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Stable Categories and Structured Ring Spectra
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
Modern Mathematical Logic
This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level.
Introduction to Proofs and Proof Strategies
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
The Strong K�nneth Theorem for Topological Periodic Cyclic Homology
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Modern Food, Moral Food
American eating changed dramatically in the early twentieth century. As food production became more industrialized, nutritionists, home economists, and so-called racial scientists were all pointing Americans toward a newly scientific approach to diet. Food faddists were rewriting the most basic rules surrounding eating, while reformers were working to reshape the diets of immigrants and the poor. And by the time of World War I, the country's first international aid program was bringing moral advice about food conservation into kitchens around the country. In Modern Food, Moral Food, Helen Zoe Veit argues that the twentieth-century food revolution was fueled by a powerful conviction that Americans had a moral obligation to use self-discipline and reason, rather than taste and tradition, in choosing what to eat. Veit weaves together cultural history and the history of science to bring readers into the strange and complex world of the American Progressive Era. The era's emphasis on science and self-control left a profound mark on American eating, one that remains today in everything from the ubiquity of science-based dietary advice to the tenacious idealization of thinness.
An Invitation to Combinatorics
A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.
An Alpine Expedition through Algebraic Topology
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
Advances in Noncommutative Geometry
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
An Introduction to Abstract Algebra
A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.
Algebraic Topology: Applications and New Directions
This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.
