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Course Criteria
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3.00 Credits
NA/QU S.Wang An introduction to functions of several variables, vector geometry, partial derivatives, maxima & minima, Taylor's Theorem, multiple integrals, line integrals, and Green's and Stokes' Theorem. Prerequisite: MATH 114 and either 115 or 116, or advanced placement. Typically offered every Semester.
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3.00 Credits
NA/QU (Cross-listed in Education) J.Sabloff A service-learning course in which students teach "math labs" to high school geometry students. Students will develop effective teaching methods through pedagogical theory and practice, and will explore the context in which mathematics is taught in high school. Offered occasionally.
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3.00 Credits
NA L.Butler An introduction to the classical theory of numbers. Topics include: primes and divisibility, congruences, the Chinese Remainder Theorem, quadratic reciprocity, sums of squares, Diophantine equations, continued fractions, approximation by rationals, Pell's equation. Time permitting, we will discuss arithmetic functions related tot the distribution of prime numbers. Emphasis will be placed on learning to generalize from examples to precise conjectures. Prerequisite: MATH 115 or instructor consent. Offered occasionally.
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3.00 Credits
NA/QU W.Miao An introduction to statistical methods used to analyze data in the natural and social sciences. It covers descriptive statistics, the binomial and normal distributions, expected value and variance, confidence intervals and hypothesis testing, comparison of two samples, regression, and analysis of variance. A required computer lab, using R, is taught alongside this course. Prerequisite: MATH 114 or advanced placement. Typically offered every Fall.
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3.00 Credits
NA/QU J.Tecosky-Feldman Ordinary differential equations: the general theory of first-order equations, linear equations of higher order, qualitative analysis of nonlinear systems, and computational methods. Other topics, such as series solutions or an introduction to partial differential equations and Fourier series, may be included. Elements of linear algebra are developed as needed. Emphasis is on applications, especially on differential equations as mathematical models in the physical, biological and social sciences. Prerequisite: MATH 114 and either 115 or 116, or advanced placement. Offered occasionally.
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3.00 Credits
NA/QU J.Tecosky-Feldman An introduction to several areas in classical and modern geometry: analytic geometry, conic sections, Platonic solids and polyhedra, tessellations of the plane, projective, hyperbolic, and differential geometry. Students will see how symmetry groups serve as a unifying theme in geometry. This course will introduce students to the skill of writing formal mathematical proofs. Prerequisite: MATH 121 or instructor consent. Typically offered in alternate years.
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3.00 Credits
NA/QU (Cross-listed in Computer Science and Economics) L.Butler Covers in depth the mathematics of optimization problems with a finite number of variables subject to constraints. Applications of linear programming to the theory of matrix games and network flows are covered, as well as an introduction to nonlinear programming and hidden Markov models. Emphasis is on the structure of optimal solutions, algorithms to find them, and the underlying theory that explains both. This course is designed for students interested in computer science, economics, or mathematics. Prerequisite: MATH 121 and instructor consent, or MATH 215. Typically offered in alternate years.
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3.00 Credits
NA/QU C.Greene An introduction to linear algebra: vector spaces, linear transformations and matrices, determinants, quadratic forms and eigenvalue problems. Applications to differential equations and linear models are discussed. Prerequisite: MATH 114 and either 115 or 116, or 121, or advanced placement. Typically offered every Semester.
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3.00 Credits
NA C.Greene Calculus of several variables: continuous and differentiable functions on Euclidean spaces, extreme value problems, inverse and implicit function theorems, multiple integration, Green's and Stokes' Theorems. Prerequisite: MATH 215. Typically offered every Spring.
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3.00 Credits
NA/QU W.Miao An introduction to probability theory. Topics include: sample spaces, combinatorics, conditional probability, independence, discrete and continuous random variables, functions of random variables, expected value and variance, the moment generating function, and some basic limit theorems. Prerequisite: MATH 116 or 121, or consent. Typically offered in alternate years.
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