Calculus: A Freshman Honors Course

This book presents the foundational mathematics curriculum taught by the eminent mathematician Emil Artin at Princeton University in the mid-1950s. Compiled from detailed course notes by G. B. Seligman, this text offers a unique window into Artin’s pedagogical philosophy, which prioritized deep comprehension, active mathematical thinking, and the elegant construction of proofs over mechanical calculation.

It covers derivatives, the definite integral, techniques of integration, and partial derivatives. Notably, Artin balances intuitive understanding with formal rigor, carefully guiding the reader through advanced topics such as Taylor’s formula, the Bernstein convergence theorem, functions of several variables, and an axiomatic foundation of the real number system.

Originally designed for a highly select group of university freshmen, the material intentionally avoids the standard, formulaic approaches found in typical textbooks of the era. Instead, it challenges readers to engage directly with the mechanics of mathematical logic.

This historical text remains a highly relevant and enriching resource today. It is ideal for advanced students seeking a deeper, more rigorous foundation in calculus, educators looking for alternative pedagogical approaches, and anyone interested in experiencing the teaching methods of one of the 20th century’s great mathematical minds.