Doctor of Philosophy in Mathematics Active
Course Units 10
Abstract Algebra
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Applications of Abstract Algebra
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Group Actions
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Group Homomorphisms and Isomorphisms
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Introduction to Groups
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Linear Transformations and Matrices
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Polynomial Rings
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Rings and Fields
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Subgroups and Lagrange's Theorem
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Vector Spaces
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Advanced Calculus
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Applications of Derivatives
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Differential Equations
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Differentiation Techniques
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Integration Methods
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Limits and Continuity
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Multivariable Calculus
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Taylor Series and Maclaurin Series
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Vector Calculus
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Differential Geometry
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Curvature and Torsion
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Curves in Space
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Differential Forms and Exterior Calculus
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Geodesics and Minimal Surfaces
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Introduction to Differential Geometry
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Lie Groups and Lie Algebras
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Riemannian Geometry
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Surfaces in Euclidean Space
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Functional Analysis
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Applications of Functional Analysis
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Banach Spaces and Hilbert Spaces
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Distributions and Sobolev Spaces
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Fourier Analysis
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Introduction to Functional Analysis
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Linear Operators and Functionals
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Metric Spaces and Normed Spaces
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Linear Algebra
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Determinants and Inverses
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Eigenvalues and Eigenvectors
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Inner Product Spaces
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Introduction to Vectors
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Linear Transformations
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Matrix Operations
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Orthogonality
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Systems of Linear Equations
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Vector Spaces
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Mathematical Logic
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Applications of Mathematical Logic
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Formal Proofs
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Gödel's Incompleteness Theorems
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Inference Rules and Proofs
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Introduction to Mathematical Logic
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Logical Equivalences
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Predicate Logic
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Propositional Logic
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Set Theory and Logic
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