2021 Winter: MATH 551, Introduction to Real Analysis
This is a new course that introduces the Lebesgue measure theory and
a few other topics in real analysis for advanced math undergraduates, masters students, and AIM and non-math Ph.D. students.
Prerequisites: Students should have a solid background in advanced Calculus (MATH 295, 297, or 451) and linear algebra (MATH 217 or 296).
We plan to cover (1) Lebesgue measure
on Rn, (2) Lebsegue integral, (3) differentiation, (4) Lebesgue-Stieltjes measure,
(5) product measures, (6) abstract metric spaces, and (7) Lp spaces.
We will cover about 2/3 of the book by Terry Tao, Introduction to Measure Theory
(which is also available as an online version on the author's website), and a few sections of Royden's book, Real Analysis.
There are some overlaps with MATH 597, alpha course for MATH Ph.D. students, but this course will proceed at a gentler pace and emphasize measures on Rn instead of general spaces.
Go to Canvas for current course information
- 2021 Winter: MATH 551, Introduction to Real Analysis
- 2020 Fall: Math/Stats 425, Introduction to Probability (2 sections)
- 2020 Winter: Math 710, Topics course in analysis; Random Matrix Theory
- 2019 Fall: Math 285, Honors Multivariable Calculus (2 sections)
- 2019 Winter: Math 525, Probability Theory (2 sections)
- 2018 Fall: Math 709, Topics in Analysis (Integrable Probability)
- 2018 Winter: Math 597, Analysis II (Real)
- 2016 Fall: Math 709, Topics in Analysis (Exactly solvable models in probability and statistical physics)
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2016 Fall: Math 596, Analysis I (Complex)
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2016 Winter: Math 597, Analysis II (Real)
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2015 Fall: Math 625, Probability and Random Processes I
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2015 Winter: Math 710, Topics in Analysis (Random Matrix Theory )
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2014 Fall: Math 596, Analysis I (Complex)
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2014 Winter: Math 215, Calculus III (2 sections)
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2013 Winter: Math 215, Calculus III (2 sections)
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2012 Fall: Math 596, Analysis I (Complex)
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2012 Winter: Math 316, Differential Equations
(2 sections)
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2011 Fall: Math 650, Fourier Analysis
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2010 Fall: Math/Stats 526 Discrete State Stochastic Processes (3 sections)
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2009 Fall: Math 709, Topics in Analysis (Random Matrix Theory)
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2009 Winter: Math/Stats 526 Discrete State Stochastic Processes (2 sections)
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2008 Fall: Math 596 Analysis I (complex)
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2008 Fall: Math/Stats 425 Introduction to Probability
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2008 Winter: Math/Stats 425 Introduction to Probability
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2008 Winter: Math 597 Analysis II (real)
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2007 Fall: Math 602 Real Analysis II (Functional Analysis)
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2006 Winter: Math/Stat 526 Discrete State Stochastic Processes
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2005 Fall: Math/Stat 525 Probability
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2004 Winter: Math 609 Toplics in Analysis (Random permutations and random matrices)
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2003 Fall: Math 555 Complex Variables and Applications
