J.S. Chahal's Books

Fundamentals of Linear Algebra

By: J.S. Chahal

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Fundamentals of Linear Algebra

By: J.S. Chahal

Fundamentals of Linear Algebra is like no other book on the subject. By following a natural and unified approach to the subject it has, in less than 250 pages, achieved a more complete coverage of the subject than books with more than twice as many pages. For example, the textbooks in use in the United States prove the existence of a basis only for finite dimensional vector spaces. This book proves it for any given vector space. With his experience in algebraic geometry and commutative algebra, the author defines the dimension of a vector space as its Krull dimension. By doing so, most of the facts about bases when the dimension is finite, are trivial consequences of this definition. To name one, the replacement theorem is no longer needed. It becomes obvious that any two bases of a finite dimensional vector space contain the same number of vectors. Moreover, this definition of the dimension works equally well when the geometric objects are nonlinear. Features: Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems

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241

Publisher

CRC Press

Published Date

ISBN 10

0429758111

ISBN 13

9780429758119

Algebraic Number Theory

A Brief Introduction

By: J.S. Chahal

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Algebraic Number Theory

A Brief Introduction

By: J.S. Chahal

This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.

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166

Publisher

CRC Press

Published Date

ISBN 10

1000402185

ISBN 13

9781000402186

Topics in Number Theory

By: J.S. Chahal

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Topics in Number Theory

By: J.S. Chahal

This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. It is intended to be an introduction to the theory of numbers. The audience consisted largely of undergraduate students with no more background than high school mathematics. The presentation was thus kept as elementary and self-contained as possible. However, because the discussion was, generally, carried far enough to introduce the audience to some areas of current research, the book should also be useful to graduate students. The only prerequisite to reading the book is an interest in and aptitude for mathe matics. Though the topics may seem unrelated, the study of diophantine equations has been our main goal. I am indebted to several mathematicians whose published as well as unpublished work has been freely used throughout this book. In particular, the Phillips Lectures at Haverford College given by Professor John T. Tate have been an important source of material for the book. Some parts of Chapter 5 on algebraic curves are, for example, based on these lectures.

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198

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1489904395

ISBN 13

9781489904393

Fertilizer sulfur and food production

Research and Policy Implications for Tropical Countries

By: J.S. Kanwar,Mohinder S. Mudahar

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Fertilizer sulfur and food production

Research and Policy Implications for Tropical Countries

By: J.S. Kanwar,Mohinder S. Mudahar

Fertilizer is a vital component of strategies for expanding foodproduction. The rapid growth in population and the widening food deficits inmany tropical countries of Asia, Africa, and Latin America call attention to those aspects of fertilization that have been neglected but are expected to yield large economic payoffs in the future. Fertilizer sulfur falls into this category. In the past fertilizer sulfur received little attention from researchers and policymakers since sulfur deficiency was not considered a serious problem. It was not a problem because of low crop yields, extensive cropping, and the incidental supply of sulfur through rain, irrigation water, manures, and sulfurcontaining fertilizers. However, the situation has changed in the last three decades. Moder nagriculture based on high crop yields, intensive cropping, improved crop varieties, and greater use of sulfur-free fertilizers and environmental regula tions restricting sulfur emissions are creating large gaps between sulfur sup ply and sulfur requirements. Sulfur deficiencies are widespread and grow ing. Consequently, the full potential of a modern agricultural system in tropical countries is not being realized. This research effort results from the recognition of the seriousness of the sulfur problem and its adverse impact on food production as well as IFDC's dedication to the development and transfer of economically ef ficient fertilizer technology to tropical countries. This study represents a comprehensive analysis of the technical and economic linkages between fer tilizer sulfur and food production, and it provides guidelines for future directions in fertilizer sulfur research and public policy.

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Page Count

249

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400943520

ISBN 13

9789400943520

Fundamentals of Linear Algebra

By: J.S. Chahal

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Fundamentals of Linear Algebra

By: J.S. Chahal

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Solve jigsaw puzzle

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Page Count

241

Publisher

CRC Press

Published Date

ISBN 10

0429758111

ISBN 13

9780429758119

Book's by J.S. Chahal

Fundamentals of Linear Algebra

Fundamentals of Linear Algebra

Algebraic Number Theory

Algebraic Number Theory

Topics in Number Theory

Topics in Number Theory

Fertilizer sulfur and food production

Fertilizer sulfur and food production

Fundamentals of Linear Algebra

Fundamentals of Linear Algebra

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