The text here is Courant's Calculus I and it in itself exceeds what is generally
taught in undergraduate Calculus. The first semester covers chapters 1-5. The
second covers chapters 6, 8-10. Each chapter includes an appendix of deeper
study, which would be included as the understanding of the students allowed.
This course is often the first college course requiring proofs,
taught as a kind of matrix arithmetic and analysis. Here, having
plenty of experience with proofs in Euclid, we can show it for the more
abstract subject that it is and keep everything within reach of the students'
understanding by restricting ourselves to spaces of two and three dimensions
where the matrix calculations are not time-consuming and the additional
ideas of n-dimensional spaces can be put off for later study by those who
actually choose to learn about them.
Decline of the West
This book, written in the aftermath of World War I, was transforming the
academic world in all disciplines when World War II intervened. Following that
war, reaction against any thought coming from a German-speaking source
(Spengler was Austrian) was rejected. Here we have another substantial road
not taken in our study of history, culture, and society. You could probably get
four years of mileage for the classroom out of this book without effort.
The Blue and Brown Books
Two Essays on Education
Wittgenstein was unique in his pursuit of critical philosophy. A
mere perusal of his works reveals that he always desired the truth and
a complete understanding and never claimed to have more of either than
he could demonstrate. The first semester's two short texts by him, written
as a guide for his own students, reveal his method. They give us a
starting point for our own original investigations and one of the
world's best examples of intellectual honesty. The second semester's
two short texts by Ivan Illich give us a basis for exercising this
method by examining public education through critical philosophy.
This book, like The Idiot, is in part Dostoevsky's reaction to
the growing socialism and nihilism (with its terrorist acts) that appeared
in Russia and Europe in his time. It allows us to expand our study into Russia
and further fills out the picture of how the 20th century was formed.
My Own Life
This is a very colorful autobiography of another unique individual. My
personal subtitle for this book is "How the Smartest Man in the World
Found Jesus, Was Saved, and Still Had Sixteen Teeth." Cardano was not
a modest man. But he is a wonderful means of expanding the Renaissance
as he was a doctor, mathematician, scientist, rogue, and an intellectual-property