Math 220, WT1 2016

The main webpage for all sections of Math 220 is here. That webpage, maintained by our Instructor in Charge, Jingyi Chen, is where you will find homework, solutions, syllabus, and announcements.

Contact Me

If you need to get ahold of me, the best way is through email: My office is in the Mathematics Building (behind the Koerner library), room 229F.

Office Hours

Wednesday, December 7th, 11am-1pm
Thursday and Friday, 15-16 December, noon-3pm

Exam Stuff

Selected problems from old exams
Hand-written notes from class, Wednesday 30 November 2016
Hand-written notes from class, Friday 02 December 2016
Long-answer problems from past four exams, sorted by topic: click on the subject in the table of contents to go to the corresponding page.

Midterm: Monday, October 17th, in class.
Topics up to and including Section 7.1.
Midterm practice questions from old midterms. Prepared by Julia Gordon (Thanks, Julia!)
Solutions to the review materials for Midterm 1 are available on the main course webpage.
Comments on midterm.


Section(s) Dates File Topics
Sept 7 Introduction.pdf Course description and resources
1.1-1.4 Sept 7 - 12 1Sets.pdf Introduction to sets, with definitions and notation; Cartesian products of sets; subsets; power sets.
1.5-1.8 Sept 12-14 2Sets.pdf Union, intersection, difference, and compliment of sets; Venn diagrams; union and intersection of indexed sets.
2.1-2.7 Sept 16-26 3Logic.pdf Statements, logical conjunctions, equivalence and quantifiers.
Extra notes on negating multiply quantified statements, courtesy of Julia Gordon.
Common mistakes from HW3
4.1-4.5 Sept 26-30 4Proofs.pdf Direct proof.
Overhead notes from Sept 30: proving propositions with cases.
5.1-5.2 Oct 3 5ContrapositiveProofs.pdf Proof by contraposition, modular arithmetic. ("Mathematical writing" is not in the course outline.)
Common mistakes from HW4
6.1-6.3 Oct 5-7 6Contradiction.pdf Proof by contradiction.
7.1-7.4 Oct 12-19 7Nonconditional.pdf Proving if-and-only-if statements, equivalent statements, proving existence (with or without uniqueness),
and the difference between constructive and non-constructive proofs.
8.1-8.4 Oct 21-24 8SetProofs.pdf Proving one set is contained in another, or two sets are equal
perfect numbers
9.1-9.3 Oct 24-26 9Disproof.pdf Proving negations of statements
10.0-10.2 Oct 28-Nov 4 10Induction.pdf Induction, strong induction, and
using the smallest counterexample to prove by contradiction.
11.0-11.5 Nov 4 - Nov 7 11Relations.pdf Relations in general, and equivalence relations in particular
Integers modulo n, relations between sets
12.1-12.6 Nov 7 - Nov 18 12Functions.pdf Functions as relations, injectivity and surjectivity,
Pigeonhole principle, composition, inverse, related vocabulary
13.1-13.3 Nov 21 - Nov 25 13Cardinality.pdf Cardinalities of sets; sizes of infinity
3.1-3.4 Nov 25 - Nov 28 3Counting.pdf Counting: lists, factorials, subsets, Pascal's Triangle and the binomial theroem
This content will not be included in the final exam

LaTeX Resources

LaTeX is a language for writing mathematics very cleanly. You type in some code, and compile a pdf. Unfortunately, this means you sometimes have to de-bug a paper. However, LaTeX provides you with a way of neatly and consistently writing highly legible and standard-looking documents.

You are highly encouraged to use LaTeX to type your homework, but it is not required.

You'll need to install two things to write LaTeX on your computer: a TeX distribution, and an editor. Articles about installation can be found for Windows, Macintosh, and Linux. To typeset LaTeX without installing anything, try TeXonWeb, Share LaTeX, or find an equivalent online program.

Googling around will give you more information that you could hope to use about LaTeX. Here's a video that gets you started from the very beginning, and here's a list of resources for beginners. Julia Gordon, who also teaches Math 220, has a list of resources here.

For the clarity of a LaTeX paper, without learning any code, you can also try LyX.

A large part of learning code is looking at what other peope have written. Provided for you is an extremely basic template for Homework 1, and a slightlier fancier version, based on a template by Prof. Andrew Rechnitzer.

If you'd like to see how I wrote something on my slides, take a look at the source files: 1Sets.tex, 2Sets.tex, 3Logic.tex, 4Proofs.tex, 5ContrapositiveProofs.tex, 6Contradiction.tex , 7Nonconditional.tex , 8SetProofs.tex, 9Disproof.tex, 10Induction.tex, 11Relations.tex, 12Functions.tex, 13Cardinality.tex, or 3Counting.tex. (I might not be updating these source files, so they might diverge slightly from the pdfs listed above.)

If at least half of your assignments are typeset in LaTeX, you will get 1% added to your final mark. You do not have to use LaTeX for pictures to get this mark--you can leave space and draw them in by hand, or use another program to generate digital images that you include in your otherwise-TeX'd homework.

Getting Help

University is meant to challenge you. However, if you find yourself struggling, I hope you'll take advantage of some of the resources available to you on campus.

Help with Registration

If you have problems registering in a math course, please find the appropriate math advisor.

If you have questions related to your major, like which flavour of calculus you should be taking, OR if you have a major life event that might prevent you from completing the semester, you should talk to your faculty advisor.

Help with Course Content

It's good for your brain to work hard! But if you find yourself feeling overwhelmed, please do take advantage of some of these marvellous resources available to you.

Help with Other Issues

Student Services at UBC has a variety of programs to help you stay happy and healthy. A good place to start is here: LiveWell

UBC provides services to address, among other things: illness and injury, mental health and wellbeing, sexual assault (for people of all genders), other violence, discrimination and harrassment, diversity, disability, and ongoing medical considerations. If you have legal issues, you might be able to get help from the Law Students' Legal Advice Program. The Office of Equity and Inclusion is a good place to go if you want more information about maintaining an environment that is respectful, especially with regards to interculturality, LGBT*QIA status, race, students who are parents, etc. The Office of Access and Diversity provides disability support.

If something comes up during the semester that interferes with your academic progress (such as an illness, or caring for a loved one) contact your faculty advising office as soon as possible. You can find them here.

The province has an excellent website with information on mental health, including an online screening tool and resources: Here To Help. The Vancouver Access & Assessment Centre (AAC) is a point of entry for concerns about mental health and substance abuse, and they also have a call line if you just want to talk to someone. The BC Crisis Centre also has phone services for someone to talk to if you are in crisis.

Education is a tool for a better life, from increased earning potential to a heightened appreciation for the beauty and complexity in the world. Your real life extends far beyond the boundaries of this campus. It's important that you don't let your education interfere with your physical or emotional health.

Addressing Issues with the Course

Full disclosure: I'm not a perfect instructor. If there's something about this course that bothers you, I'd like the chance to address it. You can contact me in person after class or during office hours, or write me an email. If you are uncomfortable discussing it with me, you can talk to the Instructor in Charge, Professor Jingyi Chen:

If it isn't feasible to change the thing that's bothering you, we still might be able to come up with strategies for addressing it. At the very least, you can get an explanation of why things are the way they are.

See you in class!