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A First Course in Modular Forms
This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms. The topics covered …
Probability-1
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random …
Partial Differential Equations
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and …
Introduction to Topological Manifolds
This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, …
Problems in Algebraic Number Theory
Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an …
Univalent Functions and Teichmüller Spaces
This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich …
Fourier Analysis and Its Applications
TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an …
Introduction to Elliptic Curves and Modular Forms
This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is …
Categories for the Working Mathematician
This new edition includes a number of revisions and additions. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The …
Elementary Functional Analysis
Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new …