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Course Criteria
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0.00 - 3.00 Credits
Semester: Fall of even years Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 818 and MTH 819 Description: Affine and projective algebraic varieties and their properties. Morphisms and singularities. Schemes and coherent sheaves. Sheaf cohomology and other related topics. Effective Dates: FALL 2004 - Open
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0.00 - 3.00 Credits
Semester: Spring of odd years Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 916 Description: Continuation of MTH 916. Effective Dates: SPRING 2005 - Open
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0.00 - 3.00 Credits
Semester: Spring of every year Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 828 Description: Hilbert spaces: Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators. Banach spaces: Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem. Effective Dates: FALL 1998 - Open View all versions of this course
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0.00 - 3.00 Credits
Semester: Fall of even years Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 829 and MTH 920 Description: Topological vector spaces, convexity, Krein-Milman theorem, Banach algebras, operators on Banach spaces, spectral theorem, C*-algebras. Effective Dates: FALL 1998 - Open View all versions of this course
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0.00 - 3.00 Credits
Semester: Fall of every year Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Description: Research on the learning and teaching of mathematics. Teaching, teacher and student learning, curriculum, and educational policy. Historical, philosophical, empirical, and theoretical perspectives. Interdepartmental With: Science and Mathematics Education, Counseling, Educational Psychology and Special Education, Teacher Education Administered By: Science and Mathematics Education Effective Dates: FALL 2005 - Open
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0.00 - 3.00 Credits
Semester: Spring of every year Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Prerequisite: SME 926 Description: Continuation of SME 926. Interdepartmental With: Science and Mathematics Education, Counseling, Educational Psychology and Special Education, Teacher Education Administered By: Science and Mathematics Education Effective Dates: FALL 2005 - Open
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0.00 - 3.00 Credits
Semester: Fall of every year Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 828 Description: Positive Borel measure, complex measures. Riesz representation theorem, Radon-Nikodym theorem, Lebesgue decomposition theorem. Differentiable transformations and change of variables, differentiation of measures, maximal functions. Effective Dates: FALL 1997 - Open
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0.00 - 3.00 Credits
Semester: Spring of every year Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 828 and MTH 829 Description: Phragmen-Lindelof method. Hadamard's theorem, Runge's thoerem, Weierstrass factorization theorem, Mittag-Leffler theorem, and Picard's theorem. Poisson integrals, Harnack's inequality, Dirichlet problem. Hp-spaces and Blaschke products. Effective Dates: FALL 1995 - Open
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0.00 - 3.00 Credits
Semester: Fall of even years Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 869 Description: Riemannian metrics, connections, curvature, geodesics. First and second variation, Jacobi fields, conjugate points. Rauch comparison theorems, Hodge theorem, Bochner technique, spinors. Further topics on curvature or submanifold theory. Effective Dates: SUMMER 2006 - Open View all versions of this course
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0.00 - 3.00 Credits
Semester: Spring of odd years Credits:Total Credits: 3 Lecture/Recitation/Discussion Hours: 3 3(3-0) Recommended Background: MTH 930 Description: Continuation of MTH 930. Effective Dates: SUMMER 2006 - Open View all versions of this course
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