mexico-mesoamerica
Hermia, Hieroglyphs, and Hyperbolas: Introducing Our Newest Electives

Comparable to college and university curriculum, Commonwealth School offers a slate of exciting electives every year, supplementing core courses and giving students a chance to delve deep into subjects of interest, from the theory of relativity to world cinema to the scientific underpinnings of their favorite artistic mediums. 

Our roster of electives for the 2021–2022 academic year is particularly exciting, introducing new classes exploring Shakespeare’s most fantastical stories, ancient Central American culture, axiomatic set theory, and more. Keep reading to get a better sense of what these courses have to offer. You can explore a comprehensive collection of our current core and elective classes for each academic discipline here. Current and incoming students will have the opportunity to enroll during our course registration period (check your email and speak with your advisor for details!). 

Related: Explore Our Curriculum

New Electives for 2021–2022

Axiomatic Set Theory
Teacher: Mr. Letarte 

Axiomatic set theory provides a formal system in which all of mathematics can be constructed from a surprisingly simple set of axiomatic assertions, expressible in a beautifully concise formal language, about a collection of pairwise distinguishable objects known as “sets.” This course is devoted to a study of ZF, the axiomatic framework due to Zermelo and Fraenkel in which this program is most often undertaken. ZF and just one additional assertion, the axiom of choice, allow us to build a hierarchy of set objects rich enough to capture all of the mathematics that anyone but a small group of logicians would ever need to do. Each model of ZFC contains a set of “natural number” objects that behave as expected; surprisingly, the axioms of set theory allow us to extend these to the classes of ordinal and cardinal numbers—both too large to be sets. Transfinite induction and recursion, generalizations of techniques of the same name on the set of natural numbers, illuminate the workings of ordinal and cardinal arithmetic, transporting us quite literally to infinity and beyond. As time permits, we will begin exploring famous assertions such as the continuum hypothesis that mark the boundaries of what can be definitively known in a model of set theory. 

The Craft of Poetry 
Teacher: Ms. Eskelund

This course is a poetry workshop for experienced writers. We will read widely, asking ourselves, “What does this poem do, and how does it do it?” Students will try out the techniques and styles we find in our readings, write poems weekly, and revise and polish a collection of their work for the end of the year. Our purpose will be to refine poetic eye and ear, to experiment with what a poem can do that prose cannot, and to develop a distinct voice in poems. (Interested students should submit a writing sample to Ms. Eskelund by the end of the course registration period.)

The Geometry of Conic Sections 
Teacher: Mr. Letarte

Parabolas, circles, ellipses, and hyperbolas are known as conics because they arise as cross sections of planes with so-called extended cones—a fact that is mentioned in modern textbooks, but seldom proved. Another conic property routinely cited without proof is the “optical property” of the parabola that underlies the use of parabolic satellite dishes to collect incoming signals at their focal points. Other conic sections have optical properties of their own, and all can be derived using vector calculus. Surprisingly, there are geometric proofs of these facts, due to ancient Greek geometers, that are elegant, beautiful, and accessible to students with no more background than a first course in geometry. In this course, we will explore the conics using purely geometric methods. Besides establishing their familiar properties, we will encounter a veritable trove of little-known results. Were you aware, for example, that if a triangle is inscribed in a circle, every point on that circle is the focus of a unique parabola that is tangent to each of the three lines determined by the sides of the triangle? That for a given ellipse, the locus of points that are intersections of pairs of lines perpendicular to one another and tangent to the ellipse is a circle containing that ellipse and concentric with it? These and other delightful surprises await! 

Introduction to Psychology
Teacher: Dr. Lasker

Psychological concepts and terms permeate our world. Yet, thinking and talking directly about this subject matter is often fraught, confusing, and/or controversial. How do we think about something as complex and shifting as identity? What do these terms we throw around all the time, such as anxiety or narcissism, actually refer to beyond some sort of “toxic” emotional thing? This course attempts to begin to address some of these questions, starting with a look at the history of the field of psychology itself and the contributions (problematic and otherwise) of Freud. The course will also delve into literature and film as “clinical material” as an access point to reflecting on themes such as identity, relatedness, and development. 

Mesoamerica 
Teacher: Mr. Conolly

Hieroglyphs carved in stone or traced in bark-paper books; pyramids aligned with the stars; an intricate calendar of intermeshing cycles; human sacrifice, royal bloodletting, a ballgame symbolizing the struggle between light and dark, life and death. These hallmarks of Maya civilization were in fact practiced throughout Pre-Columbian Mesoamerica, a region stretching from central Mexico to Honduras. They will loom large as we examine the development of Olmec, Maya, and Aztec cities (among others), from the second millennium BCE to the conquest of Mexico in 1521, with a focus on the dazzling city-states of the lowland Maya during the Classic Period (c. 250-925 CE). We will necessarily engage with a variety of evidence, including material remains, works of art, inscriptions, and even literature. (For instance, we will rely heavily on the K’iche’ epic Popol Vuh to reconstruct Maya religion.) You will therefore use all the skills you have honed in your history and English classes (plus a little math), and learn about some of the techniques archeologists and anthropologists use to reconstruct the past, such as ceramic analysis and the ethnology of indigenous peoples. 

Problem Solving
Teacher: Ms. Boppana

Imagine you host a (pre-pandemic) party at which people are freely shaking hands. Are you guaranteed to have two people at the party who shook the exact same number of hands? You are placing dominoes on a chessboard with two opposite corners removed. Can you completely cover the board without overlapping dominoes? Many problems we face in math, and beyond, are unfamiliar, not addressed anywhere in the typical math curriculum from algebra to calculus. This course is about how to solve those problems. Problem Solving will guide students through advanced topics such as number theory, combinatorics, and graph theory, which are often reserved for college or extracurricular math. So we will see new content, but our emphasis will equally be on the skill of breaking apart complex problems to gain a foothold in solving them. A typical day in Problem Solving will involve hands-on practice in small groups. 

Shakespeare and the Fairy Tale
Teacher: Ms. Tyson

When we think of Shakespeare’s most famous (or at least culturally prized) plays, we often think of the tragedies—and yet Shakespeare wrote nearly twice as many plays that fall under the headings of comedy and romance: plays that focus on wonder, miracle, magic, and reunion. Why was Shakespeare so drawn to the genres of fairy tale, medieval romance, and myth? What did those types of stories allow him to do? How might the idea of character be influenced by the more fantastical elements of these plays? This elective will explore some of these plays, with an eye toward answering these and other questions. Texts will include A Midsummer Night’s Dream, Twelfth Night, The Winter’s Tale, and another play to be determined.

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