All the Mathematics You Missed: But Need to Know for Graduate School 1st Edition by Thomas A. Garrity (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “This book will fill an interesting niche in a library collection…it should be used by browsing students interested in making sure that they are prepared for success in their graduate programs.” Choice”All the Mathematics You Missed…is a help for students going on to graduate school..Since many students beginning graduate school do not have the mathematical knowledge needed, All the Mathematics You Missed aims to fill in the gaps.” Berkshire Eagle, Pittsfield, MA”From the preface: ‘The goal of this book is to give people at least a rough idea of many topics that beginning graduate students at the best graduate schools are assumed to know.” Mathematical Reviews”The writing is lucid mathematical exposition, at a level quite appropriate to beginning graduate students.” The American Statistician”Before classes began, I jump started my graduate career with the help of this book. Even though I didn’t believe that I could have missed much math, it became clear that my belief was wrong during the first week of class. While proving a theorem, my professor asked if anyone remembered a previous result from calculus. While I did not remember it from my days as an undergraduate, I had read about the theorem and had even seen a sketch of the proof in Garrity’s book…This will be one of the books that I keep with me as I continue as a graduate student. It has certainly helped me understand concepts that I have missed.” Elizabeth D. Russell, Math Horizons”Point set topology, complex analysis, differential forms, the curvature of surfaces, the axiom of choice, Lebesgue integration, Fourier analysis, algorithms, and differential equations…. I found these sections to be the high points of the book. They were a sound introduction to material that some but not all graduate students will need.” Charles Ashbacher, School Science and Mathematics Book Description An essential resource for advanced undergraduate and beginning graduate students in quantitative subjects who need to quickly learn some serious mathematics.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Depending on what graduate school you go to (of course) students may or may not know such-and-such about field X but know a lot about field Y. For example, a student who does applied mathematics may not necessarily know a lot about topology. Instead of going over to Munkres, one need only skim the few pages that this book has on it to get the general idea.That being said, this book is not (or, at least, should not be considered) the be-all-end-all of any topic. This is more like a chocolate sampling pack: it’s a little bit of a lot of things. I’m glad, for example, that they included something about the Zariski topology, but I’m upset that they never actually calculate anything substantial in the parts about multivariable calculus. In particular, one of the questions asks the reader to “interpret” what the Jacobian means in such-and-such a case, but little is said in the chapter about such a thing.I’ve read this book in the following way: skim the parts I knew well, read the parts I didn’t know well, and write down topics that came up for the parts I didn’t know well. Afterwards (using, in fact, the suggested reading that is conveniently at the end of each chapter) I would read in greater detail.One last irritation: there are no solutions to any of the exercises. Normally, this is not such a bad deal, but for a number of the questions it would be nice to at least verify that my calculations are correct, or that my interpretation is what he wanted.All in all, it’s a nice book.

⭐It said like it said but missing the earlier part of it is arithmetic algebra 1 geometry and algebra 2 these u have to master before college algebra precalculus trig and calculus. One thing note I need geometry prior to discrete math.

⭐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.

⭐fun

⭐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.

⭐Well, don’t expect this book can help you pass the math prelims. But it indeed helps if you are in a quantitative discipline other than pure math and want to grab the math you need with limited time budgets.

⭐Sent to my adult daughter. She is boning up well.

⭐I had high hopes on reading this book, im an engineer just starting my PhD, I thought that the book would be taylored to engineering or physics students who needed a review of all the math they would need for grad school. Instead, it is a book directed towards math majors wanting to do graduate studies on math, it assumes you already have knowledge of all the topics covered in the book. Since it is directed towards math majors, you can expect to come across the math lingo used in math oriented books such as definitions, theorems, etc.. not practical at all, plus, the topics are very briefly covered so you wont get a good understanding of the topic. The author mentions that this book should be considered a guide more than a definite source of knowledge, so the recommended books at the end of each chapter are the truly precious info.

⭐This book provides a great overview of almost all the major maths I covered in my undergraduate degree. This is highly recommended to any aspiring postgraduates and is a great reference.

⭐See title. It’s not a comprehension review, but it is a great way to quickly freshen up some topics. Happy with the book! 🙂

⭐I didn’t expect the book to come in such a great condition. Thumbs up!

⭐Too few licenses. The default should be six, but this seems to have only 4.

⭐Excellent book. It helps you review essential undergrad math quickly.

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