All the Mathematics You Missed: But Need to Know for Graduate School

I will admit upfront that I got suckered in by the title. As I write this, I'm somewhere on the downhill slope of my own graduate studies in mechanical engineering, at a university with a very strong mechanics program. I've struggled in some of said mechanics classes because of my relatively limited mathematics background, so this sounded like a book that was right up my alley. Garrity picks a wide range of mathematical topics, from sets to vector analysis to geometry to differential equations, and briefly covers the main points of each of the fields. He lacks true rigor (even admits it in the preface), but that isn't the point- the book is a survey, and Garrity references many books in and at the end of each chapter. If you find yourself working in one of the areas covered, I would image that this book would be an excellent place to go for an introduction/refresher to the main concepts, and then point you in the proper direction for further study. Despite the content, I found this book to be quite readable. There are a few typos, but nothing too distracting. The tone is more casual/conversational than what I have seen in other mathematics books. The book didn't satisfy my expectations/goals of the purchase, but it wasn't written for engineers...or maybe after all of my fancy book learnin' I am already familiar enough with the topics that form the base of engineering mathematics (PDEs and vector calculus). I would still recommend the book for current or soon-to-be graduate students in math or the sciences. It seems like this will be quite the helpful tool.