Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity 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 explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.
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All the Math You Missed
Original price was: $31,99.$18,99Current price is: $18,99.
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Euclid –
I studied mathematics in graduate school 50 years ago, then worked as an actuary for 30 years. Thus I really enjoy reading a clear summary of the various topics one should know after a bachelor’s degree, review, nostalgia and catching up on what I missed. It is very enjoyable to read succinct accounts of the most central parts of mathemtics. Highly recommended!
Man –
If youβre headed through school on a STEM plan, this title is worth it.
Patrick –
I studied physics as an undergrad (a long time back), and have recently return to self-studies. This book provides an excellent summary of the essential theorems of advanced graduate mathematics, as needed for advanced undergraduate, and 1st/2nd year graduate study in physics. I’m not sure why the preview is virtually empty, not even a table of contents. That is usually a “red flag” for a book with no value, but here there is great content, clear organization, strong and graspable writing, and connections between different areas of math of well elucidated. This book is not for mathematicians, the proofs are brief or omitted altogether. But excellent for physicists, and probably for EEs, mech Es, material scientists, etc.
If/when I have time, I may edit this to at least post the outline of the table of contents. Anyway — lacking a decent preview, I decided I could afford a few $$ to give the book a test run. I am glad I did.
G. Cheves –
Good survey of undergraduate mathematics but there is no logic, set theory and scant discrete mathematics coverage, with the exception of combinatorics and probability
Table of Contents
Preface; On the structure of mathematics; Brief summaries of topics; 1. Linear algebra; 2. e and d real analysis; 3. Calculus for vector-valued functions; 4. Point set topology; 5. Classical stokes’ theorems; 6. Differential forms and Stokes’ theorem; 7. Curvature for curves and surfaces; 8. Geometry; 9. Complex analysis; 10. Countability and the axiom of choice; 11. Algebra; 12. Lebesgue integration; 13. Fourier analysis; 14. Differential equations; 15. Combinatorics and probability; 16. Algorithms; A. Equivalence relations.
Bill P –
I have the original book. This is a nice update and the author has done a good job with it. If you are looking for an overview of advanced mathematics for your studies, this is a great book to have.
Vivianna –
This book is definitely not for beginners. I have an MA in Economics and I wanted to brush up and improve my maths. The book is quite a challenge (for me anyway) but enjoyable at the same time. I bought it on the recommendation of The Maths Sorcerer on YouTube. If maths was difficult for you at school (eg at ‘O’ level), then you might be better with something a bit easier. Very good book though.
Emmanuel Gutierrez –
If you think you will learn graduate level mathematics from this book, you are very mistaken, this is a review of undergraduate level mathematics, some of it itβs useful for physicists, and engineers, from this book and itβs references you can expand your knowledge a lot.
Marco Shinobu Matsumura –
A nice resource in the style of the Princeton Companion. Helps give a quick overview of a subject and guide you through the literature. Great for those reviewing long forgotten material.
W. A. Svrcek-Seiler –
I (re-)learned a lot by reading this book. But some topics I already knew about beforehand seem
presented in a needlessly unintuitive way. Still I recommend the book for everyone who wants to brush up
his/her math.
OldScold –
If you just need to brush up on calculus or differential equations, this has more than you need, including math I never heard of, not being a math major. A good insight into that mysterious world, and maybe even good for some self-teaching. But be aware the bias is towards training mathematicians, not engineers or economists.
Alun –
This was a 3/5, but in writing this review I realized that unfair. Still, I feel a bit bad giving a 4/5, but truthfully I felt that this rehashed too much of a standard undergraduate curriculum (I do realize that’s the point), but not necessarily even one from a top school, which is more what I was hoping for. The chapter on category theory was well-received, as were the number theories (there is a bias, to be sure) — and I very much appreciated the inclusion of a section on Fourier analysis. Perhaps the (hopeful) algebraist in me is showing, or perhaps my analysis classes were particularly good, but I found myself skimming quite a lot. Still, it is a book I would have no qualms recommending to a friend desiring a different mathematical education to mine.
devilseedchild –
It showed me that mayh can be fun
Ace lastone –
Very easy to read very explanatory I would suggest this for anybody in graduate school. Or anybody who’s interested in just math
A. Dark –
The book serves two purposes. The stated goal is to allow a prospective grad student in mathematics or a closely related subject to easily examine subject matter that will be regarded as core material at the graduate level, but might have been missed at the undergraduate level. A second purpose the book could serve is to provide a list of advanced mathematical topics that might have broad value beyond that of progressing toward a degree. The book’s approach serves both of these goals very well. Twenty discrete topics are reviewed separately, each of which provide definitions, theorems, examples, and problems that cover the core concepts. This gives the reader a very clear idea as to whether the subject has been mastered, or if it demands a brush-up review or more substantial study to get up to speed. The casual rather than formal style helps with this task, and highlights the fact that this isn’t a mathematics textbook. If it turns out the reader is weak on a topic, each chapter ends with a list of recommended books with indications of the contents, depth and style of coverage that each book offers.
