The Math Major
CSU Fresno Mathematics Department
Vol 1. No. 6
Editor: Dr. Larry Cusick.
The Math Department Colloquia are a series of talks intended for a general
audience. Students, in particular, are encouraged to attend.
- Date: Monday, November 18th
- Speaker: Dr. Colin Adams from the Williams College Department of Mathematics
appearing as Mel Slugbate
- Title: "Real Estate in Hyperbolic Space: Investment Opportunities
for the 90's"
- Time: 2:30-3:20pm
- Location: Science 143
- Abstract: Have you found the new investment climate a bit on the chilly
side? Nervous about stocks, bonds and mutual funds? Afraid of risky investments
in Euclidean space? Then real estate in hyperbolic space is for you. We
will discuss the enormous potential of this new investment opportunity
and describe the many fascinating properties of hyperbolic space that make
it such an attractive place to live. This is the financial equivalent of
the 1980's junk bond. Don't miss it. Bring your checkbook and credit references!
No previous math or real estate background necessary!
Spring Math Courses
The math department will offer 11 upper division and 4 graduate level
mathematics courses this spring. In the last issue you saw descriptions
of maths 101-161. Here are the rest.
- 171A: (Intermediate Analysis I(A)--Haslam) This course revisits Math
75 but the material is covered from a theoretical point of view, where
definition, theorem and proof are the main concerns rather than computational
techniques. The course is difficult and demanding.
- 171B: (Intermediate Analysis I(B)--Nur) To introduce the calculus of
complex valued functions and its applications. The presentation of the
subject (derivatives, integration and series) is basic and should be accessible
to any one who has had three semesters of calculus. The purpose of the
course is to present the beauty of complex valued functions and their value.
- 181: (Differential Equations--Cohen) The course deals with the theory
and solution of important classes of linear differential equations that
occur in mathematics and the sciences. An introduction to nonlinear differential
equations is also presented.
- 223: (Principles \& Techniques of Applied Analysis--Cohen) The
course deals with a unified operator approach to most of the functions
of mathematics and the sciences, consolidating the study of orthogonality,
expansion problems, generating functions, and recurrence relations.
- 252: (Abstract Algebra--Cleary) We will carry on working through Artin's
book, covering aspects of group representations, ring theory, factorization
of polynomials, fields and Galois theory. We will use Galois theory to
show the impossibility of the classical problems of trisecting an angle
or duplicating a cube with only a ruler and compass as well as the impossibility
of a quintic solution by radicals.
- 271: (Real Variables--Sun) Real analysis studies point sets on the
real line, Lebesgue measure and integration, convergence theorems, topological
spaces and Banach and Hilbert spaces.
- 291: (Seminar: Topics in Combinatorics--Sun) Combinatorics studies
counting numbers, generating functions, recurrence relations, M\"obius
theory, Polya theory, graphs, the four color theorem and Ramsey theory.
Tutor Jobs
The CSUF/UC Davis Medi-Corp Program is now hiring math/science tutors
for Junior High and High School students in the Fresno area. It pays $6-7
per hour for 10-12 hours per week (may work on Saturdays). If you are interested,
pick up an application in the SCOP office Science 136 (278-4748).
Bounty Math
Math pays! The Bounty
Math web page lists open mathematics problems whose posers offer cash
awards for correct solutions. Awards range from $50 to $10,000. Here is
a $1,000 offer from John H. Conway (inventor of the "Conway's Game
of Life" and Princeton mathematics professor):
The Thrackle Problem ($1,000): Is there a graph drawn in the plane such
that each edge is a straight or curvy line segment, every pair of edges
makes either an X (crosses once) or a V (shares exactly one vertex) but
not both, and which has more edges than vertices?
The Bounty Math web page lists about two dozen problems.
Problem Corner
Problem 1.5: A list of consecutive positive integers beginning
with 1 is written on a black board. One of the numbers is erased. The average
(arithmetic mean) of the remaining numbers is 35 7/17. What number was
erased?
Solution to Problem 1.5: Suppose the original list is 1, 2, ...,
n. If 1 were erased, the resulting average would be (n+2)/2, where as if
n were erased, the average would have been n/2. This gives us the inequality:
n/2 less than or equal to 35 7/17 less than or equal to (n+2)/2. Solving
for n we see that n must be 69 or 70. Since 35 7/17 is the average of n-1
integers, (35 7/17)(n-1) must be an integer. Thus n = 69. Let x be the
number erased. Then x must satisfy ((1/2) (69)(70) - x)/68 = 35 7/17 from
which we can solve for x = 7.
Correct solutions to problem 1.5 were received Anar Ahmeov, Bryan Sheldon,
Patrick Villa and David Yoshihara.
New Problem
Problem 1.6 The sides of a triangle are proportional (all with
the same proportionality constant) to the roots of the cubic equation x^3
- a x^2 + b x - c = 0. Find the sum of the cosines of the angles of the
triangle.
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 November 7, 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.
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