Math 457, Introduction to Mathematical Logic, Spring 2016

Course details

Instructor:     Jason Rute
Email:    
Lecture:     MWF 10:10 am - 11:00 am
206 Osmond Lab
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 1:00 - 2:00 pm 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

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.

Mathematics in general

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 2014) for notes from the last time this course was taught.

Week Date Topics Book Sections Lecture Notes Remarks
1 01/11/16 Mon Introduction 1.1 notes  
01/13/16 Wed Language of sentential logic, wffs 1.1 notes  
01/15/16 Fri Induction other, 1.1 notes  
2 01/18/16 Mon MLK Jr Day (No class)      
01/20/16 Wed Induction on wffs 1.1 notes  
01/22/16 Fri Truth assignments 1.2 notes  
3 01/25/16 Mon Definition of |=, truth-tables 1.2 notes  
01/27/16 Wed Some facts about |= 1.2 notes  
01/29/16 Fri Parsing, Polish notation, induction, & recursion 1.3, 1.4 notes  
4 02/01/16 Mon Sequential connectives 1.5 notes  
02/03/16 Wed Compactness 1.7 notes  
02/05/16 Fri Natural deduction proof trees handout handout  
5 02/08/16 Mon Natural deduction examples handout handout  
02/10/16 Wed Induction on proofs handout handout  
02/12/16 Fri Soundness for sentential logic handout handout  
6 02/15/16 Mon Review   notes  
02/17/16 Wed Midterm 1 (in class)   solutions  
02/19/16 Fri Completeness for sentential logic handout handout  
7 02/22/16 Mon Completeness, elementary set theory handout, 0 notes  
02/24/16 Wed Functions, relations, sequences 0 notes  
02/26/16 Fri Cardinality, countability 0 notes  
8 02/29/16 Mon Cardinality, axiom of choice 0, 1.7 old notes   
03/02/16 Wed Effectiveness 1.7 notes  
03/04/16 Fri Logic Puzzles! N/A    
SB   SPRING BREAK. NO CLASSES THIS WEEK.      
9 03/14/16 Mon Languages of first order logic 2.1 notes  
03/16/16 Wed Languages of first order logic 2.1 notes  
03/18/16 Fri Structures 2.2 notes  
10 03/21/16 Mon Satisfiability 2.2 notes  
03/23/16 Wed Models, logical implication 2.2 notes  
03/25/16 Fri Definability in a structure 2.2 notes  
11 03/28/16 Mon Definability of a class of structures 2.2 notes  
03/20/16 Wed Homomorphisms 2.2 old notes  
04/01/16 Fri Homomorphism theorem, non-definable relations 2.2 old notes  
12 04/04/16 Mon Review   notes  
04/06/16 Wed Midterm 2 (in class)   solutions  
04/08/16 Fri Deduction rules for quantifiers handout, (2.4) handout  
13 04/11/16 Mon Equality handout, (2.4) See prev. handout  
04/13/16 Wed Additional examples handout, (2.4) handout  
04/15/16 Fri Provability, consistency, satisfiability handout, (2.4) handout  
14 04/18/16 Mon Applications of Compactness handout, (2.5) handout  
04/20/16 Wed Soundness handout, (2.5) See prev. handout  
04/22/16 Fri Completeness handout, (2.5) handout  
15 04/25/16 Mon Completeness handout, (2.5) See prev. handout  
04/27/16 Wed Halting problem and Godel's incompleteness   old notes  
04/29/16 Fri Review   notes  
FW 05/04/16 Wed Final Exam (8:00 - 9:50 am, 106 Osmond)