Books

Here is a list of technical books that I find useful or like in particular.

Maths

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

Markov theory

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

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
  • 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

Probability

  • 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.

Queueing theory

Computers

  • Chassell, R.J.: An introduction to Programming in Emacs Lisp

Algorithms

  • 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

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; 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

General

Operations management

  • 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