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Math 623 Fall 2016

Real Analysis I

(archived course page from Fall 2016)

This class covers the basics of Lebesgue integration in n-dimensional Euclidean space (construction of the Lebesgue integral, covering lemmas, the Lebesgue differentiation theorem), measure spaces in general, basics of functional analysis (Hilbert and Banach spaces) and a bit of harmonic analysis (integral operators, inequalities). The topics covered permeate all areas of mathematics (from number theory to applied mathematics) and are essential to all mathematicians.

**Lectures:**MWF 1:25 pm - 2:15 pm at LGRT 1234.

**Office hours:**MW 3:00-5:00 pm, or by appointment.

**Virtual Office hours:**Thursday-Friday 9 am - 11 am.

**Textbook:**Real Analysis: Measure Theory, Integration and Hilbert Spaces, by E. Stein and R. Shakarchi. Princeton University Press.

### Grading policy:

Problem sets (12 total) 40%(Lowest 2 grades dropped, late homeworks are counted as zero)

Midterm: 20%

Special writing assignment 10%

Final 30%

### Problem Sets

Solve all problems, except those marked with a * (those are optional).Problem Set #1. Due Wednesday September 16th.

Problem Set #2. Due Wednesday September 23rd.

Problem Set #3. Due Wednesday September 30th.

Problem Set #4. Due Wednesday October 7th.

Problem Set #5. Due Friday October 16th.

Problem Set #6. Due Friday October 23st.

Problem Set #7. Due Friday October 30th.

Problem Set #8. Due Friday November 20th.

Problem Set #9. Due Monday December 7th.

Problem Set #10. Due Monday December 14th (optional problem set).

### Important dates

September 16th. Problem set #1 is due (and then problem sets will be due each week**uninterrupted**through the first week of November).

November 4th: Midterm will be from 5 to 8 pm (location TBA).

November 30th: Special writing assignment is due.

December 11th: Last day of classes.

December 17th: The day we find out if J.J. Abrams ruined/saved Star Wars.

December 18th: Final 1-3 pm (LGRT 1234)