6630    Mathematical Analysis of Computer Algorithms  Discrete algorithms (number-theoretic, graph-theoretic, combinatorial, and algebraic) with an emphasis on techniques for their mathematical analysis. 8315    Sheaves and Cohomology Main results and techniques for sheaves on topological spaces and their cohomology. Veronese and Segre varieties, Grassmannians, algebraic groups, quadrics. Topics include the spectrum of a ring, "gluing" spectra to form schemes, products, quasi-coherent sheaves of ideals, and the functor of points. 6600    Probability  Discrete and continuous random variables, expectation, independence and conditional probability; binomial, Bernoulli, normal, and Poisson distributions; law of large numbers and central limit theorem. Courses numbered 6000-6999 are taken by senior undergraduates as well as by beginning Masters degree students. Some topics covered include the Sylow theorems, solvable and simple groups, Galois theory, finite fields, Noetherian rings and modules. 8250    Differential Geometry I  Differentiable manifolds, vector bundles, tensors, flows, and Frobenius' theorem. Introduction to homology:  simplicial, singular, and cellular. Probability, Stochastic Processes and Combinatorics. 6690    Graph Theory  Elementary theory of graphs and digraphs. 6450    Cryptology and Computational Number Theory  Recognizing prime numbers, factoring composite numbers, finite fields, elliptic curves, discrete logarithms, private key cryptology, key exchange systems, signature authentication, public key cryptology. 8150    Complex Variables I  The Cauchy-Riemann Equations, linear fractional transformations and elementary conformal mappings, Cauchy's theorems and its consequences including: Morera's theorem, Taylor and Laurent expansions, maximum principle, residue theorem, argument principle, residue theorem, argument principle, Rouche's theorem and Liouville's theorem. All other trademarks and copyrights are the property of their respective owners. Gauss-Bonnet theorem. 6670    Combinatorics  Basic counting principles: permutations, combinations, probability, occupancy problems, and binomial coefficients. 8700    Applied Mathematics: Applications in Industry  Mathematical modeling of some real-world industrial problems.Topics will be selected from a list which includes air quality modeling, crystal precipitation, electron beam lithography, image processing, photographic film development, production planning in manufacturing, and optimal control of chemical reactions. 8450    Topics in Algorithmic Number Theory  Topics in computational number theory and algebraic geometry, such as factoring and primality testing, cryptography and coding theory, algorithms in number theory and arithmetic geometry. More sophisticated methods include generating functions, recurrence relations, inclusion/exclusion principle, and the pigeonhole principle. 8010    Representation Theory of Finite Groups Irreducible and indecomposable representations, Schur's Lemma, Maschke's theorem, the Wedderburn structure theorem, characters and orthogonality relations, induced representations and Frobenius reciprocity, central characters and central idempotents, Burnside's theorem, Frobenius normal p-complement theorem. All rights reserved. This is MATH 2410H for graduate students in Mathematics Education. A number of algorithms and applications are included. Smoothness and tangent spaces, singularities and tangent cones. It's free! Must be 24 years of age or older and a high school graduate for a Bachelor's, Masters degree applicants must have a Bachelors, Doctorate degree applicants must have a Masters degree, Afterwards, you'll have the option to speak to an independent 6150    Complex Variables  Differential and integral calculus of functions of a complex variable, with applications. 8180    Functional Analysis II  Introduction to operator theory, spectral theorem for normal operators, distribution theory, the Schwartz spaces, topics from C*-algebras and von Neumann algebras. Some courses may require special math and graphics editors, such as TeX and MathType. An intensive review of techniques and material essential for graduate study in mathematics, including background in calculus and linear algebra. Topics include proofs, induction, the metric structure of the reals, the Bolzano-Weierstrass theorem, and the diagonalization theorem. Preparing for the Math portion of the GED can be quite difficult; you must, after all, answer a number of different types or... 3.14159265… Math lovers out there will recognize this number as pi, a mathematical constant that's as delicious as, well, pie.... An admission advisor from each school can provide more info about: Get Started with Southern New Hampshire University, Get Started with Colorado State University Global, Get Started with University of Pennsylvania, Get Started with University of Notre Dame. A mathematical software package will be used to implement iterative techniques for nonlinear equations, polynomial interpolation, integration, and problems in linear algebra such as matrix inversion, eigenvalues and eigenvectors. 6300    Introduction to Algebraic Curves  Polynomials and resultants, projective spaces. Connect with 8320    Algebraic Curves  The theory of curves, including linear series and the Riemann Roch theorem.

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