Laura Alcock works in the Mathematics Education Center at the University of Loughborough in the United Kingdom. In recent months I have been compiling my various notes on mathematics to put together all the tools I use in mathematical physics so I don't have to go back to original sources. In the process, I have been using more modern notation than I was taught and am writing the notes formally so that my students can use them as a starting point in reading more mathematically formal papers, particularly those that are being published on entropy, weak value quantum mechanics, and quantum computing. Alcock's book has a lot to offer and specifically talks about making the transition from calculational mathematics to advanced formal mathematics. As well as talking about this transition, Alcok reviews major definitions and provides a useful entry to formal mathematics.
The items that I mentioned in the paragraph above would make the book useful. But, the book doesn't end there, it has additional material on proofs, on reading mathematics, on good writing in mathematics, study skills, time management, and it describes what mathematicians and mathematics professors actually do. While some information applies to British universities almost everything in the book is universal. Having attended universities in both the US and the UK, I would say that Ms. Alcock has made an effort to address students at US universities.
In summary, I recommend this book to everyone who teaches mathematical topics and to all mathematics and physics students.
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