December 8, 2008

Just in time for the 10th anniversary

Just published and received in the Math Library:

Robert J. Zimmer and Dave Witte Morris. Ergodic theory, groups, and geometry: NSF-CBMS regional research conferences in the mathematical sciences, June 22-26, 1998, University of Minnesota. Regional conference series in mathematics ; no. 109. Providence, R.I.: American Mathematical Society, 2008. Mathematics Library QA1 .R33 no.109
Link to MNCAT record

The editing obviously took a while. However, given the gap between entries on this blog, it would be unwise to throw stones.

October 1, 2007

How Euler Did It

The latest book in the MAA Tercentenary Euler Celebration series collects 40 online columns from Ed Sandifer's "How Euler Did It". One of these gives the results of a poll of Euler's most important results, such as the Konigsberg bridge problem, the polyhedral formula V – E + F = 2, and of course eπi + 1 = 0, which has also figured on lists of the most beautiful equations.

You'll have to check the continuing online column to find out why "Euler" is in the Euler Identity.

How Euler Did It by C. Edward Sandifer. The MAA tercentenary Euler celebration v. 3. Washington, DC: Mathematical Association of America, 2007. Mathematics Library QA29.E8 S264 Link to MNCAT record

September 12, 2007

hoa in R: case studies

A new book of statistical case studies shows "how higher order asymptotics may be applied in realistic examples with very little more effort than is needed for first order procedures" with "resulting improved inferences." This approach depends on the hoa package bundle in R, available at Applied here to an interesting range of topics: evidence for the top quark, traffic accidents (related to cell phones and speed limits), construction costs of nuclear power stations, radioimmunoassays of drug concentrations, failure times of PET films used as electrical insulation, wasp predator-prey experiments, etc.

Applied Asymptotics: Case Studies in Small-Sample Statistics, by A. R. Brazzale, A.C. Davison, and N. Reid. Cambridge, UK; New York: Cambridge University Press, 2007. Mathematics Library QA277 .B73 Link to MNCAT record

August 9, 2007

Math curse

The conference proceedings Math Everywhere quotes Jacques-Louis Lions: "Do you really want to mathematize everything?"

That's the theme of great kids' book:
"On Monday in math class, Mrs. Fibonacci says, 'You know, you can think of almost everything as a math problem.'
On Tuesday I start having problems. . . .
I take the milk out for my cereal and wonder:
1. How many quarts in a gallon?
2. How many pints in a quart?
3. How many inches in a foot?
4. How many feet in a yard?
5. How many yards in a neighborhood? How many inches in a pint? How many feet in my shoes?
I don't even bother to take out the cereal. I don't want to know how many flakes in a bowl.
Mrs. Fibonacci has obviously put a MATH CURSE on me. Everything I look at or think about has become a math problem."

Not to worry, there's a happy ending.

Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics And Industry; dedicated to the 60th birthday of Vincenzo Capasso. Berlin; New York: Springer, 2007. Mathematics Library QA36 .M28
Link to MNCAT record

Math Curse by Jon Scieszka and Lane Smith. New York, N.Y.: Viking, 1995. Andersen Library Children’s Lit PZ7.S41267 Mat 1995 Non-Circulating Link to MNCAT record

May 15, 2007

Stochastic hat trick

All three new books arriving today are on the same subject, a coincidence demonstrating the widespread interest in all things stochastic. (No surprise if another arrives tomorrow from yet a fourth continent.)

Stochastic Tools in Mathematics and Science, by Alexandre J. Chorin and Ole H. Hald. Surveys and tutorials in the applied mathematical sciences vol 1. New York: Springer Science + Business Media, 2006. Mathematics Library QA274 .C5 2006 Link to MnCat Record
Based on a first-year graduate course at UC-Berkeley.

Introduction to Stochastic Integration, by Hui-Hsiung Kuo. Universitext. New York, NY: Springer Science+Business Media, 2006. Mathematics Library QA274.22 .K86 2006 Link to MnCat Record
Based on a course at Cheng Kung University, later given and revised at Meijo University, University of Rome "Tor Vergata," and Louisiana State University.

