The Math Major Vol. 3, No. 3
The Math Major
CSU Fresno Mathematics Department
Vol 3. No. 3 (Sep 30, 1998)
Editor: Dr. Larry Cusick.
Math Department Video Series
The department video series is Thursdays at 12:30 (refreshments and social) with film showing at
1 pm, in PB 390. Every one is cordially invited. There are two videos coming up.
- Date: October 1
- Title: "Discrete Mathematics: Cracking the Code"
- Description: This video is an introduction to the mathematics of cryptography,
data compression and electronic information transmission.
Encryption and ciphers are introduced as tools for communication
in a wide variety of settings including postal codes, Universal
Product Codes, as well as public key cryptography, a widely
used data security tool.
- Date: October 8
- Title: "Fractals, the Colors of Infinity"
- Description: The Mandelbrot set is a beautiful and remarkable
discovery. This video, narrated by Arthur C. Clark,
illustrates how simple formulae can lead to complicated
results. The video explains the Mandelbrot set, what
it means, and some of the mathematical revolutions
inspired by its discovery.
The Putnam Competition
The fifty-ninth annual William Lowell Putnam Mathematical Competition will
be held on Saturday, December 5. This is a national level competition of college mathematics
students that is run by the Mathematical Association of America. Any undergraduate college
student may enter. The deadline for registration is Tuesday October 13, but if you wish to
participate you must contact Dr. Larry Cusick by Thursday October 8 so that the
registration materials can be sent in time to meet October 13 deadline. The CSU Fresno
mathematics department is offering a $100 first prize and a $75 second prize for the two top
scoring Fresno contestants. (To qualify, you must receive a non-zero score--no mean feat in
itself.) The Fresno contestants will take the exam in Fresno.
Job Search
Career Development and Employment Services is sponsoring two employment days in October:
- Career Day on Wednesday, October 7
on the balcony of the University Student Union from 9:30 a.m. to 12:30 p.m. Representatives from
business, industry and government will be available to discuss general career information.
- Holiday Job Fair on Wednesday, October 14, in the Free Speech Area from 9:30 a.m. to
12:30 p.m. Employers from local retail stores will be available to discuss part-time work
opportunities and accept applications for the upcoming holiday season.
For
more information, call 278-2381 or 278-7849. Visit the Career Development and Employment services
web site
A Mathematical Quote
"It is more important that a proposition be interesting than that it be true. This statement
is almost a tautology. For the energy of operation of a
proposition in an occasion of experience is its interest and is its importance. But of course a true proposition is more apt to be interesting than a
false one."
--Alfred North Whitehead (1861 - 1947)
A. N. Whitehead
Problem Corner
Problem 3.2: Draw a triangle ABC and a triangle DEF interior to
triangle ABC. Let G, H,
I, J, K, L be the respective centroids of the triangles (moving clockwise around) triangle
ADB,
triangle BDE, triangle BEC, triangle CEF, triangle CFA and triangle AFD (see picture below).
Prove that the three line segments GJ, HK and IL are concurrent.
Solution to Problem 3.2: Put the triangle in a coordinate system. The
coordinates of the centroid of a triangle ABC is then (A+B+C)/3. Using this idea, we can
compute the points G, H, .... For instance, G is (A+B+D)/3 and J is (C+E+F)/3.
The midpoint of segment GJ is (G+J)/2, which simplifies to (A+B+C+D+E+F)/6. By
symmetry, we can see that this is also the midpoint of the two other segments IL and HK.
Thus, the three segments meet at their common midpoint. This common point is also the midpoint of
the segment joining the respective centroids of the triangle ABC and triangle DEF.
Correct solutions were received from Anar Ahmedov, Sandra Atkins and Linda
LeRoux (jointly), Brian Chaffe, and Ramiro Mata and Inpaeng Vannasone
(jointly).
New Problem
Problem 3.3: (Due Thursday October 8, 3 p.m.) Prove that there is a unique collection of
positive integers a1, a2, ..., an such that
a1 + a2 + ...+ an= 1998
and the product a1a2... an is as large as possible
Solutions may be delivered to the
math department office (for Dr. Cusick) or by e-mail.
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