All the Mathematics You Missed: But Need to Know for Graduate School
Thomas A. Garrity | 2001-11-12 00:00:00 | Cambridge University Press | 376 | Mathematics
Few beginning graduate students in mathematics and other quantitative subjects possess the daunting breadth of mathematical knowledge expected of them when they begin their studies. This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.
Reviews
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.
Reviews
If you need to learn the math this is not for you. If you know the math and need a refresher this is an excellent reference. If you travel a lot an need a reference but don't want to carry around a 10 lbs. book, this is a life saver.
Reviews
This book is not comprehensive and doesn't explain things well at all. It should have been titled, "All the Mathematics I, the Writer, Missed But Needed to Know For Graduate School," because that's exactly what it is. Do not misunderstand me: it is a good book and covers some interesting topics. However, it's not a book that will prepare you for graduate school. It's more of a collection of mathematical topics that the writer found interesting. It's similar to having dinner with a mathematician who can't stop talking about the topics they love.
Reviews
A previous reviewer pointed out that this book is meant to organize ones knowledge about math- not supplement for lack of knowledge. I agree. It gives recaps of the main ideas, and helps one to see the big picture about various subfields of math. Of course, NO ONE BOOK could POSSIBLY teach all of those subfields with a significant level of detail. So one should not attempt to use it for that purpose.
I'm a math undergrad, starting my senior year soon. I've been using this book to preview areas of math before taking a class in that area. It's been tremendously helpful to me to have an idea about the big picture and the context before grinding into specifics. I would highly recommend this book for that purpose. I don't know about other purposes, but for that it has been great for me.
The author gives many insights that nobody bothers to tell you in textbooks or in any specific class. For example, in the preface he explains that mathematics on the whole is about sets of certain types of objects and certain types of functions between those objects. This is a major simplification- but that's the point! I applaud Garrity for having the guts to say this, though he makes himself a target for ridicule by making such a gross simplification. Students like me need to hear it. The rest of the book begins each chapter by telling the reader what types of objects are studied in that field of math, and what the functions are that map between said objects.
It's a blurry, bird's-eye view of the big picture. But it motivates me. I have an idea about what to look forward to in a given class. I love this book. I had it out from my university's library for almost an entire year, and then realized I wanted my own copy so I could keep it.
Reviews
This book sucks. It has lots of useful mathematics in it, if you can decipher it. Most math classes you'll ever take involve mindless number shuffling and you never truly understand what you're doing. Colleges just want to produce marketable products (students) instead of good classes so most of us just repeat mathematical processes without understanding the theory behind it. This book assumes you understand those theories. I read of over some of the sections I had already learned about in college and they looked like total jibberish. Why? Because the definitions are so clinical and use notations that most of us have never seen. Not in class. Not in text books. Never! This book will make you appreciate your math teachers. It's light on examples and the ones given don't clearly demonstrate the logic involved.
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