The Math Major Vol. 2, No. 6
The Math Major
CSU Fresno Mathematics Department
Vol 2. No. 6
Editor: Dr. Larry Cusick.
Spring Math Courses Part II
The math department will offer 12 upper division and 3 graduate level mathematics courses this spring. In
this issue and the next you will find a short description of each in the words of the instructor who will
teach the course.
- 107: (Introduction to Probability & Statistics--Dr. Harbertson) Many models in mathematics,
science, engineering, and business involve uncertainty. In order to approach such problems from a
mathematical viewpoint, Math 107 introduces the concept of a Probability space and a
Random variable defined on the space. The probability
distributions of events that occur most frequently in applications are
covered in some depth along with practical calculations involving these
distributions. Both single and multi-dimensional models are discussed.
- 108: (Statistics--Dr. Harbertson) Math 108 covers theory and
applications of descriptive and inferential statistics. That is, the numeric and graphic description and
analysis of data, and how to draw accurate and correct conclusions based on data.
Topics include hypothesis testing, parameter estimation,
regression (prediction), analysis of variance, and nonparametric methods.
- 110: (Symbolic Logic--Dr. Zane)
We will take a two-fold approach; first are informal discussions and
then a more formal presentation. The emphasis will be on making the student aware of the following
distinctions: (1) the use of informal mathematical reasoning in ordinary math courses; (2) an informal
abstraction of the basic principles underlying this process and (3) a formal axiomatic edification of the
mathematical reasoning process itself.
- 123: (Topics in Applied Mathematics--Dr. Franco) This should be a useful course for math, science
and engineering students. We will develop the qualitative, numeric
and analytic approaches in the study of ordinary (non-linear) differential equations
using current technology. More traditional
topics like the special function, Fourier methods and PDE's will probably be
included as well. A survey of the background and interests of students that
enroll in the class may influence the choice and/or the amount of
time spent on some of the topics.
- 151: (Principles of Algebra--Dr. Haslam) In Math 151 we approach arithmetic from an axiomatic
point of view. The operation of adding two integers, for example, amounts to a function +:ZxZ->Z. We will look at sets S
with one or more binary operations on S. Given such an operation, say
*, we ask questions like when can we solve equations such as a * x = b, what subsets of
S inherit the binary operation, etc. Although there are many concrete examples to guide us--from unions
of sets to multiplication of matrices--the investigation is purely abstract. Thus the emphasis is on
definition, theorem, proof and counterexample--the very cornerstone of pure mathematics. The material is
challenging but elegant and rewarding.
- 171: (Intermediate Mathematical Analysis I--Dr. Haslam) In Math 171 we revisit the calculus, but
approach the material from a theoretical point of view rather than from a computational point of view as
was done in Math 75. In particular, we will pay close attention to the concepts of limit, continuity,
differentiability and integrability. We ask questions like "if a function is differentiable, is it
continuous?" rather than ask how to compute derivatives. The answer will come in the form of a proof if
the statement is true or a counterexample if false. Like math 151, the emphasis wil be on definition,
theorem, proof and counterexample.
- 252: (Abstract Algebra II--Dr. Velasquez) As with Math 271, we will proceed in the course according
to the interests and preparations of students. Together, we will
select a textbook that is mutually satisfactory. Students should bring suggested texts to
the first class meeting. From there we will devise a course outline best
suited to all. A tentative outline is module theory, field
theory, perhaps some linear algebra, coding theory and group representations.
Video Presentation: The Proof
Thursday, November 13, 3:10-4:00 p.m. San Ramon 6, Room 6. This video documentary film covers some of the
history and flavor of Andrew Wiles' proof of the famous conjecture known as
Fermat's Last Theorem. Many mathematicians in the last 350
years have tried to prove or disprove Fermat's Last Theorem,
which is that xn+yn=zn has no positive integer solutions
for n>2.
The video is not a technical descripition of the proof itself,
which is very complex, but instead describes some of the
personalities, interactions and emotions felt by those
involved in completing the proof. Free popcorn and soda!
Problem Corner
Problem 2.5: In the semi-circle shown, diameter P0P1
= 2. Angle P0P1P2 = 1 degree; angle P1P2P3 = 2 degrees; angle P2P3P4 = 3 degrees; ...,
Pk-1PkPk+1 = k degrees. If PkPk+1 is the first chord whose length is less than 1,
compute k.
Solution to Problem 2.5: Since the radius is 1, a 60 degrees arc is subtended by a chord of length
1. Therefore we are looking for the first chord whose arc is less than 60 degrees. Minor arc P1P2 =
180 - 2; in degrees minor arc P2P3 = 180 - (2+4) = 180 - 2(1+2). In general minor arc
PkPk+1 = 180 -2 (1 + 2 + 3 + ... +k) = 180 - 2 k(k+1)/2 < 60, which implies that k(k+1)> 120, so
k = 11.
Correct solutions were received from Anar Ahmedov and John Jamison.
New Problem
Problem 2.5: (Due no later than Thursday November 20, 4pm) There are several values for a prime,
p, with the property that any five digit multiple, m, of p remains a multiple of p under every
cyclic permutation of the digits of m. One such value is p = 41 (for example, 50635 is a
multiple of 41, so are 55063, 35506, 63550 and [0]6355). Another such value of p is 3. Compute the value
of p that is greater than 41.
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.
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