Welcome to Mathematical Logic! Please let me know if you have any questions at all, about our course or anything else.
Instructor Information
Instructor: 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:
- In person: Monday 2–3 PM and Wednesday 2–3 PM [Brighton 144]
- Virtual: Thursday 1–2 PM [only via Zoom]
- Also by appointment. Just send me an email.
Course Information
Meetings and books
Class times: Mon + Wed + Fri from 10:00–10:50 AM [Alpine 204]
Book: A Friendly Introduction to Mathematical Logic, 2nd Edition, by Christopher C. Leary and Lars Kristiansen. The book is free if you use the pdf version—a print version can be purchased for less than $35. Here is a link to the book.
Catalog Description
Advanced study of logic with special application to mathematics. This is a 3 unit class.
Prerequisites
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.
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 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
- understand basic concepts of logic including languages, terms, formulas, deductions, and structures;
- understand the Soundness and Completeness theorems;
- understand the Compactness Theorem and be able to apply it to create structures with various properties;
- understand the Löwenheim-Skolem Theorems and some of their implications;
- understand Gödel’s First Incompleteness Theorem and the main ingredients of a proof of it.
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
Grade composition
Overall grades for the course will be determined from the course components listed above with the following weighting:
- Homework 50%
- Participation 15%
- Final Project 35% (Paper: 20%, Presentation 15%)
Homework
There be regular homework, typically due on Fridays. The goal of this is to critically engage with the material, uncover points of confusion, and deepen understanding. 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 the due date. 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.
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.
Outside Resources
Please do not use any resources or tools (e.g. A.I., Chegg, tutors, etc.) to solve your homework problems for you. However, you are most welcome to use resources and tools to explore the concepts. When working with peers or tutors, please make sure they are guiding you to a solution and better understanding as opposed to doing most of the work for you. Let me know of you have any questions about this.
And please remember that you are allowed and encouraged to discuss anything with me!
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 attendance. Please let me know if you need to miss class, and I’ll be happy to discuss excusing the absence.
Final Project
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 Tuesday, May 19 from 8:00–10:00 AM.
Final Paper Rubric
Please aim for 3–5 pages. The paper should contain the following items:
- Introduction and/or Background Material: try to situate your topic within the history of mathematics or within our class and provide the necessary background definitions and theorems to understand your main topic
- Main Topic Content: provide definitions of the main concepts, examples (if appropriate), statements of lemmas/theorems, and a proof (or partial proof) of at least one lemma/theorem or example
- References: please use at least two citable sources in addition to our book (one of which could be Wikipedia) and include references in a bibliography at the end of the paper
The paper will be graded on a 10 point scale with points distributed as follows:
| [5] | Content + Detail | Did the paper contain the three items listed above (Introduction and/or Background Material, Main Topic Content, References), and were they addressed with sufficient depth? Were sufficient precise mathematical details provided, e.g. rigorous definitions, examples, statements of theorems, or proofs? |
| [5] | Clarity + Thoughtfulness | Were ideas clearly presented, explained at an appropriate level, and contextualized within the history of mathematics and/or within our class? Were statements (mathematical and otherwise) correct and without errors/typos? |
Final Presentation Rubric
Please aim for 10–15 minutes. The presentation will be graded on a 10 point scale with points distributed as follows:
| [5] | Content + Detail | Was the main idea of the project conveyed, and was sufficient precise mathematics presented, e.g. rigorous definitions (perhaps accompanied by intuitive explanations), examples, statements of theorems, or proofs (or proof outlines)? |
| [5] | Clarity + Thoughtfulness | Were ideas clearly presented (in speaking and writing) and well organized to help audience follow arguments and see main ideas? 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? |
Schedule of Topics
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 | Terms + Formulas |
| 3 | Truth in Structures |
| 4 | Logical Implication + Substitutions |
| 5 | Deductions |
| 6 | Rules of Inference |
| 7 | Soundness |
| 8 | Completeness |
| – | Spring Break (no classes) |
| 9 | Compactness |
| 10 | Löwenheim-Skolem + Intro to Incompleteness |
| 11 | Representability |
| 12 | Coding + Gödel Numbering |
| 13 | Representability Results |
| 14 | Self-reference + Incompleteness Theorems |
| 15 | Presentations |
| 16 | Final Exam Time (used for presentations) |
Policies and Accommodations
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. I will also take attendance for your participation grade. 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.
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. Please also reach out to the Disability Access Center (DAC) to discuss eligibility.
Safety, Wellness, and COVID-19
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.
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: sacramentostate.policystat.com/policy/11300038/latest.
Getting Extra Help.
Please come talk with me if you have any questions! It is acceptable to watch a video or go to our Math Lab for general conceptual questions, but please do not use such resources for direct assistance with the problems.
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. Students also have access to the Basic Needs Resource Center (BNRC). Whether you need groceries, clothes, toiletries, parenting supplies, or a couch surfing kit, everything at the BNRC is free and just for Sac State students. No barriers. No judgment. Just confidential support when you need it.
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.
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
Disability Access Center (DAC)
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.
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/
More Resources
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!