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Adelic line bundles on quasi-projective varieties
A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In th...
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Elliptic curves
An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come togethe...
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Enlightening symbols
An entertaining look at the origins of mathematical symbolsWhile all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before th...
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How students think when doing algebra
This book bridges research and practice to help teachers understand students' algebraic thinking. It covers five domains tied to CCSS topics and aims to accelerate early career teachers' experience with student misconceptions and struggles. The book is a valuable resource for both new and veteran...
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How to fall slower than gravity
An engaging collection of intriguing problems that shows you how to think like a mathematical physicistPaul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Alway...
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Negative math
A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? ...
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Numerical methods
A rigorous and comprehensive introduction to numerical analysisNumerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing...
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Pentagons and pentagrams
A fascinating exploration of the pentagon and its role in various culturesThe pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, ...
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Representation theory of semisimple groups
In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and r...
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Supersingular p-adic l-functions, maass-shimura operators and waldspurger formulas
A groundbreaking contribution to number theory that unifies classical and modern resultsThis book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to...
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Taming the unknown
What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved a...
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Totally nonnegative matrices
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, histo...
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Unipotent ideals and harish-chandra bimodules
A groundbreaking book that applies new geometric tools to one of the oldest problems in representation theory, expanding the field and paving the way for further progressIn the 1920s, Hermann Weyl gave a complete classification of the irreducible unitary representations of a compact Lie group G. ...
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