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Upper Division Mathematics Courses

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Undergraduate

Instructor: Steve Gubkin
Textbook: Visual Complex Analysis by Tristan Needham
School: Cleveland State University, Fall 2016

Description
Fundamentals of complex analysis, including basic properties of complex numbers, analytic functions, harmonic functions, integration, Taylor and Laurent series.

Instructor: Ivan Soprunov
Textbook: Introductory Combinatorics by Richard Brualdi
School: Cleveland State University, Fall 2016

Description
A study of combinatorial methods for enumeration, analysis and optimization of discrete structures, such as arrangements, partially ordered sets, graphs, and polytopes. The methods include binomial coefficients and other combinatorial functions, recurrence relations, and generating functions.

Instructor: John Oprea
Textbook: Differential Geometry by John Oprea
School: Cleveland State University, Spring 2017

Description
Focuses on the calculus, linear algebra, and geometry of curves and surfaces, as well as applications to engineering and science. Material covered will include the curvature and torsion of curves, Gaussian and mean curvatures of surfaces, minimal surfaces, and geodesics, Course makes extensive use of a computer system, such as Maple.

Instructor: Johnathan Scott
Textbook: Topology Now! by Phillip Straffin and Robert Messer
School: Cleveland State University, Spring 2017

Description
Introduction to topology. Point set topology, Surface Classification, Knots, Knot Embedding, Seifert-Van Kampen, Fundamental Group, Functors.

Instructor: Ivan Soprunov
Textbook: Algebraic Curves by William Fulton
School: Cleveland State University, Spring 2017

Description
Solutions to multivariate polynomials, Bezout’s Theorem, Polynomial Factorization, Projectives Planes, Division Algorithm.

Graduate

Instructor: Enrique Thomann
Textbook: Lebesgue Integration on Euclidean Space by Frank Jones
School: Oregon State University, Fall 2017

Description
Properties of metric spaces and normed spaces, including lp spaces. Completeness and applications, including fixed point theorems. Compactness. Equicontinuity and the Arzela-Ascoli theorem. Uniform continuity and uniform convergence, including applications.

Instructor: Enrique Thomann
Textbook: Lebesgue Integration on Euclidean Space by Frank Jones
School: Oregon State University, Winter 2018

Description
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini’s theorem, and applications to Fourier transforms and probability.

Instructor: Enrique Thomann
Textbook: Real Analysis by Gerald Folland
School: Oregon State University, Spring 2018

Description
Topological concepts in metric, normed, and inner-product spaces. Properties of continuous functions, including the Stone-Weierstrass theorem. Introduction to function spaces, contraction mappings, fixed points, and applications. Lebesgue measure and integration in one and several variables, basic convergence theorems, Lebesgue spaces, Fubini’s theorem, and applications to Fourier transforms and probability.

Instructor: Ren Guo
Textbook: Topology by James Munkers
School: OregonState University, Fall 2018

Description
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology.

Instructor: Christine Escher
Textbook: Topology by James Munkers
School: Oregon State University, Winter 2019

Description
Topological spaces and maps. Separation axioms, compactness, convergence, extension theorems, metrizability and compactification. Product spaces and simplicial complexes. Definition and basic properties of the fundamental group functor, with applications to the theory of covering spaces. Selected topics from dimension theory, manifold theory, and other areas of topology.

Instructor: Bill Bogely
Textbook: Linear Algebra by Friedberg, Insel, and Spence
School: Oregon State University, Fall 2017

Description
Abstract vector spaces. Linear transformations, eigenvalues and eigenvectors, the Jordan canonical form, inner product spaces.

Instructor: Malgorzata Peszynska
Textbook: Numerical Linear Algebra by Trefethen and Bau
School: Oregon State University, Fall 2017

Description
Computation of solutions of linear systems using direct and iterative methods; least-squares solution of overdetermined systems; computation of eigenvalues and eigenvectors.

Instructor: Malgorzata Peszynska
Textbook: Numerical Linear Algebra by Trefethen and Bau
School: Oregon State University, Winter 2018

Description
Numerical solution of initial-value problems using Runge-Kutta methods and linear multistep meth- ods; introduction to boundary-value problems. Analysis of stability, accuracy, and implementation of methods.

Instructor: Malgorzata Peszynska
Textbook: Numerical Linear Algebra by Trefethen and Bau
School: Oregon State University, Spring 2018

Description
Numerical solution of boundary value problems and initial-boundary value problems using finite difference and finite element methods. Analysis of stability, accuracy, and implementation of meth- ods.

Instructor: Clayton Petsche
Textbook: Complex Analysis by Stien and Shakarchi
School: Oregon State University, Spring 2018

Description
Basic theory of analytic functions of a complex variable, including Cauchy’s theorem, residue theorem, analytic continuation, conformal mappings, entire, and meromorphic functions.

Instructor: David Finch
Textbook: Functional Analysis by John Conway
School: Oregonstate University, Fall 2018

Description
Topological vector spaces, generalized functions, operator theory. Hahn-Banach The- orem, Open Mapping Theorem, Closed Graph Theorem, The Principle of Uniform Boundedness, Compact Operators, Spectral Theorem.

Instructor: Elaine Cozzi
Textbook: Vorticity and Incompressible Flow by Majda and Bertozzi
School: Oregon State University

Description
Introduction to compressible and incompressible fluids including Navier-Stokes and Euler equations. Topics include conservation laws, classic solutions, weak solutions, conditions for existence and uniqueness.

Instructor: Elane Cozzi
Textbook: Partial Differential Equations by Shearer
School: Oregon State University, Fall 2018

Description
Partial differential equations of physics, including those of potential theory, wave prop- agation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.

Instructor: Elane Cozzi
Textbook: Partial Differential Equations by Shearer
School: Oregon State University, Winter 2019

Description
Partial differential equations of physics, including those of potential theory, wave prop- agation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.

Instructor: Elane Cozzi
Textbook: Partial Differential Equations by Shearer
School: Oregon State University, Spring 2019

Description
Partial differential equations of physics, including those of potential theory, wave prop- agation, and heat flow, treated by classical means, generalized functions and variational principles. Square summable function methods and integral equations.

Instructor: Thomas Schmidt
Textbook: Abstract Algebra by Dummit and Foote
School: Oregon State University, Winter 2018

Description
Group Theory. Introduction to Symmetric Group, Dihedral Group, Quaternions, and Matrix groups. Development of cosets, Isomorphism Theorems, Group actions, Sylow Theorems, Semi Direct and Direct product, p-groups, Nilpotent groups and Solvable groups.

Instructor: Holly Swisher
Textbook: Abstract Algebra by Dummit and Foote
School: Oregon State University, Spring 2019

Description
Rings, Fields and Galois Theory. Classification of Rings and Ideals. Isomorphism Theorems, Chinese Remainder Theorem, Unique Factorization, Quotient Rings.

Instructor: David Koslicki
Textbook:
School: Oregon State University, Winter 2019

Description
General theory of probability measures and random variables, including weak conver- gence, characteristic functions, central limit theory, conditional expectations, martingales.

Instructor: David Koslicki
Textbook:
School: Oregon State University, Spring 2019

Description
General theory of probability measures and random variables, including weak conver- gence, characteristic functions, central limit theory, conditional expectations, martingales.

Upper Division Science Courses

Undergraduate

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Graduate

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Intelligent agents. Problem-solving as heuristic search. Adversarial search. Constraint satisfaction methods; Arc-consistency. Knowledge representation and reasoning. Propositional logic. Reasoning with propositional logic: algorithms for satisfiability. First-order logic. Proof theory, model theory, resolution refutation, forward and backward chaining, representing events and actions.