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Math at George School

With courses ranging from basic algebra to beyond calculus, statistics to computer science and robotics, George School’s mathematics curriculum will build your skills while it stimulates your imagination. The goal is to help you think mathematically—to analyze, to synthesize, and to hypothesize—making use of mathematics as both a language and a methodology.

If you love math, you can take calculus, statistics, computer science and robotics, artificial intelligence, and several IB options, including Further Math, which is beyond the regular Higher Level course. You can join our nationally ranked math team, or coach other students as part of our Math Help program.

Math by the Numbers

30+

math courses from basic algebra to data analysis and number theory

AI Seminar

covering topics in artificial intelligence including basic techniques for building intelligent computer systems and real-world applications

12

astute faculty members, 75% with advanced degrees

Opportunities in University-Level Math

Math Department faculty member Hamilton Davis imagines a next-generation mathematics education for George School students.

Math Department Courses

Math 1

This 5-mod course is designed to allow entry at various points depending on a student’s background in algebra. In the first mod, students review and strengthen prealgebra skills. The three core mods cover the content of a college preparatory Algebra 1 course. The optional extended topics mod, which moves at a much swifter pace than the first four, covers much of the algebraic content of Math 2 and enables students to progress directly to Math 3.

Taken over the course of 9th and 10th grades, Math 1 and Math 2 prepare interested students to begin IB SL Mathematics: Applications in 11th grade.

Min-Max Credit Hours: 1.0-5.0

Prerequisite: none

Open to: 9

Math 2

This 4-mod course takes an integrated approach to the content of traditional college preparatory Algebra 2 and Geometry courses, and covers most IGCSE Core/IBMYP 5 Core topics not covered in Math 1. Students do extensive work with linear and quadratic functions and their graphs, including consideration of quadratic inequalities and quadratic equations with complex roots, and are introduced to polynomial and exponential functions, arithmetic and geometric sequences and series, and descriptive statistics.

Students need not take all four mods in the same year. Students who have mastered the content of the optional fifth mod of Math 1 may elect to take the Math 3/4 sequence instead of this course.

Taken over the course of 9th and 10th grades, Math 1 and Math 2 prepare interested students to begin IB SL Mathematics: Applications in 11th grade.

Min-Max Credit Hours: 1.0-4.0

Prerequisite: Math 1 or an Algebra 1 course.

Open to: 9, 10

Math 3

This 3-mod course, which places a strong emphasis on developing the student’s ability to construct, communicate, and justify mathematical arguments, consists of one mod of algebraic content and two mods of geometric content, covering the first third of a typical yearlong “honors” Algebra 2 course and the first two thirds of a typical yearlong “honors” geometry course (or about half of the topics in the IGCSE Extended curriculum not already covered in Math 1 and 2). In the algebra mod, the focus is on understanding the concept of a function in general, with particular attention to linear, quadratic, and exponential functions. The connections to sequences and series are explored. In the geometry mods, the focus is on formalizing a student’s existing geometric knowledge through the lens of mathematical proof.

Taken over the course of 9th and 10th grades, Math 3 and Math 4 prepare interested students to begin IB SL Mathematics: Analysis 11th grade. With the addition of the first two mods of precalculus in 10th or 11th grade, students are prepared to begin IB HL Mathematics: Applications in 11th grade.

Sophomores who have taken Math 2 in 9th grade typically take only the algebra mod of this course.

Min-Max Credit Hours: 1.0-3.0

Prerequisite: Math 1 with extended topics mod (A-), Math 2 (B), or Accelerated Algebra 1 (A-)

Open to: 9, 10, 11

Math 4

This course, which builds on the skills of constructing, communicating, and justifying mathematical arguments developed in Math 3, consists of two mods of algebraic content and one mod of geormetric and trigonometric content, covering the final two-thirds of a typical yearlong “honors” Algebra 2 course and the final third of a typical yearlong “honors” geometry course (or most topics from the IGCSE Extended curriculum not covered in Math 1-3, along with some content of IGCSE Additional Mathematics). The algebraic content is focused around the concept of functions and their inverses, with a focus on polynomial, rational, exponential, and logarithmic functions.The geomety/trigonometry mod includes circle theorems, right triangle trigonometry, three-figure bearings, and the laws of sines and cosines.

