Last updated: 2/26/98
TEXTS: What Is Mathematical Logic? by J.N. Crossley
et al. (Oxford,1972)
Logic for Mathematicians by A.G. Hamilton
(Cambridge,1978+)
Set Theory and related topics by S. Lipshutz
( Schaum/ Mcgraw Hill,?)
| Week | Tuesday | Thursday | Reading | Problems
Due on Thursday of the next week |
|---|---|---|---|---|
| 1 Informal
Statement Calculus |
1/20
Introduction:1.1,1.2 Statements, Connectives, and Truth Functions |
1/22
Products of sets, Truth Tables |
C:1-History-(4 weeks)
H: 1.1,1.2 L: 4,5,14 |
H. ch.1: 1,2,3(a-e,h),5(a,c),6a,7
L: ch 5: 7,25,26,32 ch 14: 26, 28, 34, 37, 38 |
| 2 | 1/27 1.3
Statement Forms and Substitution |
1/29 1.5
Connectives Arguments Preview |
H: 1.3-1.5 | H. ch.1: 8, 9, 11a, 14a, 15a, 16, 17 |
| 3
Formal Statement Calculus |
2/3 1.6, 2.1
Arguments Begin Formal Logic (L) |
2/5 2.1 Proofs | H: 1.6,2.1 | H. ch.1:20, 21
ch.2: 1(a,b), 2(a,b), 3(a,b) |
| 4 | 2/10
2.1 The Deduction Theorem |
2/12 2.2 Valuations-Completeness of L (Adequacy) | H: 2.2 | H. ch. 2: 6-8,10,11 |
| 5
Informal Predicate Calculus |
2/17 Completeness continued
|
2/19 Complete and consistent extensions- Adequacy finished!
|
||
| 6 | 2/24
3.1 Begin Predicates and quantifiers. |
2/26
3.2 First Order Languages. |
H: 3.1,3.2
L: 6,15 |
H. ch. 3: 1,2, 6, 7, 9(a,b) |
| 7
Formal Predicate Calculus |
3/3 3.3 Interpretations | 3/5 3.4 Valuations
|
H: 3.3, 3.4
L: 17 C: 2 (2 weeks) |
H. ch. 3: 11, 12, 14(a-c), 15(a-c),16 |
| 8 | 3/10 3.4 Truth and Validity | 3/12 3.4 Truth and Validity | H: 4.1 | |
| 9
Spring Break |
3/17 No Class | 3/19 No Class | ||
| 10 | 3/24 Finish Truth and validity
4.1 Begin KL.Axioms,Rules,Proofs |
3/26 Soundness
The Deduction Theorem Preparing for Adequacy |
H:4.1,4.2 | H:4.1: 1 - 3 |
| 11 | 3/31 The Adequacy Theorem | 4/2 Adequacy. | H:4.4
C: ch 2 |
H: 4.4: 12-14 |
| 12 | 4/7 More on Adequacy | 4/9 Finish Adequacy
Begin Models |
H:4.5, 5.1,5.2
C:ch 3 |
H: 4.5:16-18,20 |
| 13 | 4/14 Equality
Equivalence relations |
4/16 1st Order Arithmetic Formal Set Theory- |
H:5.4, 5.5
C:ch 6 SOS: 6,7,9 |
H:5.2: 2,5,6 SOS: Ch.7:12-14,28 |
| 14 | 4/21 Axiom of Choice and The Continuum Hypothesis Begin work on formal arithmetic |
4/23 Recursive functions and relations | H: 6.1,6.2,6.3
C: ch 4 |
|
| 15 | 4/28Godel's Incompleteness Theorem | 4/30 Breath | C: ch 5 | |
| 16 | 5/5 | 5/7 |