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Course Criteria
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3.00 Credits
An introductory course on number systems. Topics will include: the development and properties of various number systems (such as integers, rational, real, and complex numbers) ; and operations and different representations in these number systems (such as those in bases other than 10) . Students will develop a conceptual understanding of the course material in a learning environment that models the pedagogical foundations of the Massachusetts Curriculum Frameworks for Mathematics and the NCTM Standards. Prerequisite: MATH 0150.
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3.00 Credits
A study of groups, rings, integral domains and fields, with special emphasis on the real and complex fields. Prerequisite: MATH 0311.
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3.00 Credits
Geometric and physical meaning of differential equations. Theory and solution of first, second and higher order linear and non-linear differential equations. Initial and boundary value problems. Finite difference equations. Prerequisites: MATH 0106 and MATH 0218.
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3.00 Credits
An integrated course consisting of intuitive, synthetic, and analytic approaches to Euclidean and other geometries. Topics will include axiomatic foundations, finite geometries, non-Euclidean geometries, and synthetic projective geometry. Prerequisite: MATH 0218.
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3.00 Credits
Topology of real numbers, Cauchy sequences, metric completeness, continuity, compactness, connectedness. Sequence and series and uniform convergence of infinite series. Derivatives and definite integrals. Prerequisite: MATH 0201.
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3.00 Credits
A simple, thorough survey of the elementary topics of point-set topology of the real line and plane topological spaces; metric spaces; mappings; connectedness; compactness. Prerequisite: MATH 0201.
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3.00 Credits
Properties of integers including congruence, primes and factorization, continued fractions, quadratic residues, linear diophantine equations and number theoretic functions. Prerequisite: MATH 0105.
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3.00 Credits
Algebra of complex numbers, analytic functions, Cauchy Riemann conditions, conformal mapping, line integrals, Cauchy integral formula, residue integration, Taylor and Laurent series. Prerequisite: MATH 0201.
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3.00 Credits
A study of mathematical modeling and of the models of interest in operations research, which may include distribution problems, linear programming, the simplex method and applications. CPM, network problems, non-linear programming problems, Markov chains, queuing models, and simulation. Prerequisites: MATH 0106 and MATH 0218.
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3.00 Credits
Intended for majors in mathematics or computer science. Methods of finding approximate numerical solutions to mathematical problems are explored using a scientific computer programming language. Standard algorithms of numerical analysis will be chosen from: numerical integration, non-linear equations, computational probability, differential equations. Prerequisites: MATH 0106 and MATH 0218.
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