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January 26, 2007

Anybody who reads this book must already know

Kabe and Gupta's new Experimental Designs: Exercises and Solutions starts with "an exposition of the basic results which are used throughout the book." But you can't get past page 2 of the Theoretical Results (which admittedly are in summary form with a bibliography for further reading) or past the first of 184 exercises without needing to know what BLUE stands for--it's not defined in the text, and there's no glossary. In contrast, Shao's recent Mathematical Statistics: Exercises and Solutions helpfully spells it out in the index as well as on first appearance in the text, Exercise 38 of 50: best linear unbiased estimator (BLUE). Perhaps not unfair, as the former book is aimed at a slightly more advanced reader, but the latter gets style as well as pedagogical points for this.

Experimental Designs: Exercises and Solutions, by D.G. Kabe and A.K. Gupta. New York: Springer, 2007. Mathematics Library QA279 .K33 2007 Link to MNCAT record

Mathematical Statistics: Exercises and Solutions by Jun Shao. New York; London: Springer, 2005. Mathematics Library QA276 .S4582 2005 Link to MNCAT record

January 2, 2007

Unique approach to number theory?

It's rather daring to claim that a new book provides a "unique approach" to number theory, as does the blurb on Fine and Rosenberger's Number Theory: An Introduction via the Distribution of Primes. Immediately one thinks of previous more or less similar books, such as Tenenbaum and Mendès France's The Prime Numbers and Their Distribution, which used the same motivation to introduce congruences, quadratic reciprocity, and other standard number theory topics. To be fair, it's probably just the normal exaggeration of marketers and blurb-writers--Fine and Rosenberger in their preface more modestly mention the "somewhat unique approach" (and their bibliography cites Tenenbaum and Mendès France's book).

Number Theory: An Introduction via the Distribution of Primes, by Benjamin Fine and Gerhard Rosenberger. Boston: Birkhäuser, 2007. Mathematics Library QA241 .F56 2007 Link to MNCAT record

The Prime Numbers and Their Distribution, by Gérald Tenenbaum, Michel Mendès France; translated by Philip G. Spain. Student mathematical library v. 6. Providence, R.I.: American Mathematical Society, 2000. Mathematics Library QA246 .T3613 2000 Regular Loan Link to MNCAT record