Upper School Mathematics
The Upper School mathematics program develops efficient problem solvers, effective communicators, independent and collaborative learners, and confident critical thinkers.
/Math_Curriculum/shot_put_main_page_mathematics.jpg)
At the conclusion of their time at Haverford, students are able to read, write, and think clearly in the language of mathematics. They explore, reason logically, and make conjectures: facilities that extend well beyond the discipline.
Our expectations are rigorous, relevant to the real world and reflect the knowledge and skills our graduates will need to be well prepared for the mathematical challenges facing global citizens of the 21st century. Our hope is that each student acquires a deep appreciation for the intrinsic beauty of mathematics as well as for its practical applicability.
Haverford students are required to complete at least three years of mathematics; most students take four years of math and many add a math elective. Below you will find descriptions of the advanced (denoted by an *) and standard course offerings in each level of a traditional mathematics journey from algebra to calculus, as well as math electives for those students who wish to pursue additional topics in mathematics.
Haverford School students compete in the 14-hour MathWorks Math Modeling (M3) Challenge.
The Upper School mathematics program sets forth clear, high-quality academic benchmarks that all students must master by the end of each course. These are designed to exceed the Pennsylvania Common Core Standards in their respective subjects. The Haverford School’s expectations are rigorous, relevant to the real world, and reflect the knowledge and skills our graduates will need to be well prepared for the mathematical challenges in life beyond Haverford.
Each of our courses offers a comprehensive set of learning objectives with the common goal of developing competent problem solvers, effective communicators, independent learners, and confident critical thinkers; these are skills that extend beyond mathematics. We are committed on an ongoing basis to improving the mathematics offerings available to our students. To that end, our instruction and curricula are monitored and adjusted to best serve our charges—the future global citizens of the 21st Century.
Mathematics Course Progression at The Haverford School
To graduate from The Haverford School, students must complete three years of mathematics, through PreCalculus.
| FOrm II | Form III | Form IV | Form V | Form VI |
|---|---|---|---|---|
| PreAlgebra | Algebra I | Geometry | Algebra II | PreCalculus |
| Algebra I | Geometry | Algebra II | PreCalculus | Calculus, and/or Statistics/* |
| Algebra I | Geometry* | Algebra II* | PreCalculus* | Calculus* or Statistics* |
| Geometry | Algebra II | PreCalculus | Calculus | Calculus* or Statistics/* |
| Geometry | Algebra II* | PreCalculus* | Calculus* | Calculus II* and/or Statistics/* |
Honors Courses
Advanced courses designated with an asterisk (*) are considered Haverford's most demanding courses and are designed to provide highly passionate students with rigorous academic experiences that move at an accelerated pace. Because we want every student to be successful, we are thorough and thoughtful in placing students in our most demanding honors courses. Entry into an honors course may vary by department and therefore students should refer to the prerequisite of each respective honors course to ensure they have met the requirements needed to successfully enroll in the course. Some departments require readiness diagnostics and other departments may require a specific grade and/or recommendation from the teacher and Department Chair in order to enroll.
Non-Haverford Courses
Credit is not granted toward the graduation requirements for courses taken at a school other than Haverford, though coursework completed in Modern and Classical Languages and Mathematics in Middle School may allow a student to take more advanced courses in those subjects in Third Form.
What are the Core Courses in the Upper School Mathematics program at The Haverford School?
Core Courses in the Mathematics curriculum of The Haverford School include the following:
- Algebra I
- Algebra II
- Geometry
- PreCalculus
- Calculus
ABOUT ALGEBRA I & GEOMETRY
Algebra is important as a modeling and problem solving tool, and it bridges the gap from computational mathematics to abstract understanding. Geometry introduces the spatial relationships that exist in two and three dimensions. The concepts learned in these introductory courses are used by each of us every day - albeit unconsciously - and form the foundation upon which subsequent math courses are built.
