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Enrichment for undergraduate math majors
Some accessible books that we recommend for college math majors who are looking to broaden their mathematical horizons and see the material that they're learning in the standard courses used in the context of deeper math are as follows. The subjects listed as prerequisites can sometimes be studied concurrently (i.e. are co-requisites).
- A Primer of Analytic Number Theory: From Pythagoras to Riemann by Jeffrey Stopple. Prerequisites: two semesters of calculus.
- A Mathematical Gift: The Interplay Between Topology, Functions, Geometry, and Algebra by Kenji Ueno, Koji Shiga, Shigeyuki Morita and Toshikazu Sunada. Prerequsites: Familiarity with calculus, complex numbers and the rudiments of topology.
- Rational Points on Elliptic Curves by Joseph Silverman and John Tate. Prerequisites: One semester of abstract algebra (in particular, the rudiments of group theory).
- Geometry of Surfaces by John Stillwell. Prerequisites: The rudiments of group theory, and calculus.
- Complex Algebraic Curves. Prerequsites: Complex analysis and the rudiments of abstract algebra and topology.