Introduction to Linear Algebra: Models, Methods, and Theory

This book provides students with a unified introduction to the models, methods, and theory of modern linear algebra. It introduces students to economic input-output models, population growth models, Markov chains, linear programming, computer graphics, regression and other statistical techniques, and more, which reinforce each other and associated theory.

This book develops linear algebra around matrices. It puts problem solving and an intuitive treatment of theory first, with a proof-oriented approach intended to come in a second course, in the same way that calculus is taught. The material is unified by the repeated use of a few linear models to illustrate each new concept and technique. These models help students visualize new ideas as they re taught and remember them after the course is complete. Although the book is often informal, it also covers several topics normally left to a more advanced course such as matrix norms, matrix decompositions, and approximation by orthogonal polynomials. This book presents a healthy interplay between mathematics and computer science, that is between continuous and discrete models of thinking.

Table of Contents:
Ch. 1 Introductory Modules
Ch. 2 Matrices
Ch. 3 Solving Systems of Linear Equations
Ch. 4 A Sampling of Linear Models
Ch. 5 Theory of Systems of Linear Equations and Eigenvalue / Eigenvector Problems

Alan Tucker teaches mathematics at SUNY Stony Brook. He started his career at Stony Brook doing research in graph theory and combinatorial algorithms. Increasingly over the past 20 years he has become more and more engaged in projects about school and collegiate mathematics education. He has been the lead author of four major reports from the Mathematical Association of America, including The Mathematical Education of Teachers (2001). He has run a number of large educational grants at Stony Brook and for the Math Association.