"Mathematical Proof"

- 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
- Office hours - Mondays 3-4pm and Tuesdays 2-4pm in my office.
- You can also make an appointment by email.

- Homework assignment 3 has been posted below. It is due February 4.
- Solutions to homework assignment 2 have been posted 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.

The midterm | The solutions |

Not yet | Ages away |

- 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 28.
- 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.__

Due Date | The problems | The template | The solutions |

Not Due | Homework Zero | template | not yet |

January 14 | Homework one | template | Solutions one |

January 23 | Homework two | template | Solutions two |

February 4 | Homework three | template | Not yet |

- From time to time we might put some extra notes up here.

Date | Topic | The notes |