Math 161 - Section 01 - Fall 2023
Subject to change.
Welcome to Mathematical Logic! 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.
Advanced study of logic with special application to mathematics. This is a 3 unit class.
Students should have successfully completed an Introduction to Formal Mathematics (Math 108) 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 mathematical logic for further study in mathematics and applications to 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.
The California Faculty Association (the labor union of Lecturers, Professors, Coaches, Counselors, and Librarians across the 23 CSU campuses) is in a difficult contract dispute with California State University management. It is possible that we will call a strike or other work stoppage this term. I promise to promptly inform you of any schedule disruption. Our working conditions are your learning conditions; we seek to protect both. For further information go to CFAbargaining.org.
This is a very rough schedule of what we will cover; please be aware that it is subject to change.
| Week | Topics |
|---|---|
| 1 | Introductions + Languages + Terms + Formulas |
| 2 | Labor day (no class on 09/04) + Terms + Formulas |
| 3 | Truth in Structures |
| 4 | Logical Implication + Substitutions |
| 5 | Deductions |
| 6 | Rules of Inference |
| 7 | Soundness |
| 8 | Completeness |
| 9 | Compactness |
| 10 | Löwenheim-Skolem + Intro to Incompleteness |
| 11 | Representability + Veteran’s day (no class on 11/10) |
| 12 | Coding + Gödel Numbering |
| 13 | Representability Results + Fall Break (no class on 11/24) |
| 14 | Self-reference + Incompleteness Theorems |
| 15 | Presentations |
| 16 | Final Exam (used for presentations on 12/13) |
There will be weekly homework; the goal of this is to critically engage with the material, uncover points of confusion, and deepen understanding. Time will be reserved at the start of most class meetings to discuss the problems.
Completed assignments are to be submitted via Canvas by the posted due date (typically on Friday). 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 are allowed to 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.
These assignments will be graded on the following ten-point system. (The score will be the highest one that applies.)
| 10 | At most one problem was skipped. All completed problems were seriously attempted with well-organized and justified work (even if not entirely complete or correct) |
| 8 | At least three problems were seriously attempted with well-organized and justified work |
| 3 | At least one problem was seriously attempted with well-organized and justified work |
| 0 | None of the above |
Learning to discuss mathematics is a highly valued part of this course. This component will evaluate your progress in areas such as ability to describe a solution (with clarity and thoughtfulness), ability to share and shed light on your difficulties, and ability to listen critically and respond accordingly. The best way to excel in this component is to be engaged in class each day, active in discussions, and prepared to present homework problems.
Participation will be graded on the following scale. (The score will be the highest one that applies.)
| E | Exceeds Expectations. Asking questions, contributing to meaningful discussion, or offering supportive comments essentially every meeting. |
| M | Meets Expectations. Asking questions, contributing to meaningful discussion, or offering supportive comments at least once per week. |
| U | Unsatisfactory. Never or very rarely participates in class or is disrespectful. |
Presentations will be graded on the following scale. (The score will be the highest one that applies.)
| E | Exceeds Expectations. Thorough and detailed solution; clear and thoughtful presentation. |
| M | Meets Expectations. Well-thought out approach capturing the key ideas; clear presentation. |
| I | In progress. Serious attempt, but has a significant flaw/gap or lack of clarity. |
| U | Unsatisfactory. Minimal or no progress was made. |
The presentation and participation rubrics will be combined as follows. (The score will be the highest one that applies.)
| 90–100% | Receives M/E for participation; has at least 2 M/E presentations over the semester. |
| 80-89% | Receives M/E for participation; has at least 1 M/E presentations over the semester. |
| 70-79% | Receives M/E for participation; has at least 1 I/M/E presentation over the semester. |
| 60-69% | Receives M/E for participation. |
| 0–60% | Receives U for participation. |
There will be periodic assignments where you are asked to carefully revise a small subset of the problems we covered to create a “final draft” of each. These will be graded both for precision of the mathematics as well as for the quality and style of writing.
Completed assignments are to be submitted via Canvas by the posted due date. Please take great care not to plagiarize or allow your own work to be plagiarized. As with the homework assignments, you are allowed to 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.
Later in the course, you will be responsible for researching a logic topic of your own choosing (but I am happy to provide options!). You do not need to prove something original, but you will be required to write up an introduction to your topic, including motivation, definitions, statements of theorems, and proofs (in your own words!) of some of the results. This will likely be 3–5 pages. You will also give an approximately 15 minute in-class presentation on your topic. We will use our final exam time for some of the presentations; it is scheduled for Wednesday, December 13 from 08:00 AM - 10:00 AM.
Please aim for 10–15 minutes. The presentation will be graded on a 10 point scale with points distributed as follows:
| [3] | Clarity and organization | Were ideas clearly presented (in speaking and writing) and well organized to help audience follow arguments and see main ideas |
| [3] | Thoughtfulness | Was the topic explained at an appropriate level (perhaps with clever use of illustrations, analogies, etc.) and was it presented in a context that would be interesting to the audience |
| [3] | Math Content | Were some mathematical details presented, e.g. rigorous definitions (perhaps accompanied by intuitive explanations), examples, statements of theorems, or proofs (or proof outlines) |
| [1] | Questions | Could speaker respond to questions or redirect to appropriate reference |
Please aim for 3–5 pages. The paper should contain the following items:
The paper will be graded on a 10 point scale with points distributed as follows:
| [2] | Completeness | Did the paper contain the three items listed above: Introduction and/or Background Material, Main Topic Content, References |
| [2] | Clarity and organization | Were ideas clearly presented and well organized to help reader follow arguments and see main ideas |
| [2] | Thoughtfulness | Was the topic explained at an appropriate level and was it contextualized within the history of mathematics or within our class |
| [2] | Correctness and precision | Were statements (mathematical and otherwise) correct and without errors/typos |
| [2] | Math Content | Were precise mathematical details provided, e.g. rigorous definitions, examples, statements of theorems, or proofs (or partial proofs) |
Overall grades for the course will be determined from the course components listed above with the following weighting:
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 an occasional missed class will not directly affect your grade. If you need to miss class, please send me a quick email in advance, so I know what is going on.
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. Please also reach out to the Disability Access Center (DAC) to discuss eligibility.
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 highly recommended for everyone on campus, and face coverings are 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.
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: sacramentostate.policystat.com/policy/11300038/latest.
Please come talk with me (or send me an email) if you have any questions! And don’t forget to check in with your classmates.
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 the Disability Access Center (DAC) to discuss eligibility. A current accommodation letter from DAC 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.
The DAC is located on the first floor of Lassen Hall in room 1008. Phone is 916-278-6955 and e-mail is dac@csus.edu. For a complete listing of services and current business hours visit www.csus.edu/student-affairs/centers-programs/disability-access-center/
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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