MATH 220: Mathematical Proof, Section 201, Winter term II, 2015/2016.
Instructor: Julia Gordon.
Where and when : TTh 11-12:30, in MATX 1101.
My office: Math 217.
e-mail: gor at math dot ubc dot ca
Office hours: Due to a variable schedule of the other course I am
teaching, the office hours will be different every week. Please see the
"Announcements" section below; they will also be announced by e-mail at
the beginning of each week. I am also somewhat available by appointment --
please e-mail well in advance though.
Text: Mathematical proofs, a transition to advanced mathematics, by G.
Chartland, A. Polimeni, P. Zhang, Second or third edition.
The common website.
The marking scheme, and all the course policies are found here.
Homework and quizzes
- All homework assignments will be posted
and will be due in class on Tuesdays.
- You are strongly encouraged (and will receive a 2 points bonus at the end of the term if you do it) to type all your homework solutions using LaTeX.
Here are some LaTeX
- Every other Thursday, the classes will be organized as workshops in
students in small groups will work problems. There will be a short quiz at the end.
- Tips for
authors by James Milne .
Please consider these before writing homework (even though these are the
tips for authors of mathematical papers). These will become more relevant
as the course progresses.
- Office hours the second week of February: Wednesday Feb 10, 10-11am,
and Thursday Feb 11,
- The alternate midterm is on Wednesday February 10, 8:30-9:50am in
(Approximate) Course outline.
Here I will post short summaries of each class and other
relevant to our secion notes, as we go along.
- Tuesday, January 5:
A few words about the course (please read the Preface and Chapter 0!); Introduction to sets; the notion of a subset.
(sections 1.1 and 1.2).
A handout about "subset" vs. "an element of"
-- please take a look if you are confused about the set notation and
- Thursday, January 7:
Cardinality of the power set. You need to know only one proof (every
element is either chosen into a subset or not). The more elaborate proof
having to do with the number of subsets of cardinality k for every k is
not required (but will be discussed in the workshop).
Operations on sets; Venn diagrams: examples. An example of a proof of
equality of sets.
We covered Section 1.3 (with some
extras), but please read everything till the end of Chapter 1!
- Tuesday, January 11:
Indexed collections of sets; Cartesian products. Sections 1.4-1.6.
- Thursday, January 13:
Workshop 1 and quiz.
- Tuesday, January 19:
Stared Chapter 2: Mathematical logic. We discussed the notion of
statement, the truth tables, conjunction, disjunction and negation of
statements. Also, defined equivalent statements as statements having the
same truth tables. Discussed open sentences, and the connection between
statements and sets. Discussed that DeMorgan's laws amount to the
rules of negating conjunctions and disjunctions. This corresponds
approximately to Sections 2.1 -- 2.3 and 2.8, 2.9.
in the text; however, we have not yet discussed the implication. Will talk
about it on Thursday.
- Thursday, Jan. 21:
Chapter 2, continued. Implication and biconditional. Quantifiers.
Sections 2.4, 2.5, 2.6, 2.10.
Here is a note discussing the common mistakes
related to the use of "such that" (we discussed this in class, too). It
also has some tricky practice problems - please look at them and feel free
to discuss in office hours! This is good preparation for the midterm.
- Tuesday, Jan. 26:
Quantifiers continued (Section 2.10).
We also will discuss the use of
define the unions and intersections of indexed collections of sets --
in particular, cover Section 1.4 more rigorously.
A brief discussion of tautologies and contradictions (Section 2.7).
Here is a note about indexed
collections of sets and quantifiers.
Here is a note discussing common
mistakes made when reading/writing statements with more than one
Please read it and make sure you do not make these mistakes.
- Thursday, Jan. 28:
Workshop 2 (this is the workshop 2
problems and quiz with solutions).
- Tuesday, Feb. 2:
Proofs involving the integers. Congruence of integers.
Sections to read:
3.2, 3.3, 3.4, 4.1, 4.2.
We will continue with 4.1-4.2 and 4.3-4.4 on Thursday.
- Thursday, February 4:
Congruences of integers, continued. Proofs involving sets. Please
read all of Chapter 4.
- Tuesday, February 9:
Counterexamples (Section 5.1); proof by contradiction (5.2-5.3)
- Thursday, February 14:
Workshop 3 and quiz