This course is for those who delight in solving challenging math problems and who would like to further develop both their problem-solving and their logical-reasoning skills. Problem solving is the activity of the mathematician, and logical reasoning is the framework for this activity. Here we give an introductory course in logic, drawing from examples outside of mathematics but focusing on the use of logic within mathematics. Students are introduced to the basics of propositional and first-order logic, and this gives them access to formal notions of familiar logical methods. Additionally, students discover how their formal understanding can be used directly to help solve certain mathematical problems. But logical reasoning is not all there is to problem solving. Good problem-solving skills include ingenuity, creativity, and the ability to apply a variety of strategies and techniques. In this course, students are taught fundamental tools and standard techniques for problem solving, and they are given the opportunity to develop their mathematical ingenuity through practice on problems in a wide range of difficulty. The mathematical subject areas that the problems are drawn from include set theory, number theory, and combinatorics - none of which require more background than algebra.
Logic and Problem SolvingMathematics
at the time of application
on the first day of session
Completion of an algebra course.