Will Graham's Tutorial Resources
About and Disclaimer
These notes have been produced on request, intended as a suppliment to the tutorials that I give. The main purpose is to provide hints for the non-homework questions; which the tutorials sometimes miss out due to time constraints, however they will also include anything from the notes that I deem worthy of highlighting and the homework hints I provide (if any). The importance of these things will range from
useful to know to
FUNDAMENTALLY IMPORTANT; and whilst I will only emphasise certain things from the notes, it is important come the exam that you are familiar with all/most of the material from the lectures and not just what I have listed here. These notes DO NOT provide a substitute for the tutorial - in fact they will often explicitly refer to the tutorial (or things I said in the tutorial), so won't make sense without it!
If there are questions about the resources you see here, drop me an email and I will do my best to answer promptly. In addition, any of my tutees will know how hopeless I am at spelling. If you spot any corrections that are required here, please point them out.
I am always happy to answer questions by email if problems arise outside the tutorial. However when typing a problem that has come up in a question, it can become cumbersome to type out the maths in full - most of the time people resort to some makeshift notation that works in context. Obviously because I have some context, this doesn't matter too much, but it would be much better if the actual mathematical expressions could be used instead, because:
- For the purposes of your general mathematical education, at some point you are going to need to get familiar with writing mathematics in reports (unless you fancy writing out a 30-page project report by hand...), so it's good practice to start now.
- It means I can understand your question faster and your point more prcisely, and give you a better answer in my response.
- It saves us all time trying to cipher/decipher the makeshift notation!
Fortunately the university email system supports writing equations and mathematical notation; provided you are using the Outlook Web App, Outlook on your personal machine, or a respectable e-mail client. Personally, I have only used a Windows OS (Operating System), and currently use Outlook as a mail client, so I only know the ins and outs of those - but in theory it is possible on any of the other clients I listed. When writing a new email in Outlook (you may need to be writing your email in a separate window for this to work), you can go to the "Insert" tab at the top of the window, and insert an equation. When you type in this box, text behaves differently, and you can insert mathematical symbols from the respective toolbar that pops up. The keyboard shortcut on Windows to insert an equation is 'Alt and ='. If you search around the help forums for other platforms, you should find an equivalent function.
A Broader Context (LaTeX):
- Those of you who can't find a function like this, consider the next paragraph, and sending your email with a .pdf or .doc file attachment.
Those of you who forsee youselves working with maths for a long time, and having to write maths-heavy reports (particularly those of you on Masters courses, including cross-departmental students) may find it useful to start familiarising yourselves with a LaTeX editor. Why you ask? Google (image) search: "ms word move image meme".
LaTeX is a typesetting system, specifically designed for scientific report writing. It is freely available and has many editors, both downloadable and online, which come ready-to-use and even include document templates. The editor can appear confusing at first, but there are plenty of tutorials to help you get started. I shalln't go into the details here, because I have literally just given a link to a whole website dedicated to guides and more, and because you can normally solve any problem you have in LaTeX simply by Google-ing it!
- LaTeX isn't perfect, so don't think I'm shooting down MS Word or iOS Pages etc; they both have their merits (in particular the spellchecking features easily surpass most LaTeX editors). However the ease of use in LaTeX, and the far less clunky way it handles images, equations and report formalities put it ahead, particularly for a scientific writer.
- Those of you who are on the MMath will have an introduction to LaTeX as preparation for your Master's project, in your 4th year. Whilst this is a long way off, it doesn't hurt to start now.
MA10207 Analysis 1A; Semester 1
Tutored 2017/18, for groups H1/2 in EB0.12, Mondays at 13:15.
Revision tutorials will be running on Monday 8th and Tuesday 9th of January (revision week) for Analysis 1A at the following times:
The format for these revision tutorials will differ slightly from the tutorials you have had throughout the year. The emphasis will be on answering questions that you have come across during revision, rather than focusing on a specific set of problems. Once any questions have been taken care of, we will be going through a past Analysis paper to help familiarise people with the thought processes that are involved.
