Happy new year and greetings to students in Math 312! I am looking forward to working with you. In this course, you will find out what we really mean when we talk, in Calculus, about such things as “limit”, “continuity”, “sum of an infinite series”, “derivative” and so on. Or, at least, you will find out what are the best answers mathematicians can currently provide to such questions.
The content of analysis is not difficult (mostly, it boils down to manipulating inequalities) but the logical structure of analysis is complicated and can be confusing. In this respect, analysis may be more like writing computer code than it is like Calculus III. When you write a program in C or Java, the individual steps are usually pretty simple; the art of coding is to fit them together into the right logical structure of loops and conditionals. So with analysis. In this course I’m going to try to build on this analogy and teach “structured proving” just as you might be taught “structured programming” in a CS course. I hope you will find this approach helpful. (Even if you have never written a program in your life.)
You can find more about my background and interests from my personal home page.