LINEAR ALGEBRA I: BASIC CONCEPTS

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This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course. The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations. In particular, the following four aspects are emphasized. How matrices arise (discretization of differential equations, description of system structures, description of transition probability) What kinds of matrices arise (sparse matrices, positive definite matrices, diagonally-dominant matrices, nonnegative matrices, integer matrices, polynomial matrices) What characteristics we are interested in (rank, eigenvalues, singular values, positive definiteness) How we can compute (expansion formulas of determinants, elementary transformation, estimates of eigenvalues) Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Matrices Contents: Preface Matrices Determinants Elementary Transformations and Elimination Rank Systems of Linear Equations Eigenvalues Quadratic Forms Singular Values and the Method of Least Squares Vector Spaces Bibliography Index Readership: Undergraduate students majoring in engineering and other mathematical sciences.

BASIC ABSTRACT ALGEBRA: EXERCISES AND SOLUTIONS

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This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a "True or False" section in each chapter. Each chapter also contains an essential background section, which makes the book easier to use. Sample Chapter(s) Introduction CHAPTER 3: Binary Relations Request Inspection Copy Contents: Introduction Sets and Logic Mappings Binary Relations Groups Rings and Fields Polynomials and Rational Fractions Bibliography Index Readership: First and second year mathematics and computer science students interested in abstract algebra. Also good for instructors.