After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning. Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A). Ancillary Materials: Online Homework System (Lyryx Learning) Partial Student Solution Manual, Instructor Solution Manual, Lecture Slides, LaTeX Source Files (all Creative Commons licensed)
Type of Material:
Open (Access) Textbook
Recommended Uses:
This is meant to be the main textbook for a linear algebra course.
Technical Requirements:
PDF viewer.
Identify Major Learning Goals:
This textbook can help the student learn all of the material from a standard linear algebra course.
Target Student Population:
Sophomore level math or hard science majors and minors.
Prerequisite Knowledge or Skills:
First year calculus.
Content Quality
Rating:
Strengths:
This textbook covers all of the topics covered in a standard sophomore level linear algebra course. Each chapter is concluded with a section or two dedicated to applications. Applications include many that are relevant to today’s students such as the Google page rank and Principle Component Analysis. The main theorems are well labeled and presented and the proofs are at an appropriate level of the target audience. All major definitions and theorems are highlighted which makes the material comprehension easier. The order of the topics work well, with the more abstract topics such as general linear transformations and inner product spaces towards the end and the more concrete topics such as matrix arithmetic and vectors in R^n towards the beginning. There are plenty of examples and homework problems.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This book is a very standard book in linear algebra, so can easily be adopted by any instructor teaching this course. The sections flow well with the theory being motivated by concrete examples. The notation is standard as is the vocabulary that is used. The quality of this textbook rises to the level of any linear algebra textbook out there, so there is no reason to make students pay for an expensive book that is not any better than this one.
Concerns:
Some questions have solution in the “back of the book” while others don’t. The choice of which have solutions seem to be somewhat random, so the creation of homework assignments will be cumbersome.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The textbook is available in pdf, so any student will be able to access it. The topics are in standard order and working through any particular section is naturally done. From the table of contents, the students can link to any section or to the answers in the back of the book.
Concerns:
The table of contents would be better placed at the very beginning of the book to make navigation easier. It would also help if there were links from vocabulary words that are used in the sections to the pages where the definitions of these words are given.
Creative Commons:
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