Mathematics Article Collection Books for Talented High School Students

Solution 1:

There is a rather large list available here.

I would add to it (for really strong students)

• V. Prasolov, Y. Solovyev Elliptic Functions and Elliptic Integrals.

This book is devoted to the geometry and arithmetic of elliptic curves and to elliptic functions with applications to algebra and number theory. It includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions. Suitable as a text, the book is self-contained and assumes as prerequisites only the standard one-year courses of algebra and analysis.

Solution 2:

I read Holme's A Royal Road to Algebraic Geometry in my sophomore year of high school. It's relatively tough to get through, but definitely doable and worth the effort.