Mathematics

This course is an introduction to algebra. Extensive attention is given to developing algebraic and graphical problem-solving skills. The coordinate geometry of lines and parabolas, fractions, rational expressions, integral exponentials, and linear and quadratic equations through the quadratic formula are included with an eye toward developing confidence and agility in problem-solving. Algebra I Enhanced is designed for students who have already been exposed to some or all of the topics of Algebra I, but who need further reinforcement to support higher levels of study in math. 

This course provides an introduction to plane and solid geometry, focusing on building confidence and developing logical reasoning and mathematical communication skills. It emphasizes foundational concepts and problem-solving in geometry.

This course pursues a deepening of students’ understanding of plane and solid geometrical figures and a building of their abilities to analyze and communicate mathematically. Much attention is given to the logical structure and the writing of mathematical arguments as well as to geometrical problem-solving.

This course reviews and then extends the study of algebra with greater attention toward functions. Topics include linear and quadratic functions and relations, polynomial functions, rational expressions and functions, exponents, logarithms, and elementary trigonometry. Students are expected to broaden their problem-solving skills and techniques. Increased attention is given to multiple representations with graphs and charts used to illustrate and enhance algebraic manipulation.

This yearlong course is for students who have completed Algebra II. It includes an introduction to the basic concepts of statistics; a review of linear, quadratic, exponential, and logarithmic functions; and a study of trigonometry. Modeling data using the functions and using statistics to verify the validity of the model is an emphasis. There is extensive use of online software programs CODAP and Desmos. Topics include: descriptive statistics, correlation, quadratic, exponential, logarithmic regression, circular trigonometry, sequences, and series. This course will not be sufficient preparation for students to take a calculus course at St. Mark’s. At the conclusion of the course, SFT students will be prepared to enter Introduction to Calculus: Data and Change. Strong SFT students may choose, with permission of the Department, to continue on to Precalculus. (Prerequisite: Algebra II. This course is not open to students who have already completed Precalculus)

Extensive discussions of polynomial, rational, exponential, logarithmic, and trigonometric functions and their properties and applications are encountered. Sequences, series, and limits are also introduced. Students gain skills in analyzing functions and drawing connections between symbolic, graphical, and numerical representations. This course is primarily designed as final preparation for the study of calculus. A graphic scientific calculator is required at this level for its aid in visualization and calculation. (Prerequisites: Algebra II and Departmental permission)

This is an accelerated course in the elementary functions that includes an introduction to the study of calculus during the second half of the year. Students are expected to have exceptional intuition and motivation for the study of mathematics. (Prerequisites: Honors Algebra II, teacher recommendation, and Departmental permission)

This is a yearlong course designed for students coming from our Statistics, Functions, and Trigonometry course. Students will work individually and in groups, and the majority of the coursework will be discovery labs, problem sets, class discussions, and projects. They will use computers and graphing calculators to enhance and inform their understanding of the essential concepts of calculus. Topics will include, but are not limited to, statistics, limits, rates, linear approximation, optimization, and accumulation. (Prerequisite: Statistics, Functions, and Trigonometry; open to V and VI Formers or others with Departmental permission).

This is an introductory calculus course designed for students who want to study calculus before college, but who do not yet feel prepared for the pace or depth of an Advanced course. The concepts of calculus are studied with problems and results expressed graphically, numerically, analytically, and verbally. Graphing calculators are used to help the students visualize critical concepts. (Prerequisite: Precalculus)

Throughout this course, students will be learning to use mathematics to tackle interesting and challenging real-world problems. They will learn about the mathematical modeling cycle and ways to best create models and present solutions to problems. While the bulk of the course will be devoted to solving problems related to social justice issues, the students will also learn about existing models for specific situations and will develop tools to use in the modeling process. This course is intended for students who enjoy mathematics, like working collaboratively, and wish to apply the mathematics they know to new and interesting problems. (Prerequisite: Completion of Precalculus or Departmental permission. This course may be taken concurrently with Precalculus with Departmental permission)

Throughout this course, students will be learning to use mathematics to tackle interesting and challenging real-world problems. As part of their problem-solving, students will learn how to best use data to reach solutions to the problems. They will learn about the mathematical modeling cycle and ways to best create models and present solutions to problems. They will also learn strategies for extracting and extrapolating useful data from large and messy data sets. While the bulk of the course will be devoted to solving problems related to finance and business, students will also learn about existing models for specific situations and will develop tools to use in the modeling process. This course is intended for students who enjoy mathematics, like working collaboratively, and wish to apply the mathematics they know to new and interesting problems in an interdisciplinary way. (Prerequisite: Completion of Precalculus or Departmental permission. This course may be taken concurrently with Precalculus with Departmental permission).

