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Название: Problems for Mathematicians, Young and Old (Dolciani Mathematical Expositions)
Автор: Halmos P.
I should preface my review by saying this is the first item I've ever reviewed on Amazon, and I've been buying from Amazon for 10 years. I felt I had to write this review as a counterpoint to an earlier negative review given to this book.
Not only are the problems in this book very interesting to work on, they also illustrate key points in algebra, calculus, set theory, etc. I would say that successfully completing the problems in this book would give you mathematical expertise comparable to that of a first year math graduate student.
When people ask me for math book recommendations, this is the book I suggest. Everyone I've suggested this book to has liked it.
For reference, I have a PhD in EECS (I minored in math) and have taught engineering for the past 12 years.