Welcome to Number Theory! I’m looking forward to meeting you all and starting our work together. Please let me know if you have any questions at all, about our course or anything else.
Instructor Information
- Name: Dr. Joshua Wiscons (he/him/his)
- Email: joshua.wiscons@csus.edu
- Physical office: Brighton Hall (BRH) Room 144
- Virtual office: csus.zoom.us/my/jwiscons
- Student office hours:
Course Information
Meetings and books
- Class times: Our class meets Mondays and Wednesdays from 1:30–2:45 PM.
- Class location: Our class meets via Zoom at the times listed above. Details and links are in our Canvas course.
- Book: Elementary Number Theory, Second Edition (Dover Books on Mathematics); by Underwood Dudley.
Catalog Description
Theory of divisibility; some number theoretical functions; congruencies (linear and quadratic); some Diophantine equations. Simple continued fractions. This is a 3 unit class.
Prerequisites
Students should have successfully completed Calculus 2 (Math 31) with a grade of C- or better before taking this course. If you have any questions or concerns about this prerequisite, please check in with me as soon as possible.
Learning Outcomes
In this course, students will (1) increase their capacity for critical thinking and fact-based reasoning, (2) develop the necessary competency with the concepts and mechanics of basic number theory for further work in mathematics and other fields, and (3) improve their written and oral communication of mathematics. Specific content outcomes are to
- understand basic properties of integers including divisibility and unique factorization;
- be able to solve Diophantine equations;
- understand congruences, congruence arithmetic, and be able to solve linear congruence equations;
- know basic theorems in number theory, such as Fermat’s, Wilson’s, and Euler’s Theorems;
- understand number theoretic functions such as the number of divisors of an integer; and
- know what a primitive root is and be able to find primitive roots.
Community Agreement
Members of this class represent a rich variety of backgrounds and perspectives. Our class commits to providing an atmosphere for learning that respects diversity and recognizes it as a source of strength. While working together to build this intellectual community, we ask all members to:
- share their unique experiences, values, and beliefs;
- be open to the views of others and honor the uniqueness of their colleagues;
- appreciate the opportunity that we have to learn from each other in this community; and
- value each other’s opinions and communicate in a respectful manner.
We will further develop this agreement together in class.
Course Components
Homework
Homework assignments usually consist of a mixture of computations and proofs. You are allowed and encouraged to work together, but please write up your solutions on your own. Please take care that your work is well-organized and fully-justified with proper grammar, punctuation, and spelling. I’m happy to discuss any aspect of any problem!
Completed assignments are to be submitted via Canvas by the posted due date and time. You may write your solutions on paper and then scan them into one pdf document with a phone. If you have a tablet to write your solutions on, that is fine too. You are also welcome to type up your solutions if you prefer. Please let me know if you have any questions.
Participation
Our class will benefit greatly from the perspective, questions, and comments of each student. I will try to make space for various ways to bring your voice to our class, but your grade for this component will based our your participation in Discussions Boards taking place in Canvas.
Exams
There are 2 take-home midterm exams. They are tentatively scheduled to start on Oct. 08 and Nov. 12, each due two days later. There is also a take-home Final Exam. It will be due at the end of our final exam time: Monday, Dec. 13 from 12:45-2:45 PM.
Course Policies and Accommodations
Grade composition
Overall grades for the course will be determined from the course components listed above with the following weighting:
- Homework 25%
- Participation 10%
- Midterm Exams 40% (20% x 2)
- Final 25%
The maximum cutoff for letter grades will be: A- 90%, B- 80%, C- 70%, D- 60%, F 59–0%.
Attendance
Please come to class as much as possible! Our community will benefit greatly from a breadth of perspectives, and class will provide an opportunity to ask, clarify, and answer questions. However, I know that you all have varied and often challenging things going on in and beyond school, so missed classes will NOT affect your grade. If you need to miss class, please send me a quick email in advance, so I know what is going on.
Late assignments
Please strive hard to meet the deadlines, but if you need an extension for any reason, I am always happy to discuss it with you. Health related reasons will always be accommodated. Please send me a quick email as soon as you realize that extra time is needed—I really want you to be successful! Although late assignments may be subject to a reduced grade, I will usually grant short extensions with no penalty.
Accommodations
If you know or think that you might need academic adjustments or accommodations, of any kind, please speak with me privately as soon as possible. If you have one, please bring a copy of your accommodation letter from the Services to Students with Disabilities (SSWD) office. All discussions will remain confidential.
Sickness
If you are sick, please do not attend any of your in-person classes, but do let your instructors know. If you are experiencing any COVID-like symptoms (fever, cough, sore throat, muscle aches, loss of smell or taste, nausea, diarrhea, or headache) or have had exposure to someone who has tested positive for COVID, please contact Student Health & Counseling Services (SHCS) at 916-278-6461 to receive guidance and/or medical care.
Academic Honesty
Academic dishonesty (including cheating and plagiarism) will result in disciplinary action and will be reported to the Office of Student Conduct. If you are unsure what constitutes cheating, please speak with me and review Sacramento State’s Academic Honesty Policy and Procedures document here: www.csus.edu/umanual/student/stu-0100.htm.
Technology
The emphasis of this course is on conceptual understanding. You may use calculators and/or computer software programs on the homework assignments unless otherwise stated. I’m a big fan of Desmos for graphing and WolframAlpha for other computations.
Getting Extra Help.
