Mathematics Courses

Course Detail: Geometry I is an introduction to Euclidean Geometry, including the nature of reasoning and proof involved in the study of geometry. Topics covered include congruent and similar figures, parallel lines, and planes, plus an introduction to the study of area, volumes and transformations involving both investigations and deductive proof. Prerequisite: none.

Course Detail: Geometry II involves Euclidean Geometry of the circle and associated concurrence theorems, the study of analytic geometry of the various conic sections, and an investigative approach to the study of elementary topology, fractal geometry and nonEuclidean geometry. Prerequisite: MA061.

Course Detail: Accelerated Algebra covers, in greater depth, many of the topics that are introduced in Intermediate Algebra. Additional topics covered include complex numbers, quadratic and rational inequalities, and inverse functions. The course is equivalent to a typical college algebra course. Prerequisite: MA100 or equivalent score on math placement test.

Course Detail: Trigonometry studies trigonometric functions, inverse trigonometric functions, graphs, identities, vectors, complex number representations, solving triangles and trigonometric equations, and applications. Prerequisite: MA101 or equivalent score on math placement test. The course must be completed by the end of the junior year.

Course Detail: Precalculus is a survey of topics necessary for calculus, including polynomials, rational, exponential and logarithmic functions, matrices, sequences and series, and the binomial theorem. Prerequisite: MA101 or equivalent score on math placement test.

Course Detail: This course is intended to provide a deeper understanding of finance, logic, and set theory. The topics included are Matrices, Linear Programming, The Simplex Method, Sets and Counting, and Probabilities. Prerequisites: MA101, or permission of the Math Department.

Course Detail: The Problem Solving Seminar/Mathematics Circle is designed to teach mathematics as a thinking tool more than as a computational tool. As such it will benefit students, whose studies lead them into any problem solving discipline, including fields as far removed from mathematics as economics, chemistry, engineering, or even business. The mission of the Problem Solving/ Mathematics Circle/Math Team Preparation is to introduce students to mathematics as a creative thinking tool through problem solving. Prerequisites: none.

Course Detail: This introduction to the theory, techniques, and applications of differential calculus includes functions, limits, derivatives, related rates, maximum/minimum problems, and curve sketching, derivatives related to exponential, logarithmic, trigonometric and inverse trigonometric functions. Prerequisites: ‘B’ or better in both MA103 and MA104 or permission of the department.

Course Detail: This introduction to the theory, techniques, and applications of integral calculus includes indefinite and definite integrals, area, volume, work, fluid force, integrals related to exponential, logarithmic, trigonometric and inverse trigonometric functions, and integration techniques. Prerequisite: ‘B’ or better in MA201 or permission of the department. NOTE: Students who plan to take the AP Calculus AB exam should complete MA201 and MA202.

Course Detail: BC Calculus studies a variety of calculus topics including infinite sequences and series, and parametric and polar equations. Other topics might include conic sections, introduction to differential equations and hyperbolic functions. Prerequisite: ‘B’ or better in MA202 or permission of the department. NOTE: Students who plan to take the AP Calculus BC exam should complete the calculus sequence through MA203.

Course Detail: This course focuses on the statistical methods and reasoning, which are used in the natural and social sciences. Topics include: organizing, classifying, and comparing data; probability distributions, sampling distributions, estimation and hypothesis testing. Prerequisite: MA104.

Course Detail: This course studies the mathematical elements of computer science including propositional logic, predicate logic, sets, functions and relations, combinatorics, mathematical induction, recursion, algorithms, matrices, graphs, trees, and Boolean logic. Prerequisite: Precalculus MA104.

Course Detail: This hands-on course emphasizes visual problem solving and teaches students how to research and write about the intersection of mathematics and the visual arts. Topics vary by term and may include but are not limited to: fractal geometry, linear perspective, tiling and tessellations, symmetry groups, knot theory, modular origami, compass and straightedge constructions, and classification of surfaces. Prerequisite: MA104.

