Reading List

1) Lara Alcock, How to Think About Analysis (OUP, 2014) ISBN 9780198723530

2) Robert G. Bartle, Donald R. Sherbert, Introduction to Real Analysis (Wiley, Third Edition, 2000), Chapters 2, 3, 9.1, 9.2.

3) R. P. Burn, Numbers and Functions, Steps into Analysis (Cambridge University Press, 2000), Chapters 2--6. [This is a book of problems and answers, a DIY course in analysis.]

4) J. M. Howie, Real Analysis, Springer Undergraduate Texts in Mathematics Series (Springer, 2001) ISBN 1-85233-314-6.

The first four books take a slightly gentler approach to the material in the syllabus, whereas the last two cover it in greater depth and contain some more advanced material.

1) Mary Hart, A Guide to Analysis (MacMillan, 1990), Chapter 2.

2) J. C. Burkill, A First Course In Mathematical Analysis (Cambridge University Press, 1962), Chapters 1, 2 and 5.

3) Victor Bryant, Yet Another Introduction to Analysis (Cambridge University Press, 1990), Chapters 1 and 2.

4) G.C. Smith, Introductory Mathematics: Algebra and Analysis (Springer-Verlag, 1998), Chapter 3 (introducing complex numbers).

5) Michael Spivak, Calculus (Benjamin, 1967), Parts I, IV, and V (for a construction of the real numbers).

6) Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner, Elementary Analysis (Prentice Hall, 2001), Chapters 1--4.