ALGEBRA I
Algebra I is an introductory course designed for incoming Third Formers who have had little or no algebra or who need a thorough review of basic algebra. The topics explored during the school year consist of:
- Problem solving skills
- Variables and proportions
- Linear graphs and equations
- Multiple representations of linear situations
- Multiplications of algebraic expressions
- Solving systems of linear equations
- Quadratics, including factoring expressions, graphing functions, and solving equations
- Solving and graphing linear inequalities
- Simplifying rational expressions
- Using laws of exponents
- Using function notation
- Appropriate use of a graphing calculator for the topics listed above
Geometry
This course provides a comprehensive introduction to Euclidean geometry. A solid foundation in Algebra I is required. The topics to be covered will include:
- Foundations of geometry
- Polygons
- Circles
- Coordinate geometry with transformations
- Inductive and deductive reasoning
- Mathematical proof
- Congruence and similarity
- Area and volume
Geometry*
This course provides a thorough year-long study of Euclidean geometry at an advanced level for qualified students from Third and Fourth Form. The course includes all of the foundational components of the standard course. Students will also be expected to connect concepts, and the most successful students will solve problems creatively. A mastery level understanding of Algebra I and a teacher recommendation are required to register for the course. In particular, the topics to be covered will include (but not necessarily to be limited to) the following:
- A rigorous treatment of mathematical proof
- Justification of the major theorems of the course
- Vectors
- Circle theorems
ABOUT ALGEBRA II
The Haverford School offers two levels of Algebra II—Honors and Standard. The goal of each is to expand and deepen your existing knowledge of Algebra I and Geometry; both courses emphasize the computational and theoretical components of the subject matter. Successful completion of these courses will satisfy the Common Core requirements for Algebra (as set by the Pennsylvania Department of Education) and will prepare students to tackle more advanced coursework in the future.
Algebra II
Prerequisite
This yearlong, standard level course is intended to meet (and surpass) the Common Core requirements. This is an exhaustive curriculum with particular emphasis on the practical/computational components of the subject and on the use of functions as mathematical models for solving real-world problems. In particular, the topics to be covered will include (but not necessarily limited to) the following:
- Properties of sets of numbers and number systems
- Solving equations, inequalities, and absolute value problems
- Functions, relations, and their graphs
- Combinations and transformations of functions
- Inverse relations and functions
- Linear functions and systems of linear equations
- Quadratic functions and introduction to complex numbers
- Properties of higher-order polynomials
- Radical functions and rational exponents (roots and powers)
- Exponential and logarithmic functions
- Rational functions
- Functions as mathematical models
- Elementary probability
ALGEBRA II*
Prerequisite
This yearlong course covers the topics outlined above, but in a much more rigorous fashion. There are a number of additional topics presented as well. One of the distinguishing features of this course over its standard counterpart is the greater commitment in both time and effort required for success. This course delves much deeper into the theory behind the basics and contemplates a wider range of topics. The curriculum reaches well beyond the Common Core requirements and prepares the students to tackle Precalculus at the honors level the following year. In particular, the topics to be covered will include (but not necessarily to be limited to) the following:
- Domain and range of functions and their inverses
- Systems of inequalities and absolute value equations
- Families of functions; transformations and graphs; end behavior of functions
- Quadratic equations (using advanced factoring techniques)
- Complex numbers/operations
- Systems of quadratic equations/inequalities
- Exponential and logarithmic functions using e and change of base
- Rational functions and their graphs–asymptotes, discontinuities, intercepts, roots and end
- behavior
- Conic sections—transformations and graphs
- Functions as mathematical models (using technology/software to solve real-world problems)
ABOUT PreCalculus
Precalculus builds on the concepts from Algebra and Geometry to create the foundation for the study of calculus and is offered in Standard and Honors levels. This challenging course includes an examination of many types of functions including trigonometric, exponential, logarithmic, rational, quadratic, and higher - order polynomials. Students will be challenged to examine mathematics graphically, algebraically, verbally and numerically. The use of the graphing calculator will be required in this course, and students will be expected to know the five basic graphical functions: minimum, maximum, value, zero, and intersection.
PreCalculus
Prerequisite
This course provides a comprehensive preparation for the study of calculus at Haverford or an introductory calculus course in college. This course requires a strong working knowledge of all the material from Algebra II, i.e. of linear, quadratic, higher-order polynomial, rational, exponential, and logarithmic functions. The concepts of trigonometry, sequences and series, and combinatorics will be developed. Mathematical models—solving real-world problems—requiring both algebraic and numerical methods will be emphasized throughout.
