Vol 1. No. 9
Editor: Dr. Larry Cusick.
None of us knew what to expect from the trip, but we all left San Diego with a new perception of mathematics. When we registered we were given a schedule of events which overwhelmed us by the choice of presentations from which we could choose. There were topics from "Education Reform" to "Careers for Math Majors" to "Topology". So, apart from Dr. Tuska's presentation on "Math History and Problem Solving" we split up and then got together to share what we had learned.
There was also a student center where we got the chance to meet other graduates from Sonoma, Los Angeles and San Diego. We socialized with other math students who shared similar interests to ourselves and learned about various programs. All the students worked together on "brain bender" games and then competed against one another at a problem solving competition which Patrick won. We also attended all the scheduled events especially for students; a workshop on "Linking Geometry and Number Theory", a lecture on "When is an Integer the Product of Two and Three Consecutive Integers?" and an ice cream social.
Another large aspect of the conference was the Exhibit Hall. This included the purchase of books, conversing with representatives from different organizations; such as AWM (the Association for Women in Mathematics) and NCTM (the National Council of Teachers of Mathematics), learning about new programs for calculators and setting up interviews for various employment opportunites in the mathematical sciences.
We witnessed mathematics as a living and continually growing subject found in areas from government to business to education. Conferences such as the one we attended allows mathematicians to learn from one another and we met mathematicians that were open to share their experiences with us and encourage us to pursue our dreams in the field of mathematics. Thanks to Dr.~Tuska, who told us of the opportunity, and the math department, who sent us. The conference touched each of our lives in a different manner. We recommend the experience of going to a conference to every one.
Problem 1.8: Suppose you want to telephone your friend, but you cannot remember the last digit of your friend's telephone number (you can remember the rest). You are at a pay telephone that costs $.25 per call and you have two quarters in your pocket. Your strategy is to guess the last digit of the number. What is the probability that you will be successful in reaching your friend with this strategy? Assume that you loose your quarter if either no one answers or it is a wrong number.
Solution to Problem 1.8: We will change the problem. The new problem though will have the same answer. The new problem is: From a bag of the digits 0 through 9, choose a number X at random and then choose Y at random (without putting X back in). You win if one of these numbers is say 0. What is the probability that you win? There are 90 possible outcomes (90 = 10x9). There are 18 winning solutions: (0, Y) where Y = 1, 2, ..., 9 and (X, 0) where X = 1, 2, .... Thus the probability of a win is 18/90 = 1/5.
The only complete correct solution was from Patrick Villa. One student gave the correct answer 1/5, but their reasoning was incorrect. There were two other incorrect submissions.
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 February 27, 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.