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instructor |
Prof. Alec N. Kercheval |
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contact me |
113 Love Building; 644-8701 (office); 644-2202 (front desk) webpage: http://www.math.fsu.edu/~kercheva/ |
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office hours | MW 2:30-3:30, R 4:30-5 | ||
eligibility |
This is a beginning graduate-level course in real analysis. You should have taken advanced calculus and be comfortable with writing proofs at the level of an upper division math major. | ||
texts |
Required: H.L. Royden and P.M. Fitzpatrick, Real Analysis, 4th Editon,
Prentice-Hall, 2010. Supplementary: G.B. Folland, Real Analysis, 2nd Edition, Wiley, 1999, and P. Billingsley, Probability and Measure, 3rd Edition, Wiley, 1995. |
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objectives |
This course contains a part of the common culture of mathematics that every graduate student in mathematics should study and every mathematician should know. It represents the culminating point of view on the real number system that began back in calculus, and is required background for anyone wishing to understand current research in analysis, probability, stochastic processes, and differential equations. The purpose of the course is to give the student a foundation for research in analysis or further study in applications. In this first semester we will aim to discuss most of the core topics, including sigma-algebras and the monotone class theorem, Caratheodory's construction of Lebesgue measure on the real line, measurable functions and Littlewood's three principles, Lebesgue integration and convergence theorems, bounded variation and absolute continuity, n-dimensional Lebesgue measure and integration, probability measures, conditional expectation and independence, signed measures and the Radon-Nikodym theorem, product measures and Fubini's theorem, L^p spaces as time permits. In the second semester we will finish discussion of the core topics and address some further topics from among Fourier Analysis, distribution theory, weak convergence and the central limit theorem, geometric measure theory, selected topics in probabiltiy and stochastic processes. |
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homework |
Homework will be assigned regularly and discussed in class. First Assignment: Page 31, #1-4. |
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exams
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There will be a one hour midterm exam on a date
to be announced, and a comprehensive final exam at the
University's designated final examination time:
Friday, December 14, 10:00 am -- 12 noon.
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grading |
Your course grade will be a weighted average of total homework grade (25%), midterm grade (25%), and final exam grade (50%). Faithful attendance is expected. Borderline grades will be resolved positively by good class participation and negatively by inconsistent attendance. | ||
makeups |
No written makeups are given. An unexcused missed exam receives a zero.
Those with prior permission or sufficient documentation
will substitute an oral exam. |
FSU Academic Honor Policy: The Florida State University Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ''. . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University.'' (Florida State University Academic Honor Policy, found at http://dof.fsu.edu/honorpolicy.htm.)
In this class, you are permitted to work together with classmates on homework problems, but you must turn in only work written by yourself. All exams and any other assignments must reflect only your own work unassisted by others.
University Attendance Policy: Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.
Americans With Disabilities Act: Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center (SDRC) and (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.
This syllabus and other class materials are available in alternative format upon request.
For more information about services available to FSU students with disabilities, contact: SDRC, 874 Traditions Way, 108 Student Services Building, FSU, Tallahassee, FL 32306-4167, (850) 644-9566 (voice), (850) 644-8504 (TDD), sdrc@admin.fsu.edu, http://www.disabilitycenter.fsu.edu
Syllabus Change Policy: Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.