PreCalculus*
Prerequisite
This course covers all of the topics in Standard Precalculus with additional and/or enhanced coverage of conic sections, parametric equations, polar coordinates, vectors and the complex plane. Honors Precalculus is fast paced and requires a mastery of all previously studied skills. Connections with the sciences, economics and other real world applications are developed throughout. This course will also develop the student’s skills in the use of the graphing calculator, in all of its modes. In particular, the topics to be covered will include (but not necessarily to be limited to) the following:
- Advanced trigonometric functions graphs of tangent, cotangent, secant, cosecant and their inverses; half-angle formulas, product-to-sum formulas
- Advanced applications of conic sections—working from first principles, i.e. definitions of foci, directrices and eccentricity
- Parametric equations—graphs and applications
- Polar coordinates and graphing polar equations
- Vectors and vector operations in 2 and 3 dimensions—dot and cross product, components of vectors, lines and planes in 3-space
- Complex numbers—trigonometric form, De Moivre’s Theorem
- Advanced treatment of sequences and series—tests for convergence of infinite series, mathematical induction
- Introduction to calculus—limits, continuity, tangent line to a curve
ABOUT Calculus
Inspired by problems in celestial mechanics, Newton and Leibniz developed the ideas of calculus more than 300 years ago. Since then, each century has extended the power of calculus to illuminate questions in mathematics, the physical sciences, engineering, and the social and biological sciences. Calculus is a powerful tool for reducing complicated problems to manageable procedures. The Haverford School offers two levels of calculus: Standard and Honors. The goal of both courses is to provide students with a clear understanding of the ideas of calculus as well as provide a solid foundation for subsequent courses. Both courses require a strong working knowledge of material from Algebra II and Precalculus, the ability to work independently, and include both computational and theoretical components.
Calculus
Prerequisite
Calculus begins with a brief review of functions including logarithmic, exponential and trigonometric. After developing the ideas of limits and continuity, the course will focus on the major concepts of differential and integral calculus. Students will learn methods for taking derivatives and antiderivatives and use these methods in various applications. Although not as theoretical as Calculus I*, this course requires a strong working knowledge of previous courses, the ability to work independently, and a desire to learn higher mathematics. The students will use the graphing calculator as well as various online resources. In particular, the topics to be covered will include (but not necessarily limited to) the following:
- Limits of functions—graphically and algebraically
- Definition of derivative—instantaneous vs. average rate of change; slope and equation of the tangent line
- Differentiation techniques-polynomials, trigonometric, and transcendental functions; implicit differentiation
- Applications of derivatives-displacement, velocity, and acceleration; optimization; related rates
- Integration—Riemann sums, definite and indefinite integrals, u-substitution
- Applications of integration—area under and between curves; accumulation
Calculus*
Prerequisite
This course is a thorough and challenging development of differential and integral calculus. In addition to numerous applications, this course includes a theoretical component and advanced methods of differentiation and integration that will not be covered in Standard Calculus. This course will prepare students to take Calculus II* at THS or move into a more theoretical calculus course in college, such as those required for mathematics, engineering or applied science majors. It is anticipated that students, having successfully completed Calculus I*, may successfully sit for the Calculus AB Examination in the spring. In particular, the topics to be covered will include (but not necessarily to be limited to) the following:
- Limits of functions—graphically and algebraically
- Definition of derivative-instantaneous vs. average rate of change; slope and equation of the tangent line
- Differentiation techniques-polynomials, trigonometric, and transcendental functions; implicit differentiation
- Applications of derivatives-displacement, velocity, and acceleration; optimization; related rates
- Integration—Riemann sums, definite and indefinite integrals, u-substitution
- Applications of integration—area under and between curves; accumulation
Calculus II*
Prerequisite
This is a rigorous and fast paced one semester course which builds on the foundation of Calculus I*. Topics covered include applications of differential equation to physics, engineering, and biology, infinite series, parametric and polar representation, and the foundations of vector calculus. It is anticipated that students, having successfully completed Calculus II*, may successfully sit for the Calculus BC Examination in the spring. In particular, the topics to be covered will include (but not necessarily to be limited to) the following:
- Differential equations—separable equations, slope fields, Euler’s Method, first-order equations and integrating factors
- Sequences and series—limits of sequences, numerical series, power series, Taylor series
- Parametrically defined curves—slope and arc length
- Polar curves—slope and area in polar coordinates
- Vector-valued functions—position, velocity, and acceleration in the plane
What are The Haverford School's Mathematics electives?
