Math 102 - Section 03 - Fall 2022
Subject to change.
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.
Theory of divisibility; some number theoretical functions; congruencies (linear and quadratic); some Diophantine equations. Simple continued fractions. This is a 3 unit class.
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.
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
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:
We will further develop this agreement together in class.
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 09/05) + 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 (10/07) |
| 7 | Linear Congruences (Section 5) |
| 8 | Fermat’s + Wilson’s Theorems (Section 6) |
| 9 | Cryptography (supplemental notes) + Divisors (Section 7) |
| 10 | Divisors (Section 7) + Euler’s Theorem (Section 9) |
| 11 | Euler’s Theorem (Section 9) + Veteran’s day (no class on 11/11) |
| 12 | Primitive Roots (Section 10) + Exam 2 (11/18) |
| 13 | Primitive Roots (Section 10) + Fall Break (no class on 11/25) |
| 14 | Quadratic Congruences and Quadratic Reciprocity (Section 11) |
| 15 | Quadratic Reciprocity (Section 11) + Pythagorean Triples (Section 16) |
| 16 | Final Exam (12/12) |
Homework assignments consist of a mixture of computations and proofs. You are allowed and encouraged to collaborate with your classmates (and with me!) on solving the problems. Completed assignments are to be submitted via Canvas and are typically due before class on Fridays. 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 take care that your work is well-organized and fully-justified with proper grammar, punctuation, and spelling. Please also take care that your solutions are written in your own words, even if you worked with others in solving the problems. When writing up your solutions, you may work with one partner on this and turn in the same document for both of you. If you do this, please make sure that you have truly collaborated on both the mathematics and the writing.
Please bring a copy of your homework solutions to class after turning it in. We will usually discuss some of the problems in class, and you are welcome to revise and resubmit your work by the end of the day it is due based on these discussions. But please remember to turn in your homework by the initial due date and time; repeated unexcused late submissions may result in a penalty to the grade on those assignments. If something comes up that prevents you from turning in an assignment on time, please send me a quick email; I’m always happy to discuss an extension.
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 during periods of in-class work, which will typically occur on Fridays. Participation will be graded on the following scale. (The score will be the highest one that applies.)
| 100% | Contributing to discussion in a respectful way during essentially every period of in-class group work. (1 unexcused absence allowed) |
| 60–90% | Contributing to discussion in a respectful way during most periods of in-class group work. (2–5 unexcused absences) |
| < 60% | Never or very rarely participates in class or is disrespectful. |
There are 2 midterm exams. They are tentatively scheduled for Oct. 07 and Nov. 18. There is also a Final Exam scheduled for Monday, December 12 from 10:15 AM - 12:15 PM.
Overall grades for the course will be determined from the course components listed above with the following weighting:
The maximum cutoff for letter grades will be: A- 90%, B- 80%, C- 70%, D- 60%, F 59–0%.
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 will only take attendance on days we do group work. In any case, please send me a quick email if you need to miss class, so I know what is going on and can support you getting caught up.
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.
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.
If you become sick, please do not attend 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.
We will be following Sacramento State’s COVID-19 policies. Vaccines are required for everyone on campus except those who have been granted a religious or medical exemption per the CSU’s COVID-19 vaccination requirement. Masks are strongly recommended indoors. Please respect your fellow students’ decision to mask or not mask. You can schedule a vaccine at My Turn California and find out more about vaccines and booster eligibility on the CDC website. Remember that COVID-19 is still a threat, even for those who are vaccinated and boosted. Please practice self-care, monitor your health for any possible symptoms of COVID-19, and contact a health care provider immediately should you believe you may be infected.
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.
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.
Please come talk with me if you have any questions! The Math Lab is located in Brighton Hall Room 118 and also operates virtually. The Math Lab provides free assistance to students in lower-division mathematics/statistics courses, but they might be able to help with this course too.
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
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:
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
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
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
Sacramento State offers many more resources to support you and your peers; learn more about some of them here:
Please reach out to me if you have any questions at all!
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