, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions.
Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on , product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions.
M W F 1000-1050
T 1700-1750
R 1300-1350
F 1200-1250
Cohn, Donald, Measure Theory, Birkhäuser, 2nd ed, 2013, https://www.springer.com/us/book/9781461469551
Stein, Elias and Shakarchi, Rami, Real Analysis: Measure Theory, Integration, & Hilbert Spaces, Princeton Princeton University Press, 2005, ISBN 9781400835560.
Bogachev, Vladimir I., Measure Theory, Springer-Verlag, 2007, https://link.springer.com/book/10.1007/978-3-540-34514-5
| Homework | 25% | ||
| Midterm 1 | 15% | March 3 | 10:00-10:25 |
| Midterm 2 | 15% | March 17 | 10:00-10:25 |
| Final (take-home written) | 25% | April 17-18 | |
| Final (10-minute oral) | 20% | April 21 | 09:00-17:00 |
| Deferred | 45% | 09:00-11:00 |
Much of the learning in this course will be done outside the classroom, solving the exercises and homework problems. Discussion with your classmates on specific homework problems is encouraged provided that you clearly acknowledge collaborators on the last page of your assignment and that you independently write up your own solutions. Assignments may be submitted any time on or before the given due date. Assignments are weighted according to their length.
On exams, you must work independently; questions of interpretation should be directed to the instructor. There will be two closed book midterm examinations, each 25 minutes long. You may not consult any books, resources, or people during the exams in this course with the exception that my lecture notes may be consulted on the take-home final exam. Calculators and formula sheets are not allowed. You may not access any websites other than the Launch/eClass link in Smart Exam Monitor. Accessing any other URL will be flagged as a potential violation, which will require investigation.
Due to the stresses caused by the Covid-19 crisis, all students will be granted double time on all exams, so please set aside double time in your calendar!
By enrolling in this course, you agree to be available for the dates and times indicated above.
The midterm examinations will be proctored with Smart Exam Monitor (SEM). Students must use SEM for the exam, it is not optional; if an exam is submitted without using SEM, it may be rejected.
Students will be given an opportunity to test SEM beforehand. On the day of the exam, I recommend setting up SEM 10 minutes before the start of the exam, so that you can sort out any technical issues and start the exam promptly. Once SEM is activated, do not open up any other websites, even before the exam opens, or this will be flagged as a violation. Please don't use earbuds or headphones or any technology other than the laptop or desktop computer that you are using to access the quizzes and exams. The only URL you are allowed to open is the link to the eClass quiz. In the exceptional event that you need to contact me during the exam, you are allowed to email me through your U of A gmail account only (the access will get flagged, but I can override that). Your student photo I.D. will be required to establish your identity; you will also need a webcam and microphone. Electronic equipment other than the computer used for access cannot be used during an exam.
The final letter grade will be determined from the course mark based on an absolute standard, taking into the account the difficulty of the exams. Assigned grades are unofficial until approved by the Department of Mathematical and Statistical Sciences and Faculty of Science.
Students will not be allowed to begin an examination after it has been in progress for 30 minutes. Electronic equipment cannot be brought into examination rooms. Cell phones are to be turned off during lectures, labs and seminars. Cell phones are not to be brought to exams.
A student who cannot write the final examination due to incapacitating illness, severe domestic affliction, or other compelling reasons can apply for a deferred final examination. Such an application must be made to the student's Faculty office within two working days of the missed examination and must be supported by appropriate documentation or a Statutory Declaration. Deferred examinations are a privilege and not a right; there is no guarantee that a deferred examination will be granted. Misrepresentation of facts to gain a deferred examination is a serious breach of the Code of Student Behaviour.
There will be no deferred midterms.
Material related to this course, including sample midterm and final exams, will be posted on the web page noted above. Additional material may be occasionally sent by email to your official U of A email address. If you do not regularly read your U of A email, it is your responsibility to forward your U of A email to your preferred email account.
Audio or video recording, digital or otherwise, of lectures, labs, seminars or any other teaching environment by students is allowed only with the prior written consent of the instructor or as a part of an approved accommodation plan.
The lectures will be recorded and posted to eClass and deleted once the course is over. To access the recordings, click on Online Classroom and then Cloud Recordings (paste in the passcode that is automatically copied to your clipboard). These recordings are made available under the following conditions:
All forms of academic dishonesty are unacceptable at the University. Any suspected offence will be reported to the Faculty of Science. Anyone who is found in violation of the Code of Student Behaviour may receive a sanction. Typical sanctions include conduct probation, a mark reduction or a mark of zero on an assessment, a grade reduction or a grade of F in a course, a remark on the transcript, and a recommendation for suspension or expulsion.
Students are expected to familiarize themselves with the Academic Integrity resources (covering the topics of cheating, collaboration, plagiarism, and substantial assistance) on the website of the Office of the Dean of Students:
https://www.ualberta.ca/current-students/academic-resources/academic-integrity/index.html