The Mathematics Department has an offering of electives available to Form VI, V, IV based on a student's interest and desire to pursue a specific topic outside of core math courses. Most electives have a prerequisite and require the recommendation of the student's current teacher. Electives that have been offered in the past include:
- Advanced Computer Science*
- Economics: Macro*
- Economics: Micro*
- Finance: Financial Literacy
- Introduction to Computer Science
- Logic
- Math Modeling
- Statistics
- Statistics*
- Advanced Topics in Math*
Example Math Electives Course Descriptions
Advanced Computer Science*
Form VI & V Prerequisite This full-year course, intended for students with experience or interest in computer programming, offers the opportunity to deep-dive into programming concepts through a collaborative, project-based approach. This curriculum immerses students in Java programming topics (abstraction, algorithms, data structures, object-oriented programming, etc.) and prepares students for college coursework and potential careers in computer science. As they progress through the year, students will solve unique, real- world problems of increasing complexity to further hone and practice their programming skills. Depending on the schedule modality, major units/projects will include:
- Introductions (Avatar Creator Project)
- Primitive Control (Resource Finder Project)
- Strings and Iteration (Language Interpreter Project)
- Objects, Classes, and Methods (Disease Diagnoser Project)
- Arrays, ArrayLists, and 2D Arrays (Air Quality Analyzer Project)
- Inheritance (Hospital Locator Project)
- Searching, Sorting, and Recursion (Data Decoder Project
Economics: Macro* (Fall)
Form VI & V
Prerequisite
This conceptually challenging elective covers the main ideas of macroeconomics, the study of the largescale structure of the national and world economy. The mathematical level is comparable to that of an introductory college class in macroeconomics. Topics include national income accounting (GDP), economic growth, unemployment and inflation, the financial sector, money and banking, aggregate supply and demand, fiscal and monetary policy, and international finance.
Economics: Micro* (Spring)
Prerequisite
This mathematically demanding elective covers the main ideas of microeconomics, the study of the decision-making processes of consumers and producers in a market economy. The mathematical level is comparable to that of an introductory college class in microeconomics. Topics include market equilibrium, elasticity, taxes and price controls, international trade, consumer and producer decisions, competition and monopoly, and externalities, such as pollution and global climate change.
Finance: Financial Literacy (F & S)
Form VI & V
Prerequisite
This course is designed to introduce the student to basic financial literacy skills to help them make responsible financial decisions. Concepts covered include financial planning, bank accounts, credit and loans, wages and taxes, investments, and insurance. Students will gain the information and skills to implement a life-long plan for financial success. A major goal of the course will be to teach students effective problem-solving techniques using real world transactions, mathematical reasoning, and spreadsheet modeling.
