I referenced some stuff in the division polynomial section for my Masters thesis. This book has some good reference stuff, the explicit formulas are nI referenced some stuff in the division polynomial section for my Masters thesis. This book has some good reference stuff, the explicit formulas are nice. I found the proofs to be EXTREMELY light on details. ...more

I used this book to learn about the Lanczos Algorithm for solving a system of linear equations over the real numbers. I was doing a project on the genI used this book to learn about the Lanczos Algorithm for solving a system of linear equations over the real numbers. I was doing a project on the generalization of the algorithm to finite fields. ...more

This book was the text book for my introduction to cryptology course. It had many typos, and the material was far too elementary.

All in all, it had soThis book was the text book for my introduction to cryptology course. It had many typos, and the material was far too elementary.

All in all, it had some good exercise, and I learned a bunch of probability from this book.

However, as a cryptology text book, it would have been better to just let the kids loose with The Code Book and lectured on the missing mathematical material.

I read this book because a professor of mine, who was retiring, gave me this book because I had displayed an interest in the material. That professorI read this book because a professor of mine, who was retiring, gave me this book because I had displayed an interest in the material. That professor was really good. I became a math major as a direct result of that action.

I learned about the elementary theory of congruences from this book. But it is referenced everywhere. I plan to read through more topics in this book later.

I have heard that it has an awesome discussion of the theory of continued fractions. ...more

This was the textbook for my Elementary Number Theory class. That class, in no small part due to this book, is the reason why I decided to major in MaThis was the textbook for my Elementary Number Theory class. That class, in no small part due to this book, is the reason why I decided to major in Mathematics and hence why I am (as of writing this) getting a graduate degree in the field.

This book is an excellent introduction to elementary number theory. The problems are very challenging, but illuminate the material deeply. Furthermore, this book serves as an excellent reference when I want to look up proofs of facts in elementary number theory. ...more

This was the textbook for my second course in abstract algebra. We mostly did module theory in that class.

I did not like this text book then, and I foThis was the textbook for my second course in abstract algebra. We mostly did module theory in that class.

I did not like this text book then, and I found it difficult to learn the material from here. However, when relearning the material in Grad School (in a more in depth fashion.) I definitely used this book as a reference.

The typesetting is really lame in this book. ...more

This was the textbook for my first course in Abstract Algebra. I found it exceptionally useful for learning basic Abstract Algebra. The mathematics isThis was the textbook for my first course in Abstract Algebra. I found it exceptionally useful for learning basic Abstract Algebra. The mathematics is presented in a very enlightening way. Now that I've moved beyond this material it is not as useful anymore. And I don't ever use this book as a reference. However, I recommend this book to anyone learning Abstract Algebra. ...more

I think this might be the best math text book ever written.

I learned Topology from this book. This book is THE text to learn topology from. This bookI think this might be the best math text book ever written.

I learned Topology from this book. This book is THE text to learn topology from. This book is a rare combination in that it teaches the material very well and it can be used as a reference later.

The treatment on algebraic topology later in the book is a little light. ...more

This was my undergrad real analysis textbook. I don't like real analysis, and I don't like this book. But compared with Rudin's text principles of matThis was my undergrad real analysis textbook. I don't like real analysis, and I don't like this book. But compared with Rudin's text principles of mathematical analysis it is quite good. If anything this book is not deep enough, but it is a good reference, and I have used it repeatedly since I finished the class. ...more

This is a good book for a high level introduction to the Mathematics behind Elliptic Curve Cryptography.

It does not go into a great amount of detail,This is a good book for a high level introduction to the Mathematics behind Elliptic Curve Cryptography.

It does not go into a great amount of detail, but it is relatively clearly written, and that definitely counts for a lot. Also, it has a very comprehensive list of references, and cites them well, so it is easy to track down the details.

So far I have used this book to learn about:

1) Isogenies - a high level introduction / definitions. 2) Complex Multiplication - I got introduced to the subject here.

I read this book because my boss Kristin Lauter suggested it was a good place to start learning about ECC. ...more

This book is not as important as the point that this book represents.

I was taking a number theory class from a professor who is one of the leading expThis book is not as important as the point that this book represents.

I was taking a number theory class from a professor who is one of the leading experts on Iwasawa Theory. This book is an introduction to Iwasawa Theory. So, I was google searching for stuff relating to the course and I found this book. All of the other books relating to the course had been checked out of the math library. So I checked out this book instead. It turned out to be really helpful, more helpful than the other books on number theory that people had checked out.

This really illustrates the point that it helps to try to figured out where your teacher is coming from.

I only used the first couple of sections of this book. The topics covered where algebraic number-theoretic properties of cyclotomic fields, and L-Series associated with those fields. ...more

This book is not the best place to learn about the general number field sieve for the first time. But it is a good way to see how the sieve was develoThis book is not the best place to learn about the general number field sieve for the first time. But it is a good way to see how the sieve was developed over time and when the various parts of the algorithm were introduced. It also helps illustrate the differences between the GNFS and the SNFS factoring algorithms.

I read this book because I was doing a project on the General Number Field Sieve for an algebraic number theory class.

UPDATE: I got this book from the library again and used it to implement the Lattice Sieve for a course project in a computational number theory course. ...more

This book is a more problem oriented approach to complex analysis. It is pretty much just calculus on the complex numbers, and how that is different fThis book is a more problem oriented approach to complex analysis. It is pretty much just calculus on the complex numbers, and how that is different from and complementary to calculus on the real numbers.

This was the textbook for my first course on complex analysis. It is a good reference material for formulas and theorems. And has some good examples on how to solve problems. It also goes into some depth about applications. Which may be useful, but wasn't used in the class I took.

There were many typos and errors, so if something looks wrong in this book, it should be checked out. ...more

This was the text book for my real analysis course. I did not like this text book. I found it dense and hard to gain relevant information from it. RudThis was the text book for my real analysis course. I did not like this text book. I found it dense and hard to gain relevant information from it. Rudin optimized this book for the shortest proofs, and that isn't particularly useful for learning the material. Important results in Mathematics are given as exercises, which is cool, except that they are really hard, and there isn't enough material in the book to cover the problems. ...more

This book is dense, which is good because it has lots of information in it. That said, it is probably not the best book to learn algebraic geometry frThis book is dense, which is good because it has lots of information in it. That said, it is probably not the best book to learn algebraic geometry from. Personally, I found it pretty difficult to learn algebraic geometry from this book.

However, I get the impression that if you already know algebraic geometry, this is an indispensable resource.

UPDATE: I also used this book to learn about Sheaf Cohomology. I actually found it quite helpful to learn about these subjects. ...more