Mathematics 201
How Mathematics Thinks: Multivariable Calculus
Taught by Guido Weiss

            This course (or seminar) is a new experience for all of us. It is designed to present to the students a fair amount of mathematics and, at the same time, teach how a mathematician thinks. Originally, I was not going to use a text; however, after looking at the book by Kennan Smith, which is the text for Mathematics 411-2, I decided to use it as the text for this course. It begins with a rather informal, not rigorous, presentation of the differential calculus of one variable. The author assumes the student is familiar with this material (which is the case here). I shall ask the student to read the first few sections rather quickly. The lectures will be complementary to this material during the first 1 ½ weeks.

I expect the students to write up these lectures and hand them in. There will also be some homework to be handed in regularly. I plan to give two exams during the semester. I urge each student to keep up with the course. Perhaps the most important feature of this course is the learning of how mathematicians communicate. MATHEMATICS IS A LANGUAGE! I want you to learn to speak it. As is the case in all languages, you cannot do this without constant practice. This course will place you at the level of having completed Mathematics 233.