🐯 Princeton Mathematics unofficial reading list, fall 2026

Freshman level
Calculus I / II / One Variable Calculus w/ Proofs MAT 103 / 104 / 210	• Thomas’ Calculus, Early Transcendentals: Single Variable by Hass et al.
Math. for Economics / Life Sciences MAT 175	◦ Calculus by Varberg et al. ◦ Thomas’ Calculus, Multivariable by Hass et al.

Sophomore level
Multivariable Calculus MAT 201	• Thomas’ Calculus, Multivariable by Hass et al.
Linear Algebra w/ Applications MAT 202	• Linear Algebra w/ Applications by Otto Bretscher
Adv. Vector Calculus MAT 203	◦ Vector Calculus by Marsden & Tromba
Numbers, Equations & Proofs MAT 214	◦ The Higher Arithmetic: An Intro. to the Theory of Numbers by H. Davenport ◦ A Classical Intro. to Modern Number Theory by Ireland & Rosen ◦ An Intro. to the Theory of Numbers by Ivan Niven
Single Variable Analysis w/ an Intro. to Proofs MAT 215	• Understanding Analysis by Stephen Abbott
Multivariable Analysis & Linear Algebra I MAT 216	◦ An Intro. to Analysis by Robert C. Gunning

Junior level
Multivariable Analysis I MAT 300	• Mathematical Analysis I by Vladimir A. Zorich
Intro. to Real Analysis MAT 320	• Real Analysis by Royden & Fitzpatrick
Numerical Analysis & Scientific Computing MAT 321	• Numerical Linear Algebra by Trefethen and Bau • An Introduction to Numerical Analysis by Süli & Mayers
Analysis II: Complex Analysis MAT 335	• Complex Analysis by Stein & Shakarchi
Applied Algebra MAT 340	• Groups and Symmetry by Mark A. Armstrong
Algebra I MAT 345	◦ Algebra by Michael Artin
Topology MAT 365	• Topology by James Munkres
Probability & Stochastic Systems MAT 380	◦ Fundamentals of Probability: With Stochastic Processes by Saeed Ghahramani ◦ Intro. To Probability by Bertsekas & Tsitsiklis ◦ Intro. to Probability Models by Sheldon M. Ross

Senior level
Geometry & Number Theory: Arithmetic of Elliptic Curves MAT 419	• The Arithmetic of Elliptic Curves by Joseph H. Silverman
Algebraic Geometry MAT 457	• Basic Algebraic Geometry 1: Varieties in Projective Space by Shafarevich & Reid