Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Science & Math

John B. Little

David A. Cox

Mathematics

Springer

Suitable for advanced undergraduates and graduate students, this text offers a complete introduction to the basic concepts of linear algebra. Interesting and inspiring in its approach, it imparts an understanding of the subject's logical structure as well as the ways in which linear algebra provides solutions to problems in many branches of mathematics. The authors define general vector spaces and linear mappings at the outset and base all subsequent developments on these concepts. This approach provides a ready-made context, motivation, and geometric interpretation for each new computational technique. Proofs and abstract problem-solving are introduced from the start, offering students an immediate opportunity to practice applying what they've learned. Each chapter contains an introduction, summary, and supplementary exercises. The text concludes with a pair of helpful appendixes and solutions to selected exercises.

A Course in Linear Algebra (Dover Books on Mathematics)

David B. Damiano

Dover Publications

Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.

Toric Varieties (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 124)

Henry K. Schenck

American Mathematical Society

Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human society's energy needs and have fewer harmful effects? How do we deal with threats such as emergent diseases? Mathematical models equations of various sorts capturing relationships between variables involved in a complex situation are fundamental for understanding the potential consequences of choices we make. Extracting insights from the vast amounts of data we are able to collect requires analysis methods and statistical reasoning. This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate liberal arts mathematics -type course but with a specific focus on environmental applications. It is suitable for introductory courses with no prerequisites beyond high school mathematics. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples. Every chapter ends with a section of problems, as well as with an extended chapter project which often involves substantial computing work either in spreadsheet software or in the R statistical package.

Modeling and Data Analysis: An Introduction With Environmental Applications

Toric Varieties (Graduate Studies in Mathematics)

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Books by John B. Little