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Week
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Date
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Notes
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Homework
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Material
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1
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Jan 12
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Hwk #1
10.5: 33, 34, 37.
10.6: 38 (a-e), 39.
Due 1/21.
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Read chapter 10.
The plan is to cover 10.5-10.7
in the first week.
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2
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Jan 19
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Hwk #2
quotient
spaces
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The plan for the week is
to cover the Banach-Alaoglu theorem and then 10.7. We will discuss some
material on locally convex vector
spaces that is not in the book. As is often the case, wikipedia has a
nice page on
this subject.
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3
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Jan 26
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Hwk #3
10.7: 48, 49 (a-h).
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4
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Feb 2
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We'll meet from 1:30-2:45. |
Hwk #4
10.8: 51, 53.
11.1: 6, 8.
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We will be going over
11.1-11.4 this week (though possibly not covering all of it). The
topics are measures, sigma-algebras and convergence theorems that are
very similar to the ones we have discussed previously for Lebesgue
measure. So much of our study will be a review of these concepts with
small changes to accomodate the more general setting of an arbitrary
measure space.
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We'll meet from 1:30-2:45. |
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Feb 6
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I'll be out of town. So there's no class today. |
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5
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Feb 9
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I'll be out of town. So there's no class
today. |
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We'll meet from 1:30-2:45. |
Hwk #5
11.2: 12, 13.
11.3: 22.
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The plan is to cover
11.2-11.4.
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We will start studying the
decomposition theorems in 11.5-11.6. These are: the Hahn decomposition
theorem, the Jordan decomposition theorem and the Radon-Nykodym theorem.
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| 6 |
Feb 16
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President's Day. No class.
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We'll meet from 1:30-2:45 |
Hwk #6
11.5: 30, 31
11.6: 34.
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This week, the plan is to
finish the decomposition theorems of 11.5-11.6 and begin studying L^p
spaces. The material of L^p spaces will involve some review but the
proof of the main theorem, the Riesz representation theorem, will be
different.
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We'll finish up the
Radon-Nikodym theorem and start into L^p spaces.
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7
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Feb 23
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Hwk #7
11.6: 35.
11.7: 42, 45.
12.1: 2.
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We'll finish up L^p spaces
and begin 12.1, 12.2
After 12.2, the plan is to discuss some applications of Caratheodory's
extension theorem. Here are some notes.
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8
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Mar 2
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Hwk #8
12.2: 8, 9.
12.3: 14.
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9
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Mar 9
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We'll meet from 1:30-2:45 |
Hwk #9
12.4: 29, 30.
12.9: 54, 55d.
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We'll meet from 1:30-2:45 |
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10
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Mar 16
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I'll be out of town. So there's no class
today. |
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Homework
10. (due after spring break)
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11
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Mar 23
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Spring Break this week. No
class. |
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12
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Mar 30
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Homework
11. |
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13
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April 6
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We'll meet from 1:30-2:45 |
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We'll meet from 1:30-2:45 |
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April 10
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Good Friday. No class. |
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14
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April 13
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I'll be out of town. So
there's no class
today. |
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There will be a midterm from 1:30-2:45.
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I'll be out of town. So
there's no class
today. |
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15
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April 20
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We'll meet from 1:30-2:45 |
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Review.
Review
Problems.
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We'll meet from 1:30-2:45 |
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16
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April 27
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17
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May 4
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May 6
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last day of instruction |
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18
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May 11
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May 15
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Official Final time,
2:15-4:15pm. |
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