Wednesday, December 7th, 11am-1pm

Thursday and Friday, 15-16 December, noon-3pm

Hand-written notes from class, Wednesday 30 November 2016

Hand-written notes from class, Friday 02 December 2016

Long-answer problems from past four exams, sorted by topic: click on the subject in the table of contents to go to the corresponding page.

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.

Section(s) | Dates | File | Topics |
---|---|---|---|

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 perfect numbers |

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.

- The Math Learning Center is staffed with tutors, and you can go there to meet other students. More information here: Math Learning Center.
- Other students in the course are an important resource. Ask the person sitting next to you if they want to work on homework together, or meet at a coffee shop to study for the next exam. Talking to strangers is hard, but having a community is helpful and important. If someone asks for help, keep in mind that teaching someone is a fantastic learning opportunity. Being able to do a problem on the homework is great, but often we learn even more when we're put in the position of explaining it to someone else.
- Free tutoring: AMS. For independent, paid tutors, check bulletin boards around the math building.
- The internet has pretty much everything. There's our class discussion board, where you can pose a question to the class. Apart from the CLP notes and problem book, there's lots of free online textbooks and notes you can search for. There's also tutoring videos, like Khan Academy. If you look hard enough, the UBC pages have old exams.
- Talk to your teacher! Office hours are time I set aside to meet with students. You can grab me after class or email me at elyse@math.ubc.ca to ask a short question, or schedule an in-person meeting if office hours don't work for you.

UBC provides services to address, among other things: illness and injury, mental health and wellbeing, sexual assault (for people of all genders), other violence, discrimination and harrassment, diversity, disability, and ongoing medical considerations. If you have legal issues, you might be able to get help from the Law Students' Legal Advice Program. The Office of Equity and Inclusion is a good place to go if you want more information about maintaining an environment that is respectful, especially with regards to interculturality, LGBT*QIA status, race, students who are parents, etc. The Office of Access and Diversity provides disability support.

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.

The province has an excellent website with information on mental health, including an online screening tool and resources: Here To Help. The Vancouver Access & Assessment Centre (AAC) is a point of entry for concerns about mental health and substance abuse, and they also have a call line if you just want to talk to someone. The BC Crisis Centre also has phone services for someone to talk to if you are in crisis.

Education is a tool for a better life, from increased earning potential to a heightened appreciation for the beauty and complexity in the world. Your real life extends far beyond the boundaries of this campus. It's important that you don't let your education interfere with your physical or emotional health.

If it isn't feasible to change the thing that's bothering you, we still might be able to come up with strategies for addressing it. At the very least, you can get an explanation of why things are the way they are.