St. Olaf Mathematics Department

Math  Mess

November 28, 2000 Volume 29, No.11

 This Week's Colloquium Title: To Infinity...And Beyond! Speaker: David Molnar, St. Olaf College Time: Thursday, November 30, 4:00pm. Cookies served at 3:45pm. Place: SC 182 Points: Min(infinity,14)

This Week's Colloquium
The Matt Groening cartoon on my office door shows a boy asking his father what the largest number is. "Infinity," his father finally tells him. "And you're not jokin'?" "Nope." "What about infinity + 100 + 14 + 28?"  Well, in most cases, that's funny. If you're working in a context where infinity + 100 + 14 + 28 is actually different from infinity, then it's not funny anymore. We'll explore such a context -the game of Blue-Red Hackenbush. That sounds funny, but it isn't. Our talk won't actually be about what is funny and what isn't, but rather a beautiful and surreal array of numbers corresponding to positions in this game, including irrationals, infinitesimals, and various ordinal numbers - different varieties of infinity.

David Molnar's interest in mathematical games is fueled by the fact that they can be used to illustrate so many different ideas. Students in his Gateways class have used basic problem-solving principles to find winning strategies for some cute little games (although he is still waiting for them to solve the donut game based on the Euclidean algorithm). David knew that he would fit in at St. Olaf when he learned that he would not be the only one who plays games in math class. There are rumors that he may be organizing a mathematical games tournament here in the spring.

Are You a Math Major?
The registrar would like to know.  Students are encouraged to register their math major when they register for courses in December.  There are a number of reasons the Math Department is interested in getting your names in the system: grants, departmental and fellowship awards, PME nominations, messages, etc.

Congratulations!
The winners of the Carlson Calculus Contest are Haley Clark and Daniel Hedges. They will each receive \$35 and their names will be inscribed on the plaque of champions. Second place goes to David Truesdale and Matthew Bills, they each get a \$25 prize. Three teams tied for 3rd place so Adam Schad, Kurt Nelson, Chris Piepho, Ben Toht, Andy Eklund, Katie Huber, Britta Anderson and David Utter will each receive \$15. The awards may be picked up in the Mathematics Department Office any time after December 4th. Congratulations to all.

Second Semester Courses
*Mathematical logic (Math 370), Prof. Kay Smith.
Math Logic uses mathematical methods to analyze reasoning and to examine what mathematicians can and cannot do. For example, are there statements that are true that are not provable?  This course will provide an introduction to three subfields of logic - set theory, which deals with formalizing infinity; model theory, which looks at the relationship between axioms and the structures that satisfy those axioms; and recursion theory, which studies what problems can be solved by algorithms.

*Software Design and Implementation (CS-272), Prof. Dick Brown. Prereqs: CS-172 or permission of instructor.
The objectives of CS-272 include introducing the C++ language and presenting the basic concepts used to design and construct software. We will focus on object-oriented software design principles that have emerged over time, based on academic computer-science research and years of practical professional experience. The course finishes with a team project that puts both C++ programming skills and software-development principles to practical use. CS-272 registration includes a scheduled two-hour weekly lab.  The lab provides supported hands-on experience with new concepts as they are encountered in the course, and extends students' backgrounds in computing tools related to software development.

*Discrete Mathematics (Math 232), Prof. David Molnar.
A list of problems which serve as a description of the course is posted at:
http://www.stolaf.edu/people/molnar/ps/232/

*Abstract Algebra II (Math 352), Prof. Jill Dietz.  Prerequisite is Math 252.
Are you one of the millions who can't get enough of Abstract Algebra?  Well, you're in luck because I'm offering a fabulous follow up course.  AAII covers more groups, rings and fields with an emphasis on finite group theory and Galois theory.  Students interested in graduate school in pure mathematics are especially encouraged to take this course.

Problem of the Week
Here's a left over from the Carlson Calculus Contest: Let f(x)= x^n + a_{n-1}x^{n-1} + ...+ a_1x + a_0 be any monic polynomial of degree n. What is the limit as x goes to infinity of [(nth root of f(x))-x]?

**Please submit all solutions to Cliff Corzatt (corzatt@stolaf.edu) by noon on Friday.  The last POW has been solved and the solution will be published next week.