WSU Retention List Stories

Fifty years ago, in 1975, Benoit Mandelbrot coined the word fractal in a French-language book entitled Les Objets Fractals. The term describes geometrical shapes that have fractional dimensions. These mind-bending shapes can make beautiful graphics, because many fractal shapes are self-similar at increasingly small scales.

The original French-language book is so rare, it is only held by two libraries in the world, both in Switzerland. Fractals took off in popularity, though, and none of the English-language books by Mandelbrot held by the Krueger Library are rare enough to be on our retention list. The one book on our retention list that features fractals is a collection of abstracts from a conference where fractals were used to study materials science, such as the fracture mechanics of polymer composites. (The book has no graphics, so I have added below a photo of a fractal shape (creative commons license).

Fractal Aspects of Materials - 1989: Extended Abstracts. Pittsburgh: Materials Research Society, 1989. 

Recap: In 2022, twenty-four Minnesota libraries joined together in a commitment to retain over a half-million print books which are scarcely-held in Minnesota. It is called the Minnesota Shared Print Collection. This is one of the stories from the Winona State share of the collection.

Today is Pi Day, the date that is closest to the value of the mathematical constant Pi (3.14159…). Mathematicians are excited about this year. 2025 is a perfect square: it is 45 squared. The number 45 itself is a special number. It is one of the “triangular numbers.” That means that, starting at one, a sequence of natural numbers sum to it. In this case, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Because of these two facts, there is a cornucopia of curious mathematical expressions that are equivalent to the number 2025, such as this one: 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ +8³ + 9³ = 2025.

The last year that had these mathematical properties was the year 1296. Such a year will not come again until the year 3025. Enjoy it while you can, math nerds!

The branch of mathematics that explores triangular numbers is Number Theory. One book on the Krueger Library retention list which discusses triangular numbers is:

Rademacher, Hans. Topics in Analytic Number Theory. Berlin: Springer-Verlag, 1973.

Recap: In 2022, twenty-four Minnesota libraries joined together in a commitment to retain over a half-million print books which are scarcely-held in Minnesota. It is called the Minnesota Shared Print Collection. This is one of the stories from the Winona State share of the collection.

(Credit for pointing out to me these mathematical details goes to Paul Weiner, the retired Chair of the Math Department at St. Mary’s University, and to his number theory chums.)

Some books make you smile, even when the subject is serious and you should be more respectful. Within the realm of finite algebraic groups, one mathematical group is referred to as the Monster. One book on Winona State’s retention list studies the Monster, and—all kidding aside—the book’s first author is named Igor. … But does he pronounce it “Eye-gor”?

Frenkel, Igor, James Lepowsky, and Arne Meurman. Vertex Operator Algebras and the Monster. Boston: Academic Press, 1988.

Recap: In 2022, twenty-four Minnesota libraries joined together in a commitment to retain over a half-million print books which are scarcely-held in Minnesota. It is called the Minnesota Shared Print Collection. This is one of the stories from the Winona State share of the collection.

Perhaps the primary criterion for a book to be on the Krueger Library's retention list is that it is scarcely-held in the State of Minnesota.

George Boole was the 19^th century mathematician who pioneered the mathematics of logic—the algebra of ANDs, ORs, and NOTs—hence, there is a great deal of interest in his work among computer scientists. Books by or about George Boole are plentiful in Minnesota and none of them are on Winona State’s retention list; however, his wife Mary was a mathematics educator, and a selection of her writings is on our list.

Boole, Mary Everest. A Boolean Anthology: Selected Writings of Mary Boole on Mathematical Education. Compiled by D. G. Tahta. Nelson: Association of Teachers of Mathematics, 1972.

Recap: In 2022, twenty-four Minnesota libraries joined together in a commitment to retain over a half-million print books which are scarcely-held in Minnesota. It is called the Minnesota Shared Print Collection. This is one of the stories from the Winona State share of the collection.