A two-course sequence including a review of algebra, trigonometry, and analytic geometry integrated with an introduction to the theory of differential and integral calculus.
An introduction to the theory of differential and integral calculus for functions of one variable. Includes the concepts of limit, continuity, derivatives, and indefinite integrals and definite integrals, culminating in the Fundamental Theorem of Calculus. Applications to related rates and optimization problems.
Differentiation and integration of logarithmic functions, exponential functions, and inverse trigonometric functions. Study of polar coordinates, conic sections, and various integration techniques. Applications to computations of volumes, surface areas, and centers of mass.
A survey of the math topics which are foundational to computer science: functions, relations, sets, basic logic, proof techniques, combinatorics, graphs and trees, discrete probability. No prerequisite. Satisfies the Abstraction and Formal Reasoning LADR.
Non-technical introduction to selected concepts of modern mathematics (such as logic, set theory, axiomatic systems, non-Euclidean geometry, number theory, graph theory, etc.) that illustrate the nature of mathematics and its connections to other areas of knowledge.
Emphasizes problem solving, fundamental mathematical concepts and applying mathematical principles to non-routine problems. Introduction to numeration systems, theory of arithmetic, combinatorics, probability, statistics, familiar number sets and their properties (naturals, integers, rationals, irrationals, reals) and functions.
Use of graphs and numerical summaries to describe data from individual variables and to investigate relationships among variables. Design of statistical experiments. Survey of fundamental concepts of probability, including sampling distributions. Use of sample data to estimate, and to test hypotheses about, unknown parameters.
An introduction to the foundations of mathematics, with emphasis on developing basic reasoning skills needed for constructing proofs.
Differentiation and integration of vector-values functions. Study of functions of several variables, including partial derivatives and multiple integrals. Detailed study of infinite sequences and series.
Systems of linear equations and their solutions. Study of the algebraic properties and applications of vectors, matrices and linear transformations.
Survey of basic techniques for describing dynamical systems by means of equations involving derivatives of functions, and of methods for finding functions which satisfy these equations.
Survey of important discoveries in mathematics and the
historical contexts in which they were made. Topics will include major mathematical developments
beginning with the Ancient Greeks and tracing the development through Hindu, Arabic and
European mathematics up to the modern developments of the 20th century.
Explores properties of the integers such as divisibility
and congruence, linear diophantine equations, prime numbers, the Fundamental Theorem of
Arithmetic, Fermat’s little theorem, Euler’s Theorem, Euler’s phi function, computing powers and
roots in modular arithmetic, and public key cryptography.
Development of the algebraic and topological properties of the real number system and the theoretical foundations of differential and integral calculus. Strongly recommended for students considering post-graduate study in mathematics.
Study of complex numbers and functions of a
complex variable. Topics include algebra and geometry of the complex plane, derivatives, integrals,
power series, Laurent series, and residue theory.
Study of concepts abstracted from algebraic properties of the classical number systems, including groups, rings, fields, order relations, and equivalence relations.
Calculus-based survey, including axioms of probability, discrete and continuous variables, standard probability functions (binomial, normal, Poisson, etc), mathematical expectation, generating functions, and a brief introduction to the estimation and hypothesis testing.
Survey of ancient, classical and modern views regarding the nature of space, the description of spatial structures and the organization of facts about space into deductive theories.
Includes selected topics from graph theory and combinatorics: connectivity, colorings, cliques, planarity, directed graphs, cuts and flows, principle of inclusion and exclusion.
Off-campus supervised experience in mathematics.
Study of concepts, growing out of and underlying geometry and calculus, which have become important in physics, chemistry, logic, and computer science. Careful development of abstract notions such as topological spaces, continuity, topological equivalence, connectedness, and dimension, and related philosophical and historical matters in mathematics and liberal arts generally.
Topics may be drawn from analysis with complex variables, introduction to functional analysis, category theory, mathematical logic and model theory, recursive function theory, topology, universal algebra, or other areas.
Individual study of topics such as those listed under 360.
Student-led inquiry/research in an area of mathematics such as real or complex analysis, topology, algebra, etc. Content varies. May be repeated for credit.
Course content will reflect the topic for the annual Capstone. Open to all juniors and seniors and may be repeated once for credit. Students may enroll in only one Capstone seminar in a given term.