Here is a list of books on maths that I liked in particular.

General maths books

  • Alexander, A: Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World
  • Borrelli, Rullière: En cheminant avec Kakeya on Kakeya’s needle problem.
  • Bressoud, D.M.: A Radical Approach to Lebesgue’s Theory of Integration
  • Bressoud, D.M.: A Radical Approach to Real Analysis
  • Bressoud, D.M.: Second Year Calculus: from Celestial Mechanics to Special Relativity
  • Courant, R: What is mathematics
  • Dunham, W., Euler the master of us all
  • Dunham, W., The calculus galery
  • Jeevanjee, N, An introduction to tensors & group theory
  • Korner, T: Fourier theory
  • Peitgen et al, Chaos
  • Vilenkin N.Ya, In search of infinity.

Probability

  • Capinski M., Tomasz Jerzy Zastawniak: Probability Through Problems. A great book, but targeted at students that like to learn a bit of measure theory.
  • Grinstead and Laurie snell, introduction to probability.
  • Lindley, D.V.: Understanding Uncertainty, A really nice book to help how to think about probability.
  • Diaconis, P and Skyrms, B: Ten Great Ideas about Chance, Also an interesting book.

Markov theory

These are some great (and sometime intuitive) books to Markov chains, martingales and optimal stopping.

  • Benaïm M. and El Karoui N: Promenade aléatoire: Chaînes de Markov et simulations : martingales et stratégie
  • Dynkin E.B. and Yushkevich A.A: Markov processes: theorems and problems
  • Laurie Snell J. and Doyle P.: Random walks and electric networks
  • Kemeny and Laurie Snell: Finite Markov Chains.
  • Norris J: Markov chains

Physics

  • Gourgoulhon E., Relativite restreint des particules a l’astrophysique. A good book to prepare yourself for general relativity. It covers all I learned as a student on special relativity, and more.
  • Zee A.: Einstein Gravity in a Nutshell

Queueing theory

Think books

Here are some books freely available for download. I encourage you to browse through all of these books. The reason I recommend these books is that they combine three enormously important skills for students with a penchant for quantitative work:

  1. Making and adapting (mathematical) models;
  2. Analyzing (quantitatively) the models with computers;
  3. Evaluating and interpreting the results.

The books are:

  • Think Stats
  • Probability and statistics for programmers
  • Think Bayes
  • Modeling and Simulation in Python *Think Complexity.
  • How to think like a computer scientist (Not strictly necessary, but nonetheless interesting.)