The Math Major Vol. 3, No. 4

The Math Major

CSU Fresno Mathematics Department

Vol 3. No. 4 (October 13, 1998)

Math Department Video Series

The department video series is Thursdays at 12:30 (refreshments and social) with film showing at 1 pm, in PB 390. Every one is cordially invited. There are two videos coming up.

Date:Thursday, October 15
Title:"Crystals and Shortest Networks"
Description: Dr. Frank Morgan, a well-known lecturer and researcher in the field of minimal structures, discusses the notion of shortest networks of paths between a collection of points. He also discusses connections between the notions of minimal size structures and crystals.
Date: Thursday, October 22
Title: "Not Knot"
Description: Not Knot is a guided tour into computer-animated hyperbolic space. It proceeds from the world of knots to their complementary spaces -- what's not a knot. Profound theorems of recent mathematics show that most known complements carry the structure of hyperbolic geometry, a geometry in which the sum of three angles of a triangle always is less than 180 degrees.

From Not Knot

Math Majors Honored

Each year the Department of Mathematics selects math majors to receive memberships to the AWM (Association for Women in Mathematics) and the MAA (Mathematical Association of America). The students are nominated by math faculty. This year's awards are as follows. To the AWM: Svetlana Grishchenko, Lina Obeid and Amy Peterson. To the MAA: Sandra Atkins, Matt Bourez, Svetlana Grishchenko, Mindy Millard, Lina Obeid and Elaine Wagner. Congratulations go out to these fine math majors.

Web Watch: Online Math Museums

If you are intrigued by the images below, then visit the American Mathematical Society's Online Math Museums link page.

A Mathematical Quote

"In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection."

--Hugo Rossi

Problem Corner

Problem 3.3: Prove that there is a unique collection of positive integers a₁, a₂, ..., a_n such that

a₁ + a₂ + ...+ a_n= 1998

and the product a₁a₂... a_n is as large as possible

Solution to Problem 3.3: If any a_i is larger than 4, it can be replaced by 2 + (a_i - 2) to get a larger product. Furthermore, any a_i that is 4 can be replaced by 2+2 and not change the product. In this way we know the largest product must occur using 2's and 3's. Finally, 2+2+2 can be replaced by 3x3 to increase the product. So we know the maximum product is realized with as few 2's as possible. Since 1998 = 3x666, we can then see that the maximum product is realized with all a_i= 3, i = 1, ..., 666.

Correct solutions were received from Anar Ahmedov, Bryan Chaffe, John Jamison and Garth Kinnier and Amy Peterson (Jointly). Several other students turned in the correct number 3⁶⁶⁶, but with insufficient proofs.

New Problem

Problem 3.4: (Due Thursday October 22, 3 p.m.) Find all real solutions (x, y) to the equation

5^x-1 + 5^3-x = 2(8 cos(xy) sin(xy) + 1). --From Dr. Tuska

Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail.

CSU Fresno Math Department Home Page

California State University, Fresno