About
Welcome to your first Mathematical Logic course. In this course, we will cover most of the basics of mathematical logic, starting from some very naive set theory, then working our way through propositional and first-order logic (culminating in Gödel's completeness theorem). After this, we'll start getting our hands a bit dirtier, working through the early development of computability theory, and then to put everything together, we will try to prove Gödel's first incompleteness theorem. A slightly more official version of the contents of the course can be found here.
If you want to learn a bit more about some of the dramatis personae of our story, I really recommend you read Logicomix, which tells the wonderful story of the early days of Mathematical Logic (you can find it online here, and if you like it, you should for sure buy it, just please not off of Amazon!)
General information
When? MonWedFri 1:00pm-1:50pm.Where? Kirwan 0102.
Who? Aris Papadopoulos (just call me Aris: "R"+"iss" or "air"+"iss").
How? That's a more multifaceted question. Here are some possibilities:
- How to reach me?
{aris}@{umd}.{edu}(without{}, obviously). - How to study? I'll be providing lecture notes.
- How to get more help? Come to my office hour (Wed. 11:30am).
Notes
Week 0: Introduction (Notes)Week 1: Pretty Naive Set Theory (Notes)
Typos corrected 09/06 and 09/16 (Thanks Matthew and Wesley!)
Week 2: Propositional Logic - Syntax and Semantics (Notes)
Typos corrected 09/09 and 09/13 (Thanks Jennifer and Matthew!)
Week 3: (a) Propositional Logic - Completeness (Notes)
Typos corrected 09/20 (Thanks Matthew!)
(b) First-Order Logic - Syntax (Notes)
Typos corrected 09/28 (Thanks Matthew!)
Week 4: First-Order Logic - Semantics and Substitutions (Notes)
Typos corrected 10/02 and 10/18 (Thanks Matthew and Matthew!)
Week 5: Gödel's Completeness Theorem (Notes)
Typos corrected 10/18, and 10/20 (Thanks Noor and Matthew, and Gary!)
Week 6: (a) Gödel's Completeness Theorem - Final Touches (Notes)
(b) Gödel's Completeness Theorem - Consequences of
Compactness (Notes)
Added 10/18.
Typos corrected 10/26 (Thanks Matthew!)
(c) Recursion Theory - Register Machines (Notes)
Typos corrected 10/18 (Thanks Matthew!)
Week 7: Recursion Theory - Primitive Recursive functions (Notes)
Typos corrected 10/18 and 10/26 (Thanks Gary and Matthew!)
Week 8: Recursion Theory - Universal Machines (Notes)
Week 9: (a) Recursion Theory - The Halting Problem (Notes)
(b) Peano Arithmetic - The Basics (Notes)
Week 10: (a) Peano Arithmetic - Representable Functions (Notes)
(b) Peano Arithmetic - Gödel's function (Notes)
Week 11: (a) Peano Arithmetic - Coding (Notes)
(b) Peano Arithmetic - Incompleteness (Notes)
Week 12: Extra topics - Set theory and Łoś (Notes)
Only the material up to (and including) Gödel's first incompleteness theorem (Week 11) is examinable. The last four weeks of the course will consist of various tasters of more advanced topics in mathematical logic (Weeks 12-14) and an exam revision week (Week 15).
Homeworks
HW 0 (here, optional!)HW 1 (here, due 09/15)
HW 2 (here, due 09/29)
Typos corrected 09/20 and 09/23 and 09/28 (Thanks Gary, Matthew, and Sky!)
HW 3 (here, due 10/08)
Typos corrected 09/28 (Thanks Gary and Matthew!)
HW 4 (here, due 10/20)
Typos corrected 10/15 (Thanks Gary, Sky, and Matthew!)
HW 5 (here, due 10/31)
Typos corrected 10/25 and 10/26 (Thanks Gary and Matthew, and Gary!)
HW 6 (here, due 11/10)
Hint added 11/08 (Thanks Gary!)
HW 7 (here, due 11/24)
Practice Final Exams
Practice Exam 1 (here)Practice Exam 2 (here)