Course Instructor:
Cristian E. Gutierrez
Instructor Email:
gutierre@temple.edu
Course Materials:
Textbook: “Measure and Integral: An Introduction to Real Analysis", Second Edition, by R. Wheeden and A. Zygmund (Chapman & Hall/CRC Pure and Applied Mathematics) ISBN-13: 978-1498702898.
Course grading scheme:
There will be regular homework assignments (20%), which must be uploaded online to Canvas; two midterms (25% each) October 1 and November 5; and a final exam (30%) December 10.
Course prerequisites:
Basic knowledge of real variables and Euclidean topology, sequences of functions, and Riemann integration.
Course goals:
This is the first semester of a year-long course covering the core areas of analysis. It focuses on the development of Lebesgue's measure and integration theory, differentiation, abstract measures and integration, Hilbert spaces, basic functional analysis, and Hausdorff's measure. Emphasis will be on exercises and problems. The course will prepare students to take the Real Analysis section of the qualifying exam.
Topics covered:
1. Functions of bounded variation and Riemann-Stieltjes integral
2. Lebesgue measure and outer measure
3. Lebesgue measurable functions
4. Lebesgue integral
5. Fubini's theorem
Exam dates:
Midterm 1: October 1
Midterm 2: November 5
Final Exam: December 10
Technology Specifications for this Course:
This is a registered Canvas course. All information and assignments will be regularly posted there.
Course materials
Textbook: “Measure and Integral: An Introduction to Real Analysis", Second Edition, by R. Wheeden and A. Zygmund (Chapman & Hall/CRC Pure and Applied Mathematics) ISBN-13: 978-1498702898.
Course grading scheme
There will be regular homework assignments (20%), which must be uploaded online to Canvas; two midterms (25% each) October 1 and November 5; and a final exam (30%) December 10.
Course prerequisites
Basic knowledge of real variables and Euclidean topology, sequences of functions, and Riemann integration.
Course goals
This is the first semester of a year-long course covering the core areas of analysis. It focuses on the development of Lebesgue's measure and integration theory, differentiation, abstract measures and integration, Hilbert spaces, basic functional analysis, and Hausdorff's measure. Emphasis will be on exercises and problems. The course will prepare students to take the Real Analysis section of the qualifying exam.
Description of topics covered
1. Functions of bounded variation and Riemann-Stieltjes integral
2. Lebesgue measure and outer measure
3. Lebesgue measurable functions
4. Lebesgue integral
5. Fubini's theorem
Exam dates
Midterm 1: October 1
Midterm 2: November 5
Final Exam: December 10
Technology Specifications for this Course
This is a registered Canvas course. All information and assignments will be regularly posted there.
Course Instructor
Cristian E. Gutierrez
Instructor Email
gutierre@temple.edu