Course Detail: This course will be a rigorous study of Euclidean ruler and compass construction. Students will learn theorems and techniques outlined in Euclid’s Elements, and extend those techniques to analyze and recreate classical Islamic geometric patterns. This interdisciplinary course will equally focus on mathematical and artistic content, and includes a research component. Prerequisites: A in Visual Mathematics, A in ASMS Geometry I & II, or permission of the instructor.

Course Detail: This is the first half of a university-level course in multivariable calculus. This course includes the theory and application of vector functions and partial derivatives. Topics include: Vectors and the geometry of space, Vector–valued functions, Continuity and differentiability of functions of several variables, Gradients and directional derivatives, Extrema of functions of two variables, Lagrange multiplies. Prerequisite: ‘B’ or better in MA202 or permission of the department.

Course Detail: This is the second half of a university-level course in multivariable calculus. This course includes the theory and application of multiple integrals and vector fields. Topics include: Multiple integrals, Jacobian and change of variables, Line and surface integrals, Green’s Theorem, Stoke’s Theorem, Divergence Theorem. Prerequisite: ‘B’ or better in MA301 or permission of the department.

Course Detail: This course is an introduction to group theory. Topics include groups, subgroups, finite groups, cyclic groups, permutation groups, and isomorphism. Prerequisite: MA104.

Course Detail: Topology is the study of surfaces in space and certain properties of those surfaces that remain unchanged under deformation. Students will learn proof techniques in point-set topology, learn how to classify surfaces based on genus, Euler characteristic, and other methods of geometric topology, and study topics in algebraic topology such as homeomorphism and homotopy. Because this course is proof-intensive, BC Calculus or Counting & Probability are recommended prior to enrollment, although not required. Prerequisites: “A” in Precalculus or permission of the instructor.

Course Detail: This course is designed for incoming students who already took Elementary Geometry in their home school, or Geometry I and II at ASMS, and continues the study of geometry, building off the techniques to explore more advanced topics to prepare them for prestigious math contests and standardized exams. We will develop essential tools for working with circles, such as inscribed angles, cyclic quadrilaterals, and Power of a Point. We will consider Concurrency of Lines in a Triangle, some theorems connected with Collinearity of Points, Symmetric Points in a Triangle. A secondary goal of the course is to teach students the elements of good mathematical exposition. Students will complete a short exposition (project) of their own. Prerequisite: Geometry

Course Detail: This course is designed to provide students with the theoretical context of concepts encountered in the Calculus sequence. Topics include sequences and series of real numbers, suprema and infima, Cauchy sequences, open sets and accumulation points in Euclidean space, completeness, compactness, connectedness, continuity, Intermediate Value Theorem, differentiation of functions of one variable, integration of functions of one variable, pointwise and uniform convergence, Mean Value Theorem, Taylor's Theorem, Inverse Function Theorem, Implicit Function Theorem. Prerequisites: “A” in both MA201 Differential Calculus and MA202 Integral Calculus or permission of the instructor.

Course Detail: This course is designed to provide students with the theoretical context of concepts encountered in the Calculus sequence. Topics include sequences and series of real numbers, suprema and infima, Cauchy sequences, open sets and accumulation points in Euclidean space, completeness, compactness, connectedness, continuity, Intermediate Value Theorem, differentiation of functions of one variable, integration of functions of one variable, pointwise and uniform convergence, Mean Value Theorem, Taylor's Theorem, Inverse Function Theorem, Implicit Function Theorem. Prerequisites: “A” in both MA201 Differential Calculus and MA202 Integral Calculus or permission of the instructor.

Course Detail: Historical survey of the general development of mathematics with a balance of historical perspective and mathematical structure. This course features a significant writing component. Prerequisite: Differential Calculus or permission of the instructor. (Fulfills graduation requirement)

Course Detail: Differential Equations introduces the theory, techniques, and applications of ordinary differential equations. Topics include first and second order differential equations, linear equations of higher order, systems of differential equations, numerical methods, Laplace transform methods, and applications. Prerequisite: ‘B’ or better in MA202 or permission of the department.

