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MATHEMATICS 221
Fourier series and integrals, orthogonal functions, convergence in the mean, geometry
of Hilbert space.
Text: The Theory of Functions, Titchmarsh.
Instructor: Michal.
Ma. 209 a, b, c. Functionals and Functional Equations. 15 units; first,
second and third terms.
Prerequisite: Graduate standing in Mathematics, including a course in Analysis.
Functional operations; permutable functions, functions of composition; integral
equations, integro-differential equations; differentials of functionals, functional
equations with functional derivatives; infinite matrices; Stieltjes and Lebesgue
integrals; abstract spaces.
Instructor: Michal.
Ma. 251 a. Seminar (I) in Algebra and the Theory of Number •• 9 units;
first term.
Prerequisite: Graduate standing.
Topics selected to suit the class.
In charge: Bell.
Ma. 251 b. Mathematical Logic. 9 units; second term.
Instructor: Bell.
Ma. 251 c. Theory of Algebraic Numbers. 9 units; third term.
Prerequisite: Graduate standing.
Instructor: Bell.
Ma. 252 a, b, c. Seminar in Continuous Groups. 9 units; first, second
and third terms.
Prerequisite: Graduate standing in Mathematics.
Lie's theory of r-parameter groups; differential geometry of the group manifold.
Groups of functional transformations; invariant functionals; differential geometries
of function space •.
In charge: Michal.
Ma. 253. Seminar in Foundations of Abstract Algebra. 6 units; first,
lecond, and third terms.
Prerequisite: Graduate standing.
Lattice theory, Boolean rings and algebras. Decomposition theorems in rings and
hypercomplex systems.
In charge: Ward.
Ma. 254 a, b, c. Seminar in Modern Theorie. of Integration. 6 unitt;
first, second and third terms.
Prerequisite: Graduate standing in Mathematic., including a course in Function
Theory.
Stieltjes and Lebesgue integrals with applications to the algebra and geometry
of functionaIs.
In charge: Michal.
Ma. 255 a, b, c. Methods of Mathematical Physic •• 11 units; fint, second
and third terms.
Prerequisites: Ma. 8, 10.
Integral equations in which the kernel is a Green', function, Fourier series and
integrals, Sturm-Liouville functions. Methods of Volterra, Fredholm and Hilbert