Linear Methods: A General Education Course

by David Hecker, Stephen Andrilli

Linear A General Education Course is expressly written for non-mathematical students, particularly freshmen taking a required core mathematics course. Rather than covering a hodgepodge of different topics as is typical for a core mathematics course, this text encourages students to explore one particular branch of mathematics, elementary linear algebra, in some depth. The material is presented in an accessible manner, as opposed to a traditional overly rigorous approach. While introducing students to useful topics in linear algebra, the book also includes a gentle introduction to more abstract facets of the subject. Many relevant uses of linear algebra in today’s world are illustrated, including applications involving business, economics, elementary graph theory, Markov chains, linear regression and least-squares polynomials, geometric transformations, and elementary physics. The authors have included proofs of various important elementary theorems and properties which provide readers with the reasoning behind these results. Authors David Hecker is a Professor of Mathematics at Saint Joseph's University in Philadelphia. He received his Ph.D. from Rutgers University and has published several journal articles. He also co-authored several editions of Elementary Linear Algebra with Stephen Andrilli. Stephen Andrilli is a Professor in the Mathematics and Computer Science Department at La Salle University in Philadelphia. He received his Ph.D. from Rutgers University and also co-authored several editions of Elementary Linear Algebra with David Hecker .

410 pages, Paperback

Published August 9, 2018

Reviews

[Tom Schulte · Rating 4 out of 5]

"...this text still offers opportunities to amplify linear methods in a college algebra course. This includes the extensive coverage of Gauss-Jordan around elementary row operations with little reliance on matrix inverses. The introduction to linear regression is based on transpose matrices over the iterative least squares sum approach typically used at this level. I find Algebra I textbooks often leave the transpose operation out there as a seldom applied technique while students find least squares sums a tedious exercise better done by a calculator and offering no real insight. I find intriguing the idea introducing linear regression as a matrix method applying newly introduced matrix operations...."

[Look for my entire review at MAA Reviews]