Elliptic Curves and Their Applications

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Lecture 2:

Lecture 3:

Lecture 4: Doubly periodic functions and Weierstrass P-function

Lecture 5: Weierstrass P-function and tori isomorphism

Lecture 6: j-Invariant for functions on SL_2(Z)

Lecture 7: Properties of j-invariant

Lecture 8: Complex multiplication

Lecture 9: Elliptic curves over reals

Lecture 10: Elliptic curves over rationals I

Lecture 11: Elliptic curves over rationals II

Lecture 12: Elliptic curves over rationals III

Lecture 13: Mordell-Weil theorem

Lecture 14: Elliptic curves over finite fields

Lecture 15: Divisors and space of differentials

Lecture 16: Riemann-Roch theorem

Lecture 17:

Lecture 18:

Lecture 19:

Lecture 20:

Lecture 21:

Lecture 22:

Lecture 23: L-functions and modular forms

Lecture 24: Shimura-Tanyama conjectures

Lecture 25: Fermat's Last Theorem

Lecture 26: Wiles modularity theorem