The Math Major Vol. 3, No. 7

The Math Major

CSU Fresno Mathematics Department

Vol 3. No. 7 (December 2, 1998)

Professor Donohue is Retiring

After thirty three years of service (which included a term as Chair of the Math Department), Professor Don Donohue will retire at the end of this Fall semester. His wit will be sorely missed.

Ten Brave Math Students Face the Putnam Exam

Intrepid math students Anar Ahmedov, Mike Chamberlin, Arkady Hanjiev, Leslie Hatcher, Jared Hayton, Rosa Huerta, Shawn Jackson, John Jamison, Alice Klepac and Matthew Zhou (this must be a record for CSU Fresno!) will participate (along with a couple of thousand other mathies from around the country) in the William Lowell Putnam Mathematical Competition on Saturday December 5. The national winner receives a full paid scholarship to Harvard. The exam lasts from 8 AM to 4 PM, with a 2 hour break in the middle, and is very difficult, with typically half of the competitors receiving a zero score. The ten will be competing for a $100 first prize and $75 second prize for CSU Fresno participants. We wish our intrepid students well.

Math Department Video Series

By popular demand, we will again show the award winning video "Not Knot".

Date & Location: Thursday, December 3, SR 6 Room 4
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"

Graduate Assistants & Tutors for Spring Semester

Applications are available from the department office for Spring semester work. There is a need for graduate assistants and tutors for the tutorial math labs.

A Mathematical Quote

"Say what you know, do what you must, come what may." (Motto on her paper "On the Problem of the Rotation of a Solid Body about a Fixed Point.")

--Sofia Vasilyevna Kovalevskaya (1850-1891)

Sofia Vasilyevna Kovalevskaya

Problem Corner

Problem 3.6: A pawn is placed in the central square of a 11x11 chessboard. Two players move the pawn in succession to any other square, but each move (beginning with the second) must be longer than the previous one. The player who cannot make such a move loses. Who wins an errorless game?

Solution to Problem 3.6: The second player will win the game if they place the pawn on the board that is symmetric with respect to the center of the last position of the pawn. Since the distance is increasing, eventually the game must stop. It is only left to show that the second player's move is always a greater distance than the previous move. Referring to the picture below: second player moves A to B, first player moves B to C and second player moves C to D. Now we just observe that BCAD is a parallelogram. One diagonal of any parallelogram is longer than the two sides. Since BC >AB, the diagonal CD must be longer than the side BC, which is what we wanted to prove.

Correct solutions were received from John Jamison and Garth Kinnier and Amy Peterson (jointly).

New Problem

Problem 3.7: (Due Thursday December 10, 3 p.m.) AB-land consists of two states: A and B. Each road in AB-land connects two towns from A and B respectively. It is known that no town is connected with more than 10 others. Prove that it is possible to color all roads in AB-land, using 10 colors, in such a way that no two adjacent roads would be the same color. We call two roads adjacent if they leave the same town.

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

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