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Study Sessions
Preparing for the Graduate Qualifying Examination at Washington State University.
Place: Hacker Lounge - Neill Hall 216
Time: Thursdays 6-8pm
- Exam Dates
- Fall: August 24
- Spring: Early January
We will meet to discuss problems and review the material covered on the exam. At least twice during the semester we will split into groups and develop practice tests.
Topics:
Advanced Calculus
Metric spaces, Cauchy sequences and completeness, limits, continuity, Intermediate Value Theorem, differentiation, Mean Value Theorem, Taylor's Theorem, L'Hospitâl's Rule, monotone functions, convexity and curvature, infinite series, sequences and series of functions, Fundamental Theorem of Calculus, Mean Value Theorem for integrals, improper integrals, partial and directional derivatives, Jacobian matrix, gradient vector, chain rule, Divergence Theorem, Stokes' Theorem, Inverse Function Theorem, Implicit Function Theorem, change of variables in multiple integrals, Lagrange multipliers
Linear Algebra
Basic matrix operations, properties of determinants, vector space, linear dependence and independence, basis and dimension, subspace, orthogonality, orthonormal basis, linear transformation, matrix representation, equivalence, similarity, range, null space (kernel), invertibility, invariant subspaces, eigenvalue and eigenvector, characteristic polynomial, projection, adjoint, Hermitian operator and unitary operator, norm, inner product, triangle inequality, Cauchy-Schwarz inequality
Image de-noising on the manifold of patches: a spectral approach