- Monday 8th, 9:15-10:05 CB4.1, by Federico Cornalba
- Monday 8th, 10:15-11:05 CB4.1, by Federico Cornalba
- Monday 8th, 13:15-14:05 CB3.5, by myself
- Tuesday 9th, 9:15-10:05 CB3.1, by myself
IMPORTANT: I talked a bit about the exam format in the last tutorial; however I have since been informed by Karsten that the format of the exam has changed, and you must now answer all questions to achieve full marks.
- Week 4 notes (23rd October) available here.
- Week 5 notes (30th October) available here.
Week 6 notes (6th November) available here.
- The week 6 notes are more detailed than other weeks. This is because there was a lot more content to get through in the tutorial, and I didn't have time to cover everything I wanted to from sheet 4 and talk about things relating to sheet 5. As such; even if you were at the tutorial on Monday 6th, I recommend reading week 6's notes to make up for what I (would have) said in the tutorial.
- Week 7 notes (13th November) available here.
- Week 8 notes (20th November) available here.
- Week 9 notes (27th November) available here.
- It is around this time that my previous groups have begun asking me questions about (a) the format of the exam and (b) questions from past exam papers. I am happy to answer questions from past exam papers in the tutorial (just bear in mind that it'll take longer than usual for me to come up with a working answer) and about the format of the exam. However please remember that I don't know anything about what will appear ON YOUR EXAM, so don't bother asking!
- Week 10 notes (4th December) available here.
Important Notice (so important I forgot to say anything about it in the tutorial):
As you may (or may not have yet) recieved an email, revision tutorials are being organised for Revision Week (8th January). I will include any details from these emails on this webpage as they are relayed to me. Currently it is planned that the tutorials will be run for groups larger than the standard size (potentially merging multiple groups) and may or may not run for longer than the standard 1 hour.
- Week 11 notes (11th December) available here.
- This is all that I have for you guys; there are no more scheduled tutorials exclusively for the group. See above for details on what will be happening in revision week.
- Thanks to everyone for turning up, being talkative, and treating me like a human despite my poor spelling and writing on the board. Best of luck to you all in the exam.
MA10207 Analysis 1B; Semester 2
Tutored 2017/18, for groups H1/2 in 8W2.24, Tuesdays at 9:15.
Tutorials start in Week 2 this semester.
Problem sheets are handed out on Thursdays. Hand-in is the following Thursday by 17:15. This is a strict deadline as the Problem Class is Friday 9:15!
- Week 2 notes (13th February) available here.
Week 3 notes (20th February) available here.
These notes include more detail on tackling proofs that require you to explicitly work with the definition of limit or continuity.
- Week 4 notes (27th February) are no longer available; in a classic "Will" move I overwrote them when writing the week 5 notes, because I'm a genius. Sorry...
Week 5 notes (6th March) available here.
- With the industrial action and the snow last week, there has been some distruption to the course. The hand-in for problem sheet 3 is now this week, rather than last.
- To compensate, this week the online notes contain an overview of the content that was taught at this time last year. This is just to give you a taste for what is to come, so don't worry about it not making perfect sense now!
- As always, drop me an email if you need anything explained (although I can't promise good explanations for questions unrelated to Analysis).
Week 6 notes (13th March) available here.
- As there are no lectures this week due to the industrial action, the online notes focus on the solution to H2 of Problem sheet 3.
- I will update the notes with anything that I find relevant, once we have more information about what is going to happen next week.
Week 7 (20th March): There are no notes because this will be the first week that we are back to normal schedule.
- You'll be given problem sheet 4 on Wednesday and sheet 5 on Friday. Do not panic, there is enough time to get through all the material in the course in the remaining lectures.
- For the problem sheet hand-in; provided the problem sheet is in the pigeonhole the Monday BACK from Easter, I will mark it.