Sequences and Series for Birmingham University Students

Lecturer: Dr Richard Kaye, Room 308 Watson building. Email: R.W.Kaye@bham.ac.uk.

Office hours: Tuesdays 12noon-1pm and Fridays 12noon to 2pm. See outside my room for any late alterations.

The group of web pages you are reading right now contain organisational information you will need for this module, such as assessment arrangements, lists of assessed questions, marking schemes etc.

The mathematical content of the course is available at http://web.mat.bham.ac.uk/R.W.Kaye/seqser/. This is an on-line textbook and may be copied as often as you like (under the terms of the Gnu Free Documentation Licence). It covers slightly more than you will need for the course. I will indicate in lectures what parts are optional. To read the web pages, you are advised to set up your browser for MathML. Firefox with some additional fonts is the recommended way. An experimental pdf alternative is available, but this may not be quite so good. If you have genuinely tried to follow all the instructions and you are still having difficult reading these pages please contact me.

You should bookmark both this page and the web-text pages. Web pages will be updated throughout the term. Look out for any changes.

This is the official syllabus, taken from the module description.

Of this, the integral test cannot be covered rigorously and although it is handy to know and may be discussed briefly, will not be examined. The detailed structure of the real numbers (in particular, completeness and consequences) will be taken towards the middle of the module, since although this should logically come first it is one of the more difficult parts of the course and will mean much more to you after you have some experience in the other parts of the course. The material on the modulus function and inequalities is more straightforward, and will be discussed briefly at the beginning and then in more detail in examples when needed. Thus, after a couple of lectures or so of introduction, the module will start with sequences.

Both MSM1B and MSM2P01 taken as a whole is worth 20 credits. Each semester is of equal weight.

The marks are calculated as follows:

G100, G103 and G141 students: 72% from one examination in the summer, 20% continuous assessment based on work handed in for supervisions and 8% from workshops.

All other students: 72% from one examination in the summer, 28% continuous assessment based on work handed in for supervisions.

The spring semester part of the module has five tutorials all weighted equally. Second year students doing MSM2P01 will have slightly different exercises, or different assessed activities in class.

An up-to-date list of all assessments for the course is kept on a separate web page here.

Your supervisor and I will provide feedback on your work in a number of ways. Some of them are less obvious than others. You cannot expect to learn the module and know what's required without taking note of all this.

Note that in most cases you will have to ask for feedback, or ask for clarification of various points. This is not a problem, but is in fact the usual mode of learning and teaching in a university environment. I will be helpful and friendly to all students who ask for help, especially if they have made some effort to read or understand the set work first. However, I do not have time to repeat large amounts of material to you that I have already given in a lecture that you didn't hear because you didn't attend. You should make every effort to attend lectures unless there are good reasons not to - in which case I will understand.

The web pages are substantial and cover the whole course. They can be freely copied and printed. (Please check the licence first.) They should be used as your main textbook and will be entirely sufficient unless you wish for a second opinion, second view or further background reading. There will be computers on campus that can display and print these pages, or you can use your own (but be careful to set it up correctly).

For additional or alternative reading, I recommend the following text books.

Burn is more abstract than Hart but contains more problems for you to do yourself. Both go further in some directions than I will do in the lectures and the web pages, so please read them carefully and don't get confused when they introduce new ideas. There is no need to purchase either book.

Note: I will not provide comprehensive printed material for the module. The beauty of web pages is that you can read them on-line where and when you need them, print the ones you find helpful, but you do not need to print them all out. Also I can add to them or correct them from time to time. However, there will be some hand-outs to help ensure you have the right material copied down in your notes.

You will also be able to find other materials available on the web. As always, be very careful with what you read on the web, including these pages! Anyone can write web pages, and web pages are often inaccurate or incorrect. However, I found one course on analysis by Bert G. Wachsmuth at http://web01.shu.edu/projects/reals/index.html that seemed pretty good. Not all the proofs you will need are there and not all the material is completely compatible with this course. (I.e., he takes the material in slightly different order or in a different way.) But with careful reading you may find it helpful. Sections 1-4 cover material that we are doing here, and later sections are more advanced for interested students.

My marking schemes will also be available. They give some idea of what I am looking for in each supervision. I don't know if they are any use to students, but they are freely available to students too, should any want to read them.