Monday Mathematics

It was back to classes on Monday morning for students on the California High School Summer Program! The past weekend was one to remember, from a competitive volleyball tournament to a beach day and shopping trip in Santa Barbara, but this morning, reenergized by their break from academics, the high schoolers were excited to try something new: their first TAC math class! 

After morning Mass and a hot breakfast, the programmers headed to their classrooms in St. Gladys Hall, where they discussed the opening pages of Euclid’s Elements, a treatise that compiles ancient proofs of arithmetic and geometric theorems. During their freshman year, students at Thomas Aquinas College work their way through the Elements, demonstrating everything from the Pythagorean Theorem to the construction of three-dimensional polyhedrons.

The high schoolers will be presenting proofs in class for the rest of the week, but today they began by discussing Euclid’s definitions, postulates, and common notions. While some of these first principles are self-evident, such as the postulate that the whole is greater than the part, others, such as Euclid’s definition of a point, line, or circle, require more discussion. “Definition day is always my favorite,” said prefect Monica Weinkopf (’25), who, now a senior, remembers her own experience with Euclid freshman year. “It awakens wonder. Do you really know what a line is? You go into class thinking you understand the definitions, and then you find out you don’t know as much as you think you did.”

TAC’s approach to geometry, as with other subjects, is about coming to a common understanding through discussion and focuses more on understanding logical arguments than memorizing definitions and formulas. “I really liked doing math without numbers,” said programmer Owen A. “I think, when I leave, I’m not going to want to go back to normal school; I’m just going to want to talk about everything!” The high schoolers will have plenty of opportunities to talk about math throughout the rest of the week, starting with their first demonstrations tomorrow. 

Many students attended midday Mass after class, then ate pulled-pork sandwiches and coleslaw for lunch, crowding around the dining tables to continue their classroom conversations or to joke and share stories. 

In their afternoon class, students had their first discussion of Boethius’s Consolation of Philosophy. In the work, which was written by Boethius while he was in prison and facing execution, the author bemoans the injustice that has befallen him, until he is visited by Lady Philosophy, the personification of human wisdom. Boethius relates the ensuing conversation, as he struggles to understand man’s nature and purpose, the problem of evil, and the inevitable failure of worldly goods to satisfy man’s desires. Since these questions are more than a bit too heavy to settle in a single afternoon, students will be able to spend two more classes unpacking the lessons from Lady Philosophy. 

For the rest of the day, the programmers have much to fill their time, including a talk on art and beauty and a prefects vs. students basketball game. Check the Summer Program Blog tomorrow for a recap!