Instructor: Doug Pickrell
Office: Mathematics 703
Office Phone: 621-4767
Email: pickrell@math.arizona.edu
Office Hours: TBA
Required Text: Real Analysis: Modern Techniques and Their Applications, by Gerald Folland, available online through the library. I will follow the outline of the text closely, and I will often refer to the text for details. Other useful texts: Lebesgue Integration on Euclidean Space by Frank Jones, Real and Complex Analysis by Walter Rudin, and Real Analysis by H.L. Royden.
Course Objectives: We will cover the basic definitions and theorems of abstract measure theory, with emphasis on Lebesgue measure and integration on Euclidean space. A minimum aim is to prepare everyone to high pass the real analysis qualifying exam.
More About the course: The basic prerequisite for the course is advanced calculus (limits and continuity, differentiation and (Riemann) integration, infinite series, uniform convergence, and the notion of a metric space). Chapter 0 summarizes the prerequisites for reading the book: (section 0.1) the language of set theory, (section 0.5) basic properties of the real numbers, and (section 0.6) the elementary properties of metric spaces. It is useful to have had some exposure to point set topology or probability, but not essential. We will aim to cover chapters 1-4 in the Fall semester. By the end of the Spring, we will aim to cover most of chapters 1-9.
Homework: I am tentatively planning on assigning homework weekly. I will email the homework assignments directly to you (It is essential that I have your email address). I will grade the homework on a very good, good, okay, not okay basis. I will email solutions for most of the problems on the due date.
Exams: There will be two midterms and a final exam. The dates of each midterm, and the material to be covered on each midterm, will be announced at least one week in advance in class and by email (The tentative dates for the midterms are TBA). The final exam is scheduled for Friday, December 10, 10:30-12:30.
Grades: The two midterms, the final exam, and the homework, will each count for 1/3 of the grade. ``A'' will mean that I believe you are on pace in preparing for the real analysis qualifying exam, ``B'' will mean that you are making significant progress, but are off pace in preparing for the exam.
Attendance: Students are expected to attend every scheduled class. • The UA’s policy concerning Class Attendance, Participation, and Administrative Drops is available at: http://catalog.arizona.edu/policy/class-attendance-participation-and-administrative-drop. • The UA’s policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable. See: http://policy.arizona.edu/human-resources/religious-accommodation-policy. • Absences pre-approved by the UA Dean of Students (or Dean Designee) will be honored. See: https://deanofstudents.arizona.edu/absences.
Classroom Behavior: To foster a positive learning environment, students and instructors have a shared responsibility. We want a safe, welcoming, and inclusive environment where all of us feel comfortable with each other and where we can challenge ourselves to succeed. To that end, our focus is on the tasks at hand and not on extraneous activities (texting, chatting, reading a newspaper, making phone calls, web surfing).
Communication: It is the student’s responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes, by email.
Students with disabilities: Our goal in this classroom is that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact the Disability Resource Center (520-621-3268) to establish reasonable accommodations. For additional information on the Disability Resource Center and reasonable accommodations, please visit http://drc.arizona.edu. If you have reasonable accommodations, please plan to meet with me by appointment or during office hours to discuss accommodations and how my course requirements and activities may impact your ability to fully participate. Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable.
Students withdrawing from the course: Must be made in accordance with University policy http://catalog.arizona.edu/policy/grades-and-grading-system#Withdrawal.
Incompletes: Must be made in accordance with University policies, which are available at http://catalog.arizona.edu/policy/grades-and-grading-system#incomplete
University Policies: • The UA Threatening Behavior by Students Policy prohibits threats of physical harm to any member of the University community, including to oneself. See http://policy.arizona.edu/education-and-student-affairs/threatening-behavior-students. • Students are encouraged to share intellectual views and discuss freely the principles and applications of course materials. However, graded work/exercises must be the product of independent effort unless otherwise instructed. Students are expected to adhere to the UA Code of Academic Integrity as described in the UA General Catalog. See: http://deanofstudents.arizona.edu/academic-integrity/students/academic-integrity. • The University is committed to creating and maintaining an environment free of discrimination; see http://policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy
Note: Information contained in the course syllabus, other than the grade and absence policy, may be subject to change with advance notice, as deemed appropriate by the instructor.