- The final exam (for all sections) is on April 21, 7-9:30 PM, in WOOD 2.
- Office hours before the final exam:
- Prof. Khosravi: office hours Friday April 17, 2-3 pm, and a review session
Friday April 17, 3-5 pm, in MATH 104.
- Prof. Laba: Wednesday April 15, 2-3 pm; Friday April 17, 2-3 pm; Monday April 20, 11am - 1 pm
- Solutions to the practice exam for Section 203.
Please note that these are here only because Prof. Rechnitzer forgot to post them before leaving.
The final exam for Sections 201 and 202 will be different (covering only the material that was
covered in our classes).
- The UBC Math Club (MATX 1119) sells study packages with several final exams from recent years with solutions, at nominal price ($10).
- Practice problems for Chapter 10 are posted here. Solutions are
posted below. We have covered Sections 10.1-10.3
in full. From Section 10.4, you need to know how to compare cardinalities of sets (the definition on
page 236: |A| < |B| if there is an injective function A -> B but no bijection). We will be going over
some practice problems for the exam next week (April 7-10).
- Practice problem solutions are now posted.
- Midterm solutions are here: Section 201 (TueTh 11-12:30),
Section 202 (TueTh 2-3:30)
- The midterm exam is scheduled on Tuesday, Feb. 24, in class. It will cover all material
up to (and including) Section 5.2. A practice exam is posted here.
(It consists of midterm and final exam problems from previous years.) Solutions are posted here.
- HW4 solutions are now posted.
- Registration issues: In Mathematics, instructors do not have the authority
to sign up students for courses. If you need assistance with
registration, you should email email@example.com, include your name, student number,
course and section number. Requests are handled and prioritized centrally by the department.
Mathematics 220 (Mathematical Proof), Winter/Spring 2015
Lecture times and locations:
Lecturer: Prof. M. Khosravi (Section 201)
- Section 201: Prof. M. Khosravi, Tue Thu 11:00-12:30, MATX 1100
- Section 202: Prof. I. Laba, Tue Thu 14:00-15:30, LSK 460
- Section 203: Prof. A. Rechnitzer, MWF 12:00-12:50, LSK 201 (CPEN student section)
Lecturer: Prof. I. Laba (Section 202)
- Math Bldg 219, (604) 822 2615, firstname.lastname@example.org
- Office hours: Tue Thu 12:30-1:30
Lecturer: Prof. A. Rechnitzer (Section 203)
- Math Bldg 200, (604) 822 4457, email@example.com
- Office hours: Tue 1-2, Th 3:30-4:30, and by appointment
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.
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 always be accommodated.
- Math Bldg 215, (604) 822 4516, firstname.lastname@example.org
- Office hours: Mon 3-4, Tue 2-4
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 pages:
Information for Sections 201 and 202:
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.
Please that homework problems will be assigned from the 3rd edition of the book.
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%),
the midterm exam (35%), and the final exam (50%). The grades may be slightly
scaled at the end of the course.
There will be one in-class 80-minute midterm scheduled in class on February 24,
and a 2.5 hour final exam in April.
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.
Homework: There will be 7 homework assigmnents, due tentatively on
January 13, January 22, February 3, Februaty 12, March 5, March 17, and March 27.
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 lectures.
To allow for minor illnesses and other emergencies, the lowest homework score will be dropped.
Homework assignments will be posted here.
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]