Professor: Jeff Johannes Section 1 MF 2:30-3:45p Sturges 105

Office: South 326A

Telephone: 5403 (245-5403)

Office Hours: Monday 8:00-9:00p, Tuesday 3:45-5:00p, Thursday 11:30a-1:30p, Friday 10:30-11:20a, or by appointment or visit.

Email Address: Johannes@Geneseo.edu

Web-page: http://www.geneseo.edu/~johannes

Textbooks

A Friendly Introduction to Mathematical Logic by Chris Leary

Overview

This is not truth tables, Philosophy 101, or a gentle continuation of Introduction to Proofs. In this course we will tell the tale of Gödel's theorems, one of the most amazing stories inside of mathematics, and about mathematics as well. Come join us for a wild ride and a trip and a half into the surprising world of vast abstraction.

Learning Outcomes

Math 301 - Upon successful completion of
Math 301 - Mathematical Logic, a student will be able to:

- State the following theorems and outline their proofs: The Soundness Theorem, The Completeness Theorem, The Compactness Theorem, Gödel's First Incompleteness Theorem, and Gödel's Second Incompleteness Theorem,
- Evaluate the development of 20th century Mathematical Logic in terms of its relation to the foundations of mathematics,
- Explain basic concepts from Recursion Theory, including recursive and recursively enumerable sets of natural numbers, and apply them to theoretical and appropriate applied problems in logic,
- Explain basic concepts from Proof Theory, including languages, formulas, and deductions, and use them appropriately, and
- Define and give examples of basic concepts from Model Theory, including models and nonstandard models of arithmetic, and use them in appropriate settings in logic.

Grading

Your grade in this course will be based upon your performance on participation (on-line and in person), problem sets, take home exams, and a final experience. The weight assigned to each is designated below:

In-class Participation 1/10

On-line Participation 3/20

Problem Sets 1/4

Take Home Exams 3/10

Final Experience 1/5

In-class Participation

If you are present and engaged in class you will receive one participation point that day. If you also participate to the class as a whole (answer a question, present a solution, ask an insightful question or offer important relevant commentary) you will receive two participation points for that day. Working each day and never speaking in class will earn 80%. Speaking every other day on which there is an opportunity to speak will earn 95%. Scores between will be scaled linearly.

On-line Participation

Our class discussion will be run via a Facebook group. Sometime between classes, write a post about the reading for the next class. I will "like" posts that are good, and they will satisfy your posting for that day. I will "superlike" (by typing something) posts that are exceptional. They will earn you a pass for any other class day. I will grade this component of the course as follows:

If you are missing fewer than 3 posts, you will earn an A

If you are missing fewer than 10 posts, you will earn a B

< 17 C

< 23 D

≥ 23 E

Problem Sets

There will be occasional problem sets due on announced dates. You are encouraged to consult with me outside of class on any questions toward completing the homework. You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions. A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity. A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions. While working on homework with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur. There are plenty of places that one can find all kinds of solutions to problems in this class. Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation. Reading them and referencing them is not quite plagiarism, but sometimes undermines the intent of the problems. Therefore, if you reference solutions you will receive 0 points when it is inappropriate, but you will *not* be reported for an academic integrity. Simply - please do not read any inappropriate solutions for problems in this class. Problems will be graded in ways appropriate for the individual assignment. Unless stated otherwise, each problem set will be of equal value.

Take Home Exams

The exams will consist of a few questions designed to emphasise a personal understanding of the fundamental learning outcomes. They will occur approximately once every three weeks. You will receive them on Fridays and they will be due the subsequent Mondays. Each exam will be equally weighted. By their nature, grading will be in a holistic sense, rather than in a points/problem sense.

Final Experience

Your final experience will be an opportunity to personally demonstrate your accomplishment of the course learning outcomes. More details to follow.

Feedback

Occasionally you will be given anonymous feedback forms. Please use them to share any thoughts or concerns for how the course is running. Remember, the sooner you tell me your concerns, the more I can do about them. I have also created a web-site which accepts anonymous comments. If we have not yet discussed this in class, please encourage me to create a class code. This site may also be accessed via our course page on a link entitled anonymous feedback. Of course, you are always welcome to approach me outside of class to discuss these issues as well.

Disability Accommodations

SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional or learning disabilities. Students should consult with the Director in the Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their individual faculty regarding any needed accommodations as early as possible in the semester.

Religious Holidays

It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me no later than September 10 of plans to observe the holiday.

Schedule (subject to change)

August 28 Introduction, S1-2

September 1 L1.1-5, uncountable proof HW

September 8 L1.6-9

11 Discuss PS, L 1.10, 2.1-2

15 L2.3-4,5? XM1 given

18 L2.5, 2.6, 3.1 XM1 due

22 L3.2

25 Discuss PS / L 3.2

29 S 3-5

October 2 S 6-7, 10

6 S 11-12 XM2 given

13 S 11 XM2 due

16 S 12-13

20 S 14

23 Discuss PS S15

27 S 16 XM3 given

30 S 17-19 XM3 due

November 3 S 19-20

6 S 21-22

10 S 22-23

13 S 24

17 S 31 XM4 given

20 XM4 due S 32-33

27 S 33-34

December 1 S 35 L 3.3

4 L 3.3, wrap up

8 wrap up

11 Exam discussions

Tuesday, December 19 wrap up final experience 12N-2:30p