The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra in a clear and easily understandable style. Over 160 computer-generated images, accessible to readers via the World Wide Web, facilitate an understanding of mathematical concepts and proofs even further.
Introduction to the Theory of GroupsAnyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions. The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange's theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.
Algebra Success in 20 Minutes a Day, 4th Edition (Skill Builders)
Algebra Success in 20 Minutes a Day, 4th Edition is a wonderful introduction or refresher course in basic algebra, including working with integers, equations, inequalities, radicals, and the quadratic formula. It offers 20 simple lessons that promote quick but thorough coverage of practical, essential skills. There is an emphasis on the applicability of algebra skills to real-world and real-work problems. Algebra Success includes a FREE online link to instantly scored practice exercises.
This book is a concise, self-contained introduction to abstract algebra which stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation- both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others. Classical results of geometry and number theory are used to motivate and illustrate algebraic techniques, and classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory.
Added by: honhungoc | Karma: 8660.27 | Black Hole | 25 November 2010
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MIT Linear Algebra Video Lectures
These video lectures of Professor Gilbert Strang teaching 18.06 were recorded live in the Fall. Support for the video production was provided by the Lord Foundation of Massachusetts under a grant to the MIT Center for Advanced Educational Services.
01 The Geometry of Linear Equations.rm 02 Elimination with Matrices.rm 03 Multiplication and Inverse Matrices.rm 04 Factorization into A = LU.rm 05 Transposes, Permutations, Spaces R^n.rm 06 Column Space and Nullspace.rm 07 Solving Ax = 0 - Pivot Variables, Special Solutions.rm 08 Solving Ax = b - Row Reduced Form R.rm 09 Independence, Basis, and Dimension.rm
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