Taken over the course of 9th and 10th grades, Math 3 and Math 4 prepare interested students to begin IB SL Mathematics: Analysis in 11th grade. With the addition of the first two mods of precalculus in 10th or 11th grade, students are prepared to begin IB HL Mathematics: Applications in 11th grade. Students who take Advanced Analysis after Math 4 will be prepared to take IB HL Mathematics: Analysis.

Min-Max Credit Hours: 1.0-3.0

Prerequisite: Math 3 (C+)

Open to: 9, 10, 11

Algebraic and Geometric Analysis

This course is designed to challenge those 9th and new 10th-grade students who have unusually strong backgrounds in algebra, geometry, or both. Students build on prior experience in algebra and geometry as a basis for investigating advanced topics, including those typically seen in math contests. Emphasis is placed on individual and group exploration of mathematical ideas in order to solve unfamiliar problems, to discover patterns, and to prove results. Creative problem solving, clear thinking, and careful articulation provide an important foundation for advanced mathematics courses at George School and beyond. The concept of proof is central to the course; a wide variety of proof strategies are explored. Topics from earlier algebra courses that are studied in greater depth include functions (polynomial, absolute value, rational, radical, exponential, and logarithmic), inverse functions, complex numbers, and nonlinear inequalities. Topics from earlier geometry courses that are studied in greater depth include congruency axioms, similarity, parallel properties, area, perimeter, and volume. Topics which may be completely new to students include set theory, vectors in two and three dimensions, parametric equations, the binomial theorem, number theory, algebraic proof, matrices, descriptive statistics, conic sections, sequences and series, Fermat primes, and theorems from Ceva, Heron, and Apollonius.

The class uses a problem book rather than a textbook. Daily homework requires students to creatively apply concepts discussed in class to thought-provoking problems with methods of solution that may not have been demonstrated by the teacher. Because many students who take this course have not previously had to study to do well in math, attention is given to techniques for efficient and effective learning of advanced mathematics. This course is taught at a rapid pace. Students are encouraged to develop the confidence to risk failure by tackling questions that deepen their understanding in class, on homework, and on tests. Strong graphing and algebraic skills are assumed, as is the ability to generalize a pattern from specific cases. Students in this class are strongly encouraged to sit for the Mathematical Association of America’s AMC exam.

Min-Max Credit Hours: 1.0-3.0

Prerequisite: Exceptionally strong background in algebra and strong background in geometry as demonstrated by skills assessment

Open to: 9, 10

Algebra 2

A thorough review of Algebra 1 skills is intertwined with the development of more advanced algebraic skills in this course. Students are introduced to the concept of a mathematical function and they do extensive work with linear and quadratic functions and their graphs. Quadratic equations with complex roots are considered and quadratic inequalities are explored. Logarithmic and exponential expressions, equations, and functions are introduced. Students deepen their understanding of rational, absolute value, and polynomial expressions and equations. Concepts are introduced or extended almost daily. Review is built in as needed. Daily homework problems are similar to problems worked through in class.

Min-Max Credit Hours: 3.0-3.0

Prerequisite: A geometry course together with either Algebra 1 (C-) or Accelerated Algebra 1

Open to: 11

Intensive Algebra 2

Extending the skills developed in Accelerated Algebra 1 and Intensive Geometry with Trigonometry, this course introduces new algebraic concepts that include rational expressions and equations; quadratic expressions, equations, and inequalities; complex numbers; sequences and series; and the binomial theorem. There is a thorough consideration of the concept of a function, including transformation of graphs and inverse functions. Polynomial, absolute value, logarithmic, and exponential expressions and functions are studied. New topics are introduced daily. While many daily homework problems are similar to problems worked in class, others require students to apply what they know to new types of problems. Strong graphing, factoring, and note-taking skills are assumed.

