I’ve discovered that a truly great textbook about a higher-level subject can often be difficult to find. These are some of my favorites. Each one provides a clear and concise explanation of its chosen subject in a way that is imminently readable. In most cases they are so easy to read that I have sat down and read them cover-to-cover. In other cases, they are so comprehensive that I keep them within arm’s reach to serve as a chosen reference for a given subject.

Obviously, this list will never be complete. I’m simply adding titles as I work back through different subjects from my undergraduate studies. If you’re interested in applications of math, however, most of these are a great introduction to a particular subject.

Mathematics

• Kline. Calculus: An Intuitive and Physical Approach. 1st ed. New York, NY: Dover Publications, Inc. 1998.
• Penney. Linear Algebra: Ideas and Applications. 4th ed. Hoboken, NJ: Wiley & Sons, Inc. 2015. (A fifth edition has also been released.)
• Savage. The Foundations of Statistics. 2nd rev. ed. New York, NY: Dover Publications, Inc. 1972.
• Hogg, McKean, & Craig. Introduction to Mathematical Statistics. 7th ed. Boston: Pearson. 2012.

Applied Mathematics

• Dixit. Optimization in Economic Theory. 2nd ed. New York, NY: Oxford University Press. 1990.
• Boas. Mathematical Methods in the Physical Sciences. 3rd ed. Hoboken, NJ: Wiley & Sons, Inc. 2006.
• Bate, Mueller, & White. Fundamentals of Astrodynamics. 1st ed. New York, NY: Dover Publications, Inc. 1971. (An updated edition has been released which looks very interesting.)
• Holmes. Introduction to Scientific Computing and Data Analysis. 1st ed. Troy, NY: Springer International Publishing. 2016
• Press, Teukolsky, Vetterling, & Flannery. Numerical Recipes: The Art of Scientific Computing. 3rd ed. New York, NY: Cambridge University Press. 2007.

Machine Learning

• Gareth, Daniela, Trevor, & Robert. An Introduction to Statistical Learning. 8th prnt. Troy, NY: Springer International Publishing. 2017
• Hastie, Tibshirani, & Friedman. The Elements of Statistical Learning. 2nd ed. Troy, NY: Springer International Publishing. 2017.
• Deisenroth, Faisal, & Ong. Mathematics for Machine Learning. 1st ed. New York, NY: Cambridge University Press. 2020.