This book provides an introduction to modular forms and the Modularity Theorem, covering topics such as elliptic curves, modular curves, Hecke operators, and Galois representations. It's designed for beginning graduate students and advanced undergraduates, with no prior knowledge in algebraic number theory required, and includes exercises throughout.
Focusing on the interplay between analysis and multivariable calculus, this book offers a conceptual approach that emphasizes their connection within Euclidean space. It covers differentiation, leading to the inverse and implicit function theorems, and integration, culminating in the general fundamental theorem of integral calculus. The text strikes a balance, providing more depth than standard calculus books while remaining less technical than typical analysis introductions, making it accessible for students seeking a comprehensive understanding of these intertwined subjects.