Min-Max Credit Hours: 3.0-3.0

Prerequisite: One of the following two options:
1. Intensive Geometry with Trig (C)
OR
2. Geometry (A-) together with Algebra 1 (A) or Accelerated Algebra 1 (B)

Open to: 10, 11

Functions and Trigonometry

This exploration-based class includes real-world applications of the skills developed. During the first mod, students review and extend the study of functions and relations begun in Math 2, with particular attention to translations and transformations of polynomial, exponential, and logarithmic functions. The second mod is devoted to trigonometry, including radian measure, the unit circle, and the graphs of sine, cosine, and tangent function. The pace is relaxed, yet purposeful. If a specific exploration is proving fruitful for a particular class, it might be extended even if that means not covering every topic on the original syllabus.

The optional third mod of this course, Advanced Functions (MAT310A), is common to IB SL Math: Applications and provides additional preparation for Precalculus (MAT340A). Some students may instead opt to go directly to Precalculus, while still others may decide to take Statistics (MAT510A) or Accelerated Statistics (MAT511A) in lieu of the Advanced Functions mod.

Min-Max Credit Hours: 2.0-3.0

Prerequisite: Math 2 (C), Algebra 2 (C-), Math 3, or Intensive Algebra 2

Open to: 11, 12

Advanced Functions

This course, which can be taken alone or as the third mod of Functions and Trigonometry (MAT310A) gives students the opportunity to advance their algebraic and trigonometric knowledge before proceeding with the IB SL Math: Applications sequence or taking Precalculus (MAT340A). The study of functions (in particular, linear, quadratic, cubic, sinusoidal, and exponential) is deepened through more advanced applications and a focus on mathematical modeling, often using a graphing device. A circular functions approach to trigonometry completes the study of trigonometry begun in Functions and Trigonometry. Real-world applications of the skills developed are central to this course. The content of this course may be modified to meet student needs.

Min-Max Credit Hours: 1.0-1.0

Prerequisite: Any of the following
1. Math 3 (B+)
2. Math 4 (C+)
3. Functions and Trigonometry (C, 2 credits)
4. Geometry (B+) or Intensive Geometry with Trig (C+), together with either Algebra 2 (B+) or Intensive Algebra 2 (C+)

Open to: 10, 11, 12

Precalculus

The concept of a function is the central theme of this course. Topics covered in depth include domain and range, composition, translation, transformation, and inverse functions. A primary goal is to help students learn to shift fluently between algebraic and graphical representations of functions. Polynomial, exponential, logarithmic, rational, and trigonometric functions are studied in-depth and the concept of a limit is introduced. Additional topics include sequences and series, vectors, and matrices.

A strong working knowledge of linear and quadratic functions is assumed. In addition, students are expected to have good algebraic skills, good graphing skills, and familiarity with right triangle trigonometry. While many daily homework problems are similar to problems worked in class, others require students to apply what they know to new types of problems. The capacity for independent work is important to a student’s success.

The first two mods of this course are part of the IB SL Mathematics: Analysis course. Students may take Intro to Calculus (MAT400A) and/or the first mod of Calculus (MAT410A) after completing these mods. Enrolling in AP Calculus – AB (MAT428A) or the final two mods of Calculus requires completion of all three mods of Precalculus.

Min-Max Credit Hours: 2.0-3.0

Prerequisite: Any of the following
1. [Advanced] Algebraic and Geometric Analysis
2. Algebra 2 (A)
3. Intensive Algebra 2 (B)
4, Math 4 (B)
5. Functions and Trigonometry (2 credits, A, or 3 credits, B+)
6. Advanced Functions (B+)

Open to: 10, 11, 12

Advanced Analysis

Students in this course develop their ability to investigate a problem mathematically and hone their proof-writing skills by exploring such topics as trigonometric functions, theories of polynomial equations, logarithmic and exponential functions, inverse functions, complex numbers, DeMoivre’s theorem, polar coordinates, vectors in three dimensions, probability, combinatorics, linear algebra, and mathematical induction. The pace is very fast. Because the class frequently takes the form of a Socratic dialogue with questions asked and solutions offered by both teacher and students, it is imperative that students have or develop the courage to write down and share their ideas.

Satisfactory performance in the first two mods of this course fulfills the prerequisite for any of the calculus courses offered at George School. The third mod is a prerequisite for IB HL Math: Analysis and a variety of other advanced courses.

