lowest homework score will be dropped.
Workshops: Every other week, there will be an in-class workshop led by Dr. Sandra Merchant, Science
Teaching and Learning Fellow at UBC, and your instructor. The workshop schedule is as follows:
At the end of each workshop,
there will be a short 10-minute quiz based on that workshop's problems. Your workshop participation mark will be based on these quizzes. As with homeworks, the lowest quiz score will be dropped.
- Section 101: Fridays, September 13 and 27, October 11, November 1, 15 and 29
- Section 102: Wednesdays, September 11 and 25, October 9 and 30, November 13 and 27
Academic concession: Missing the midterm, or handing in a homework
after the deadline, will result in a mark of 0.
Exceptions may be granted in two cases: prior consent of the
instructor, or a documented medical reason.
Your course mark will then be based on your remaining coursework.
Additional course related resources:
- Tim Gowers has a series of blog posts on mathematical logic. Highly recommended as supplementary reading for Chapter 2. (Update: the link has been fixed to point only
to the subcategory of posts on logic, not to the larger "teaching" category.)
See in particular:
- Robert Talbert's videos on set theory,
logic and proof techniques. They are paired with a different textbook, but cover roughly the same material
as this course and are identified by topic, so you should have no trouble finding the videos you need.
- "Dangerous Knowledge", a BBC documentary featuring the mathematicians Georg Cantor, Ludwig Boltzmann, Kurt Godel, and Alan Turing.
The first part talks about Cantor and his discovery of infinities of different sizes, something that
we plan to cover near the end of the course. The documentary is a bit overwrought and sensationalized at times, but
it does a good job conveying both the general thrust of Cantor's work and the impact it had on the development of mathematics.
- Please read the UBC
policy on Student Conduct and Discipline.
- Mathematics Learning Centre:
The Math Department runs a drop-in tutorial centre for undergraduate
Math courses, staffed by Graduate Teaching Assistants. This centre is
located in Rooms 300, 301, and 302 in the Leonard S. Klinck (LSK)
Building, and is open Monday through Friday, 9:00am to 7:00pm. Check
the website above for any changes to hours and announcements. All
tutors provide assistance with first- and second-year calculus and
linear algebra and will attempt to help with any undergraduate Math
course. In addition to regular assistance, the MLC offers Quick Help
for students who are looking for fast support for minor snags. There
is no charge for the services MLC provides.
Past final exam database
- UBC Math Club,
located in Math Annex 1119, sells
math exam packages (old exams together with solution sets)
for a nominal price before each final exam session.
[University of British Columbia]