Introduction to Modern Number Theory

Part I. Problems and Tricks

1. Number Theory

2. Some Applications of Elementary Number Theory

Part II. Ideas and Theories

3. Induction and Recursion

4. Arithmetic of algebraic numbers

5. Arithmetic of algebraic varieties

6. Zeta Functions and Modular Forms

7. Fermat’s Last Theorem and Families of Modular Forms

Part III. Analogies and Visions

8. Introductory survey to part III: motivations and description

9. Arakelov Geometry and Noncommutative Geometry (d’après C. Consani and M. Marcolli, [CM])

10. Arakelov Geometry and Noncommutative Geometry (d’après C. Consani and M. Marcolli, [CM])

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Keywords: MATHEMATICS / General MAT000000