Back to Mark McLean's Homepage

MAT 324: Real Analysis

General information about the course


Date Topic Reading Assignments
Aug 28 Introduction, Riemann Integration 1 Homework 1
Solutions
Aug 30 Null Sets, Outer Measure 2.1, 2.2
Sept 4 Lebesgue Measure, σ-fields 2.3 Homework 2
Solutions
Sept 6 Properties of Lebesgue Measure 2.4 Homework 1 due at 10:00am in Physics P-124.
Sept 11 Borel Measure. 2.5. Homework 3
Solutions
Sept 13 Probability Spaces,
Measurable Functions
2.6,2.7,
3.1,3.2,3.3
Homework 2 due at 10:00am in Physics P-124.
Sept 18 Properties of Measurable Functions 3.4 Homework 4
Solutions
Sept 20 Random Variables, Probability Distributions, Independence of Random Variables 3.5 Homework 3 due at 10:00am in Physics P-124.
Sept 25 Lebesgue Integral of non-negative measurable functions 4.1 Homework 5
Solutions
Sept 27 Monotone Convergence Theorems. 4.2 Homework 4 due at 10:00am in Physics P-124.
Oct 2 Integrable Functions. 4.3 Homework 6
Solutions
Oct 4 Dominated Convergence Theorem. 4.4 Homework 5 due at 10:00am in Physics P-124.
Oct 9 No Classes in Session
Oct 11 Relation to Riemann Integral 4.5
Oct 16 Approximation of measurable functions 4.6
Oct 18 Probability 4.7 Homework 6 due at 10:00am in Physics P-124.
Oct 23 L1 spaces. 5.1
Oct 25 Midterm Exam 10-11:20am in Physics P-124
Exam (Solutions)
Covers: 1,
2.1-2.7,
3.1-3.5,
4.1-4.7

Except: 2.6.3, 3.5.5, 4.7.4, 4.7.5
Practice 1, (Solutions)

Practice 2, (Solutions)
Oct 30 L2 spaces. 5.2 Homework 7
Solutions
Nov 1 Lp spaces. 5.3
Nov 6 Lp spaces continued. 5.3 Homework 8
Solutions
Nov 8 Product Measures Page 1-6 from here. Homework 7 due at 10:00am in Physics P-124.
Nov 13 Fubini's Theorem Page 6-9 from here. Homework 9
Solutions
Nov 15 Product Measures Continued. Page 9-12 from here. Homework 8 due at 10:00am in Physics P-124.
Nov 20 Joint Distributions 6.5.1,6.5.2
Nov 22 No Classes in Session
Nov 27 Joint Distributions continued.
Radon-Nikodym Theorem.
6.5.2,6.5.3
7.1
Homework 10
Solutions
Nov 29 Radon-Nikodym Theorem continued. 7.1,7.2 Homework 9 due at 10:00am in Physics P-124.
Dec 4 Radon-Nikodym Theorem continued and statement of the Lebesuge Decomposition Theorem. 7.2
Dec 6 Review Session Homework 10 due at 10:00am in Physics P-124.
Dec 20 Final Exam 8:00am-10:45am in Physics P-124. Exam Information Practice 1, (Solutions)

Practice 2

Practice 3 (Except Question 10).




Student Accessibility Support Center (SASC) Statement:
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the staff at the Student Accessibility Support Center (SASC). For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities.

Academic Integrity Statement:
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website, http://www.stonybrook.edu/commcms/academic_integrity/index.html.

Critical Incident Management Statement:
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.