The Math Major Vol. 2, No. 5

The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 5

Spring Math Courses

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.

101: (Statistical Methods--Dr. Ganter) Descriptive statistical measures, continuing onto statistical procedures and applications to biology and social sciences. Standard probability distributions; chi-square; analysis of variance and regression; non-parametric methods.
128: (Applied Complex Analysis--Dr. 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 anyone who has had three semesters of calculus. The purpose of the course is to present the beauty of complex valued functions and their value.
143: (History of Math--Dr. Tuska) The history of the development of mathematical concepts in algebra, geometry, number theory, analytical geometry, calculus, probability, and set theory from ancient times through modern times. The mathematics is connected to the lives and works of the most influential mathematicians as well as to the role of mathematics in a variety of cultures. Students are required to participate in a group project.
152: (Linear algebra--Dr. Woo) Linear Algebra is an important component of mathematics. It is a valuable introduction to mathematical abstraction and logical reasoning. The topics to be covered are: vector spaces, linear transformations, matrices, determinates, eigenvalues, eigenvectors, inner-product spaces, quadratic forms and orthogonal and unitary transformations. This course stresses both practical computations and theoretical principles and centers on the principle parts of the above topics. Hopefully, students will have a clear understanding of linear algebra after taking this course.
161: (Principles of Geometry--Dr. Duncan) Next semester in Math 161 we will be taking a winding tour through the realm of Geometry. I would hope to begin with Euclidean Geometry but not stay there too long. The course should evolve more as a geometric sampler to include elliptic, projective and hyperbolic geometries. The history of the subject and its influence on other subjects (not limited to the sciences) will also be covered. Use of computer software programs to aid in visualization will also be encouraged.
182: (Partial Differential Equations--Dr. Nur) The purpose of this course is to acquaint the students with some of the techniques of applied mathematics and to provide them with basic material helpful for further study in partial differential equations. This course also attempts to strike a balance in emphasis between theory and application. Several techniques of applied mathematics--such as the method of eigenfunctions expansion, the Fourier transform, and the use of Green's functions--are developed and the theory discussed.
271: (Real Variables--Dr. Velasquez) We will do some preliminary work in set theory and point-set topology to study measures, Lebesgue integrals, L ^p spaces and other topics according to students' interests.
291: (Seminar in "Group Theory"--Dr. Sun) The content is mostly finite groups, a bit of free groups and infinite abelian groups. Finite groups include the theorems of Sylow, Cauchy, Cayley, Frobenious, Jordan-Holder-Schreier and Burnside, p-groups, solvable groups, nilpotent groups, simple groups, permutation groups, linear groups, etc. Infinite abelian groups include the Fundamental Theorem of Finitely Generated Abelian Groups.

Next week: math 107, 108, 110, 123, 151, 171 and 252.

Math Alliance News--Chess Tournament

(From Dr. Velasquez) The Math Alliance is planning a chess tournament. The date is still unknown, but could be as soon as in one or two weeks. Contact Dr. Velasquez for more information.

Graduate Assistants for Spring Semester

If you are interested in a Graduate Assistant position for this Spring semester, contact the department office as soon as possible.

Reminder: The Proof on TV

Don't forget about the NOVA broadcast of The Proof --The drama behind Andrew Wiles' proof of Fermat's Last Theorem. This will be shown on local channel 18 (PBS) on Tuesday October 28 at 7 p.m.

Problem Corner

Problem 2.4: The letters a, b and c represent different digits, a is a prime, and a-b = 4. If the number aaabbbc is a prime, find the values of a, b and c.

Solution to Problem 2.4: The test for divisibility by 3 shows that 3a+3b + c must not be a multiple of 3; therefore c \= 0, 3 or 9. Also, for the number to be prime, c \= 2, 4, 5, 6 or 8. Therefore c = 1 or 7. The test for divisibility by 11 shows that

(2a + b + c)-(2b + a) = (a-b) + c = 4+c

must not be a multiple of 11. Therefore c \= 7, so c = 1. Since a-b = 4 and a is prime we can only have have (a, b) = (5, 1) or (a, b) = (7, 3). Since c = 1, the answer is (a, b, c) = (7, 3, 1). The number 7,773,331 is a prime number.

Correct solutions were received from Anar Ahmedov, John Jamison and Lina Obeid.

New Problem

Problem 2.5: (Due no later than Thursday November 6, 4pm) In the semi-circle shown, diameter P₀P₁ = 2. Angle P₀P₁P₂ = 1 degree; angle P₁P₂P₃ = 2 degrees; angle P₂P₃P₄ = 3 degrees; ..., P_k-1P_kP_k+1 = k degrees. If P_kP_k+1 is the first chord whose length is less than 1, compute k.

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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