The Cantor-Schroeder-Bernstein Theorem material is posted
in the Workbook. (See the link below.)

The course will concentrate on "discrete" mathematics for
computer science and engineering. The term "discrete" signifies
areas of mathematics normally thought of as not involving
calculus. Such a veiwpoint is fundamentally misguided, but
servicable for the purposes of the course. The topics are
generally more advanced than calculus. The goal of the course
is not to learn about topics in
discrete math. The goal is to
see clearly in a certain kind of rational
cognitive sense. One learns how to see
clearly in this sense
by fine-tuning a rationally skeptical attitude relentlessly
devoted to it, that is, to seeing clearly.

TheObjective of this course is to
equip participants with a way of
seeing based upon mathematics and the fundamental
building blocks of mathematics: sets, relations, and
functions.

ThePurposeof this way of seeing is
to empower one to engineer anything in the design space that is
the mathematical universe, the only limits being those imposed by
logical consistency.

Course Rationale

The mathematical universe displays extreme
consilience; in
particular, the structure and function of any part of it impacts the
structure and function of every other part.

Artifacts of technology as well as the the virtual
worlds of computing are realizations of structures in the mathematical
universe.

Therefore, the greater one's powers to
roam at will through the design space that is the mathematical
universe, the
greater will be one's powers to create and to wield artefacts of
technology and the virtual worlds of computing.

Course Outcomes

To realize the course's purpose, upon completion of the course
participants will be able to:

Begin to read mathematical research papers in computer science
and engineering.

Recognize rigorous mathematical reasoning.

To use mathematical reasoning to facilitate
deep learning of new technical concepts on one's
own.