The Math Major Vol. 2, No. 9

The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 9

Math Department Colloquia

Date: Thursday, February 26, 3:10 pm
Speaker: Anar Ahmedov, Graduate Student
Title: "Fermat's Last Theorem"
Location: Science 141
Abstract: Fermat's Last Theorem states that there are no non-zero integer solutions to the equation xⁿ + yⁿ = zⁿ for any whole number n larger than 2. Fermat, in a scribbled marginal note, claimed to have had a proof, but never delivered. In 1993, Andrew Wiles, a Princeton mathematician, claimed to have a proof, but a fatal flaw was discovered during the review process. But in 1994 Wiles, with mathematician Richard Taylor, produced a proof that did survive the review process.

Math Club Film Series

The Math Club will sponsor a Math Film Series this semester beginning February 24. The video presentations will be Tuesdays at 5 pm in Peters Building Room 428. The first film in the series will be "N is a number", a documentary on one of the most extraordinary mathematicians of the twentieth century: Paul Erdos. Everyone is cordially invited to attend.

Paul Erdos (1913-1996)

Paul Erdos was born in Budapest, Hungary on March 26, 1913. He was a mathematical prodigy and he has stayed among the very first among mathematicians for all his life. He obtained his Ph.D. in mathematics in 1934 from the University of Budapest. He spent four years in Manchester as a postdoc - this is the longest time he ever spent at the same place. It would be impossible to list the universities, academies and research institutes where he has lectured, or even those where he obtained honorary degrees. It would be impossible to outline the topics of his more than 1200 papers or even count those papers that cite Erdos's work as their main motivation. Let it suffice to mention the Wolf prize, one of the highest recognitions in mathematics, which he received in 1984. (From Paul Erdos is 80 by L. Lovasz.)

Summer REU Programs

Are you curious about mathematics research? Do you think you would like to give it a try? If so, think about applying to one of the many REU summer programs around the country. REU stands for Research Experience for Undergraduates. Participants work in groups with other undergraduate students and with a supervising university mathematician on a research project. This is an excellent opportunity to work with other motivated students on an interesting mathematics problem. Visit the Undergraduate Research Programs web site at Swarthmore's Math Forum for more information on the many REU sites around the country.

Summer Jobs

The CSU Fresno Career Development & Employment Services (278-2703) will sponsor the Internship & Summer Job Fair on Wednesday February 25 from 10 am to 2 pm at the Satellite Student Union. More than 50 employers will be represented to meet with and hire students for Summer `98.

Graduate Program

If you are interested in applying to any graduate program, you will most likely be required to take the GRE (Graduate Records Examination). Some graduate programs require the subject GRE as well as the general GRE. The next Fresno test date for the GRE is April 4. It is not too early to register for this important exam. Registration information, along with other test locations and dates, can be found at the ETS GRE web site. For information regarding CSU Fresno's math graduate program, contact the department graduate advisor Dr. Hugo Sun.

Problem Corner

Problem 2.8: You have 12 coins, one of which is counterfeit. The 11 non-counterfeit coins all weigh the same, but the counterfeit is either heavier or lighter--you don't know which. Using a balance scale three times, determine which coin is counterfeit.

Solution to Problem 2.8: First divide the coins into 3 groups of 4 and balance say group 1 against group 2. If they balance, then the counterfeit coin is in group 3. We can determine the counterfeit in 2 more balances: compare coin 1 with coin 2 then compare coin 1 with coin 3--we leave the details to you.

Now suppose group 1 does not balance with group 2, say group 1 is heavier. Label the coins A, B, C, D in group 1 and E, F, G, H in group 2. We perform the two comparisons: (ABE) with (CDF) and then (BCH) with (ADG). There are 8 possible outcomes which can be summarized in the chart below. (+, - and = stand for heavier, lighter and the same respectively. For instance, the first entry +--+ means that (ABE) was heavier than (CDF) and (BCH) was lighter than (ADG).)

Odd Coin	Balance Result
A	"+--+"
B	"+-+-"
C	"-++-"
D	"-+-+"
E	"-+=="
F	"+-=="
G	"==+-"
H	"==-+"

This gives us a total of 3 weighings.

John Jamison submitted the only correct solution.

New Problem

Problem 2.9: (Due Thursday February 26 by 4 pm) The ancient Babylonians used the formula K = (a+c)(b+d)/4 for the area enclosed by a quadrilateral with consecutive side lengths a, b, c, d. Prove that the formula is valid only if the quadrilateral is a rectangle.

Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail at larryc@csufresno.edu. There is a $75 dollar first prize and a $50 second prize to be awarded at the end of the semester to the student(s) who submit the most correct solutions.