MAT 3120 – Real Analysis
Real Analysis代写 In this course, we build on rudimentary proof-theoretic analysis, to explore the new settings of metric spaces and normed vector spaces.
Prerequisites:
MAT2125/2525 (Introduction to real analysis)
In this course, we build on rudimentary proof-theoretic analysis, to explore the new settings of metric spaces and normed vector spaces. This serves not only to reinforce the techniques of reasoning found in your previous analysis course, but also to see a unified approach to convergence and related notions.
Almost all results presented in class will be accompanied by a proof and students will be expected to do proofs on assignments and exams.
Tests and assignments: Real Analysis代写
o There will be 4 assignments and 1 midterm test. Assignments may include bonus questions, which can earn you extra marks.
o Late assignments will not be accepted, there will be no make-up midterm test, and no make-up quizzes. If you miss a midterm test or an assignment its weight will be automatically transferred to the final exam (no justification needed)1.
o If you do better at the final exam than any of the assignments, quizzes, or the midterm, then the grade for those assignments/quizzes/midterm test will be automatically replaced by the grade of the final exam.
o Your assignments and midterm will normally be handed back to you approximately one week after the test/assignment due date.
After this, they can always be picked up from the professor’s office during regular office hours.
o Assignments will be posted on Virtual Campus two weeks before they are due. Quizzes will be available one week before they are due.
Evaluation Scheme:
If the final exam grade is less than 45%, then your final grade is your final exam grade (regardless of your midterm/quiz/assignment grades).
If the final exam grade is more than or equal to 45%, then the total final grade is computed as follows:
4 Assignments: 20%
Midterm Exam: 30%, Final exam: 50%.
Midterm rules: Real Analysis代写
o The midterm will be held during the regular lecture time (10-11:20; 75 minutes) on Thursday October 29.
o Notes, calculators, and communication devices are not allowed.
o Students may not enter after 20 minutes have passed from the beginning of the midterm exam.
o Students must present their ID and student cards during the midterm.
o Any attempt at copying is treated as a case of academic fraud, as is the facilitation of copying by others. Students must take reasonable care to prevent others from copying their work.
Collaboration and academic fraud:
Students are encouraged to discuss assignment questions with each other, and even to work together towards a solution. However, students must generate their solution themselves, and understand what they write down. It is not allowed to copy another students solution or to allow another student to copy yours. It is not allowed to tell another student exactly how solve a problem. It is not allowed to copy your solution from anywhere else (e.g., a forum on the internet). You should acknowledge any assistance or collaboration, by writing, for example “[so-and-so] helped me with question X”, “[so-and-so] and I worked together on question Y”, “I consulted [wikipedia/other source] for help with question Z”. Please see the university’s regulations concerning academic fraud here:
http://www.uottawa.ca/academic-regulations/academic-fraud.html
Content of the course: Real Analysis代写
Metric spaces: definitions, examples, basic concepts (1-2 weeks).
Contractive mappings and fixed points (1 week). Topological concepts;
compactness (2-3 weeks). Completeness and the Baire categorytheorem (1-2 weeks). Normed vector spaces (3-4 weeks). Hilbert spaces (1 week).
Lecture notes:
Lecture notes written by Prof. Savage are available on Virtual Campus, and may be purchased from the DocUcentre. Reading the course notes is advised, but it is not a substitute for coming to the lectures and taking your own notes. There will be some departures from the course notes, most notably:
- We will not discuss topological spaces in much detail (although we will talk about topological concepts, such as open and closed sets, in the context of metric spaces)
- The topic of the Baire category theorem is not in the notes. I will type up separate notes for this topic and put them on Virtual Campus.
Textbooks: Real Analysis代写
The following supplementary textbooks are recommended (but optional):
- W.A. Sutherland. Introduction to metric and topological spaces. Oxford University Press
- G.L. Cohen. A course in modern analysis and its applications. Cambridge University Press
Need help?
o If you have difficulties with the material presented in the course, please see your professor during office hours or make an appointment by e-mail.
o Students who require accommodations or academic support because of learning disabilities, health, psychiatric or physical conditions, are invited to register with the Access Service:
in person: UCU 339 / by Telephone: 562-5976 / via TTY: 562-5214 / by E-mail: adapt@uottawa.ca
