This course may be known at other schools as Introduction to Abstract Mathematics, Transition to Higher Mathematics, Bridge to Advanced Mathematics, etc. The objective of the course is to give students a chance to become more comfortable with the major elements of theoretical mathematics before they are asked to create proofs in content courses such as abstract algebra, real analysis, and topology. At Stetson, this course is a prerequisite for all upper level math courses.
Modern mathematics is based on the axiomatic system.
This organization dates back only about a century, when logic and the foundations of mathematics were intensively studied. A student's first acquaintance with logical structure is usually in Euclidean geometry, where the axioms are made explicit, and the student may be asked to write proofs. It is rarely mentioned at this time that arithmetic and algebra, fields possibly more familiar to students, have their own axioms and theorems. I try to combine lecture, discussion, and student presentation of exercises and proofs. In some classes I have been able to use the Moore Method part of the time.