This page contains material for the course MAA140 and MAA143 aka Analysis 1. The module specifications can be found here. Here is a list with suggested reading.
- How to study for Analysis 1
- Polya's Algorithm to solve Problems
If you can not solve the proposed problem do not let this failure afflict you too much but try to find consolation with some easier success, try to solve first some related problem; then you may find courage to attack your original Problem again. Do not forget that human superiority consists in going around an obstacle that can not be overcome directly, in devising some suitable auxiliary problem when the original one appears insoluble.
Could you imagine a more accessible related problem? You should now invent a related problem, not merely remember one; I hope that you have tried already the question: Do you know know a related problem? (G. Polya)
- Learning Analysis (by Dr. Lara Alcock)
In this lecture, I follow the outline of Dr. Lara Alcock very closely.The Lecture Notes will be completed during the semester. They will consist of gappy notes which I will upload in advance of every week's session and you should fill in in class. Sometimes you might want to write a note that I do not write. If you have no experiece in taking real notes, the University Library provides workshops and materials.
Homework Problem Sheets
You should start working on homework them as soon as you have been to the first lecture(s) in any given week (even just reading them will help you to listen more effectively in lectures). When you get stuck, ask your fellow students, your tutor or a member of MLSC staff for hints and help. When you are pretty confident, ask other students to read and critique your answers. You need to get good at writing clear mathematical arguments, and this will help.
Mathematics is not a spectators sport. Please take the problem sheets seriously and always try to attempt them. Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics. Sometimes this means doing even more than the assigned problems. This is how to avoid the common pitfall of understanding everything in class but blanking out on the exams.
- Review your lecture notes and understand all the definitions and relevant theorems.
- Write down the problems from the sheets and work out what you have to show.
- Play around with related inequalities, identities and so forth.
- Don't give up too soon. Some questions are very hard and only few will solve them alone but if you use the right techniques, you will always learn something.
- Use tools as GeoGebra and Wolfram alpha for visualisation and confirmation of results.