Having read the book, and being familiar with about half a dozen of the topics covered, I consider the approach very effective and the material to be well chosen. If there are any less important topics included, I would guess that these would be the four chapters added to the second edition, all of which involve number theory. I’ve also found the casual style beneficial for looking up mathematical concepts. A simple web search yields strict technical definitions and rough illustrative analogies of terms and concepts in advanced mathematics, but it’s harder to find a quick, well-informed summary clarifying topical questions.
I am not a mathematics graduate student, but I found the book invaluable, and I’m convinced I would have benefitted from having this book as a freshman in college, or even as a junior in high school. It’s not a mathematics textbook, it’s a list of places to direct one’s attention in the field of advanced mathematics.
Victor –
bom
Marc –
For me it’s not “all the math I missed” but “a lot of the math I forgot”. … Now that I’m old it’s interesting to see if I can still do it … and, I’m doing okay.
The book is not very deep but is pretty broad. So, if that’s what you’re looking for I would recommend it.
Grant Eastland –
The book arrived in excellent condition, and I find that it well written and fairly good explanation of the included mathematics. The book covers several different areas and topics of mathematics utilized in physics but is not a comprehensive mathematics book. There are several topics and details that I found that I didn’t learn in the course I took 20+ years ago and appreciate that proofs are not the emphasis.
Someone with a fundamental understanding of calculus and mathematical notation would be able to follow most things in this book.
Dr. L. G. Fugate –
I’m using this book as a review. It would also be helpful for college students learning the subjects for the first time. The presentation is a bit different from other textbooks; I think it’s very helpful to read at least two different perspectives.
Bill Roth –
The bibliography lists almost 200 authoritative resources and is itself worth the price of the book. This book will inspire readers to discover topics they may not have ever encountered.
Marcelo Alves de Oliveira –
Γ um resumo dos principais tΓ³picos de um curso de graduação, com alguns exercΓcios e uma bibliografia para aprofundamento. Indicado para quem quer se preparar para uma pΓ³s-graduação em MatemΓ‘tica. Muito bem escrito, mas sucinto como se propΓ΄s.
WP –
The book is an overview of the math you might be expected to encounter in graduate school when studying Math and/or one or more of the hard sciences.
Brian Chown –
This book is for students attending University.
Lettore –
Libro stupendo, contenuto stupendo. Raccomando.
monte –
Great Book AAA+++
qirong29 –
I’ve not quite finished reading this book, but I find its choice of topics as “the maths missing” very good indeed. It’s also piqued at just the level I wanted.
Geronimo OrdoΓ±ez –
A couple of more exercises could help.
RUSSELL L STEAD –
I enjoyed reading the 1st edition more than 20 years ago. This 2nd edition has 4 more topics and is very well written and just as enjoyable to read. Although I never made it to grad school. I think anyone interested in a “survey” of important mathematics would enjoy and benefit from reading this book. Like his fellow Williams College colleague Colin Adams’ book on knots, this book is a very well done effort!
Ron Toolsie –
For those who pursue graduate degrees in STEM fields, the mathematical tools that are required in graduate school are way deeper than those needed as an undergrad-where formal training usually ends with Calculus3 and diff-eq. This book is a nice and fairly short compendium of the skills that are expected very early on in graduate school.
There are other excellent, well written texts for non-mathematicians who need deeper knowlege of applied mathematical techniques. Boas ‘Mathematic Methods for the Physical Sciences’ is one that immediately springs to mind, as do the books by Bryon and Arfken. There is no SINGLE book that will fill the needs of every graduate student, but this one should be one of the first you turn to.
Kelvin D. Meeks –
I was looking for a text that would help me renew some of my math skills – and also provide a holistic roadmap for broadening and deepening my efforts to prepare for graduate-level course work.
The writing in this book is clear, concise, and well written.
I especially appreciated the commentary in the “Books” section at the end of the chapters – offering the author’s person insights & suggestions on which books to explore a given topic further.
Swapnil Varpe –
I like this book alot. This gives overview and important topics of higher mathematics. As title says this book gives all maths that we need to know for higher studies
ASdni –
Good book
mike –
Great idea. Great book. Thank only wished that the format is smaller – like the first edition.
Jansen Fisher –
The content of this book is still too shallow for students majoring in mathematics. However, for non-math majors, it can be very helpful.
John –
Great book in general covering a wide breadth of topics, but the section on category has several errors. Within the first few pages, there are several examples of function composition arguments in the wrong order, as well as referring to morphisms as functors. Thankfullu, the commutation diagrams are correct, so it’s likely just sloppiness on the part of the author. Still frustrating though.
R. Finley –
I had the previous edition of this book and it is great for reviewing and finding your weak spots in mathematical physics. I like it!