Resolution of Curve and Surface Singularities in Characteristic Zero
Resolution of Curve and Surface Singularities in Characteristic Zero

Author: K. Kiyek

Publisher: Springer Science & Business Media

Published: 2012-09-11

Total Pages: 506

ISBN-13: 1402020295

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The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

A History of Modern Psychology
A History of Modern Psychology

Author: Duane Schultz

Publisher: Academic Press

Published: 2013-10-02

Total Pages: 433

ISBN-13: 1483257940

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A History of Modern Psychology, 3rd Edition discusses the development and decline of schools of thought in modern psychology. The book presents the continuing refinement of the tools, techniques, and methods of psychology in order to achieve increased precision and objectivity. Chapters focus on relevant topics such as the role of history in understanding the diversity and divisiveness of contemporary psychology; the impact of physics on the cognitive revolution and humanistic psychology; the influence of mechanism on Descartes's thinking; and the evolution of the third force, humanistic psychology. Undergraduate students of psychology and related fields will find the book invaluable in their pursuit of knowledge.

A Beginner's Guide to Scientific Method
A Beginner's Guide to Scientific Method

Author: Stephen Sayers Carey

Publisher: Wadsworth Publishing Company

Published: 2012

Total Pages: 146

ISBN-13: 9781111726010

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This concise yet comprehensive guide provides an introduction to the scientific method of inquiry. You will not only learn about the proper conduct of science but also how to recognize and question factors such as pseudoscience, untestable explanations and fallacies. Compact enough to be used as a supplementary book, yet comprehensive enough in its coverage to be used as a core book, this book assists users in using the scientific method to design and assess experiments.

Matrix Algebra for Applied Economics
Matrix Algebra for Applied Economics

Author: Shayle R. Searle

Publisher: Wiley-Interscience

Published: 2001-09-13

Total Pages: 0

ISBN-13: 9780471322078

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Coverage of matrix algebra for economists and students ofeconomics Matrix Algebra for Applied Economics explains the important tool ofmatrix algebra for students of economics and practicing economists.It includes examples that demonstrate the foundation operations ofmatrix algebra and illustrations of using the algebra for a varietyof economic problems. The authors present the scope and basic definitions of matrices,their arithmetic and simple operations, and describe specialmatrices and their properties, including the analog of division.They provide in-depth coverage of necessary theory and deal withconcepts and operations for using matrices in real-life situations.They discuss linear dependence and independence, as well as rank,canonical forms, generalized inverses, eigenroots, and vectors.Topics of prime interest to economists are shown to be simplifiedusing matrix algebra in linear equations, regression, linearmodels, linear programming, and Markov chains. Highlights include: * Numerous examples of real-world applications * Challenging exercises throughout the book * Mathematics understandable to readers of all backgrounds * Extensive up-to-date reference material Matrix Algebra for Applied Economics provides excellent guidancefor advanced undergraduate students and also graduate students.Practicing economists who want to sharpen their skills will findthis book both practical and easy-to-read, no matter what theirapplied interests.

A First Course in Mathematical Modeling
A First Course in Mathematical Modeling

Author: Frank R. Giordano

Publisher: Cengage Learning

Published: 2008-07-03

Total Pages: 640

ISBN-13: 9780495011590

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Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.