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Math For Business And Finance: An Algebraic Approach ISE
Math for Business & Finance: An Algebraic Approach provides modern examples for students to understand business mathematics and make connections with real-world applications.The course covers mathematical concepts from an algebraic approach, combined with Business applications.Every chapter is devoted to a Personal Finance theme, with topics that include Payroll and the Cost of Purchasing a Home.There is also extensive integration of scientific calculator notation, and also has the Wall Street Journal and Kiplinger news clips that have been widely popular in Jeffrey Slater's other two Business Math texts.Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, and how they need it, so that your class time is more engaging and effective.
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Algebraic Topology
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology.This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally.The author emphasizes the geometric aspects of the subject, which helps students gain intuition.A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find.Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers.Researchers will also welcome this aspect of the book.
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Algebraic Geometry
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P.Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years.In 1972 he moved to California where he is now Professor at the University of California at Berkeley.He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles.His current research interest is the geometry of projective varieties and vector bundles.He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively.Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons.He has travelled widely, speaks several foreign languages, and is an experienced mountain climber.He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.
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Algebraic Number Theory
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Introduction to Algebraic Geometry
The goal of this book is to provide an introduction to algebraic geometry accessible to students.Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts.In many places, analogies and differences with related mathematical areas are explained.The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra.The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.
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Elements Of Algebraic Topology
Elements of Algebraic Topology provides the most concrete approach to the subject.With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.
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Lectures On Algebraic Topology
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics.These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT.The style is engaging and student-friendly, but precise.Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
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Algebraic Geometry and Arithmetic Curves
This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem).This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups.Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory.The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field.Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces.Castelnuovo's criterion is proved and also the existence of the minimal regular model.This leads to the study of reduction of algebraic curves.The case of elliptic curves is studied in detail. The book concludes with the fundamental theorem of stable reduction of Deligne-Mumford. This book is essentially self-contained, including the necessary material on commutative algebra.The prerequisites are few, and including many examples and approximately 600 exercises, the book is ideal for graduate students.
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