All the Math You Missed

Great review of math concepts for getting your master's or phd. Great consolidation of things you need to know vs don't need to know and it is very well written. Highly recommend!

I like it very much.

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.

Great book in general, covering a wide breadth of topics, but the chapter on category theory has several errors. Within the first few pages, there are several examples of function composition arguments in the wrong order, as well as some typos referring to morphisms as functors. Thankfully, the commutation diagrams are correct, so it's likely just a bit of sloppiness on the part of the author. Still frustrating though.

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.

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.

Dense but relatively easy to absorb

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!