Mathematics 301 :  Mathematical Logic
Fall 2017

Introduction

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

Textbooks
An Introduction to Gödel's Theorems, Second Edition by Peter Smith
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.

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

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