This book presents a graduate student-level introduction to the classical  theory of modular forms and computations involving modular forms, including  modular functions and the theory of Hecke operators. It also includes  applications of modular forms to such diverse subjects as the theory of  quadratic forms, the proof of Fermat s last theorem and the approximation  of  pi . It provides a balanced overview of both the theoretical and  computational sides of the subject, allowing a variety of courses to be taught  from it.    Contents:  Historical Overview; Introduction to Modular Forms; Results on  Finite-Dimensionality; The Arithmetic of Modular Forms; Applications of  Modular Forms; Modular Forms in Characteristic  p ; Computing with  Modular Forms;  Appendices:  ; MAGMA Code for Classical Modular  Forms; SAGE Code for Classical Modular Forms; Hints and Answers to Selected  Exercises.

Modular Forms: A Classical and Computational Introduction PDF

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