From vaccine effectiveness to disease modeling to electoral politics, math provides insight into so many of the world’s challenges.

Bay’s math program pairs the mastery of foundational skills with the mathematical reasoning that prepares students to pursue the subject at a high level. The core curriculum integrates algebra, geometry, trigonometry, and statistics in the three-year Math 1, 2, and 3 sequence. By layering these in the core series, our teaching reinforces concepts and skills while also showing the connections between the various math branches. Teachers look for demonstrated understanding through regular assessments, presentations, and documentation of work.

Whiteboard collaboration and process discussions figure largely in Bay’s teaching: Research shows that skills and retention are improved when students discuss the problem-solving process. At Bay, it is not enough to know the formula: you have to know what it means, understand its parts, and be able to explain it to others. Our math department also works to align course content with the concepts that students need to know in our science courses.

We offer a variety of electives and honors courses to cater to diverse interests, with options in both theoretical and applied mathematics. All incoming students take a placement test to determine their starting point in our math sequence.

## Courses Offered

Students must complete six semesters in mathematics. Students typically complete this requirement in their first three years at Bay; they are encouraged to continue their studies beyond this requirement.

This two-semester course is the first in a three-year sequence of integrated courses (Math 1, Math 2, and Math 3) that form the core math curriculum at The Bay School. Math 1 introduces students to problem-solving approaches built on mathematical “habits of mind.” Students explore problem solving using tables, graphs, visuals, and algebraic methods. Students work with linear models and real-world scenarios, exponents and functions, statistics, and geometry. Math 1 students also spend time building fluency in basic algebraic manipulations and techniques. **No prerequisite.**

This two-semester course is the second in a three-year sequence of integrated courses (Math 1, Math 2, and Math 3) that form the core math curriculum at The Bay School. In Math 2, students extend their study of algebra and geometry. The course focuses on functions and mathematical proofs. Students analyze, compare, and apply different function models in various representations, and use these to analyze scenarios and make predictions. Students also study probability, parallel line postulates, proofs involving two-dimensional shapes, and right triangle trigonometry. **Prerequisite: **Math 1 **or** placement test

This two-semester course is the third in a three-year sequence of integrated courses (Math 1, Math 2, and Math 3) that form the core math curriculum at The Bay School. Math 3 covers a variety of topics drawn from advanced algebra, geometry, trigonometry, and statistics, including but not limited to: circles, trigonometric functions, exponential and logarithmic functions, and statistical inference. The course’s major throughlines include the use of functions and other mathematical tools to explore, model, and analyze real-world phenomena. **Prerequisite**: Math 2 **or** placement test

### Electives

Analysis of Functions is a two-semester course in which students make the transition from the conceptually-oriented approach of previous mathematics courses to the more rigorous deductive approach often seen in higher-level mathematics and science courses. Students who think they may have any desire to study a math- or science-related field in college should take this course, as it prepares students for the study of calculus and other advanced mathematical studies. Topics covered include function transformations, the theory of inverse functions, logarithms, polynomial and rational functions, analytic trigonometry, and advanced algebraic manipulations. Students work on a culminating project about how math connects to an area of personal interest. **Prerequisite:** Math 3

This one-term course has two guiding questions. First, *How can one collect meaningful data about a population without examining every single member of the population?* Secondly, *How can one analyze this data quantitatively to reach statistically valid conclusions about a population?* Students learn topics through case studies that illustrate how statistical concepts apply to various situations, events, and data sets. Connections between statistics and current events are highlighted throughout the term. Students also use statistical software, graphing calculators, software applets, and online labs. **Prerequisite:** Math 3

The guiding question for this course is: *How can we utilize data science to expose, argue for, and stay curious about social justice topics? *Much of today’s interactions occur under the guise of machine learning algorithms that attempt to anticipate our actions and manipulate our decisions. With the age of Artificial Intelligence afoot, we must be capable of understanding the social justice implications that arise from its use, and be able to peel back the curtain to reveal what is truly going on. In this one-term course students explore how “Big Data” is used, and address the ethical issues that come with its misuse. Students learn how to program their own machine learning algorithm, including a neural network, and explore the impact of overlooking structural and systematic biases within the data that is used to build them. This course has three principal objectives: To solidify our understanding of statistical analysis and build an understanding of machine learning algorithms and neural networks; to learn the basics of python programming and how to create prediction algorithms; and to apply the learned data science skills to explore and argue for systemic changes to support social justice. In this class students explore topics such as, but not limited to, climate change, mass incarceration, and neighborhood dynamics. During the last third of the course, students demonstrate and further their learning by conducting in-depth research on a topic of their choosing. **Prerequisite:** Math 3

