Although Euclid’s definitions, axioms and logical proofs were a great advance for his time, we have since discovered that there are a lot of unclear definitions and unstated assumptions in them, and that his proofs, at certain critical places, seem to depend on visual evidence rather than on the axioms alone. We will explore these issues, and show how modern mathematicians have found an approach that clarifies the foundations of Euclidean geometry, showing how they can be explained in a way that does away with visual imagery, and develops all theorems purely logically from the axioms.

Learn to pronounce the names of people and places you read in the newspaper. We will cover spelling/pronunciation rules for German, Spanish, and Italian, as well as for the usual Romanized forms of Arabic, Russian, and Chinese.

Learn how mathematicians have found a neat but curious way to extend the plane so as to represent the behavior of algebraic and analytic functions at infinity in a natural way. The resulting closed surface is one-sided, like a Möbius strip or Klein Bottle, and has the properties that any two lines intersect in exactly one point, but a line does not divide the plane into two parts—both sides of the line are the same region! This unique surface obeys elliptic geometry, a variant of spherical geometry. It is also used in projective geometry, where it is called the real projective plane.

Ever puzzled at how to pronounce foreign names you come across in the news? Learn to recognize and pronounce common languages such as german, spanish, italian and romanized russian, arabic and chinese.

Explore the many subtle connections between words. Class will trace out themselves such word families as (carry, car, cart, carriage, chair, care), (house, home, hovel, hive, hut, hutch, hotel, hospital) and (glare, gold, glitter, glisten, glory, gloat, glad, glade, glamor, gleam, gloom). Learn both historical (etymological) connections and phonosymbolic connections (certain sounds innately expressing certain meanings by analogical structure or symbolism). We will see how these principles work in English, in languages related to English, and in unrelated languages. This will be an activity with much class participation. Bring an English dictionary, as well as some foreign-English dictionaries if you have them.

There is a simple relationship between the numbers of vertices, edges and faces in a diagram consisting of points (vertices) ...

The famous 4-color map problem was only recently solved, with the help of a computer. (How many colors do we ...

Learn how to pronounce those foreign names and phrases you see all the time, and to recognize what language they ...

Why do words have the sounds and meanings that they do? How are different words and languages related to each ...

We will explore a new topic every week or two, including games such as Nim, Go-Moku and Othello. Students will ...

We will depart from MIT, across Mass. Ave. from the main entrance, bike up the Charles to the end of ...

If you are a history or war buff, or simply like vernacular poetry, you will love these poems, which tell ...

Hughes was the greatest Black American poet of the mid-twentieth century. Hear him vividly illustate the life and times of ...