# Math 557: Mathematical Logic

I am Stephen G. Simpson, a mathematician at Penn State University.

Math 557 is an introductory graduate-level course in mathematical logic. It is suitable for all mathematics graduate students. It is one of two first-year graduate courses in mathematical logic, the other being Math 558.

I am teaching Math 557 in Fall 2013. We are meeting Tuesdays and Thursdays, 9:45-11:00 AM, in 315 McAllister Building. My office hours are by appointment. Grades will be based on homework and an in-class midterm exam. Homework is due at the beginning of class on the specified due date.

Here are some course materials.

• Notes on Mathematical Logic: PDF, PS, DVI.
• Notes on Foundations of Mathematics: PDF, PS, DVI.
• Notes on Undecidability and Incompleteness: PDF, PS, DVI.
• Syllabus: PDF, PS, DVI.
• Homework #1, due August 29: ML notes, Exercises 1.1.16, 1.2.14, 1.2.15.
• Homework #2, due September 3:
• Read Exercise 1.2.16 and construct and solve a similar exercise.
• Exercises 1.3.3.1, 1.3.3.6, 1.3.4.
• Exercise 1.3.5.2, and give an example showing that A => (B => C) is not always logically equivalent to (A => B) => C.
• Hamlet problem: PDF, PS, DVI.
• Homework #3, due September 10: Exercises 1.8.2, 1.8.6.
• Homework #4, due September 17: Exercises 2.3.8, 2.3.9, 2.3.10. (Also, study the worked exercises in Sections 2.1, 2.2, 2.3.)
• Homework #5, due September 24: Exercises 2.4.2, 2.4.4, 2.4.5, 2.4.13, 2.4.16, 2.4.18.
• Homework #6, due September 26: Exercises 2.5.12, 2.5.13, 2.5.14, 2.5.15.
• Homework #7, due October 1: Exercises 2.6.4, 2.6.5.
• Homework #8, due October 3: Exercise 3.3.14.
• Homework #9, due October 15: Exercises 3.4.7, 3.4.16, 3.4.17, 3.4.18.
• Midterm Exam, October 22: PDF, PS, DVI.
• Homework #10, due October 29: Exercises 4.2.5, 4.2.8, 4.2.9, 4.4.2, 4.4.3, 4.4.7, 5.1.11.
• Homework #11, due November 12: Exercises 5.3.15, 5.5.4.
• Homework #12, due December 5: FOM notes, Exercises 1.4.4, 1.5.8, 1.5.9.
• Homework #13, due December 10: Exercises 1.6.8, 1.7.9, 1.7.12.
• Homework #14, due December 12: Exercises 1.9.6, 1.9.11, 1.9.20, 1.9.21, 2.2.4, 2.2.16-2.2.21, 2.2.24, 2.2.25, 2.3.5, 2.3.6.
I have taught Math 557 several times before. Some old course materials are available.

Information about Penn State's Mathematical Logic Research Group is available. Also of interest is the Penn State Logic Seminar.

```t20@psu.edu / 5 December 2013
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