Introduction

This module deals with the theory behind integration, differentiation, and “infinite sums”. From High School and MATH101 you will remember many useful formulas and procedures when it comes to integration and differentiation. This is good, but for the moment, try to forget them as we are going to build up everything from scratch. You will understand why all that you have learnt in the past about this topic is true, how you could prove it to somebody who has no idea about all this, and how you could extend it to a wider context. You will also understand a bit more about the general structure of mathematics and proofs. All this provides a good preparation for future modules.

Since the topic is not the easiest one, there are several kinds of exercises:

• A

  Assessment: to be done as homework, will directly contribute to your overall mark, solutions provided on Moodle week by week

• W

  Workshop: in the Workshop classes, solutions provided on Moodle week by week

• P

  Problem Solving classes: not contained in these lecture notes

• L

  Lecture: to be done interactively during the lectures

• X

  Extra: for individual training or curiosity, not examinable and sometimes quite challenging, no solutions provided, but you may discuss them with your lecturer or possibly your problem solving or workshop tutor

To bring along to the lectures: pencil, eraser, ink pens in three different colours, notepad, lecture notes.

Some useful textbooks for complementary reading and exercises (you do not have to buy any of them at this point, rather have a look at them in the library):

• •

  BARTLE, R.G. and SHERBERT, D.R.: Introduction to real analysis (4th ed), John Wiley and Sons (2011). [a thorough real analysis textbook that goes beyond the aim of this module and that will be useful throughout your whole undergraduate studies, very (!) expensive though]

• •

  BINMORE, K.G: Mathematical analysis (2nd ed), Cambridge University Press (1982). [a thorough real analysis textbook that goes beyond the aim of this module and that will be useful throughout your whole undergraduate studies]

• •

  HART, F.M.: Guide to analysis (2nd ed), Palgrave Macmillan (2001). [a gentle example-focused introduction to real analysis]

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  LIEBECK, M.: A concise introduction to pure mathematics (4th ed), Taylor and Francis (2015). [a good introduction to general university mathematics, its language and structure, including part of the content of this module]