Min-Max Credit Hours: 2.0-3.0

Prerequisite: Any one of the following
1. [Advanced] Algebraic and Geometric Analysis (C+)
2. Intensive Geometry with Trig (A) and Intensive Algebra 2 (A)
3. Math 3 (A) and Math 4 (A)

Open to: 10, 11

Intro to Calculus

In this course, which can be taken independently or as part of IB SL Math: Applications, students work with derivatives and antiderivatives of polynomial functions to explore the central calculus concepts of rates of change and accumulation. Applications include linear approximations, function analysis, optimization, and finding the area under a curve. Students use technology as an aid in developing and exploring calculus-based models.

Min-Max Credit Hours: 1.0-1.0

Prerequisite: Functions and Trig (3 credits, B), or Advanced Functions (B), or Precalculus (2 credits, C-)

Open to: 11, 12

Calculus

The first mod of this course is a common mod with IB SL Math: Analysis (MAT637Y) and IB HL Math: Application (MAT627Z). In this mod, students learn to differentiate polynomials, the sine and cosine functions, the exponential function, and the natural log function, and work with both definite and indefinite integrals of these derivatives. Applications to function analysis, optimization, kinematics, and areas between curves are considered.

In preparation for college-level calculus (including AP Calculus), the second and third mod of this course considers limits in substantially more depth, including the limit definition of the derivative, and rectangle and trapezoid approximations to the area under a curve. The Fundamental Theorem of Calculus is introduced, and derivatives (and associated integrals) of the other four trig functions, exponential functions of bases other than e, and some inverse trig functions are studied. Further applications include volumes, related rates, accumulation in various contexts, and probability functions.

Students may take the first mod of this course after completing the first 2 mods of Precalculus. Enrollment in subsequent mods requires completing the third mod of Precalculus. Students who have taken all three Precalculus mods but do not meet the grade prerequisite may enroll if they first earn a B- or better in Intro to Calculus.

Min-Max Credit Hours: 1.0-3.0

Prerequisite:
For 22-23: either Intensive Precalculus (B) or Advanced Precalculus with Discrete Math
For 23-24 and later: either Precalculus (B) or Advanced Analysis

Open to: 11, 12

AP Calculus – AB

This course covers all topics included in the College Board syllabus for AP Calculus AB. It is designed to be the equivalent of a college-level Calculus 1 course. Throughout the course, problems are considered from graphical, numerical, and analytical perspectives with an aim toward developing students’ ability to shift easily from one perspective to another. There is an emphasis on learning to understand, use, and appreciate the value of the precise technical language (definitions, theorems, etc.) of mathematics. An awareness of the historical context of the development of calculus and an appreciation of its importance as a human achievement are cultivated. Students learn to discern situations in which technology can be a helpful tool in the solution of a problem. Graphing calculators are used extensively. The pace is fast. Students are expected to work as mathematicians do in that they are asked frequently to try problems without having been explicitly taught how to find the solutions. Excellent algebraic, graphing, and organizational skills are assumed, as is a very good understanding of trigonometric functions.

Students are required to sit for the AP exam.

Min-Max Credit Hours: 3.0-3.0

Prerequisite:
22-23: Intensive Precalculus (A) or Advanced Precalculus with Discrete Math (C) or IB SL Calculus (B)
23-24: Precalculus (3 credits, A), or Advanced Analysis (2 credits, C), or Calculus (A if 1 credit of Calculus, B if 2 credits)

Open to: 11, 12

AP Calculus – BC

This course covers all topics included in the College Board syllabus for AP Calculus BC. It is designed to be the equivalent of college-level Calculus 1 and 2 courses. Because of this, the course moves extremely quickly, and the Calculus 1 material is covered at a particularly fast pace. Throughout the course, problems are considered from graphical, numerical, and analytical perspectives with an aim toward developing students’ ability to shift easily from one perspective to another. There is an emphasis on learning to understand, use, and appreciate the value of the precise technical language (definitions, theorems, etc.) of mathematics. An awareness of the historical context of the development of calculus and an appreciation of its importance as a human achievement are cultivated. Students learn to discern situations in which technology can be a helpful tool in the solution of a problem. Graphing calculators are used extensively. Students are expected to work as mathematicians do in that they are asked frequently to try problems without having been explicitly taught how to find the solutions. Excellent algebraic, graphing, and organizational skills are assumed, as is a very good understanding of trigonometric functions.

