Material to be
covered
The following chapters/sections of the textbook will be covered:
Chapter 6:
Sections 6.1 - 6.5
Chapter 7:
Sections 7.1 - 7.4, 7.7 - 7.8
Chapter 8:
Sections 8.1 - 8.2
Chapter 9:
Sections 9.3, 9.5
Chapter 10:
Sections 10.3 - 10.4
Chapter 11:
Sections 11.1 - 11.10
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 Integral Calculus and Infinite Series, 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.