Basic Information

• Syllabus (pdf file)
• CRN: 22266
• Course Credit: 3 credit hours
• Official Department Course Description Page
• Course Page in Brightspace
• Meeting Location/Modality: This course is "Online on-site". The lectures and office hours will be synchronously live-streamed online using Zoom. Please see the “Zoom Ground Rules” at the end of the syllabus document (above) for more information. The connection details can be found in Brightspace . Lectures (not office hours) will be recorded and made available later in Brightspace for those who cannot join synchronously (but it is expected that students attend synchronously if they can).
  Please note: it is currently planned that there will be two in-person midterms (see below for tentative schedule). It is of course possible that plans will be required to change because of changing circumstances (either university-wide, campus-wide, course-wide, or on a case-by-case basis). You should keep monitoring this site and Brightspace for updates. Please email me if you have any concerns.
• Auditing: If you wish to audit the course, you must first enrol in the course, and then request to audit in the form of a "Grade Mode Change" by following these instructions . This process generates a request for your advisor (not instructor) to approve the request to audit. You are then free to participate in the course to the extent that you wish, but you will not receive a grade or any credits at the end.
• Dates: Lectures and office hours held during August 24th - December 5th 2020 (except on US Thanksgiving, Thursday November 26th 2020); Final Exam period is December 7th - 12th 2020.
• Meeting Times: Lectures on Tuesdays and Thursdays 1:30pm-2:45pm EDT/EST (always in the current time zone of Purdue WL campus).
• Office Hours: Tuesdays 2:45-3:30pm AND 5:15-6:00pm, and Thursdays 4:00-5:30pm Tuesdays 4-5:30pm and Thursdays 3-4:30pm EDT/EST (always in the current time zone of Purdue WL campus).
• Office Location: MATH 638
• Contact: Via email to memthomas at purdue.edu. Please include include MA58500 in the subject line.

Course Information

• Official Course Description: Propositional and predicate calculus; the Gödel completeness and compactness theorem, primitive recursive and recursive functions; the Gödel incompleteness theorem; Tarski's theorem; Church's theorem; recursive undecidability; special topics such as nonstandard analysis.
• Prerequisites: Some background in Abstract Algebra or Real Analysis would be highly beneficial (and it would make studying the material in this course much more meaningful).
• Primary Textbook (required): E. Mendelson, Introduction to Mathematical Logic (6th Edition) (earlier editions, especially 4th and 5th, may also be viable). We'll discuss in class various ways of accessing a copy of the book.
  Secondary Textbook: Since some of the course material may be dependent on how the coverage of material in class develops, secondary, optional reading materials may be recommended in due course.
• Assessment Methods:
  • Eleven written assignments consisting of problems from the textbook (Mendelson). These will be due almost every week by Wednesday at 1:30pm (see tentative schedule below).
    Assignments are to be submitted via Gradescope, which will be accessed via Brightspace . You should submit your answers as a .pdf file, which can be a scan (using your phone or other suitable device) of your handwritten work. Instructions on how to make a good quality scan your work and upload it to Gradescope can also be found on Brightspace ; please read these instructions before submitting.
    As always, please make sure that your name is legible! If you work together with others, then you must write up your own version of the answers, and please also write at the top of your submitted work the names of the people with whom you worked.
  • Two Midterm Tests. Two written, closed-book tests in person (see tentative schedule below).
  • Final Examination. One cumulative written, open-book exam, made available online at a pre-announced time with answers to be submitted via Gradescope by a given deadline during Finals week (see tentative schedule below).
• Course Evaluation:
  • Assignments 25%;
  • Midterm Tests 50% (2x25%);
  • Final Examination 25%.
• Grading Scale: Students who get at least 97% of the total points in this course are guaranteed an A+, 93% guarantees an A, 90% an A-, 87% a B+, 83% a B,80% a B-, 77% a C+, 73% a C, 70% a C-, 67% a D+, 63% a D, and 60% a D-; for each of these grades, it's possible that at the end of the semester a somewhat lower percentage will be enough to get that grade.
• The instructor reserves the right to adjust the course evaluation mechanism or the grading scheme at the end of the course; this adjustment will be applied uniformly and in a manner which only increases individual grades.

Assessments

TENTATIVE SCHEDULE for assignment due dates and midterm tests is as follows.

