MAT315H1Y: Elementary Number Theory Summer 2021 University of Toronto
I. Instructor and Teaching Assistants Course Instructor
Name: Gaurav Digambar Pa0l
Email: gpa0l@math.toronto.edu
Office Hours: Thursdays 12:00pm-2:00pm, By appointment
TA(s)
Name: Nicolo Fellini, Ali Pirhosseinloo
Email: n.fellini@mail.utoronto.ca, ali.pirhosseinloo@mail.utoronto.ca
Office Hours (on Piazza): Nick Fellini Fridays 2pm-4pm, Ali Pirhosseinloo Wednesdays 12pm-2pm
II. Course Overview
Course DescripMon
Elementary topics in number theory: divisibility; arithme7c func7ons; the residue classes modulo m and the structure of unit group; Hensel’s Lemma; quadra7c reciprocity law, representa7on of numbers as sums of squares; Gaussian integers.
Prerequisites
(MAT223H1/ MATA23H3/MAT223H5/MAT240H1/ MAT240H5, MAT235Y1/ MAT235Y5/(MATB41H3, MATB42H3)/MAT237Y1/ (MATB41H3, MATB42H3, MATB43H3)/MAT237Y5, MAT246H1/ CSC236H1/ CSC240H1)/MAT157Y1/ MAT157Y5/MAT247H1/ MAT247H5
Textbooks/ Course Readings
Main Textbook: Elementary Number theory by Gareth A. Jones and J. Mary Jones.
Other reference books: A comprehensive introducMon to Number Theory-Alan Baker, An introducMon to the theory of numbers-Ivan Niven/ Herbert S. Zuckerman and Hugh L. Montgomery, An introducMon to the theory of numbers-Hardy and Wright. A friendly introducMon to number theory-Silverman.
Course Website
hBps://q.utoronto.ca/courses/219785
How this course is organized:
This course will consist of three weekly one hour lectures and a weekly tutorial. Due to the Covid-19 pandemic, all components of the course will be delivered online synchronously/ asynchronously on Zoom. Lectures will be recorded and posted on the course site following each class.
.
Technical Requirements
In order to par0cipate in this course, students will be required to have:
• Reliable internet access. It is recommended that students have a high speed broadband connec0on
(LAN, Cable, or DSL) with a minimum download speed of 5 Mbps.
• A computer sa0sfying the minimum technical requirements (haps://
www.viceprovoststudents.utoronto.ca/covid-19/tech-requirements-online-learning/)
Other recommended items include headphones, microphone, webcam, and a tablet.
If you are facing financial hardship and are unable to meet these requirements, you are encouraged to contact your college or divisional registrar (haps://future.utoronto.ca/current-students/registrars/) to apply for an emergency bursary so that you can obtain the required items.
III. EvaluaMon/ Grading Scheme Mark Breakdown
Weekly Quizzes 10% Assignments 60% Midterm Assessment 10% Final Assessment 20%
Weekly Quizzes
There will be weekly quizzes on Quercus. There will about 9-11 of them all of which will count towards your grade. You will be given a period of 24 hours to aaempt a quiz. (You will only have three hours once you begin. Though these should be short and not require more than half an hour.)
Assignments
There will be 6 assignments on crowd mark, of which the one with lowest grades will be dropped (late submissions will receive a mark of zero).
Problem Set 1 due May 16, 10:00 pm Problem Set 2 due May 30, 10:00 pm Problem Set 3 due June 13, 10:00 pm Problem Set 4 due July 11, 10:00 pm Problem Set 5 due July 25, 10:00 pm Problem Set 6 due August 8, 10:00 pm
Midterm Assessment
The Midterm Assessment will be held on June 22, 12:00pm to June 23, 12:00pm
Final Assessment
The final assessment will be held during the final assessment period in June/August 2021 and will be scheduled by the registrar. Informa0on about the format will be provided during the semester.
