MATH 3325 -- Transitions to Advanced Mathematics
Course Meeting Times and Place: MW 4 - 5:20 pm, S 116
Office Hours: M 3 - 4, and by appointment. Email me for an appointment.
Text: Proofs by Jay Cummings
Course Description:
This course is an introduction to proofs and the abstract approach that characterizes upper level mathematics courses. It serves as a transition into advanced mathematics, and should be taken after the initial calculus sequence and before (or concurrently with) mid-level mathematics courses. The goal is to give students the skills and techniques that they will need as they study any type of advanced mathematics, whether it be in pure mathematics, applied mathematics, or application-oriented courses. In particular, this course covers topics that are ubiquitous throughout mathematics (e.g. logic, sets, functions, relations) and helps prepare students for classes such as Real Analysis, Abstract Algebra, and Advanced Linear Algebra, that are required for majors and minors.
A major objective of the course will be to teach students how to read, write, and understand proofs. Throughout the course students will be exposed to the notation, language, and methods used by mathematicians, and will gain practice using these in their own proofs. In addition, great emphasis will be placed on writing and communication.