Alan Noell

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 5083.Prerequisite(s): MATH 4023 with grade of “C” or better.

Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 4083.Prerequisite(s): MATH 4023 with grade of “C” or better.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 5083.Prerequisite(s): MATH 4023 with grade of “C” or better.

Differentiation with respect to measures. Aspects of point set topology: nets, locally compact spaces, product spaces. Elementary functional analysis: Hahn-Banach, uniform boundedness, open mapping theorems, weak topologies, Hilbert spaces. Riesz representation theorems: duals of Lebesgue spaces and spaces of continuous functions. Other topics may include: elements of Fourier analysis, distribution theory, Stone-Weierstrass theorem.Prerequisite(s): MATH 5143.

A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and Hermitian forms, and dual spaces. Meets with MATH 4063. May not be used for degree credit with MATH 4063.Prerequisite(s): MATH 3013 and MATH 3613 with grades of “C” or better; grades of “B” or better recommended.

A continuation of MATH 2144, including techniques of integration, series and their applications, parametric equations, and polar coordinates. Previously offered as MATH 2155, MATH 2163, and MATH 2365.Prerequisite(s): MATH 2144 with grade of 'C' or better.

Theory of topological vector spaces including metrizability, consequences of completeness, Banach spaces, weak topologies, and convexity.Prerequisite(s): MATH 4613 or MATH 5003 or MATH 5023, MATH 5153, MATH 5303.

Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 5083.Prerequisite(s): MATH 4023 with grade of “C” or better.

Continuation of MATH 4023. Review of limits and continuity. Properties of continuous functions, uniform continuity, the derivative, the Mean Value Theorem. The Riemann integral, the Fundamental Theorem of Calculus. Infinite series, power series, pointwise and uniform convergence of series of functions. May not be used for degree credit with MATH 4083.Prerequisite(s): MATH 4023 with grade of “C” or better.

Differential and integral calculus of functions of several variables, vector analysis, Stokes’ Theorem, Green’s Theorem and applications. May not be used for degree credit with MATH 5063.Prerequisite(s): MATH 2163 and MATH 3013 with grades of 'C' or better.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

A continuation of MATH 2153, including differential and integral calculus of functions of several variables and an introduction to vector analysis.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Basic topology of the plane, functions of a complex variable, analytic functions, transformations, infinite series, integration and conformal mapping.Prerequisite(s): MATH 4153 or MATH 5053.

A continuation of MATH 2153, including differential and integral calculus of functions of several variables and an introduction to vector analysis.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Measure theory, measurable functions, integration and differentiation of functions.Prerequisite(s): MATH 4153 or MATH 5053.

A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and hermitian forms, and dual spaces. Honors and regular sections are offered and meet with MATH 5023. May not be used for degree credit with MATH 5023.Prerequisite(s): MATH 3013 and MATH 3613 with grades of “C” or better; grades of “B” or better recommended.

A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and Hermitian forms, and dual spaces. Meets with MATH 4063. May not be used for degree credit with MATH 4063.Prerequisite(s): MATH 3013 and MATH 3613 with grades of “C” or better; grades of “B” or better recommended.

A rigorous treatment of vector spaces, linear transformations, determinants, orthogonal and unitary transformations, canonical forms, bilinear and hermitian forms, and dual spaces. Honors and regular sections are offered and meet with MATH 5023. May not be used for degree credit with MATH 5023.Prerequisite(s): MATH 3013 and MATH 3613 with grades of “C” or better; grades of “B” or better recommended.

A continuation of MATH 2153, including differential and integral calculus of functions of several variables and an introduction to vector analysis.Prerequisite(s): MATH 2153 with grade of 'C' or better.

An introduction to analysis of functions of one real variable emphasizing the reading and writing of mathematical proof. Basic logic, set theory, functions and relations, cardinality of sets. Structure of the real numbers, completeness, open and closed sets, compact sets. Convergence of sequences bounded and monotone sequences, subsequences. Limits of functions, continuity. May not be used for degree credit with MATH 4023.Prerequisite(s): MATH 2153 and MATH 3613 with grades of 'C' or better, or consent of instructor.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

An introduction to analysis of functions of one real variable emphasizing the reading and writing of mathematical proof. Basic logic, set theory, functions and relations, cardinality of sets. Structure of the real numbers, completeness, open and closed sets, compact sets. Convergence of sequences bounded and monotone sequences, subsequences. Limits of functions, continuity. May not be used for degree credit with MATH 5073.Prerequisite(s): MATH 2153 and MATH 3613 with grades of 'C' or better, or consent of instructor.

An introduction to analysis of functions of one real variable emphasizing the reading and writing of mathematical proof. Basic logic, set theory, functions and relations, cardinality of sets. Structure of the real numbers, completeness, open and closed sets, compact sets. Convergence of sequences bounded and monotone sequences, subsequences. Limits of functions, continuity. May not be used for degree credit with MATH 4023.Prerequisite(s): MATH 2153 and MATH 3613 with grades of 'C' or better, or consent of instructor.