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Course Criteria
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3.00 Credits
A continuation of MAT 330, in which key properties from the integers and the real numbers are used as models for the algebraic structures known as rings and fields. Students construct and examine a rich collection of examples including rings of polynomials, Gaussian integers, and finite fields. Topics include prime factorization, integral domains, ideals, ring homomorphisms, and extension fields. Prerequisite: MAT 330.
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3.00 Credits
A study of functions of one complex variable, the course extends notions from the calculus of real-valued functions. Topics include complex numbers, limits, continuity, differentiability, Cauchy-Riemann equations, analytic functions, elementary transformations, complex integration, Cauchy's Theorem, the annulus theorem, Cauchy's Integral Formula, Morera's Theorem, complex power series, Laurent series, and the theory of residues. Prerequisite: MAT 230.
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3.00 Credits
This course describes the many physical and social phenomena that involve a change in some quantity with respect to time and are described mathematically via differential equations. Topics include techniques for solving first-order differential equations (exact, separable, linear, integrating factors, homogeneous), solving higher order linear differential equations (constant coefficients, undetermined coefficients, variation of parameters), and the Laplace transform methods and series solutions of differential equations. Prerequisite: MAT 230 or permission of the instructor.
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3.00 Credits
A study of how computers obtain numerical estimates of solutions when people apply mathematics to diverse disciplines (e.g. physics, economics, medicine, etc.). In this course we discuss and develop various algorithms that form the basis for computer applications including root finding, interpolation, differentiation and integration, differential equations, and systems of equations. Prerequisite: MAT 240 and CSC 117.
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3.00 Credits
A systematic exploration of how calculus provides profound insights into explaining and understanding our world and its phenomena. The study of real analysis discusses the theoretical foundations of single variable calculus to arrive at a deep understanding of why calculus works. Topics include properties of the real numbers, limits, continuity, differentiation, and integration. Prerequisite: MAT 230 and MAT 290.
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3.00 Credits
A study of geometry from an algorithmic perspective, this course examines classic problems such as The Art Gallery Problem, The Post Office Problem, and The Piano Movers' Problem. Computational Geometry focuses on the design and analysis of efficient algorithms to solve problems which can be stated in terms of basic geometric objects like points, lines, segments, polygons, etc. We will consider various strategies for building convex hulls, Voronoi diagrams, and Delaunay triangulations; finding nearest neighbors and closest pairs; as well as line segment intersection, linear programming, polygon triangulation, point location, and range searching. Prerequisite: MAT 290; or MAT 230 and CSC 117; or permission of the instructor.
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1.00 Credits
The Putnam Exam is a notoriously challenging annual mathematical competition. This is a course on problem-solving focusing on Putnam-style problems. Students learn strategies for tackling such problems and become familiar with the style by working out problems from past Putnam exams, discussions, and presentations to the group. The semester culminates in taking the Putnam exam. Prerequisite: MAT 230.
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1.00 Credits
Students meet weekly to discuss and present undergraduate research topics in math ematics. Students are individually mentored by mathematics faculty in the study and in the oral and written presentation of a research topic at increasing levels of sophistication. Prerequisite: MAT 290.
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3.00 Credits
An introduction to music theory, including standard music notation, key signatures, and recognition of simple chords and chord symbols. Designed for those with little or no previous training in music.
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3.00 Credits
An introduction to Western musical culture and style. Through careful listening to music from the Middle Ages to the present, students study the historical and cultural context of a wide range of music and learn critical listening skills. While the primary focus is on music of the Western classical tradition, regular comparisons with contemporary popular music and culture forms an integral part of the course. Special emphasis is also placed on music that students hear live at the Norton Center or in other area concert venues. No prerequisite; the ability to read music is not required.
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