The Math Major Vol. 3, No. 8

The Math Major

CSU Fresno Mathematics Department

Vol 3. No. 8 (February 2, 1999)

Editor: Dr. Larry Cusick.

Problem Corner Winners For Fall 1998

Congratulations to Anar Ahmedov (first place--$75) and Bryan Chaffe and John Jamison (tied for second place--$25 each) for submitting the most correct solutions to the Problem Corner last semester. Anar provided correct solutions to 6 problems while Bryan and John submitted 5 correct solutions each. Other students who turned in correct solutions were Sandra Atkins, Garth Kinnier, Linda LeRoux, Ramiro Mata, Amy Peterson and Inpaeng Vannasone. A new Problem Corner competition begins this semester. Good Luck!

Spring 1999 Video and Colloquium Series

(From Dr. Cleary) Our spring video and colloquium series will be meeting Thursdays from 2:10-3pm. Each week at this time we will either be showing a mathematical video or having a colloquium talk suitable for undergraduates. Please join math undergrads, grads and faculty for these interesting videos and talks. Refreshments will be provided.

Here are two upcoming videos:

Feb 4: "Nova: The Man who Loved Numbers." This NOVA documentary describes the life and work of Srinvasa Ramanujan, a remarkable mathematical prodigy who did important and surprising work in a number of fields, particularly number theory, early in this century. His highly original and unusual genius has prompted the title. (2:10pm-3pm in PB 390 on Thurs Feb 4th.)

Feb 11: "The Mathematics of Juggling." Ron Graham, an internationally recognized mathematician and computer scientist is also a world-class juggler. One of his great contributions to the overall field of juggling was to devise an efficient notation for representing various patterns. In this video, he describes and demonstrates his mathematical approach to juggling. There will be juggling balls available for those who want to follow along! (2:10pm-3pm in PB 390 on Thurs Feb 11th.)

Field Trip to the Mathematical Sciences Research Institute

Saturday, February 13th in Berkeley, the Pacific Northwest Geometry Seminar will be holding its winter meeting. There should be some interesting talks suitable for motivated students. Dr. Cleary is planning to take a group of students to the conference for the day. If you are interested in coming, please let him know. MSRI in Berkeley, located in the hills above the Berkeley campus, is not only an important international mathematical center, but is in a beautiful setting.

LISTSERVs for Math Majors

There are two email listserv accounts for distributing information, asking questions, and discussion. They are called "mathmajors" and "mathgrads" and are easy to join. To join the "mathmajors" listserv, you need to send mail from the email account which you would like to receive your listserv mail to the listserv manager. Send a one-line email message to listserv@listserv.csufresno.edu with the following line in the body of the message: subscribe mathmajors YourFirstName YourLastName.

Replace "mathmajors" with "mathgrads" for the listserv for math graduate students. Make sure that command is in the body, not the subject. In a little while, you will receive a confirmation message from the listserv. Reply to the message, with a single line in the body of the message OK within 48 hours and then you are set! You will get an informative message from listserv with further instructions about administrative features, but from then on you will receive mail which people send to the mathmajors list. For more information ask Dr. Cleary or see the ITS website about Listserv membership.

A Mathematical Quote

"It isn't that they can't see the solution. It is that they can't see the problem."

--G. K. Chesterton (1874-1936) from The Point of a Pin in The Scandal of Father Brown.

Problem Corner

Problem 3.7: 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.

Solution to Problem 3.7: Use induction on the number of roads. Suppose that all roads but one are colored according to our rule and that the only uncolored road connects towns X and Y. Then there are roads of color 1 starting at X and roads of color 2 starting at Y, but there are no roads of color 2 starting at X and no roads of color 1 starting at Y. Consider the path, passing through the greatest number of roads, that starts at X and consists of roads of color 1 and 2 only. These colors necessarily alternate. This path cannot pass more than once through any town, and it cannot finish at Y. Now, we reverse the colors of all roads in this path; color 1 changed to color 2, and vice versa. After this operation, which keeps the specified property, we can color the road XY with color 1.

Correct solutions were received from Anar Ahmedov; Garth Kinnier and Amy Peterson (Jointly).

New Problem

Problem 3.8: (Due Thursday February 11, 3 p.m.) At a party, assume that no boy dances with every girl and each girl dances with at least one boy. Prove that there are two couples (girl1, boy1) and (girl2, boy2) which dance whereas boy1 does not dance with girl2 nor does girl1 dance with boy2.

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