The Math Major Vol. 2, No. 8

The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 8

Summer Math Programs for Undergraduates

Many universities host summer academic programs for motivated undergraduate math majors. These include Research Experience for Undergraduates (REU) and other mathematics enrichment programs. If you think you might be interested, visit Swarthmore's Undergraduate Research Programs in Mathematics web site .

Job Search

A couple of items.

Roosevelt High School needs Math majors to tutor/TA in Algebra I classes ($8.35 per hour). For more information call Marilyn Oskanian, 441-3777, extension 1621.
For job information (summer or permanent) visit the CSU Fresno Career Development & Employment Services in Joyal Administration Room 256. Visit their web site.

Math Awareness Week and the Math Field Day

Every year the Joint Policy Board for Mathematics designates a week in Spring to be Math Awareness Week (MAW). This year it will be April 26 to May 2, and the theme will be Mathematics and Imaging. Information on MAW can be found at the web site.

For our part, the department of Mathematics will sponsor its annual Mathematics Field Day on Saturday April 18. Local high school students are invited to participate in various mathematics competitions, with awards going to winning individuals and schools. Student volunteers will be needed for the Field Day. Contact Dr. Della Duncan.

New Prime Number News

Euclid proved that there are infinitely many prime numbers and Gustave Lejeune Dirichlet (in 1837) proved that there are infinitely many prime numbers in any arithmetic sequence a, a+d, a + 2d, .... in which a and d are relatively prime. But beyond this, there has not been much success in finding natural sequence of numbers that include infinitely many primes that are not too "sparse.'' (That is, they contain so many non-prime numbers that, as lenses for examining prime numbers, they do not provide a very sharp focus.) This changed recently when two mathematicians--John Friedlander of the University of Toronto and Henryk Iwaniec of Rutgers University in New Jersey--proved that there are infinitely many prime numbers in the form a² + b⁴. Their work solved a hundred year old problem and has given experts in the field new tools for studying prime numbers. More information can be found at the web site.

Calculus Help

Where can you go for Calculus help? The math department tutorial lab is located in EE 167. There you will find a tutor at the following times:

M, 8:00-10:00 & 11:00-7:00
T & Th 8:00-2:00
W, 8:00-10:00 & 11:00-5:00
F, 10:00-4:00

The University Learning Resource Center (Lab School 137) also has calculus tutors available at various times of each day.

Problem Corner Winners For Fall 1997

Congratulations to John Jamison (first place--$75) and Anar Ahmedov (second place--$50) for submitting the most correct solutions to the Problem Corner last semester. John provided correct solutions to all 7 problems while Anar submitted 6 correct solutions. Other students who turned in correct solutions were James Dunn, Lina Obeid, Robert Seidel and Patrick Villa. A new Problem Corner competition begins this semester. Good Luck!

Problem Corner

Problem 2.7: Consider the equation

100 ... 00_b + 100... 00_b+1 = 100... 00_b+2,

where each term contains exactly n zeros and each subscript b, b+1, b+2 is the base in which the term is written. For how many values of n, n >=2, will a solution (i.e., a positive integer value of b) exist for the equation?

Solution to Problem 2.7:The equation becomes

bⁿ + (b+1)ⁿ = (b+2)ⁿ.

According to Fermat's Last Theorem (proved by Princeton University mathematician Andrew Wiles in 1994) the equation xⁿ + yⁿ = zⁿ (where x, y, z and n are positive integers) has no solution for n = 3, 4, 5, .... So our equation can only have solutions for n=2 (one value of n), specifically b = 3.

John Jamison submitted the only correct solution.

New Problem

Problem 2.8: (Due Thursday February 14, by 4pm) 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.

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.