"Mathematical Proof"

- Section 203 is taught by Andrew Rechnitzer
- Monday, Wednesday and Friday 1:00pm - 2:00pm in Woodward Room 6

- 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.

- I have removed all the pdfs and tex files.

- The old exam I showed in class is here.
- Pre-exam office hours = 2-4pm on Wednesday 23, Thursday 24 and Friday 25 April.
- Note that while we did a quick introduction to graph theory, the other sections worked on suprema and limits. Hence graphs will be on our exam, but not suprema or limits (and theirs will have suprema and limits but not graphs).
- There are some old exams with solutions here. The 2005 exam is not really relevant, but the other two are helpful.
- There are more old exams here - no solutions though.

- The solutions for homework 11 have been posted.
- Homework 11 has been posted. It is due at the start of class on Friday April 4th. Note you will need to draw some graphs for this homework. I recommend that you either learn to use a vector graphics editor such as inkscape or just leave some blank space and draw the graph in by hand after you print the page.
- I have posted notes on graphs.
- There was a small error in EQ4 in homework 8. See the updated version - the change is underlined.
- There was a small error in the solutions to Q9.12(a) in homework 7. See the updated version - the change is underlined.
- Your homework solutions
**must be typeset**- see notes here.

- 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
- Weekly homework assignments

- 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 Friday February 28th.
- We 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 |

The paper | The solutions (updated) |

- Homework will be assigned week-by-week.
- 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 in 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 17 | Homework 1 | template | The solutions |

January 24 | Homework 2 | template | The solutions (updated) |

January 31 | Homework 3 | template | The solutions (updated) |

February 7 | Homework 4 | template | The solutions |

February 14 | Homework 5 | template | The solutions |

February 26 | Homework 6 | You don't need one anymore | The solutions |

March 7th | Homework 7 | You don't need one anymore | The solutions (updated) |

March 14th | Homework 8 UPDATED | Bah! No more templates. | The solutions |

March 21st | Homework 9 | Nope. | The solutions |

March 28th | Homework 10 | Nope. | The solutions |

April 4th | Homework 11 | Nope. | The solutions |

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

Date | Topic | The notes |

March 23 | Graphs | The notes |

Please note that I will likely revise the above document before the end of term.

Additionally, I apologise to my students for the copyright notice at the bottom of the page. Of course I grant students in my class the right to copy and print these notes.

I am required to append the copyright statement because on February 20th 2014 the UBC Board of Governors passed "Policy 81" which (roughly speaking) allows UBC to take any notes and teaching materials that I share with people in the UBC community and use them as they see fit. This happens unless I specifically opt-out of the policy - which I do. This policy was passed despite vigorous opposition from faculty. The Canadian Associate of University Teachers has begun proceedings to censure the UBC administration over this policy.