# Modern Calculus

## Table of Contents

## Part 1A Michaelmas

This is the first term of the Mathematical Tripos where we learn how to do university level math, here we learn basic real analysis/calculus since it's only taught in Lent but we'll need it now in Michaelmas.

I do this P/T whenever I can, usually on a phone over lunch, so there will be spelling mistakes and other uncaught errors that will briefly persist as I complete the materials.

### Course

We will be examined on this as *Analysis I* in Easter term.

- Project DIRACC taught at ASU (reading only)
- The Calculus Integral by B. S. Thomson (2010)
- A Radical Approach to Real Analysis by David Bressoud (2007)

#### Supplementary Reading

- Solving Problems in Mathematical Analysis, Part I by Radozycki 2020

Cambridge recommendations:

- T.M. Apostol Calculus, vol 1. Wiley 1967-69
- † J.C. Burkill A First Course in Mathematical Analysis. Cambridge University Press 1978
- D.J.H.Garling A Course in Mathematical Analysis (Vol 1). Cambridge University Press 2013
- J.B. Reade Introduction to Mathematical Analysis. Oxford
- M. Spivak Calculus. Addison–Wesley/Benjamin–Cummings 2006
- Bressoud's book which we are reading

Apostol will drill you on countless trig identities for some reason if there's nothing to say at the end of a chapter. Spivak will mix in extremely difficult problems with easy problems and not tell you.

TODO