1. Euclid’s Elements – Euclid
Euclid’s Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria, Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.
2. Principia Mathematica – Alfred North Whitehead and Bertrand Russell
Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. It is considered one of the most important works in mathematical logic and philosophy of mathematics. The work attempted to describe a set of axioms and inference rules in symbolic logic from which all mathematical truths could be derived.
3. Introduction to Mathematical Thinking – Keith Devlin
Introduction to Mathematical Thinking is a book written by Keith Devlin, a professor of mathematics at Stanford University, which provides an introduction to the basic concepts of mathematics and how to think mathematically. The book is intended for students who have had limited exposure to mathematics and its applications.
4. The Art of Computer Programming – Donald Knuth
The Art of Computer Programming is a comprehensive monograph written by computer scientist Donald Knuth that covers many kinds of programming algorithms and their analysis. It is widely recognized as the seminal work on the subject and is often referred to as "the Bible of computer programming".
5. Gödel, Escher, Bach: An Eternal Golden Braid – Douglas Hofstadter
Gödel, Escher, Bach: An Eternal Golden Braid is a 1979 book by Douglas Hofstadter. It is a work of philosophical science fiction, exploring common themes in the fields of logic, mathematics, art, music, and consciousness. The book won the 1980 Pulitzer Prize for general non-fiction.
6. How to Solve It – George Pólya
How to Solve It is a 1945 book by mathematician George Pólya. It is a classic work on problem-solving and mathematical thinking. The book is intended for use by teachers and students of mathematics, and is a popular resource for anyone interested in problem solving.
7. Concrete Mathematics – Ronald Graham, Donald Knuth, and Oren Patashnik
Concrete Mathematics is a textbook on mathematics written by Ronald Graham, Donald Knuth, and Oren Patashnik, and published in 1989. It is a comprehensive treatment of discrete mathematics, covering a wide range of topics from basic counting techniques to graph theory and algebraic structures.
8. Mathematical Analysis – Tom M. Apostol
Mathematical Analysis is a classic textbook on real and complex analysis written by Tom M. Apostol and published in 1967. The book is intended for use by undergraduate and graduate students, and is a popular resource for anyone interested in learning the fundamentals of analysis.
9. Mathematical Methods in the Physical Sciences – Mary L. Boas
Mathematical Methods in the Physical Sciences is a textbook on applied mathematics written by Mary L. Boas and published in 1983. The book is intended for use by undergraduate and graduate students, and is a popular resource for anyone interested in learning the basics of mathematical methods used in the physical sciences.
10. A Course in Mathematical Analysis – Walter Rudin
A Course in Mathematical Analysis is a classic textbook on real and complex analysis written by Walter Rudin and published in 1964. The book is intended for use by undergraduate and graduate students, and is a popular resource for anyone interested in learning the fundamentals of analysis.