Year Three

Mon-Wed-Fri

Tue-Thu

Mathematics I

Algebra

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.

Mathematics II

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 algebra text.

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.

History

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.

Thought

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.

Long Narrative

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.

Humanity

Lewes's Goethe

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.


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