Introduction to Computer Science
Form VI, V, IV Prerequisite This yearlong course offers an introduction to computational thinking and programming skills through collaborative, open-ended authentic, and collaborative projects. Students will spend time examining how computing shapes society by investigating and debating issues such as cybersecurity, data privacy, and digital literacy. The course will also explore introductory programming concepts, first through blockbased coding and eventually working towards text-based (Python or equivalent). Students will leave this course with an overarching understanding of computer science principles and prepare for further coursework if desired. Depending on the schedule modality, major units/projects will include:
- Algorithmic Thinking (Password Generator Project)
- Programming (Scratch Programming Project)
- Data Representation (Unintend'o Controler Project)
- Digital Media Processing (Image Filter Project)
- Big Data (TEDxKinda Project)
- Innovative Technologies (Prototyping the Future Project)
Logic (S)
Form VI & V
Prerequisite
This semester-long course introduces students to methods of reasoning, inference, and argument. It is open to all students who wish to improve their abilities to think carefully and critically with respect to any claim with which they are confronted, whether that be claims of societal significance such as those pertaining to civic, economic, or political outcomes, or of cultural aesthetics such as those pertaining to art, food, and sports. Not only will students have the opportunity to develop and practice their analytical thinking skills, but they will also develop their understanding of the concepts, systems, and processes of logic and their metacognitive awareness of thought patterns and habits (both their own and others). Students will find many parallels between the methods developed in this course and the equation solving processes of Algebra and the proof processes of Geometry, as well the use of formal abstract language to generalize arguments and derive structure from repeated patterns. More specifically, students will learn the foundational principles of proof techniques that they may have seen in their core math courses such as Proof by Induction and Proof by Contradiction. In particular, students will learn to:
- contrast the nature of arguments from that of explanations, opinions, and beliefs,
- understand the principles of deduction vs induction including the conditions of validity and soundness identify and define logical fallacies
- make claims of equivalence and inference based categorical propositions and class using tools such as Venn Diagrams and the Boolean Square of Opposition
- apply the language of symbolic logic in formal proofs of validity
Math Modeling (F)
Form VI & V
Prerequisite
This semester-long course introduces students to the concepts and techniques of mathematical modeling. The course is designed to answer the fundamental question, “How can I use mathematics to better understand and solve real-world social challenges?” The course draws from skills students have acquired across all of their math experiences including those in Algebra, Trigonometry, Statistics, and some ideas of Calculus, though students need only have a strong working knowledge of material from Algebra II, more broadly:
- state and build from valid assumptions,
- target desired outcomes and define variables,
- use mathematical techniques to find solutions,
- analyze and model results,
- report conclusions and use the evidence they have acquired to argue compellingly a position
The course will address real-world social challenges such as housing disparities, food insecurity, educational outcomes, and equitable resource distribution.
Statistics
Form VI & V
Prerequisite
This yearlong course is intended to provide students a framework to think about the world “statistically.” Real world problems will be solved using 21st century methodologies, i.e. by incorporating useful technologies and working collaboratively; the process will be project-based, highly interactive, and engaging. It is ideally suited for students who have completed FST or Precalculus and are now looking to expand their mathematical horizons. The course utilizes an online textbook for readings and exercises.
Statistics*
Form VI & V
Prerequisite
This is a yearlong comprehensive survey of the foundations of probability theory and statistical methods for collecting, organizing, displaying, analyzing and drawing conclusions from data. Emphasis is placed on clear and accurate reporting of the results obtained from these activities. Statistics* is a demanding course (both in time commitment and complexity), open to qualified Fifth or Sixth Form students who wish to study statistics at a level comparable to a rigorous college course. It is anticipated that students, having successfully completed Statistics*, may successfully sit for the AP Examination in the spring. Technology will be used extensively for solving problems in the course. No specific textbook shall be required (although classroom copies of Stats: Modeling the World by: Bock, Velleman & De Veaux will be available for reference). Students may take this course concurrently with Calculus
Advanced Topics in Math* (S)
Form VI & V
Prerequisite
In this semester course we will explore either the foundations of linear algebra or multivariable calculus. The course will alternate topics each year to allow advanced Form V students to take the course two years in a row. This is this highest level mathematics course offered at Haverford and students who enroll should be prepared for rigorous and challenging study.
Linear Algebra (Odd Numbered Years)
- Linear Combinations of Vectors
- Basic vector operations
- Matrix operations and their use in solving linear systems of equations
- Vector Spaces and Subspaces
- Orthogonality
- Determinants of Vectors
Multivariable Calculus (Even Numbered Years)
- Functions of multiple variables
- Partial differentiation
- The gradient and directional derivative
- Vector Analysis
- Applications from physics, economics, and engineering
What distinguishes the mathematics program at The Haverford School?
The Haverford School's mathematics program balances rigorous foundational coursework with meaningful real-world application. Students build deep mathematical understanding while applying quantitative reasoning to authentic challenges through advanced electives, research, competitions, and collaborative problem-solving. The program emphasizes not only mastering mathematics, but also developing the analytical, communication, and critical thinking skills students will use in college and beyond.