Assessment	Material	Due date and time
Assignment 1	Wednesday September 2nd 2020, 1:30pm EDT	Exercises: 1.4 b, g, h; 1.5 c, d; 1.6 e, g; 1.12; 1.16 d; 1.19 e, j; 1.21 a, c; 1.22 d; 1.25; 1.27 a, b. (Please provide some form of explanation for those exercises that have answers in the back of the book.)
Assignment 2	Wednesday September 9th 2020, 1:30pm EDT	Exercises: 1.31; 1.33 g, i; 1.34 b, c; 1.35; 1.37; 1.38; 1.42 d(iii) (see part c for the definition of "full"); 1.45; 1.46; 1.48 e, f (for the definitions of the "shorthands" (i.e. other connectives!) used in the wffs in 1.48, see right before Lemma 1.8).
Assignment 3	Wednesday September 16th 2020, 1:30pm EDT	Exercises: 1.50; 1.59; 2.6 b, c, d; 2.8 e, i, l, m, o; 2.9 b, d, e; 2.11 b, c, d, e; 2.15 b, c, d, e, f.
Assignment 4	Wednesday September 23th 2020, 1:30pm EDT	Exercises: 2.10 b, c; 2.12 IV, VII; 2.14 b, c, e; 2.17 b; 2.18 d; 2.21 e, f, h; 2.26.
Assignment 5	Wednesday September 30th 2020, 1:30pm EDT	Exercises: 2.27 b, e; 2.31 b, f, l; 2.32 d; 2.34; 2.35; 2.36; 2.38; 2.40; 2.44; 2.50. (For the formal proof questions, please try to pay attention to which section of the textbook they are in and which derived rules have already been introduced in the book by that point, and limit yourself to those if at all possible!)
Midterm Test 1	Thursday October 8th 2020, 1:30pm EDT	Logistical details: UNIV 201; 60 minutes closed-book test (further information circulated by email).
Assignment 6	Wednesday October 14th 2020, 1:30pm EDT	Exercises: 2.50, 2.51, 2.53, 2.54, 2.56, 2.59.
Assignment 7	Wednesday October 21st 2020, 1:30pm EDT	Exercises: 2.65 b, e; 2.71; 2.72; 2.73; 2.75; 2.78; 2.84 b.
Assignment 8	Friday October 30th 2020, 6:30pm EDT Wednesday October 28th 2020, 1:30pm EDT	Exercises: 3.1; 3.2; 3.4; 3.5 a; 3.8; 3.9; 3.10; 3.11; 3.13; 3.14.
Assignment 9	Friday November 6th 2020, 6:30pm EDT Wednesday November 4th 2020, 1:30pm EST	Exercises: 3.16, 3.17, 3.18, 3.19, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.31.
Midterm Test 2	Thursday November 12th 2020, 1:30pm EST	Logistical details: UNIV 201; 60 minutes closed-book test (further information circulated by email).
Assignment 10	Friday November 20th 2020, 6:30pm EST Wednesday November 18th 2020, 1:30pm EST	Exercises: 3.32 c, d, e; 3.33; 3.34 b (keep your answer as a product of prime powers!); 3.36 (in part c it should read "If ... the identity relation $x=y$ is expressible in $K$ by the wf $\bf{x=y}$ ..."); read about Robinson's System RR (pp.202-204) and answer 3.37 and 3.38.
Assignment 11	Tuesday December 1st, 2020, 6:30pm EST Tuesday November 24th 2020, 11:30pm EST (because of Thanksgiving break)	Exercises: 3.41, 3.42, 3.43, 3.44, 3.55, 3.56, 3.58; read Section 3.7 (pp. 228-230) and complete Exercise 3.65.
Final Examination	Monday December 7th, 2020 5:30pm EST - Wednesday December 9th, 2020 5:30pm EST	Logistical details: The exam will be posted to Gradescope (link in Brightspace ) at 5:30pm EST on Monday December 7th, 2020, and all your answers must be uploaded before 5:30pm EST on Wednesday December 9th, 2020. You should expect to spend no more than around 2 hours in total completing it (but you are allowed to take longer if you wish). You may consult the course textbook, any notes from the course (including your own notes or anything posted to the course page in Brightspace ), anything posted to the course page in Piazza (accessed through Brightspace ) and any previous work from the course that you have done. You may NOT consult any other resources; in particular, you may NOT consult any online resources except those just listed. You may NOT collaborate or communicate in any way about the exam with anyone else between the release of the exam and the deadline (this includes NOT posting or answering questions on Piazza, publicly or privately; the course page in Piazza will be locked to new posts during the window of the final examination). This restriction (on discussion with others during the exam window) applies even if you have already submitted your answers. You will be asked to write out and sign the Purdue Honor Pledge as part of your examination submission, in order to indicate that you have abided by these instructions for the final examination.

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Attendance policy during COVID-19

Students should stay home and contact the Protect Purdue Health Center (496-INFO) if they feel ill, have any symptoms associated with COVID-19, or suspect they have been exposed to the virus. In the current context of COVID-19, in-person attendance will not be a factor in the final grades, but the student still needs to inform the instructor of any conflict that can be anticipated and will affect the submission of an assignment or the ability to take an exam. Only the instructor can excuse a student from a course requirement or responsibility.

When conflicts can be anticipated, such as for many University-sponsored activities and religious observations, the student should inform the instructor of the situation as far in advance as possible. For unanticipated or emergency conflict, when advance notification to an instructor is not possible, the student should nevertheless contact the instructor as soon as possible. When the student is unable to make direct contact with the instructor and is unable to leave word with the instructor’s department because of circumstances beyond the student’s control, and in cases of bereavement, quarantine, or isolation, the student or the student’s representative should contact the Office of the Dean of Students via email or phone at 765-494-1747.

