Toshitsune Miyake Books

Focusing on clarity for beginners, the book delves into linear algebra, starting with matrices and their operations as abstractions of tables. It emphasizes the connection between linear equations and linear algebra, using row-reduction methods akin to Gauss elimination for solving systems. Unique to this text is the vertical arrangement of matrices for easier calculations. Additionally, it covers advanced topics like Hermitian products, Jordan normal forms, and the application of determinants to polynomial resultants, while also introducing abstract vector spaces.

This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition. It offers the basic knowledge of elliptic modular forms necessary to understand recent developments in number theory. It also treats the unit groups of quaternion algebras, rarely dealt with in books; and in the last chapter, Eisenstein series with parameter are discussed following the recent work of Shimura.