Students with a 5 on the AP Calculus AB exam may opt-out of the first mod of this course.

Students are required to sit for the AP exam.

Min-Max Credit Hours: 2.0-3.0

Prerequisite:
For 22-23: Advanced Precalculus with Discrete Math (A-) or AP Calculus AB (B-)
For 23-24: Advanced Analysis (2 credits: A or 3 credits: A-) or AP Calculus AB (B-)

Open to: 11, 12

Statistics

The first two mods of this course introduce students to the concepts, symbols, terminology, and process of statistics. Students formulate questions that can be addressed with data; collect, organize, and display relevant data to answer statistical questions; select, use, and evaluate descriptive methods to analyze data, and critique graphs and descriptive data analyses that they encounter outside of class. Concepts include graphical methods, descriptive analyses of univariate and bivariate data, sampling, and experimental design. Students learn how to perform analyses using paper and pencil, and a statistical calculator, with an emphasis on the interpretation of results. The third mod is Data Analysis (MAT560D).

Min-Max Credit Hours: 2.0-3.0

Prerequisite: Any of the following
1. B in either Algebra 2 or Math 3
2. C+ in Functions and Trigonometry (2 credits)
3. C- in any of Intensive Algebra 2, Math 4, Advanced Functions, or Functions and Trigonometry (3 credits)

Open to: 11, 12

Accelerated Statistics

The Accelerated Statistics course aims to help students understand basic statistical analysis. It covers similar content to Statistics (MAT510A) but moves nearly twice as fast. Topics studied include univariate analysis; graphs of single variables; bivariate analysis; graphs of two variables; probability; and probability distributions.

Students interested in applying the content learned in this course to a project of their own design can do so by taking the optional second mod, Data Analysis (MAT560D).

If taken as part of the IB SL Math Applications course, this course must follow the first two mods of that sequence; it is recommended that SL Applications students take this course in the exam year (typically 12th grade).

Min-Max Credit Hours: 1.0-2.0

Prerequisite: One of the following
1. B+ in Functions and Trigonometry (2 credits)
2. C+ in Intensive Algebra 2, Math 4, Advanced Functions, or Functions and Trigonometry (3 credits)
3. C in [Advanced] Algebraic and Geometric Analysis
4. 2 credits in either Precalculus or Advanced Analysis

Open to: 10, 11, 12

AP Statistics

This course follows the College Board syllabus, which includes all of the topics covered in Accelerated Statistics plus concepts of variation, especially as related to statistical inference, sampling distributions, estimation and confidence intervals, and hypothesis testing at least through two-sample t-tests. Students learn how to perform analyses using paper and pencil, a statistical calculator, and the computer, with an emphasis on the interpretation of results. Class activities consist of lecture, problem solving, and group discussion, with a heavy emphasis on analytical discussion. The pace is rapid and the topics are complex. Students are expected to be inquisitive about data, analysis, and interpretation and to contribute their thoughts actively to class discussions.

Students interested in applying the content learned in this course to a project of their own design can do so by taking Data Analysis (MAT560D) at any time after completing the first mod (which is common to this class and both IB HL courses.)

Students–except those who have taken Accelerated Statistics (MATH511A) and earned a B or better–are required to complete a summer assignment in preparation for class.

Students enrolled in this course must sit for the AP exam.

Min-Max Credit Hours: 3.0-3.0

Prerequisite: 2 credits in either Precalculus (B+) or Advanced Analysis (C)

Open to: 11, 12

Data Analysis

In this course (which can be taken multiple times), students apply their understanding of univariate and bivariate descriptive statistics to independent data analysis projects of their own design. Students use statistical software for calculations and graphs. Students also write final reports with an emphasis on clear communication of their findings. Additional topics in data collection and inference are taught as needed to support student work.