IV. Course Policies
Policy on Missed Term Work: As flexibility for missed or late course assignments have been built into the
marking scheme, late and missed assignments will not be accepted for any reason.
Please note that Verifica0on of Illness forms (also known as a “doctor’s note”) are temporarily not required. Students who are absent from class for any reason (e.g., COVID, cold, flu and other illness or injury, family situa0on) and who require considera0on for missed academic work should report their absence through the online absence declara0on. The declara0on is available on ACORN under the Profile and Seongs menu.
If you miss the midterm or the final assessment, then you must inform your course Instructor within 72 hours of the test. No excep0ons. If your request is approved, you may receive an accommoda0on in the form of an oral exam, wriaen make-up test, or a re-weigh0ng of your assessments.
Email Policy:
Should you have a ques0on that is not answered on the course site (please check there first!) please note that all communica0ons with the Course Instructor or TA’s must be sent from your official utoronto email address, with the course number included in the subject line. If these instruc0ons are not followed, your email may not be responded to.
Online EMque`e/ParMcipaMon
Be Excellent to one another!
V. InsMtuMonal Policies and Support
Academic Integrity
All suspected cases of academic dishonesty will be inves0gated following procedures outlined in the Code of Behaviour on Academic Maaers (haps://governingcouncil.utoronto.ca/secretariat/policies/code-behaviour- academic-maaers-july-1-2019). If you have ques0ons or concerns about what cons0tutes appropriate academic behaviour or appropriate research and cita0on methods, please reach out to your Course Instructor. Note that you are expected to seek out addi0onal informa0on on academic integrity from me or from other ins0tu0onal resources (for example, the University of Toronto website on Academic Integrity hap://academicintegrity.utoronto.ca/).
Copyright
This course, including your par0cipa0on, will be recorded on video and will be available to students in the course for viewing remotely and arer each session.
Course videos and materials belong to your instructor, the University, and/or other sources depending on the specific facts of each situa0on and are protected by copyright. Do not download, copy, or share any course or student materials or videos without the explicit permission of the instructor.
For ques0ons about the recording and use of videos in which you appear, please contact your instructor.
Accessibility
The University provides academic accommoda0ons for students with disabili0es in accordance with the terms of the Ontario Human Rights Code. This occurs through a collabora0ve process that acknowledges a collec0ve obliga0on to develop an accessible learning environment that both meets the needs of students and preserves the essen0al academic requirements of the University’s courses and programs.
Students with diverse learning styles and needs are welcome in this course. If you have a disability that may require accommoda0ons, please feel free to approach your Course Instructor and/or the Accessibility Services office as soon as possible. The sooner you let us know your needs the quicker we can assist you in achieving your learning goals in this course.
Link to Accessibility Services website: haps://studentlife.utoronto.ca/department/accessibility-services/
Equity, Diversity and Inclusion
The University of Toronto is commiaed to equity, human rights and respect for diversity. All members of the learning environment in this course should strive to create an atmosphere of mutual respect where all
members of our community can express themselves, engage with each other, and respect one another’s differences. U of T does not condone discrimina0on or harassment against any persons or communi0es.
Important Academic Dates & Deadlines
The academic dates include enrolment dates, drop deadlines, exam periods, pe00on deadlines and more.
haps://www.artsci.utoronto.ca/current/dates-deadlines/academic-dates
Other Academic and Personal Supports
• Wri0ng Centre haps://wri0ng.utoronto.ca/wri0ng-centres/arts-and-science/
• U of T Libraries haps://onesearch.library.utoronto.ca/
• Feeling Distressed? haps://studentlife.utoronto.ca/task/support-when-you-feel-distressed/
• Academic Success Centre haps://studentlife.utoronto.ca/department/academic-success/
• College/Faculty Registrars haps://future.utoronto.ca/current-students/registrars/
AddiMonal Supports
– Geong Ready for Online: haps://onlinelearning.utoronto.ca/geong-ready-for-online/