Please come talk with me if you have any questions! The (Virtual) Math Lab provides free assistance to students in lower-division mathematics/statistics courses, but they might be able to help with this course too.
Schedule of Topics
This is a rough schedule of what we will cover, but please be aware that it is subject to change. The section numbers refer to our book.
| Week | Topics |
|---|---|
| 1 | Introductions + Integers (Section 1) |
| 2 | Labor day (no class on 09/06) + Integers (Section 1) |
| 3 | Unique Factorization (Section 2) |
| 4 | Linear Diophantine Equations (Section 3) |
| 5 | Congruences (Section 4) |
| 6 | Linear Congruences (Section 5) + Exam 1 (take home) |
| 7 | Linear Congruences (Section 5) + Fermat’s Theorem (Section 6) |
| 8 | Wilson’s Theorem (Section 6) + Cryptography (supplemental notes) |
| 9 | Cryptography (supplemental notes) + Divisors (Section 7) |
| 10 | Divisors (Section 7) + Euler’s Theorem (Section 9) |
| 11 | Primitive Roots (Section 10) + Exam 2 (take home) |
| 12 | Primitive Roots (Section 10) |
| 13 | Quadratic Congruences and Quadratic Reciprocity (Section 11) |
| 14 | Quadratic Congruences and Quadratic Reciprocity (Section 11) |
| 15 | Pythagorean Triples (Section 16) |
| 16 | Final Exam (take home) |
Student Resources
Crisis Assistance & Resource Education Support (CARES)
If you are experiencing challenges with food, housing, financial or other unique circumstances that are impacting your education, help is just a phone call (916-278-5138) or email (cares@csus.edu) away. The CARES office provides case management support for any enrolled student.
Learn more about your options and resources here: www.csus.edu/student-affairs/crisis-assistance-resource-education-support
Basic Needs Support
The ASI Food Pantry provides food and basic necessities to Sac State students in need at no cost. You just need to present a valid student OneCard. You can also utilize the Sacramento Food Bank & Family Services (SFBFS). In fact, SFBFS offers more than just food. From clothing for a newborn baby or a teenager heading out on a job interview, to Immigration Legal Services or English as a Second Language classes, and more, SFBFS is proud to offer support to the people of Sacramento County in a variety of different ways.
Learn more here:
- ASI Food Pantry: www.asi.csus.edu/programs/food-pantry
- SFBFS: www.sacramentofoodbank.org
Sexual Misconduct
If you or someone you know has experienced any type of sexual violence (including harassment, assault, dating or domestic violence, or stalking), there are many confidential and non-confidential resources available on campus. So you know, the University requires faculty and staff to report any personal disclosures of sexual misconduct including rape, dating/domestic violence and stalking to the Title IX Coordinator. Students who do not wish to report their experience to me or the Title IX Coordinator may speak to someone confidentially by contacting Student Health and Counseling Services (916) 278-6461. You can also contact WEAVE, Inc. Sacramento, which provides confidential support 24 hours a day at (916) 920-2952.
If you are in immediate danger or need immediate assistance, please call 9-1-1 or if you are on campus, campus police at 916-278-6000. If it is after hours or the weekend and you need immediate advocacy, please call WEAVE’s 24-hour hotline at 916-920-2952.
Learn more here: www.csus.edu/student-life/health-counseling/sexual-violence-support
Student Health and Counseling Services
Your physical and mental health are important to your success as a college student. Student Health and Counseling Services (SHCS) in The WELL offers medical, counseling, and wellness services to help you get and stay healthy during your time at Sac State. SHCS offers: Primary Care medical services, including sexual and reproductive healthcare, transgender care, and immunizations; urgent care for acute illness, injuries, and urgent counseling needs; pharmacy for prescriptions and over-the-counter products; mental health counseling, including individual sessions, group counseling, support groups, mindfulness training, and peer counseling; athletic training for sports injury rehabilitation; wellness services, including nutrition counseling, peerled health education and wellness workshops, and free safer sex supplies; violence and sexual assault support services. Most services are covered by the Health Services fee and available at no additional cost.
Confidential counseling services are available for Sacramento State students. Counselors are located on the second floor of the WELL. Appointments can be made 8:00am–5:00pm, Monday–Friday. Call 916-278-6461 or go here shc-pncweb.saclink.csus.edu/ to make an appointment.
If you are in immediate crisis, please call 9-1-1 or the Suicide Hotline at 1-800-273-TALK (8255).
Learn more here: www.csus.edu/student-life/health-counseling
Services to Students with Disabilities (SSWD)
Sacramento State is committed to ensuring an accessible learning environment where course or instructional content are usable by all students and faculty. If you believe that you require disability-related academic adjustments for this class (including pregnancy-related disabilities), please immediately contact Services to Students with Disabilities (SSWD) to discuss eligibility. A current accommodation letter from SSWD is required before any modifications, above and beyond what is otherwise available for all other students in this class will be provided. Please be advised that disability-related academic adjustments are not retroactive. If you know or think you need academic adjustments or accommodations of any kind but do not have a letter from SSWD, please speak with me privately as soon as possible.
SSWD is located on the first floor of Lassen Hall 1008. Phone is 916-278-6955 and e-mail is sswd@csus.edu. For a complete listing of services and current business hours visit www.csus.edu/student-affairs/centers-programs/services-students-disabilities
More Resources
Sacramento State offers many more resources to support you and your peers. Reach out to me if you have any questions, or go here to learn more about many of them: webpages.csus.edu/wiscons/more/SacStateCampusResources.html.