Material to be
covered:
This course will cover most of Chapters 1 - 5 of the book, as time
allows. We will tentatively aim to cover the following sections:
Chapter 1: Sections 1.1 - 1.3, 1.5, 1.6
Chapter 2:
Sections 2.2 - 2.8 (read 2.1 on your own)
Chapter 3:
Sections 3.1 - 3.6, 3.10
Chapter 4:
Sections 4.1 - 4.5, 4.7 - 4.9
Chapter 5:
Sections 5.1 - 5.5 as time allows
The actual section coverage may slightly differ from this list,
depending on our progress. The particular week-by-week schedule of
the course will correspond to the weekly homework assignments,
which will be displayed on the class webpage as we progress.
Teaching philosophy:
The main goal of this liberal arts GE course is to present the
mathematical way of thinking, centering on rigorous logic and
analytical reasoning. We will do this on the example of the
classical material of Differential Calculus, going back to the
fundamental 17th century work of Isaac Newton and Gottfried
Wilhelm Leibniz and its 19th century presentation by
Augustin-Louis Cauchy and Karl Theodor Wilhelm Weierstrass, along
with other important mathematicians. The approach we take will be
largely theoretical, aiming to not only demonstrate computational
methods, but also to understand what makes them work. While we
will not be able to prove all the results presented, we will see
some proofs and discuss the underlying logic behind the main
concepts. In this way, this course will also serve as an
introductory exposition of the art of mathematical proof, which
may be different from a more computational approach to Calculus
taken in many high school courses.