Modular Forms (ePub)

Modular Forms is 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 various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added. Request Inspection CopyContents:Historical OverviewIntroduction to Modular FormsResults on Finite-DimensionalityThe Arithmetic of Modular FormsApplications of Modular FormsModular Forms in Characteristic pComputing with Modular FormsThe Future of Modular Forms?Modular Forms ProjectsAppendices:Magma Code for Classical Modular FormsSage Code for Classical Modular FormsHints and Answers to Selected ExercisesReadership: Graduate students studying or taking a course in modular forms.Key Features:Covers the computational side together with the theoryHas a wide variety of exercisesHistorical asides and references to modular forms in mathematical culture which help ground the subject and motivate student interest