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