Stochastic Analysis and Partial Differential Equations: emphasis year 2004-2005 on stochastic analysis and partial differential equations, Northwestern University, Evanston, Illinois, edited by Gui-Qiang Chen, Elton Hsu, and Mark Pinsky. Contemporary mathematics vol. 429. Providence, R.I.: American Mathematical Society, 2007. Mathematics Library QA274.2 .S77135 2007 Link to MnCat Record
Obviously based on events at Northwestern. Includes both research and expository papers.

May 10, 2007

Recommended math finance books

Motivated by the new Master of Financial Mathematics program, here's a list of books recommended by the Director, Professor Scot Adams:

May 3, 2007

Mathematical epigraphs

Every recreational math book will quote from Lewis Carroll--that's understood. Even quotations from John Locke and Roger Bacon are not unexpected. But George Carlin, Seamus Heaney, and John Glenn? All six of these, and more, provide the chapter mottoes in Julian Havil's "Nonplussed! Mathematical Proof of Implausible Ideas."

How were the nonmathematicians worked in?

Carlin: "I'm sixty years of age. That's 16 Celsius." (introducing the chapter on the Birthday Paradox)

Heaney: "We want the surprise to be transitive like the impatient thump which unexpectedly restores the picture to the television set, or the electric shock which sets the fibrillating heart back to its proper rhythm." (for the chapter on transitivity: Effron's dice, coin tossing, etc.)

Glenn, when asked what went through his mind while he was crouched in the rocket nose-cone, awaiting blast-off: "I was thinking that the rocket has 20,000 components, and each was made by the lowest bidder." (a perhaps tenuous connection to "Hyperdimensions")

Nonplussed! Mathematical Proof of Implausible Ideas, by Julian Havil. Princeton, N.J.: Princeton University Press, 2007. Mathematics Library QA99 .H38 2007 Link to MnCat Record

Unfortunately full citations for the epigraphs are not provided. Some of the more traditional ones, such as Bacon comparing mathematics to tennis, can be found in

Memorabilia mathematica; or, The philomath’s quotation-book, by Robert Edouard Moritz. New York: The Macmillan Company, 1914. Mathematics Library QA3 .M7 Link to MnCat Record
Mathematically Speaking: A Dictionary of Quotations, selected and arranged by Carl C. Gaither and Alma E. Cavazos-Gaither; illustrated by Andrew Slocombe. Bristol; Philadelphia: Institute of Physics Pub., 1998. Mathematics Library QA99 .M363 1998 Link to MnCat Record

April 4, 2007

In what sense do statistical methods provide scientific evidence?

Bill Thompson's The Nature of Statistical Evidence addresses this intriguing question. Along the way, he discusses whether statistics meets the predictive and experimental verification criteria of the scientific method; critiques Bayesian inference (e.g., "Randomness Needs Explaining"); investigates various interpretations of probability and "attitudes toward chance;" offers a framework for statistical evidence as an alternative to the "true value" model; and more. Many thought-provoking points in very few pages--a practical slant on the philosophy of statistics, from a Professor Emeritus of Statistics (University of Missour-Columbia) who has also consulted for the National Bureau of Standards and the U.S. Army Air Defense Board, among others. And more diplomatically phrased than the initial statement that "the purpose of this book is to discuss whether statistical methods make sense."

The Nature of Statistical Evidence by W. A. Thompson. Springer, 2007. Mathematics Library QA276.16 .T488 2007 Link to MnCat Record

March 22, 2007

Matrix Door

There's a striking cover image on Rajendra Bhatia's Positive Definite Matrices (Princeton series in applied mathematics. Princeton, N.J.: Princeton University Press, 2007. Mathematics Library QA188 .B488 2007 Link to MNCAT record)


This is credited on the back cover: "Doors of the Florence Baptistery show an example of a 4 x 7 matrix." Further investigation shows that these must be the gilded bronze North Doors, by Lorenzo Ghiberti (1404-24). Close-ups of the individual reliefs are available: North Doors, Florence Baptistry. The earlier south doors (by Pisano) are similarly structured, but the later east "Doors of Paradise" (also by Ghiberti) are a 2 x 5 matrix.

