Teachers of lower-division college mathematics classes are often concerned about student deficiencies. Some students didn't master particular concepts when they studied them in class; some students need additional work or explanation on current topics; others are returning to school and are in need of a review. Maths: A Student's Survival Guide offers a collection of topic-specific materials for such students. This book begins with a review of early algebra topics (e.g., use of letters to represent unknowns, order of operations); moves through algebra and trigonometry; includes sections on series; continues with differential and integral calculus; and ends with a study of the complex number system. The book does not include material from matrix algebra, high school geometry (e.g., area, perimeter, similarity, congruence), or multivariable calculus. The first two chapters (only) include "self-tests" that students can use to determine where they should start their review.
The book reminds me of other review materials, such as the Schaum's Outline Series. The most obvious difference is the inclusion of all of the topics in one volume rather than the topic-specific volumes that the Schaum's Series offers. The sections are self-contained -- so a student could look for a particular topic without needing to read the rest of the book. Yet at key points, the author offers suggestions for review in other sections if the student is feeling lost in a particular topic. She also writes in a more conversational tone than the Schaum's books use, and her explanations are more extensive than the Schaum's books offer -- as if she is tutoring the student. The format cues students to engage in their reading in specific ways; for example, after presenting the primary Pythagorean trigonometry identity in a box, she writes: "This is an enormously useful result and it is worth surrounding its box with bright colour." She goes on to derive one of the other Pythagorean identities, and then asks the students to derive the third one -- she use a thick horizontal line across the page beneath a question to remind the students to pause in their reading to consider the question before reading her answer. She also manages explanations that are not jargon-filled but which also do not lack mathematical terminology. Furthermore, the book is black-and-white with grayscale graphics rather than color pictures -- a different presentation style from typical textbooks on the market these days..
In the preface to the book, phrases such as "this friendly and gentle self-help workbook" are used to describe the book. If this were the only part of the book I had read, I might have been "put-off" by this almost patronizing tone. However, beyond the preface the tone is more conversational and explanatory -- a tone that facilitates learning for some groups of students. So, I recommend just moving on past that first page. Of course, the book uses British terminology (e.g., "factorising"). Although some U.S. students may find this distracting or unfamiliar, I believe that the benefits of the book outweigh this mild inconvenience.
The reviewer asked graduate students attending the Undergraduate Curriculum and Pedagogy Research Seminar in the Department of Mathematics at the University of Oklahoma to offer their thoughts on this book and its possible uses. The group included students with experience outside the U.S., a community college mathematics instructor, and an eighth grade mathematics teacher. Even such a diverse group agreed unanimously that this book is an essential for every library. We could all think of students who would benefit from access to the book. We think the book would be especially useful to students returning to school or to mathematics after some hiatus. We also believe that the book might be useful for preservice or new teachers who want some examples of explanations for these topics. Even experienced instructors might use it when preparing lessons as a resource for examples or additional explanations and connections.
Teri J. Murphy (firstname.lastname@example.org) is assistant professor of mathematics at the University of Oklahoma. Her research specialty is undergraduate mathematics education.