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