Reddit mentions of Introduction to Mathematical Statistics (7th Edition)

Took a numerical statistics course first year of my masters which used C&B as well. I found Hogg, McKean, and Craig - Introduction to Mathematical Statistics to be a really good companion volume. It covers a lot of the same material, but in a more accessible fashion.

Try the two:

https://www.amazon.com/Introduction-Mathematical-Statistics-Robert-Hogg/dp/0321795431

https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

introduction to mathematical statistics by craig and statistical inference by george casella.

found it! Apparently they've gone through several editions and added a coauthor since I bought my copy.

My father is a statistician and he is the one who recommended Hogg and Craig when I complaining about Casella and Berger. I spent a summer working my way through Hogg and Craig and then reviewed everything from my classes that previous year as my way for studying for the written quals. I passed so it worked. And then I promptly forgot everything.

Since you're an applied math PhD, maybe the following are good. They are not applied though.

This is the book for first year statistics grad students at OSU.
http://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126/ref=sr_1_1?ie=UTF8&qid=1368662972&sr=8-1&keywords=casella+berger

But, I like Hogg/Craig much more.
http://www.amazon.com/Introduction-Mathematical-Statistics-7th-Edition/dp/0321795431/ref=pd_sim_b_2

I believe each can be found in international editions, and for download on the interwebs.

I think it's this: https://www.amazon.com/Introduction-Mathematical-Statistics-Robert-Hogg/dp/0321795431/ref=mt_hardcover?_encoding=UTF8&me=

But really, if I remember right, they "use" it the same way we "used" the textbook in 400. (I do like both books though.)

For probability I'd recommend Introduction to Probability Theory by Hoel, Port & Stone. It has the best explanations of any probability book I've seen, great examples, and answers to most of the problems are in the back (making it well-suited for self-study). I think it's still the best introductory book on the subject, despite its age. Amazon has used copies for cheap.

For statistics, you have to be more precise as to what you mean by an "average undergraduate statistics" course. There's a difference between the typical "elementary statistics" course and the typical "mathematical statistics" course. The former requires no calculus, but goes into more detail about various statistical procedures and tests for practical uses, while the latter requires calculus and deals more with theory than practice. Learning both wouldn't be a bad idea. For elementary stats there are lots of badly written books, but there is one jewel: Statistics by Freedman, Pisani & Purves. For mathematical statistics, Introduction to Mathematical Statistics by Hogg & Craig is decent, though a bit dry. I don't think that Statistical Inference by Casella & Berger is really any better. Those are the two most-used textbooks on the subject.

My math stats textbook is Hogg McKean Craig. I don't think the math would be too much for a computation statistics major, but it would give you a great overview if you're interested in that direction.

http://www.amazon.com/Introduction-Mathematical-Statistics-7th-Edition/dp/0321795431