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A First Course in Linear Algebra: Study Guide for Undergraduate Linear Algebra Course

Mohammed Kaabar
CreateSpace Independent Publishing Platform
Publication Date: 
Number of Pages: 
Student Helps
[Reviewed by
Tom Schulte
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The five chapters of this volume touch upon linear systems, vector spaces, characteristic equations of matrices and vector operations such as the dot product. Exercises conclude each chapter with solutions to odd-numbered exercises at the end of the book. This book assumes the reader has taken at least one semester of calculus.

This text suffers from a lack of editing. The resulting printed errors or incomplete statements can confuse the reader new to the topic. This ranges from the minor typographical (the first variable in consideration may be referred to both as x1 and x1 in the same sentence) to logic pernicious for its incompleteness. An exercise that asks “Find Span{(1,2),(2,3)}” concludes “Hence, {(1,2),(2,3),(5,8)} \(\in\) Span{(1,2),(2,3)}” with spacing, etc. as in the text. No suggestion is made that the complete linear span has not been arrived at or how to describe it generally, a key topic largely foregone here. Other examples are merely abrupt and without context.

Lacking a cohesive exposition of the topic at large, the result is islands of unassimilated facts, merely related trivia from the larger subject.

Any work that advertises itself as a “first course” should be comprehensive on fundamentals for the topic at hand and self-contained enough to not require additional introductory texts on the same topic. This text reads like unfinished lecture notes that cannot be presented to or relied upon by a student without the preface of detailed lecture or another, more complete text. The subtitle of “study guide” fits better. This could be a checklist for a student looking for self-assessment.

Tom Schulte works hard to introduce students to topics in mathematics and lectures at Oakland Community College.

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