This course develops an understanding of the major concepts of calculus. Applications and techniques of differential and integral calculus are illuminated. Students will develop an understanding of the concepts of calculus and will be provided with experiences that enable them to apply these concepts. The course will emphasize a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Graphing calculators are used to help the students visualize critical concepts. Students enrolled in this course will take a strong role in the ownership of the concepts covered in this course and are expected to be able to apply concepts covered in previous courses. (Prerequisites: Precalculus and Departmental permission)

This course is an extension and enhancement of Advanced AB Calculus. It is a more rigorous course, with a more extensive syllabus, including an introduction to power series expansions, vector calculus, and the calculus of polar curves. Successful completion of this course is roughly equivalent to a full year of college calculus. (Prerequisites: Honors Precalculus, teacher recommendation, and Departmental permission)

This course introduces the major concepts of an introductory college-level statistics course. Students will develop statistical reasoning by analyzing data, drawing meaningful conclusions, and expressing their findings clearly and precisely in writing. In the study of descriptive statistics, students learn to represent and summarize data effectively, while in inferential statistics, they use samples to estimate population characteristics (confidence intervals) and test hypotheses about populations. Key principles underlying survey and experimental research are also explored. By completing the course, students will be prepared to apply statistical methods in a wide range of fields that rely on data analysis, such as psychology, political science, and economics. (Prerequisites: Precalculus and Departmental permission)

Topics of study are chosen to allow students to take multiple versions of the course over several semesters and have recently included Multivariable Calculus, Linear Algebra, Differential Equations, Probability, Abstract Algebra, Number Theory, and Graph Theory. (Prerequisites: Advanced BC Calculus and Departmental permission) 

MA-601F | Multivariable Calculus (fall semester)

This course re-examines the differentiation and integration processes by looking at them from the perspective of more than one variable. Topics will typically include partial derivatives, level curves, and gradients, double and triple integrals, Lagrange multipliers, and optimization in several variables.

MA-602S | Probability (spring semester)

The purpose of this course is to enable students to extend their understanding of statistics, acquire additional modes of mathematical reasoning at an introductory level, and develop skills necessary for the further study of mathematics and natural and social sciences. Topics will build from basic counting methods to include distribution functions: binomial, geometric, hypergeometric, and Poisson distributions. The other topics that may be covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes’ theorem; joint distributions; Chebyshev inequality; the law of large numbers; and the central limit theorem.

St. Mark’s believes in fostering the multidisciplinary study of science, technology, engineering, and mathematics (STEM), understanding that this study extends beyond the walls of the classroom and involves more than the acquisition of information from textbooks. While innovative electives can provide students with the opportunity to understand and appreciate this idea, active participation in authentic research and real-world exposure to the applications and illustrations of STEM topics is far more powerful. The STEM Fellowship aims to provide students such an opportunity through advanced independent STEM research, collaborative work within a team, a focused interdisciplinary approach, mentorship from an expert in the corresponding discipline of study, and the potential application of research to real-world challenges. This program is intended to provide an opportunity for students to work beyond the Advanced level in their chosen course of study. Acceptance to and successful participation in this program requires a commitment to an academic endeavor spanning an entire calendar year and requiring significant independent scholarship. The culmination of research will be a public presentation to peers, faculty, and experts in the field. (Prerequisite: Departmental permission. STEM Research fellows will be selected through an application process that will take place in the spring of 2026. This class is cross-listed with the Math department. Students in the STEM Fellowship should have taken or be concurrently enrolled in the highest-level science and/or math  course related to their research topic)