Min-Max Credit Hours: 1.0-1.0

Prerequisite: Statistics (B), Accelerated Stats (B-), or the common IB HL/AP Statistics mod

Open to: 11, 12

Basic Tax Preparation

This course is cross-listed as MUL560T (Extradisciplinary). See MUL560T (Extradisciplinary) in the Extradisciplinary section of the catalog for description.

Min-Max Credit Hours: 1.0-1.0

Prerequisite: none

Open to: 10, 11, 12

IB SL Math: Analysis

The topics covered in this survey course are those of the IB SL Mathematics: Analysis and Approaches syllabus. The fundamentals of differential and integral calculus are covered. Topics include limits; continuity; understanding derivatives as functions, slopes, and rates of change; derivatives of polynomial, rational, trigonometric, exponential, and logarithmic functions; analysis of graphs; optimization; related rates; rectilinear motion; anti-differentiation; the Fundamental Theorem of Calculus; integration by substitution; and applications of integration to the area, volume, rectilinear motion, and accumulation problems. Statistics topics introduced in Intensive Precalculus are reviewed and extended. These include discrete random variables and normal distributions. Students complete an IB mathematics exploration in this class. Strong algebraic and graphing skills are assumed.

Students who enroll in this course must sit for the IB exam.

Min-Max Credit Hours: 3.0-3.0

Prerequisite: One of the following options:
1. Intensive Precalculus (B)
2. Advanced Precalculus with Discrete Math

Open to: 12

IB SL Math: Applications

The IB SL Mathematics Applications course aims to help students understand the world through a mathematical lens. This two-year course of study focuses on mathematical applications, with particular emphasis on the meaning of mathematics in context. The focus is on topics that are often used in applied situations or mathematical modelling. Topics studied include number and algebra; functions; geometry and trigonometry; statistics and probability; calculus. As their IB Internal Assessment, students complete a project–including a formal paper—usually with a statistical focus. A capacity for independent work is important to a student’s success.

This course consists of six mods, the first of which is Advanced Functions (MAT310D). The next two mods, Intro to Calculus (MAT400A) and Accelerated Statistics (MAT511A), may be taken in either order. At least one of these two must be taken in 11th grade. The final three mods are unique to this course, and the first of these may be taken in either 11th or 12th grade. The final two mods must be taken in 12th grade.

Students who have already taken Intensive Algebra 2 or Math 4 (MAT140A) do not need the Advanced Functions mod. Students who have already taken AP Statistics do not need MAT511A.

Students who enroll in this course must sit for the IB exam.

Min-Max Credit Hours: 4.0-6.0

Prerequisite: Any of the following
1. Math 2 (4 credits, B+)
2. Math 3 (3 credits, C+)
3. Math 4 (3 credits, C)
4. Functions and Trigonometry (2 credits, B)
5. Advanced Functions (C)
6. Precalculus (1 credit)
7. Geometry (B) or Intensive Geometry with Trig (C), together with either Algebra 2 (2 credits, B) or Intensive Algebra 2 (1 credit, C)

Open to: 11, 12

IB HL Math: Applications

The IB Mathematics Applications and Interpretation course aims to help students understand the world through a mathematical lens, with particular emphasis on mathematical modeling and statistical analysis, both of which leverage the power of technology. This two-year course of study develops theory in order to tackle applications. As their IB Internal Assessment, students complete a project–including a formal paper–with a strong mathematical modeling focus. Topics studied include descriptive statistics, probability, inferential statistics, and Markov chains; calculus and differential equations; graphs and graph algorithms for trees, the traveling salesman problem and the Chinese postman problem; vectors, matrices, complex numbers, and linear algebra. This course assumes strong algebraic, function analysis, and graphing skills. Students with a desire to tackle practical, concrete problems in the areas of biology, ecology, economics, business, urban planning, and other applied domains will find the techniques developed in this class useful (and hopefully fulfilling!).

This course consists of five mods, the first three of which can be taken in any order. At least one of these first three mods must be taken in 11th grade. The final two-mod sequence is taken in 12th grade. One of the first three mods and the final two mods are specific to this course, the other two are the first mod of Calculus (MAT410A) and the common AP/IB HL statistics mod. Students who have already taken a calculus course do not need the calculus mod. Students who have already taken AP Statistics do not need the statistics mod.