This is a two-semester course in single-variable differential and integral calculus with an emphasis on applications to the physical, life, and social sciences. Major concepts are developed through the investigation of practical, real-world scenarios. Topics covered include applications of the derivative as a rate of change and a slope, symbolic formulas for computing derivatives, applications of the definite integral as an accumulation function and an area, creation of mathematical models using Riemann sums, symbolic techniques of anti-differentiation, and the creation of mathematical models. Time-permitting, students may also study additional Calculus topics and their applications. [This course is an Honors course; see __Honors information__ for details.] **Prerequisite: **Analysis of Functions A/B

Students in this course will sharpen their logical and critical reasoning skills as they dive into an entirely new way of describing mathematics known as abstract algebra. This proof-based course will hone students’ skills in mathematical reading and writing. The course will start from first principles to find similarities and differences between the groups of integers, rationals, real, and complex numbers. Students will examine Abelian groups, symmetries of polygons, homomorphisms, cyclic and permutation groups, matrix operations, and other topics. Group theory gives mathematicians a whole new way to think about numbers—though you might not see many numbers in this course—that is different from what students have seen so far. [This course is an Honors course; see __Honors information__ for details.] **Prerequisite:** Analysis of Functions A/B

For much of a high school student’s math education, one dwells in the world of two or possibly three dimensions. In this course we will delve into the generalization of solving linear equations in higher dimensions, and more abstractly in Rn. Students will practice their mathematical reading and writing skills as we explore topics of linear dependence, matrix properties, vector spaces, orthogonality, determinants, and linear transformations. To ground our understanding of what will be for many, unfamiliar territory, we will relate theory to applications in fields such as physics, geometry, economics, biology, and computer science. [This course is an Honors course; see __Honors information__ for details.] **Prerequisite:** Calculus A/B

Imagine a world where everything is made of a stretchy material that can be molded into whatever you like…but can’t be torn apart. In this world, bowls and plates are the same because each can be changed into the other, but a coffee mug is different because of the hole made by the handle. Topology is the branch of math which studies shapes and spaces but does so while ignoring things like size and angle. In topology, squares, rectangles, parallelograms, trapezoids, and circles are all considered to be the same. But here’s the tricky question: if we ignore these ways of measuring, how can we tell when two shapes are different? Students enrolled in this one-term course start by examining questions like this and quickly progress to speculations about the shape and fundamental nature of the universe. Mobius strips, Klein bottles, tori, gluing, orientability, and dimension—including ways to represent the fourth dimension—are all ideas that students examine and investigate. [This course is an Honors course; see __Honors information__ for details.] **Prerequisite:** Analysis of Functions A **Can be taken concurrently with Analysis of Functions B.

### Immersives

The depiction of human and animal forms--figural representation--is generally considered to be forbidden in Islam. This course explores the artistic traditions that emerged in Islamic art with the absence of figural representations. Geometry, calligraphy, and biomorphic design are all disciplines of Islamic art. The interweaving of the three creates works of mathematical complexity and great beauty. Students study constructions, symmetry, and tiling groups in order to better understand the ways that geometry can be used to create works of art, and the ways in which art can help us better understand and illuminate geometrical relationships. This course centers around using straight-edge and compass and their technological equivalents to construct geometric designs, and considering the ways in which Islamic (and other) artists use geometry to create art. The class culminates in the creation of a work of art that showcases the concepts and themes from the course. **No prerequisite.**

In this course, students explore the math behind digital animation and modeling. Using Pixar films as a starting point, students learn about various stages in the digital animation process, from character development to fine-tuning digital animations. Students interact with these elements through digital tools, hands-on activities, hearing from professionals in the industry, and local field trips. Essential questions guiding our study include: *How can mathematics help us to model characteristics and phenomena we observe (or imagine)? How do we analyze and strategically set up the representations we use a computer to manipulate? How does the iterative design process relate to both our work in mathematics and the creation of a digitally animated film? ***No prerequisite.**

In this interdisciplinary math and social studies course, students explore voting and representation, the fundamental features of democratic government, through a mathematical lens. Students learn about the history of representational government as well as analyze current election and representation systems. The course examines a variety of voting and representation schemes that are currently in use or that have been proposed, and looks at how these methods influence election strategies and outcomes. In addition to democratic systems themselves, students learn how representation is distributed to each state and how changes in the creation of districts may influence the outcome of elections. Essential questions guiding our study include: *What is the function of representation in a democracy? How can/should groups of people make decisions? How can an individual make an impact on policy?* **No prerequisite.**