Vol 1. No. 7 (Final Edition for Fall 1996)
Editor: Dr. Larry Cusick.
Mathematics professor Detlev Lindae will retire at the end of this semester. He has been on the faculty at CSU Fresno since 1971. You might want to stop by his office and wish him a happy retirement.
The third International Mathematics and Science Study, funded by the National Science Foundation, has been completed.
U.S. science and math teaching "is a mile wide and an inch deep," when compared to our international competitors, notes NSF's Larry Suter, who oversaw the research summarized in A Splintered Vision: An Investigation of U.S. Science and Mathematics Education.
Other conclusions:
There is much more. This can be found on the MAA (Mathematical Association of America) Online web page http://www.maa.org/news/timss.html.
The Scholarship Program at CSUF will award approximately $800,000 to entering, transferring, and continuing undergraduate/graduate students for the 1997-98 academic year. Deadline for application is Feb. 3, 1997. Eligibility: 3.0 or better GPA; Involvement in school, university, and/or community activities; Full-time student at CSUF. More information and application forms available in the Math Department office.
Congratulations to students Joy Bjerke, Juliet Hauser, Todd Kandarian, Lisa Kenney, Leonel Verduzco and Scott Wilson. Each was nominated by the department to receive an honorary membership to the MAA (Mathematical Association of America). Also congratulations to Sandra Atkins, Joy Bjerke, Juliet Hauser, Lisa Kenney, Li Kang Liu, Nalla Lorton, Deborah Marshall, Natalia Moore, Lina Obeid and Robyn Whitaker who were nominated for honorary memberships to the AWM (Association of Women in Mathematics).
Anar Ahmedov, Robert Van Bindsbergen and Patrick Villa will participate (along with a couple of thousand other mathies from around the country) in the William Lowell Putnam Mathematical Competition on Saturday December 7. The national winner receives a full paid scholarship to Harvard. The exam lasts from 8 AM to 4PM, with a 2 hour break in the middle, and is very difficult, with typically half of the competitors receiving a zero score. The three will be competing for a $100 first prize and $75 second prize for CSU Fresno participants. We wish our intrepid trio well.
Applications for Graduate Assistantships (for Spring semester) are due in the Math department office by 5pm December 6 (Friday).
Final grades will be available to students via STAR on January 8 from 8:00 am to 8:00 pm.
Problem 1.6: The sides of a triangle are proportional (all with the same proportionality constant) to the roots of the cubic equation x3 - a x2 + b x - c = 0. Find the sum of the cosines of the angles of the triangle.
Solution to Problem 1.6: Let p, q, r denote the roots of the equation; kp, kq, kr the sides of the triangle; A, B, C the angles respectively opposite. Then
cos A = (q2 + r2 - p2)/(2qr), cos B = (p2 + r2 - q2/(2pr), cos C = (p2+ q2- r2)/(2pq), and so
cos A + cos B +cos C = [(pq2 + pr2 + p2q + qr2 + p2 r + q2r) - (p3 + q3 + r3)]/(2pqr).
But we have the further equalities
p+q+r = a, pq + qr + pr = b, pqr = c;
and so
pq2+ pr2+ p2q + q r2+ p2r + q2r = ab - 3c,
p^3 + q^3 + r^3 = a^3 - 3ab + 3c
and cos A + cos B + cos C = (4ab - a^3 - 6c)/(2c).
The only correct solution to problem 1.6 was received from Roden Macalma.
Problem 1.7 Find six square numbers whose sum is a square, and the sum of their roots plus the root of their sum is a square.
Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail at larry_cusick@csufresno.edu. no later than Thursday December 6, 3pm. 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.