Highlights of the program include:
- Applied mathematics with real-world impact: Beyond the core sequence through calculus, students can pursue electives in statistics, economics, finance, advanced topics in mathematics, math modeling, and computer programming, exploring how mathematics informs business, technology, engineering, and the social sciences.
- Math Club: where students deepen their appreciation for mathematics by tackling challenging problems, collaborating with peers, and preparing for competitions.
- 14-Hour MathWorks Math Modeling (M3) Challenge teams: giving students the opportunity to work collaboratively on open-ended, real-world problems that require creativity, data analysis, and mathematical modeling.
- Participation in the American Mathematics Competitions (AMC): allowing students to test their problem-solving abilities against top young mathematicians from across the country.
- Regional competition opportunities: including Temple University's OWLympiad and Math Madness, where students collaborate, compete, and strengthen advanced mathematical reasoning.
- Newton's Notebook, Haverford's student-led STEM journal, which showcases pure and applied mathematics alongside scientific inquiry through articles written by students, faculty, and staff. Published since 2017, the journal encourages students to communicate complex mathematical ideas, share original research, and inspire curiosity throughout the school community.
Together, these opportunities create a mathematics program that extends well beyond the classroom. Students graduate not only fluent in the language of mathematics but also prepared to use quantitative reasoning, creativity, and collaboration to solve complex problems in an increasingly data-driven world.
What are the outcomes of the mathematics education at The Haverford School?
Rather than viewing mathematics as a collection of abstract formulas, Haverford students regularly connect mathematical concepts to authentic problems. Project-based learning, applied mathematics electives, economics, finance, statistics, programming, and mathematical modeling encourage students to use quantitative reasoning to analyze data, make informed decisions, and solve complex interdisciplinary problems.
Haverford School graduates can be found pursuing careers in engineering, finance, medicine, technology, research, entrepreneurship, consulting, and other analytical fields. While these alumni often credit multiple aspects of their Haverford education, they consistently point to habits developed in rigorous academic programs—including disciplined problem-solving, intellectual curiosity, collaboration, and clear communication—as foundational to their success.
A Haverford mathematics education produces graduates who are more than proficient mathematicians. They become analytical thinkers who ask thoughtful questions, collaborate across disciplines, communicate complex ideas with clarity, and confidently apply mathematical reasoning to solve real-world problems. Whether pursuing STEM, business, economics, medicine, or the humanities, Haverford graduates leave with the intellectual curiosity and quantitative fluency needed to thrive in an increasingly complex and data-driven world.
What are people saying about the mathematics program at The Haverford School?
Haverford School graduates express gratitude to their teachers and for the program for building the habits of mind, analytical thinking, and quantitative reasoning that have brought them success in their careers and lives.
I came to realize that success in customer insights was based on a skill I first learned at Haverford: build a thesis and support it with data.
Michael Lewis '99, Head of Customer Strategy & Insights, Dropbox
Haverford's finance and accounting classes helped me realize what I wanted to do with my professional career. I had grown up in an entrepreneurial family, so I knew I was interested in being a business major, but his classes helped me figure out my specialization. The introduction to these financial topics inspired me to want to learn more about them and some concepts that I learned from his classes are used on a daily basis.
Nicholas Dodds '07, High Net Worth Client Manager, Vanguard
Develop and cultivate your intellectual curiosity. Find the things that interest you, and dive deeply into them. Haverford teachers are unique in that they're willing to go as deep on a subject with you as you would like.Josh Collins '13, entrepreneur and technology executive
Who teaches math at The Haverford School?
The Mathematics department faculty at The Haverford School includes teachers with advanced degrees in their field, professional experience, and internationally-recognized teaching. Our faculty regularly attend and present at conferences advancing boys' school education, such as those offered by the International Boys' Schools Coalition (IBSC).
Where do I go to learn more about the Mathematics department at The Haverford School?
To learn more about the Mathematics department at The Haverford School, read the Math department's philosophy here.
To learn more about The Haverford School, reach out to our admissions team at admissions@haverford.org or submit an inquiry form to begin the admissions process.
To explore other aspects of our curriculum, browse our offerings here.
Last updated July 2026