March 9, 2007

The tempo of Ricci flow

Bennett Chow, who recently left Minnesota for UC-San Diego and East China Normal University, has collaborated on another book on the Ricci flow, that hot topic involved in the attempts to prove the Poincaré conjecture:
Hamilton’s Ricci flow, by Bennett Chow, Peng Lu, and Lei Ni. Graduate studies in mathematics v. 77. Providence, R.I.: American Mathematical Society/Science Press, 2006. Mathematics Library QA670 .C455 2006 Link to MNCAT record

As implied by the series, it is accessible to graduate students. The previous book was aimed at researchers:
The Ricci flow: an introduction, by Bennett Chow and Dan Knopf. Mathematical surveys and monographs v. 110. Providence, R.I.: American Mathematical Society, 2004. Mathematics Library QA1 .M758x v.110 Link to MNCAT record

In explaining the difference between these "cousins," the authors compare the style of the 2004 book to jazz--"dive right into Ricci flow and then proceed at a metric pace, taking the time to appreciate the intricacies and nuances of the melody and structure of the mathematical music"--whereas the style of the 2006 book is more like rock 'n' roll--"after starting from more basic material, as a connection to Ricci flow, the tempo is slightly more upbeat. The recital is defined on a longer page interval, and consequently more ground is covered, with the intention of leading up to the forefront of mathematical research."

A further book is to appear in May: The Ricci flow: techniques and applications: Part I: Geometric Aspects, by Chow et al. Mathematical Surveys and Monographs v. 135. Providence, R.I.: American Mathematical Society, 2007.
Given the ten authors credited, perhaps its style will be orchestral.

February 19, 2007

Demand for history of geometry course

Jeremy Gray mentions that "well over a hundred" students elected each year to take his history of geometry course at the University of Warwick (2001-2004). Not just enrolled, but also "completed the course and reported positively on their experiences. . . Individually and collectively they demonstrated a hugely encouraging desire to grapple with difficult material." A remarkable testament to the professor, the course, and the university--especially when some major universities offer no math history courses at all.

Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century. Springer undergraduate mathematics series. London: Springer, 2007. Mathematics Library QA443.5 .G73 2007 Link to MNCAT record

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

December 22, 2006

Musical combinatorial designs

The new edition of Handbook of Combinatorial Designs points to Tom Johnson's musical compositions based on

1. Kirkman's Schoolgirls Problem: "Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once." [T. P. Kirkman, Query VI. Lady's and Gentleman's Diary (1850), 48.] Johnson's 2005 score for three flutes or solo harp, "Kirkman's Ladies," is based on the solution to the follow-on problem (solved by Denniston in 1974): can all 455 triples from a 15-element set be arranged into 13 disjoint Kirkman Triple Systems of order 15, thereby allowing a walk for each of the 13 weeks of a school term, without any three girls walking together twice?

2. The specific t-(v, k, λ) design given in the Handbook's 4.6 Example. In describing his piece "Block Design for Piano," Johnson gives the definition of a 4-(12, 6, 10) design in musical terms: "There are 12 notes, distributed into 6-note arpeggios, in such a way that every combination of four particular notes comes together exactly 10 times in 10 different arpeggios."

See Recent works by Tom Johnson for more information on the compositions. For more information on the combinatorial designs, see pages 13 and 79 of

Handbook of Combinatorial Designs, 2nd ed., edited by Charles J. Colbourn, Jeffrey H. Dinitz. Boca Raton, FL: Chapman & Hall/CRC, 2007. Mathematics Library Quarto QA166.25 .H36 2007 Link to MNCAT record

December 14, 2006

Kurt Gödel: The Album

Photographs of Kurt Gödel, his family, friends, colleagues, houses and schools. Facsimiles of letters and telegrams to/from/about Gödel. Copies of his degree notices, lecture announcements, awards. Odd snippets like his lending library card, the bill from his wedding dinner, the sales receipt from his copy of Whitehead and Russell's Principia Mathematica. All helpfully captioned in both German and English. Unfortunately no index, but it's a pleasure to browse through the sections: Gödel's Life, Gödel's Work, Gödel's Vienna.

Kurt Gödel: Das Album = The Album, by Karl Sigmund et al. Wiesbaden: Vieweg, 2006. Mathematics Library QA29.G58 S54 2006 Link to MNCAT record