Problems in Lower Mathematics
In the first semester, chapters I-IX, XV-XXI of Todhunter's Algebra are
used to solidify the arithmetic use of algebraic expressions. In the second
semester, chapters IX-XV and XX-XXIV are combined with chapter 16 in
Finkel to learn what is modelled by first- and second-degree equations and
how one creates these models. This is generally referred to as "word problems,"
which are presented as individual puzzles and as such are despised by both
De Morgan and Todhunter. Here we learn how to classify the situation in the
world according to types of models.
Everymind's De Morgan's Elements: Trigonometry
This text section of the text
quickly dispenses with the relatively trivial solution of angles and sides of
triangles. It focuses on an introduction to complex numbers, the complex
plane, and related infinite series, building upon what was learned in De Morgan's
Everymind's De Morgan's Elements: Calculus
This is a very short text for a full semester. But if you were to intelligently
examine how the best mathematicians compose their introductory Calculus
texts, you would find that this text is an excellent introduction to the fundamental
ideas in those best of Calculus texts. Undergradute Calculus is sufficiently trivial
to be considered the Last Arithmetic with the beginnings of real mathematics
added on. This text provides a basis to understand those real mathematics.
Renaissance in Italy
I consider this the best book of history ever written. It begins with a chapter
as exciting as any novel I have ever read. From there, it builds up a very large,
varied, and complete picture of the Renaissance. It is extraordinary. It gives
the student a real benchmark for excellence.
Goethe's Theory of Colours
This is one of the most original texts of natural philosophy ever written.
It is basically the story of the road not taken in our study of nature. But like
Walden, it is an influential book and pops up where least expected, as in the
writings of Ludwig Wittgenstein.
Our Mutual Friend
This is one of the four pillars of Dickens's later work. The other three examine
business, poverty, and the law. This one examines money, its uses and abuses in
English society. Given a year for its study, the course would begin by viewing the
excellent PBS version of the work. Then the book would be read and analyzed
in class to deepen our understanding of the long narrative.
Again, this text is used both to expand the knowledge of the subject of
the Thought class and to increase the understanding of the world. This
would broaden our understanding of Europe from England across the channel
to Germany. Goethe, peculiar man that he was, would also deepen our study
of the possibilities of a human life.