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UofT Real Analysis Course Guide

This document provides information about the MAT 337 H1S Introduction to Real Analysis course, including required textbooks, the instructor, grading policy, syllabus, academic integrity policies, and accessibility services. The course will cover topics such as the least upper bound principle, convergence of sequences, topology, functional limits, continuity, differentiation, integration, and the fundamental theorem of calculus. There will be 5 quizzes, 2 midterm exams, and a final exam. Students are expected to uphold the University's code of behavior on academic matters and should contact accessibility services if any accommodations are required.

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492 views2 pages

UofT Real Analysis Course Guide

This document provides information about the MAT 337 H1S Introduction to Real Analysis course, including required textbooks, the instructor, grading policy, syllabus, academic integrity policies, and accessibility services. The course will cover topics such as the least upper bound principle, convergence of sequences, topology, functional limits, continuity, differentiation, integration, and the fundamental theorem of calculus. There will be 5 quizzes, 2 midterm exams, and a final exam. Students are expected to uphold the University's code of behavior on academic matters and should contact accessibility services if any accommodations are required.

Uploaded by

JOHNATHAN WANG
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MAT 337 H1S Introduction to Real Analysis

Books:
“Understanding Analysis”, Second Edition by Stephen Abbott The textbook is provided as
a free electronic resource to all of the University of Toronto students through the library website:
http://myaccess.library.utoronto.ca/login?url=http://books.scholarsportal.info/viewdoc.html?id=/ebook
07-09/1/9781493927128
You maybe asked to enter your UTORid and password.

Supplementary Books:
“Principles of Mathematical Analysis”, by W. Rudin

Instructor
Regina Rotman 6262 Bahen Building
Office Hours Friday, 9:30-10:30, or by appointment
Grading Policy:
5 Quizzes 4 points each, 20 points in total
written in the tutorials based on the suggested problems
Two Midterm Exams 20 points each towards the final grade
Final Exam 40 points towards the final grade
Syllabus:
Sep. 6 Review (sections 1.1-1.2)
Sep. 9 The Least Upper Bound Principle, Convergence of Sequences
(sections 1.3, 1.4)
Sep. 16 Sequences and Series (sections 2.1-2.7 )
Sep. 23 Topology of lR: The Cantor Set, Open and Closed Sets, Inte-
rior, Exterior, and Border Points, Compact Sets (sections 3.1
- 3.3)
Sep. 30 Perfect Sets, Connected Sets, Heine-Borel Theorem. Baire’s
Theorem (sections 3.3-3.5)
Oct. 7 Functional Limits (sections 4.1-4.2), October 11: Midterm
Exam
Oct. 14 Continuity and Compact Sets, Uniform continuity (sections
4.3-4.4, 4.6)
Oct. 21 The Intermediate Value Theorem, Differentiability, The Mean
Value Theorem (sections, 4.5, 5.2, 5.3 )
Oct. 28 Nondifferentiability, (section 5.4), Sequences and Series of
Functions, (section 6.1)
Nov. 11 Uniform Convergence, Uniform Convergence and Differentia-
tion (sections 6.2, 6.3), November 15: Midterm Exam
Nov. 18 Power Series, Riemann Integration (sections 7.2, 7.3, 7.4)
Nov. 25 The Fundamental Theorem of Calculus, Lebesgue’s Criterion
for Riemann Integrability (sections 7.5, 7.6)
Dec. 2 Review
Academic Integrity: Plagiarism is a form of academic fraud and is treated
very seriously. The work that you submit must be your own and cannot con-
tain anyone else’s work or ideas without proper attribution. Familiarize yourself
with the University of Toronto Code of Behaviour on Academic Matters, available at
http://www.governingcouncil.utoronto.ca/policies/behaveac.htm You are expected to know
these rules. Keep in mind that not being aware of a rule is not an acceptable excuse for
not having followed it. Potential offences include, but are not limited to:
Using or possessing unauthorized aids during an exam or test;
Looking at someone else’s answers during an exam or test;
Misrepresenting your identity;
Falsifying institutional documents or grades;
Falsifying or altering any documentation required by the University, including (but not limited
to) doctor’s notes;
Both receiving and providing unauthorized assistance is an academic offence.
The University of Toronto treats cases of academic misconduct very seriously. All suspected
cases of academic dishonesty will be investigated following the procedures outlined in the Code.
The consequences for academic misconduct can be severe, including a failure in the course and
a notation on your transcript.
Accessibility Needs: The University of Toronto is committed to accessibility. If you
require accommodations for a disability, or have any accessibility concerns about the course,
the classroom or course materials, please contact Accessibility Services as soon as possible at
http://www.studentlife.utoronto.ca/as

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