MWF 2:00 - 4:00 pm or by appointment.
I plan to keep an up-to-date list of the topics, examples etc. covered in class.
Lecture #
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Date
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Material covered / special events
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Remarks/ additional material
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WELCOME TO MATH 418/516 !!
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1
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Wed 4 Sep
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Preliminaries: linear algebra; the contraction mapping theorem.
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Handout: Preliminaries.
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2
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Fri 6 Sep
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Preliminaries: metric topology, completeness and completion(s), compactness.
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3
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Mon 9 Sep
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Convex sets and functions. Normed spaces.
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4
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Wed 11 Sep
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Basic properties of norms. Banach spaces.
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5
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Fri 13 Sep
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First examples.
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Homework #1 posted on eClass - due 25 September.
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6
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Mon 16 Sep
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Series in normed spaces: (absolute; unconditional)
convergence; summability.
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7
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Wed 18 Sep
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Quotients and products. More examples.
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8
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Fri 20 Sep
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L^p spaces - a very brief review.
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9
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Mon 23 Sep
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Finite- vs. infinite-dimensional spaces. Equivalent norms.
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10
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Wed 25 Sep
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Riesz lemma. Characterizations of
finite-dimensionality. Examples.
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11
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Fri 27 Sep
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Schauder bases. Linear operator basics.
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Homework #2 posted on eClass - due 16 October.
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12
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Mon 30 Sep
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Spaces of linear operators.
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13
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Wed 2 Oct
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Examples. (Isometrically) isomorphic spaces.
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14
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Fri 4 Oct
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Banach-Mazur distance. Dual spaces.
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15
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Mon 7 Oct
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Dual operators. Examples.
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16
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Wed 9 Oct
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Extending linear functionals.
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17
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Fri 11 Oct
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The Hahn-Banach Theorem.
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Mon 14 Oct
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No class.
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Happy Thanksgiving! |
18
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Wed 16 Oct
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The bidual. Reflexive spaces. The uniform boundedness theorem.
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Homework #2 deadline extended to
4pm on 18 October.
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19
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Fri 18 Oct
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The Banach-Steinhaus and open mapping theorems.
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Homework #3 posted on eClass - due 6
November.
Practice midterm I posted on eClass.
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20
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Mon 21 Oct
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The closed graph theorem. Applications.
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Wed 23 Oct
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MIDTERM TEST 1.
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Good luck!!
Model solutions posted on eClass.
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21
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Fri 25 Oct
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The dual of C[0,1].
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22
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Mon 28 Oct
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Complemented subspaces. Consistent summation schemes.
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23
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Wed 30 Oct
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Semi-inner products.
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24
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Fri 1 Nov
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The Cauchy-Schwarz inequality and the parallelogram law.
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25
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Mon 4 Nov
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Examples. Orthogonality and the closest point property.
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26
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Wed 6 Nov
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Orthogonal complements and projections.
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Homework #4 posted on eClass - due 20
November.
Graduate project posted on eClass - due 6
December (last day of class).
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27
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Fri 8 Nov
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The Fréchet-Riesz theorem. Orthonormal systems.
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Enjoy Reading Week. |
28
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Mon 18 Nov
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Orthonormal bases. Examples.
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29
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Wed 20 Nov
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Orthonormal bases in L2[0,1].
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Homework #5 posted on eClass - due 6 December.
Practice midterm II posted on eClass.
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30
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Fri 22 Nov
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Fejér's Theorem and some consequences.
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31
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Mon 25 Nov
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Classical Fourier series.
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Wed 27 Nov
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MIDTERM TEST 2.
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Good luck!!
Model solutions posted on eClass.
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32
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Fri 29 Nov
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Linear operators on Hilbert spaces.
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Please consider
completing the online MATH 418/516 course survey. It only takes a
few minutes. Thank you. |
33
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Mon 2 Dec
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The spectrum. Definitions and examples.
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34
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Wed 4 Dec
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Properties of the spectrum.
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35
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Fri 6 Dec
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The spectral radius. Concluding
remarks.
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Good bye and good
luck !! |
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Fri 13 Dec
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office hours (also for MATH 201):
10am - 3pm in CAB 683.
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Mon 16 Dec
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office hours:
2pm - 5pm in CAB 683.
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Tue 17 Dec
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Final exam !
Please see box on the left for details.
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Good luck !! |
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