# Math 457, Introduction to Mathematical Logic, Spring 2017

## Course details

 Instructor: Jason Rute Email: To reduce unsolicited e-mail this address is javascript encoded. Note to self: Use JavaScript Escape Unescape Converter Tool on the web. Lecture: MWF 10:10 am - 11:00 am 302 Willard Building Textbook: A Mathematical Introduction to Logic, 2nd Edition by Herbert B. Enderton(See this errata list, which used to be on the author's website.) Office: 421 McAllister Building Office Hours: T 4:00--5:00 pm and R 2:00--3:00 pm or by appointment (email me to set up a meeting), or feel free to drop by unannounced (I may not be in).

See the course syllabus for additional details. Grades will be recorded on ANGEL.

## Supplementary resources

### Mathematical Logic (Fun)

Mathematical logic has captured the public interest. These popular science resources are not mathematically deep, but they are interesting, fun, and provide a general overview.
• Logicomix (highly recommended, although not entirely historically accurate)
• Gödel, Escher, and Bach (a meandering path through logic, zen koans, art, music, and meta-ness)
• Infinity and the Mind (an insightful look at infinity, self reference, and Gödel's theorems)
• More to be added...

## Homework Assignments

Please read my instructions for homework assignments.

## Schedule

The schedule below is tentative. The lecture notes may differ from what was presented in lecture. See Math 475 (Spring 2016) for notes from the last time this course was taught.

 Week Date Topics Book Sections Lecture Notes Remarks 1 01/09/17 Mon Introduction 1.1 notes 01/11/17 Wed Language of sentential logic, wffs 1.1 01/13/17 Fri Induction other, 1.1 2 01/16/17 Mon MLK Jr Day (No class) 01/18/17 Wed Induction on wffs 1.1 01/20/17 Fri Truth assignments 1.2 3 01/23/17 Mon Definition of |=, truth-tables 1.2 01/25/17 Wed Some facts about |= 1.2 01/27/17 Fri Parsing, Polish notation, induction, & recursion 1.3, 1.4 4 01/30/17 Mon Sequential connectives 1.5 02/01/17 Wed Compactness 1.7 02/03/17 Fri Natural deduction proof trees handout 5 02/06/17 Mon Natural deduction examples handout 02/08/17 Wed Induction on proofs handout 02/10/17 Fri Soundness for sentential logic handout 6 02/13/17 Mon Review 02/15/17 Wed Midterm 1 (in class) 02/17/17 Fri Completeness for sentential logic handout 7 02/20/17 Mon Completeness, elementary set theory handout, 0 02/22/17 Wed Functions, relations, sequences 0 02/24/17 Fri Cardinality, countability 0 8 02/27/17 Mon Cardinality, axiom of choice 0, 1.7 03/01/17 Wed Effectiveness 1.7 03/03/17 Fri Logic Puzzles! N/A SB SPRING BREAK. NO CLASSES THIS WEEK. 9 03/13/17 Mon Languages of first order logic 2.1 03/15/17 Wed Languages of first order logic 2.1 03/17/17 Fri Structures 2.2 10 03/20/17 Mon Satisfiability 2.2 03/22/17 Wed Models, logical implication 2.2 03/24/17 Fri Definability in a structure 2.2 11 03/27/17 Mon Definability of a class of structures 2.2 03/29/17 Wed Homomorphisms 2.2 03/31/17 Fri Homomorphism theorem, non-definable relations 2.2 12 04/03/17 Mon Review 04/05/17 Wed Midterm 2 (in class) 04/07/17 Fri Deduction rules for quantifiers handout, (2.4) 13 04/10/17 Mon Equality handout, (2.4) 04/12/17 Wed Additional examples handout, (2.4) 04/14/17 Fri Provability, consistency, satisfiability handout, (2.4) 14 04/17/17 Mon Applications of Compactness handout, (2.5) 04/19/17 Wed Soundness handout, (2.5) 04/21/17 Fri Completeness handout, (2.5) 15 04/24/17 Mon Completeness handout, (2.5) 04/26/17 Wed Halting problem and Godel's incompleteness 04/28/17 Fri Review FW TBA