Algebraic Number Theory and Fermat's Last Theorem (eBook)

I. Algebraic Methods. 1. Algebraic Background. 2. Algebraic Numbers. 3. Quadratic and Cyclotomic Fields. 4. Pell's Equation. 5. Factorisation into Irreducibles. 6. Ideals. II. Geometric Methods. 7. Lattices. 8. Minkowski's Theorem. 9. Geometric Representation of Algebraic Numbers. 10. Dirichlet's Units Theorem. 11. Class-Group and Class-Number. III. Number-Theoretic Applications. 12. Computational Methods. 13. Kummer's Special Case of Fermat's Last Theorem. IV. Elliptic Curves and Elliptic Functions. 14. Elliptic Curves. 15. Elliptic Functions. V. Wiles's Proof of Fermat's Last Theorem. 16. The Path to the Final Breakthrough. 17. Wiles's Strategy and Subsequent Developments. VI. Galois Theory and Other Topics. 18. Extensions and Galois Theory. 19. Cyclotomic and Cubic Fields. 20. Prime Ideals Revisited. 21. Ramification Theory. 22. Quadratic Reciprocity. 23. Valuations and p-adic Numbers.