## Course Summary

Though most people agree that mathematics is a cornerstone in a person's education, few realize that the math is not synonymous with algebra, trigonometry and calculus, or even that it is a vibrant research discipline. Quite to the contrary, mathematics is a discipline that continues to grow, and where unanswered questions far outweigh well understood phenomena. For example, in 2010 there were 20,000 papers submitted to an online repository of math articles; even if only a fraction of these are new and publishable, this is still a lot of math being generated in one year!

Math 125 (Mathematical Thought & Proof) is a course designed to show math enthusiasts what life is like after calculus. The heart of the course is in learning proof, the defining quality of mathematics and the source of its timeless truth. Students will spend the semester learning about the basic mathematical objects and proof techniques that will carry them through the rest of the undergraduate major (and, if interested, beyond). A secondary goal in the class is to show students some of the incredibly interesting mathematical results from the past several hundred years. For instance, a portion of the class will be devoted to discussing why there are certain infinite sets which are quantifiably larger than other infinite sets. In fact, there are infinitely many sizes of infinity!

The basic goals for the course are for students to

- develop the art of mathematical proof;
- become critical of their own work and the work of others in a courteous, productive way;
- gain insight into the process of how mathematics is created;
- become independent learners and thinkers; and
- learn how to capitalize from mistakes.

## Course Instructor

The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours will be scheduled at the beginning of the semester. You are highly encouraged to attend office hours, and you never need an appointment to do so. If these office hours don't fit with your schedule, contact the instructor so that he can either adjust when official office hours are held or set up an appointment to help you outside of office hours. You can also try dropping by his office to chat; if his door is open and he has time to talk, he'll be more than happy to help you with whatever calculus questions you have.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").

The college also sponsors a "help room" to give you extra assistance if you need it. You can find out more information about the help room here.