Students who enroll in this course must sit for the IB exam.

Min-Max Credit Hours: 4.0-5.0

Prerequisite: 2 credits of either Precalculus (A-) or Advanced Analysis (B-)
[Prior to 22-23 these courses were called Intensive Precalculus and Advanced Precalculus with Discrete Math]

Open to: 11, 12

IB SL Math: Analysis

The topics covered in this two-year survey course are those of the IB SL Mathematics: Analysis and Approaches syllabus and include fundamentals of function analysis, trigonometry, differential and integral calculus, and statistics. Students are encouraged to appreciate the links between different concepts and branches of math. The course moves at a swift pace, with a focus on developing an in-depth understanding of concepts and using that understanding to solve abstract problems as well as those set within a specific context. There is a strong emphasis on the ability to construct, communicate and justify mathematical arguments. Students learn to discern situations in which technology can be a helpful tool in the solution of a problem. Students develop the skills needed to apply mathematics in other fields and continue their mathematical studies in other learning environments.

This course consists of six mods: the first two mods of Precalculus (MAT340A), the first mod of Calculus (MAT410A), Accelerated Statistics (MAT511A), and two mods specific to this course. The mods specific to this course must be the last mods taken. In these final two mods, in addition to covering additional content, students complete the IB Mathematics Exploration (which includes a paper of approximately 12-20 pages in length), and spend time on test preparation.

Students typically take both precalculus mods in 11th grade. (Students who had George School’s Precalculus or Advanced Analysis in 10th grade do not need these mods.) The calculus mod can be taken any time after the precalculus mods and before the final two mods. (Students who take an AP Calculus course do not need the Calculus mod). The Accelerated Statistics mod can be taken at any time prior to the final two mods. (Students who take an AP Statistics course do not need the Accelerated Statistics mod.)

Students who enroll in this course must sit for the IB exam.

Min-Max Credit Hours: 4.0-6.0

Prerequisite: Any of the following
1. [Advanced] Algebraic and Geometric Analysis
2. Algebra 2 (A) with Intensive Geometry with Trig (B) or Geometry (A)
3. Intensive Algebra 2 (B) with Intensive Geometry with Trig (B) or Geometry (A)
4, Math 4 (B)
5. Functions and Trigonometry (2 credits, A, or 3 credits, B+)
6. Advanced Functions (B+)

Open to: 11, 12

IB HL Math: Analysis

This course covers topics from the IB HL Mathematics: Analysis and Approaches syllabus. Unlike a single-topic AP calculus or statistics exam, the IB HL Mathematics exam requires an advanced level of mastery of a wide range of mathematical topics and their interconnections. The HL Analysis curriculum is more abstract than the HL Applications curriculum, and less tied to modeling and technology. There is an emphasis on learning to understand, use, and appreciate the value of the precise technical language (definitions, theorems, etc.) of mathematics. Students are expected to work as mathematicians do in that they are asked frequently to try problems without having been explicitly taught how to find the solutions. Excellent algebraic, graphing, and organizational skills are assumed, as is a very good understanding of trigonometry.

This course begins with the common AP/IB HL Statistics mod, and–for those students coming from AB rather than BC Calculus– a calulus mod, and ends with two mods comprising additional calculus and statistics topics, an IB exploration, and test preparation. The first two mods can be taken in either order. The final mod must be taken in 12th grade. The others may be taken in either 11th or 12th grade. The calculus mod must come after AB Calculus has been completed.

Min-Max Credit Hours: 3.0-4.0

Prerequisite: AP Calculus - AB (B) or AP Calculus - BC (B)

Open to: 11, 12

Linear Algebra

Linear algebra begins with a study of vectors, linear systems of equations, and matrices. Students develop the mathematical theory behind vector spaces, matrix factorizations, determinants, eigenvalues, and eigenvectors, and applications in dynamical systems, geometry, graph theory, least squares approximation, and more. Proof writing and use of technology (particularly for handling large datasets) are central to the course.

Min-Max Credit Hours: 2.0-2.0

(This course will not be offered in 2022-23.)