Course Detail: Linear Algebra studies the theory, techniques, and applications of linear algebra including systems of linear equations, matrices, determinants, vectors, vector spaces, and eigenvalues/eigenvectors. Prerequisite: ‘B’ or better in MA201 or permission of the department.

Course Detail: This course is an introduction to the analysis of complex functions. Topics covered: arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus or residues; conformal representation; applications. Prerequisite: 'B' or better in MA202 or permission of the department.

Course Detail: This course is an introduction to classical number theory with a balance of theory and computation. Topics include mathematics induction, divisibility properties, and properties of prime numbers, the theory to congruencies, number theoretic functions, and continued fractions. Prerequisite: MA104.

Course Detail: This course is an investigation of methods of numerical computation with an emphasis on application of numerical approximation techniques in the solution of problems frequently encountered in engineering and science. Topics will include error analysis, solutions of equations, interpolation, quadrature, and linear systems. Prerequisite: MA202.

Course Detail: Topics covered include: Basic counting and probability techniques, Inclusion-exclusion, 1-1 correspondences, Pigeonhole Principle, Constructive expectation, Fibonacci and Catalan numbers, Recursion, Conditional probability, Generating functions , Graph theory. Prerequisite: MA104.

Course Detail: In this class students will continue their exploration of more advanced counting and probability topics. This class is the follow-up to Counting and Probability I. Topics include inclusion-exclusion, 1-1 correspondences, the Pigeonhole Principle, constructive expectation, Fibonacci and Catalan numbers, recursion, conditional probability, generating functions, graph theory, and much more. The class is structured to inspire the students to explore and develop new ideas. Important counting and probability techniques and powerful problem solving approaches are taught throughout the class. Prerequisite: MA104

Course Detail: This course will focus on preparation for the AP Calculus exam. Prerequisite: students who plan to take the AP Calculus AB exam should complete MA201 and MA202; students who plan to take the AP Calculus BC exam should complete the calculus sequence through MA203.

Course Detail: This course follows the AP Statistics curriculum set by the College Board and is designed to prepare students for the AP Statistics exam. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will learn how to use graphing calculators and read computer output in an effort to enhance the development of statistical understanding. During this course, the student will be exposed to four broad conceptual themes and will be expected to demonstrate proficiency in: Exploring data: describing patterns and departures from patterns; Sampling and experimentation: planning and conducting a study; Anticipating patterns: exploring random phenomena using probability and simulation; Statistical inference: estimating population parameters and testing hypotheses. Prerequisites: MA205 or Permission by the Math Department.

Course Detail: Algebra A and Algebra B provide an in-depth analysis of polynomials, factoring, exponents and radicals, linear and quadratic equations, complex numbers, functions, graphs, systems of equations, and applications complex numbers, quadratic and rational inequalities, inverse functions, and conic sections.

Course Detail: Algebra A and Algebra B provide an in-depth analysis of polynomials, factoring, exponents and radicals, linear and quadratic equations, complex numbers, functions, graphs, systems of equations, and applications complex numbers, quadratic and rational inequalities, inverse functions, and conic sections.

Course Detail: This course is an introduction to the theory of two-person games. It focuses on fundamentals of game theory including basic concepts and techniques and various ways of describing and solving games. It covers topics such as optimal responses to specific strategies, the maximum strategy, the minimax strategy, solutions of zero-sum games, dominance, symmetric games, mixed strategies for nonzero-sum games, and mixed Nash equilibria for 2x2 nonzero-sum games. It also introduces applications of game theory in economics, political sciences, business, and biology. Prerequisites: Precalculus or permission of the department.

Course Detail: Financial mathematics involves applying mathematics to situations that involve financial transaction. This course provides an introduction to financial mathematics and a brief introduction to financial economics. Students will learn about the time value of money; annuities; loans; bonds; general cash flows and portfolios; immunization; general derivatives; options; forwards and futures; swaps; and hedging from the point of view of an actuarial scientist. A secondary goal of the course is to teach students the elements of good mathematical exposition. Students will complete a short exposition (project) of their own. Prerequisite: MA202.