Classroom Guidance Regarding Protect Purdue

The Protect Purdue Plan , which includes the Protect Purdue Pledge , is campus policy and as such all members of the Purdue community must comply with the required health and safety guidelines. Required behaviors in this class include: staying home and contacting the Protect Purdue Health Center (496-INFO) if you feel ill or know you have been exposed to the virus, wearing a mask in classrooms and campus buildings , at all times (e.g., no eating/drinking in the classroom), disinfecting desk/workspace prior to and after use, maintaining proper social distancing with peers and instructors (including when entering/exiting classrooms), refraining from moving furniture, avoiding shared use of personal items, maintaining robust hygiene (e.g., handwashing, disposal of tissues) prior to, during and after class, and following all safety directions from the instructor.

Students who are not engaging in these behaviors (e.g., wearing a mask) will be offered the opportunity to comply. If non-compliance continues, possible results include instructors asking the student to leave class and instructors dismissing the whole class. Students who do not comply with the required health behaviors are violating the University Code of Conduct and will be reported to the Office of the Dean of Students with sanctions ranging from educational requirements to dismissal from the university.

Any student who has substantial reason to believe that another person in a campus room (e.g., classroom) is threatening the safety of others by not complying (e.g., not wearing a mask) may leave the room without consequence. The student is encouraged to report the behavior to and discuss next steps with their instructor. Students also have the option of reporting the behavior to the Office of the Student Rights and Responsibilities (OSRR) . See also Purdue University Bill of Student Rights .

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Academic Integrity

As a Boilermaker pursuing academic excellence, I pledge to be honest and true in all that I do. Accountable together – we are Purdue.

Academic integrity is one of the highest values that Purdue University holds. Individuals are encouraged to alert university officials to potential breaches of this value by either emailing integrity@purdue.edu, or by calling 765-494-8778, or by contacting the Office of the Dean of Students . While information may be submitted anonymously, the more information that is submitted provides the greatest opportunity for the university to investigate the concern.

Purdue prohibits "dishonesty in connection with any University activity. Cheating, plagiarism, or knowingly furnishing false information to the University are examples of dishonesty" (Section B.2.a of the Student Regulations concerning Conduct ).

Furthermore, the University Senate has stipulated that "the commitment of acts of cheating, lying, and deceit in any of their diverse forms (such as the use of ghostwritten papers, the use of substitutes for taking examinations, the use of illegal cribs, plagiarism, and copying during examinations) is dishonest and must not be tolerated. Moreover, knowingly to aid and abet, directly or indirectly, other parties in committing dishonest acts is in itself dishonest."

Incidents of academic misconduct in this course will be addressed by the course instructor and referred to the Office of the Student Rights and Responsibilities (OSRR) for review at the university level. Any violation of course policies as it relates to academic integrity will result minimally in a failing or zero grade for that particular assignment or test, and at the instructor’s discretion may result in a failing grade for the course. In addition, all incidents of academic misconduct will be forwarded to OSRR, where university penalties, including removal from the university, may be considered.

Commercial Note Taking in Classes

Notes taken in class are generally considered to be “derivative works” of the instructor’s presentations and materials, and they are thus subject to the instructor’s copyright in such presentations and materials. No individual is permitted to sell or otherwise barter notes, either to other students or to any commercial concern, for a course without the express written permission of the course instructor. See the Regulations on Student Conduct: Miscellaneous Conduct Regulations .

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Nondiscrimination

Purdue University is committed to maintaining a community which recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her own potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life. Purdue’s nondiscrimination policy can be found at here .

Academic Accommodation of Students with Disabilities

Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center (DRC) at: drc@purdue.edu or by phone: 765-494-1247.

In this mathematics course accommodations are managed between the instructor, student and DRC Testing Center. If you have been certified by the Disability Resource Center (DRC) as eligible for accommodations, you should contact your instructor to discuss your accommodations as soon as possible. Here are instructions for sending your Course Accessibility Letter to your instructor: Course Accessibility Letter on myPurdue .

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Mental Health

If you find yourself beginning to feel some stress, anxiety, and/or feeling slightly overwhelmed, try WellTrack . Sign in and find information and tools at your fingertips, available to you at any time.

If you need support and information about options and resources, please see the Office of the Dean of Students , for drop-in hours (M-F, 8am-5pm).

If you find yourself struggling to find a healthy balance between academics, social life, stress, etc. sign up for free one-on-one virtual or in-person sessions with a Purdue Wellness Coach at RecWell . Student coaches can help you navigate through barriers and challenges toward your goals throughout the semester. Sign up is completely free and can be done on BoilerConnect. If you have any questions, please contact Purdue Wellness.

If you’re struggling and need mental health services: Purdue University is committed to advancing the mental health and well-being of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of mental health support, services are available. For help, such individuals should contact Counseling and Psychological Services (CAPS) at 765-494-6995 during and after hours, on weekends and holidays, or by going to CAPS office on the second floor of the Purdue University Student Health Center (PUSH) during business hours.

Major Campus Emergency

In the event of a major campus emergency, course requirements, deadlines, and grading are subject to change that may be necessitated by a revised calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted on course websites. You are expected to read your @purdue.edu email on a frequent basis.

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