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Theodore Smith
Theodore Smith

Abstract Algebra: A First Course

A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra, and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose. This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Gröbner bases. Key to the 8th Edition has been transforming from a print-based learning tool to a digital learning tool. The eText is packed with content and tools, such as mini-lecture videos and interactive figures, that bring course content to life for students in new ways and enhance instruction. A low-cost, loose-leaf version of the text is also available for purchase within the Pearson eText.

Abstract Algebra: A First Course

MAT* 274 - Linear AlgebraCredit(s): 4Prerequisite(s): MAT* 256 A first course in linear algebra for students in mathematics, science and engineering. Topics include systems of linear equations and their solutions; matrices, matrix algebra, and inverse matrices; determinants; real n-dimensional vector spaces, abstract vector spaces and their axioms; linear transformations; inner products (dot products), orthogonality, and their applications; subspaces, linear independence, bases for vector spaces, dimension, and matrix rank; eigenvectors, eigenvalues, and matrix diagonalization. Applications from various disciplines will be considered throughout the course. This course requires a graphing calculator and may include use of a computer software package.

This course provides an introduction to the ideas and methods of linear algebra, which you will learn by understanding them geometrically, justifying them algebraically, and using them to solve problems in various disciplines. In addition, the course serves as an introduction to abstract reasoning and mathematical proof. It is a prerequisite for all advanced courses in mathematics and provides excellent preparation for graduate work in the natural sciences and quantitative social sciences.

If you think you may need accommodations in this course due to the impact of a disability please meet with me privately during the first week of class. You should also contact the Resources for Disabled Students office to confirm your eligibility for appropriate accommodations. Doing so early in the semester will help prevent unnecessary inconvenience.

Beginning with the work of Dehn, geometric group theory has studied the structure of groups via their actions on metric spaces. Classical problems in geometric group theory include algorithmic problems, such as the word and conjugacy problem, and questions about the structure of subgroups. In the first part of the course, we will discuss these and other problems in the context of CAT(0) spaces, and particularly CAT(0) cube complexes. In the second part of the course, we will explore groups acting on trees and spaces of trees.

This course is a study of sets, mappings, operations, relations, partitions, and basic algebraic structures, including groups, rings, integral domains, fields, and vector spaces. This is the second course in a two-semester sequence which introduces the student to algebraic structures; it builds on the introduction to vector spaces which is begun in the first course, MT 325 Linear Algebra. Prerequisite: MT 315 or MT 320, and MT 325. 041b061a72

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