## Book suggestions

Book suggestions for undergrad/master students
Suppose you already learnt some abstract algebra (rings, ideals, modules etc.):
1. You should learn Galois theory. I recommend Hungerford's book ``Algebra" Chapter V (try to solve most of the exercises there).
2. More algebraic preparations:
Learn some language of categories, e.g., Hungerford's book ``Algebra" Chapter X.

Learn some commutative algebra. Standard book: Atiyah-Macdonald ``Introduction to Commutative Algebra" (try to solve most of the exercises there).

Learn some homological algebra. For example, Hilton-Stambach: ``A Course in Homological Algebra", Chapter 1-4. (some of Chapter 5, 6 if you like).
3. Venturing into AG and NT.
For AG, can start with Hartshorne ``Algebraic Geometry" Chapter 1-3.

For NT, Local class field theory, Serre: ``Local fields". Global CFT, Neukirch book; and/or Cassels-Frohlich book.

With some AG learnt, can learn Elliptic curves. Silverman, ``The Arithmetic of Elliptic Curves".

Relation between EC and MF, Diamond-Shurman, ``A First Course in Modular Forms".
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