Mathematics 220 - Term 2 2014-2015
"Mathematical Proof"

Lecture details

Section 203 is taught by Andrew Rechnitzer
- Monday, Wednesday and Friday 1:00pm - 2:00pm in LSK Room 201
Sections 201 and 202 of Maths220 will follow a slightly different syllabus. See here.
It is worth looking at the homework problems set in those sections, but some material covered in 203 will not be covered in 201/202 and vice-versa.

Mathematics Building Room 215
Email: andrewr@math.ubc.ca
- Please put "MATH220" in the subject line of your email.
Phone: 604-822-4516
Please make an appointment by email.

Andrew will be away from April 8th and will not have email. Sorry.
Andrew's last office hours = Wednesday April 1st 10-12.
Jingyi Chen will take classes on April 8th and 10th
Professor Chen will hold pre-exam office hours for 220 on April 20th
- Time = April 20th @ 11-12pm and 2-4pm
- Place = Mathematics Annex room 1212
You can also email Professor Khosravi questions about maths220 during the exam period.
"Homework" 8 on induction is posted below with solutions to some problems. Please attempt the problems before looking at the solutions.
A practice exam (last year's paper) with solutions (not just yet) is posted below.
- The structure of this year's exam will be very similar (Andrew is not that creative).
- Any topics covered in class - up to and including induction - may appear on the exam.
- Please note that we did not cover any graph theory this year. So some questions on the practice paper are not examinable.

Solutions to homework assignment 7 have been posted below.
The midterm solutions have been posted. See below
The midterm has been posted. See below
Solutions to the practice midterm have been posted. See below.
Your homework solutions must be typeset - see notes here.
Homework assignment 0 is already posted below. This is just an exercise to help you learn latex. You do not need to hand it in.

The main aim of the course is to learn how write clear and correct mathematical proofs. It provides the gateway to more advanced mathematics.
A little more precisely (though this is provisional and order / content may change)
- Sets - definitions, set operations (chapter 1)
- Logic - logical connectives, quantifiers (chapter 2)
- Proofs - direct and contrapositive. (chapters 3 and 4)
- Equivalence realtions (chapter 8)
- Functions - injective, surjective, bijective, inverses and compositions (chapter 9)
- Proofs - existence and contradiction (chapter 5)
- Cardinality of sets - finite sets and different types of infinite sets (chapter 10)
- Induction (chapter 6)
The chapters refer to the textbook. We will then apply these methods to the following two topics (which unfortunately are not in the text)

Elementary combinatorics — basic rules of counting, combinations and binomial theorem, recursive counting.
Graphs and trees — definitions, handshaking theorem, isomorphism and planarity, graph representations, DAGs, spanning trees, Eulerian and Hamiltonian tours.

The learning goals for the standard version of Maths220 can be found here. These do not precisely align with the CPEN version, but they should give you a good idea of what is expected.

Gary Chartrand, Albert D. Polimeni and Ping Zhang: Mathematical Proofs - A Transition to Advanced Mathematics (Second or Third Editions).
The course will (mostly) follow the text and the homework will also be assigned from it.
We will mostly cover material in the same order as the text.

The assessment for this course will consist of
- Final exam
- One midterm
- Homework assignments every 2 weeks
Your final grade will be computed by the following formula
- Homework = 10%, Midterm = 30%, Exam = 60%
If a homework or quiz is missed for a documented medical or other reason, it will be ignored.
Note that, original written documentation, for example a doctor's note or letter from a coach, is required; otherwise, a score of 0 will be given for the missed homework or midterm.
Permission to write a makeup midterm or reweighting of other course components may be granted in the following two circumstances:
- (a) prior notice of a valid, documented absence (e.g. out-of-town varsity athletic commitment) on the scheduled date; or
- (b) notification to the instructor within 72 hours of absence due to medical condition.
Please do not eat leftover sushi before your midterms or exam. It is surprising how many students become ill because of this.

The midterm will be in class on Wednesday February 25th.
I will put up more information about the midterms and exam here as it becomes available.
Calculators, notes and books are not allowed in the midterms or the final exam.
Some exams from previous years can be found here. Note that the material covered in 220 does change from term to term, and so there may be questions on previous exam on material we have not studied.
You should use the learning goals to help your exam and midterm prepartion - these are designed for the more standard version of Maths220, but should give you a good idea of what is expected.

Homework will be assigned approximatelt every 2 weeks.
There will be 7 homework assigmnents, due tentatively on January 14, January 23, February 4, February 13, March 6, March 18, and March 27.
Your homework solutions must be typeset - handwritten solutions will not be marked.
I strongly suggest that you use latex to typeset your homework. See notes here.
Homework will be due at the beginning of the last lecture each week and we will try to return it to you within 1 week.
Solutions will be posted immediately after the homework is to be handed in.
You should also attempt other questions from the text as we cover each topic.
Please read these notes on plagiarism and academic integrity.
We will not accept late homework.

Date	Topic	The notes
March 30	Practice exam	Solutions coming soon