Basic facts

My contact information:

• Paul Johnson
• paul.johnson@sheffield.ac.uk
• Office Hicks J6b

The second semester will be lectured by Anna Barbieri.

Lectures:

• Thursday 2, LT6
• Friday 10, F41

Office hours are currently scheduled for:

• Tuesday 2-3
• Wednesday 10-11

I picked these as time slots where there did not appear to be level 4 modules, so hopefully they will work for everyone, but if you’d like to come to office hours regularly and neither slot works for you let me know, and I may change with input from the class later in the semester. Additionally, always feel free to ask questions during or after class, in an email, or to set up a time to chat in person.

Marking

There is no exam for this module. Instead, there will be weekly assessed problem sets.

Problem sets will be assigned in lecture every week, and will be due the next week at the beginning of the Friday lecture. You can email the problem sets to me before lecture starts, hand a paper copy in at the beginning of lecture, or slip it under my door before lecture starts.

You are allowed, and in fact encouraged, to meet in small groups to discuss the course, including the problem sets. Working with friends is a great way to learn and is usually more fun. Small’’ here means two or three people; larger groups are not allowed, as it becomes too easy to just listen and not contribute.

Every student must hand in their own solutions, and the group shouldn’t write up’’ the proofs together. On the front of each problem set put your name, a list of the members of your group that you worked with the problems on, and your registration number.

What’s allowed to be done on the group?

Doing mathematics typically has two parts: the informal what is even going on here?’’ way we work in our heads, and the formal proofs and definitions that we read and write. We are constantly going back and forth between these, and solving a problem set will typically involve

1. Digesting the formal statement of the problem into an informal
2. Coming up with an informal solution
3. Refining that informal solution into a formal, written proof

The first two steps are what can be down with your group, the third step should be done alone. Obviously, the steps blend together some and separating the exact line is not really feasible. But you should not be discussing the line-by-line organization of the proof together, or sitting next to each other and asking questions as you write up the proof.

Writing proofs

I recommend latexing your assignments, but this is not required. A previous incarnation of the course had the following handout, which has some useful discussion of writing proofs. We will take time to have discussions about writing proofs as the course continues.

Proofs are not perfect platonic objects living in a vacuum, they are social constructs that are a form of communication. As such, neatness and style are important and will be evaluated.