• 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
• Needham T: Visual complex analysis
• Peitgen et al, Chaos
• Vilenkin N.Ya, In search of infinity.

• Lindley, D.V.: Understanding Uncertainty, A really nice book to help how to think about probability.
• Jaynes E.T Probability theory: the logic of science. I like his opinionated writing a lot. It’s funny at times, but often very to the point.
• Diaconis, P and Skyrms, B: Ten Great Ideas about Chance, Also an interesting book that discusses general probability concepts.
• Grinstead and Laurie snell, introduction to probability.
• Capinski M., Tomasz Jerzy Zastawniak: Probability Through Problems. Targeted at students that like to learn a bit of measure theory.
• Ash, R. B., Real analysis and probability, if you like something tougher.

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
• Baez J.C. and Biamonte J: Quantum Techniques for Stochastic Mechanics
• Stachurski J: Economic Dynamics: Theory and Computation

• 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
• Flanders H.: Differential forms with applications to the physical sciences
• Nahin, P.J.: Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph (2020) (It is a petty that Nahin appears not to have read the book of Korner on Fourier theory. There is a lot of overlap, and I like Korner’ account better.)
• Nahin, P.J.: In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions

• Cormen, T.H. et al: Introduction to Algorithms
• Hetland, M.L.: Python Algorithms, Mastering Basic Algorithms in the Python Language
• Kopec, D.: Classic Computer Science Problems in Python

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; 1. Analyzing (quantitatively) the models with computers; 1. 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

• Goldratt, E.M.: The goal
• Womack, J.P. and Jones, D.T.: The Machine That Changed the World: The Story of Lean Production– Toyota’s Secret Weapon in the Global Car Wars That Is Now Revolutionizing World Industr