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Course Criteria
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3.00 Credits
Systems of Linear Equations; Determinants; Vector Spaces; Subspaces; Subspaces Spanned by Vectors; Inner Product; Inner Product Vector Spaces; Special Subspaces - Orthogonal Complements; Orthogonalization; Projections. Vector Space of Free Vectors; Applications in Elementary and Analytic Geometries; Vector Space Homomorphisms (Linear Transformations); Isomorphisms; Endomorphisms; Automorphisms; Matrix Representations of Homomorphisms; Special Subspaces Genrated by Homomorphisms: Kernels, Images, Eigenspaces; Applications - Diagonalization of Matrices; Regressions (Least Squares Solutions); Special Linear Transformations: Projections, Reflections. MT 2145 or Permission of Instructor
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3.00 Credits
Percent, ratio, and proportion, powers and roots, simple equations, equations in more than one unknown, quadratic equations, exponents, and logarithms, variation, plane geometry, trigonometry. Prerequisite: MT 1513 or equivalent.
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3.00 Credits
Well-ordering and induction, Integer Representations (different bases), Primes, Divisibility, Euclid's Algorithm, Fundamental Theorem of Arithmetic; Equivalence Relations Mod m (Congruences), System of Linear Congruences; Fermat's Little Theorem, Euler's Function, PythagoreanTriples, Diophantine Approximation and Pell's Equation; Application in Cryptology.
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4.00 Credits
The second course in a three-semester course of unified calculus and analytic geometry including transcendental functions, hyperbolic functions, various methods of integration, areas and volumes as limits, applications of integration, and series. Prerequisite: MT 2145.
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3.00 Credits
A continuation of Calculus II. Power series, expansion of functions into series with applications, definition and meaning of ordinary partial derivatives, multiple integrals and vector calculus. Prerequisite: MT 3624 or equivalent.
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3.00 Credits
A rigorous treatment of calculus of one and several variables. Elementary topology of Euclidean spaces, continuity and uniform continuity, differentiation and integration. Prerequisites: MT 2145, MT 3624, MT 3633.
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3.00 Credits
A study of the complex number system, functions of a complex variable, differentiation, integration, series, residues and poles, conformal mappings, and applications to the physical sciences. Prerequisites: MT 2145, MT 3624, MT 3633.
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3.00 Credits
Sets, relations, and functions; Operations on Sets; Operational Compatible with Equivalence Relations; Algebraic Structures; Sub-Algebraic Structures; Quotient Algebraic Structures; Algebraic Structure Homomorphisms; Groups: Rings; Fields; Vector Spaces; Applications of Algebraic Structures in Number Theory, Cryptology (Modular Rings), and Galois Theory. MT 3223 or Permission of Instructor
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3.00 Credits
Sets, inequalities and sums, graphs and coordinate geometry, lines, linear programming, determinants and vectors, matrices, probability, statistics, correlation, and introduction to game theory. Prerequisite: MT 3313 or equivalent. the Funamental Theorem of Arithmetic; Generating Fucnstions, Partitions of integers, and the Summation Operator; The Principle of inclusion and Exclusion, derangements and arrangements with forbidden positions, Rook Polynomials; Some algebraic Structures, Ring Structure and Modular Arthmetic, Homomorphisms and Isomorphisms; Finite Fields and Combinatorial Designs, polynomial rings, Latin Squares, finite geometries and affine planes, blosk designs and projective planes. MT 2145
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3.00 Credits
The algebraic development of formulas used in statistical methods, frequency curves, curve fitting, correlation, probability, the binomial distribution, the Poisson distribution, random sampling, large sample theory, testing hypotheses, small methods, Chi-squared distribution, analysis of variance. Prerequisites: MT 2145 or permission.
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