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A course on surgery theory
An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. ...
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A primer on mapping class groups
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time g...
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Beautiful geometry
An exquisite visual celebration of the 2,500-year history of geometryIf you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite ...
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Curves for the mathematically curious
Ten amazing curves personally selected by one of today's most important math writersCurves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an acco...
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Discrete and computational geometry
An essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet w...
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Discrete and computational geometry, 2nd edition
The essential introduction to discrete and computational geometry—now fully updated and expandedDiscrete and Computational Geometry bridges the theoretical world of discrete geometry with the applications-driven realm of computational geometry, offering a comprehensive yet accessible introduction...
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Flatland
In 1884, Edwin Abbott Abbott wrote a mathematical adventure set in a two-dimensional plane world, populated by a hierarchical society of regular geometrical figures-who think and speak and have all too human emotions. Since then Flatland has fascinated generations of readers, becoming a perennial...
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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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How to solve it
The bestselling book that has helped millions of readers solve any problemA must-have guide by eminent mathematician G. Polya, How to Solve It shows anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or findi...
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Intermittent convex integration for the 3d euler equations
A new threshold for the existence of weak solutions to the incompressible Euler equationsTo gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solut...
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Introduction to topology and geometry
A concise and unified introduction to the foundational concepts of modern topology and geometryTopology and geometry are branches of mathematics with applications in fields ranging from physics and chemistry to computer science and economics. This textbook offers a rigorous yet accessible approac...
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Lectures on the h-cobordism theorem
Important lectures on differential topology by acclaimed mathematician John MilnorThese are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the o...
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Mathematical excursions to the world's great buildings
How mathematics helped build the world's most important buildings from early Egypt to the presentFrom the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular b...
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Office hours with a geometric group theorist
Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instru...
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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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Perspective and projective geometry
Through a unique approach combining art and mathematics, Perspective and Projective Geometry introduces students to the ways that projective geometry applies to perspective art. Geometry, like mathematics as a whole, offers a useful and meaningful lens for understanding the visual world. Explorin...
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The man who saved geometry
An illuminating biography of one of the greatest geometers of the twentieth centuryDriven by a profound love of shapes and symmetries, Donald Coxeter (1907–2003) preserved the tradition of classical geometry when it was under attack by influential mathematicians who promoted a more algebraic and ...
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The structure of groups with a quasiconvex hierarchy
This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory that generalizes ideas...
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Viewpoints
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of es...
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