Prerequisite: Advanced Precalculus with Discrete Math (A), or Advanced Analysis (A), or AP Calculus BC (B)

Open to: 11, 12

Number Theory

Number theory is the branch of mathematics devoted primarily to studying the integers and integer-valued functions. Lauded as the “queen of mathematics” by none other than Karl Friedrich Gauss, number theory is a delight of pure mathematics with deep applications in cryptography and other computational realms. Students undertake the study of prime numbers, divisibility, Fermat’s little theorem, modular arithmetic, arithmetic functions, as well as generalizations of the integers and applications in cryptography. Emphasis is placed on proof writing, as well as the creation of computer algorithms intended to visualize and access the far reaches of the field.

Min-Max Credit Hours: 2.0-2.0

Prerequisite: Advanced Precalculus with Discrete Math (A), or Advanced Analysis (A), or AP Calculus BC (B)

Open to: 11, 12

Discrete Math – Combinatorics & Graph Theory

Discrete mathematics studies mathematical structures that are discrete in nature. This is the mathematics that underlies algorithms in computing. This course will study topics in combinatorics and graph theory, in particular: counting arguments and combinatorial proof, binomial coefficients, recurrence relations, generating functions, properties of graphs, graph algorithms, planar graphs, coloring, and matching problems. Topics will be approached through theoretical and computational lenses, with an emphasis on problem-solving.

Min-Max Credit Hours: 2.0-2.0

Prerequisite: Advanced Precalculus with Discrete Math (A), or Advanced Analysis (A), or AP Calculus BC (B)

Open to: 11, 12

AP Computer Science A

AP Computer Science A is an introductory course in computer science for those who already have some basic programming experience. The course emphasizes object-oriented programming methodology with a concentration on problem-solving and algorithm development and is the equivalent of a first-semester college-level course in computer science.

The central activity of the course is the design and implementation of computer programs to solve problems; the goal of the course is to develop and hone skills that are fundamental to the study of computer science. Creating computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of classes and fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. The responsible use of these systems is an integral part of the course.

The computer language studied is Java, as required by the AP curriculum. The prerequisites for entering this course include knowledge of algebra, a foundation of mathematical reasoning, and experience in problem-solving. In addition, because documentation plays a central role in the programming methodology, competence in written communication is a requirement.

Students who enroll in this course must sit for the AP Computer Science A exam.

Min-Max Credit Hours: 3.0-3.0

Prerequisite: Intensive Physical Computing and Robotics (A) or placement test

Open to: 11, 12

Advanced Programming: Artificial Intelligence

Advanced Programming: Artificial Intelligence is an advanced course in computer science for those who have ample mathematical and programming experience.

The first two mods of the course survey some of the common methodologies in artificial intelligence through project work and discussion of algorithms and theory. Students in this class implement computer programs that apply artificial intelligence techniques such as genetic algorithms, neural networks, decision trees, random forests, and others as time or interest warrants. The goal is to not merely use the various algorithms being discussed but to understand how they work so that improvements to them can be proposed and evaluated. Extensive programming proficiency is required.

Furthermore, discussion of the ethics and the responsible use of these systems is an integral part of the course. Topics to consider include: algorithmic biases, artificial intelligence vs. artificial consciousness, exploring how AI are developed differently in cultures, and the ramifications of those differences. A significant portion of the course is devoted to the understanding of formal logic. Topics include: natural language representation, syntax and semantics, truth tables, resolution, inference, propositional (sentential) logic, first-order (predicate) logic, and ontology construction. Reasoning about uncertain knowledge could be included pending time.

In the optional third mod, students apply their work and understanding from the previous mods to independent projects of their own design. Students can choose to dig deeper into AI or take this opportunity to pursue cross-disciplinary work. Examples of such work include: image analysis and creation with the arts, textual analysis of historical documents, applying AI to issues in social justice, and data mining of scientific, athletic, and/or medical (or other) datasets. Additional topics will be taught as needed to support student work.

Min-Max Credit Hours: 2.0-3.0

Prerequisite: AP Computer Science (A) and one of AB Calculus (A-), BC Calculus (B) or at least 3 credits in an IB HL math course (B)

Open to: 12

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