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Course Criteria
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3.00 Credits
3 credits Prerequisite: MTH 142. Corequisite: MTH 253. First order differential equations, linear differential equations with constant coefficients, methods of undetermined coefficients, variation of parameters, series solutions. Concepts of linear algebra applied to systems of first order equations, higher order equations. Introduction to numerical methods. Applications.
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4.00 Credits
4 credits Corequisite: MTH 141 or permission of department. Matrix algebra, determinants, solutions of systems of linear equations. Real vector spaces: linear independence, basis, and dimension. Linear transformations. Applications.
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1.00 Credits
1 credit Prerequisites: MTH 141 and 253 and permission of department. May be taken for credit up to six times. This seminaris required of all students who wish to earn honors in mathematics.
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3.00 Credits
3 credits Prerequisites: MTH 142, CSC 156. Logic: truth tables, connectives, and quantifiers. Proof: formal and informal reasoning, strategies, proof by contradiction, existence, counterexamples. Set Theory: sets, operations on sets. Cartesian product, relations, functions, equivalence relations. Mathematical induction. Groups: modular arithmetic, permutation groups, isomorphism. Number systems: construction of the integers and rationals, ordered fields, the completeness axiom.
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3.00 Credits
3 credits Prerequisite: MTH 142 and MTH 301, or permission of instructor. A critical treatment of the foundations of Euclidean geometry. The parallel postulate, absolute and non-Euclidean geometries. Defects in Euclid’s treatment and a modern axiomatization of Euclidean geometry. Independence, consistency, and completeness of a system of axioms; model of system of axioms. Coordination of Euclidean geometry.
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3.00 Credits
3 credits Prerequisites: MTH 142 or permission of instructor. This course pursues geometry from a computational point of view, using coordinates (including homogeneous coordinates), vectors, matrices, scalar products, and norms to study important structures such as lines, planes, and spheres, and important transformations such as isometries and projective transformations. Applications will be strongly emphasized, especially in computer graphics, computer vision, and robotics.
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3.00 Credits
3 credits Prerequisites: MTH 243 and 253, or permission of instructor. Antiquity to the present: fundamental concepts and their historical background. Survey of the main fields of current mathematics.
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3.00 Credits
3 credits Prerequisite: Permission of instructor. Divisibility properties, Euclidean algorithm, prime factorization, arithmetic functions, indeterminate problems, congruences, quadratic reciprocity.
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3.00 Credits
3 credits Prerequisites: MTH 142 and MTH 301. Sentential and predicate calculus. Proof theory. Recursive function theory. Godel’s theorem. Lambda conversion.
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3.00 Credits
3 credits Prerequisites: MTH 142 and 253. Laws of probability. Distribution functions, means and variance, moment generating functions, joint distributions, functions of random variables. The Law of Large Numbers. Binomial, Poisson, geometric distributions. Introduction to the normal distribution and the Central Limit Theorem.
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