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.
- 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.
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
- 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
- Van Foreest, N.D., Analysis of Queueing Systems with Sample Paths and Simulation, which is free, constains lots of problems and solutions.
- Tijms, H.C: A First Course in Stochastic Models, Wiley, 2003.
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:
- Making and adapting (mathematical) models;
- Analyzing (quantitatively) the models with computers;
- 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.)