Last updated: 4/08/02
TEXTS: What Is Mathematical Logic? by J.N. Crossley
et al. (Oxford,1972)
Logic for Mathematicians by A.G. Hamilton
(Cambridge,1978+)
| Week | Monday | Wednesday | Friday | Reading | Problems
Due on Wednesday of the next week |
|---|---|---|---|---|---|
| 1 Informal
Statement Calculus |
1-21 MLK Day | 1-23 Introduction:1.1,1.2
Statements, Connectives, and Truth Functions |
1- 25
Truth Tables |
C:1-History-(4 weeks)
H: 1.1,1.2 |
Due :1-30:
H. ch.1: 1,2,3(a-e,h),5(a,c),6a,7 |
| 2 | 1-28 1.3
Statement Forms and Substitution |
1-30 | 2-1 1.5
Connectives Arguments Preview |
H: 1.3-1.5 | Due: 2-6:
H. ch.1: 8, 9, 11a, 14a, 15a, 16, 17 |
| 3 Formal
Statement Calculus |
2-4 Products of sets | 2-6 1.6, Arguments | 2-8 2.1 Begin Formal Logic (L)
Proofs |
H: 1.6, 2.1 | Due 2-13:
H. ch.1:20, 21 ch.2: 1(a,b), 2(a,b), 3(a,b) |
| 4 | 2-11 2.1 More on proofs and The Deduction Theorem | 2-13 Deduction applications.
Begin valuations. |
2-15 2.2 Valuations-Soundness and Completeness of L (Adequacy) | H: 2.2 | Due 2-20 Extended to 2-27!
H. ch. 2: 6-8,10,11 |
| 5
Informal Predicate Calculus |
2-18 Completeness continued | 2-20 Extensions: Complete and consistent
...a proof of adequacy. |
2-22 Complete and consistent extensions- Adequacy finished! Begin Predicates and Quantifiers? | H: 2.2 cont'd.
H: 3.1 |
Due 2-27 (Extended from 2-20.)
H. ch. 2: 6-8,10,11 H. ch. 3: 1,2 |
| 6 | 2-25 3.1 Begin Predicates and quantifiers. | 2-27More on Predicates... valuations | 3-1 3.2 First Order Languages.
3.3 Interpretations 3.4 Valuations ,Truth and Validity |
H: 3.1,3.2 | Due : 3-6
H. ch. 3: 6, 7, 9(a,b) |
| 7
Formal Predicate Calculus |
3-4 3.4 Truth and Validity | 3-6 Truth and validity | 3-8 Finish Truth and validity | H: 3.3, 3.4
C: 2 (2 weeks) |
Due 3-13
H. ch. 3: 11, 12, 14(a-c), 15(a-c),16 |
| 8 | 3-11 Finish Truth and validity. | 3-13
4.1 Begin KL. Axioms,Rules,Proofs Soundness |
3-15More on Proofs: The Deduction Theorem.
Preparing for Adequacy |
H: 4.1 | Due: 3-27
H:4.1: 1 - 3 |
| 9
Spring Break |
3-18 No Class | 3-20 No Class | 3-22 No Class | ||
| 10 | 3-25 The Adequacy Theorem. | 3-27More on Adequacy | 3-29 Adequacy | H:4.1,4.2, 4.4
C: ch 2 |
Due: 4-5 (Friday)
H: 4.4: 12-14 |
| 11 | 4-1 NO Class!
CC Day |
4-3 finish Adequacy.
Begin Models |
4-5 Begin Equality and
Equivalence relations |
H:4.4.4.5, 5.1,5.2
C:ch 3 |
Due: 4-17 !!!
H: 4.5:16-18,20 |
| 12 | 4-8 More Equality and Equivalence relations and Normal models. | 4-10 1st Order Arithmetic | 4-12 Reading Day- NO class
Watch Video: A Non-Euclidean Universe. |
H:5.1, 5.2,5.4,5.5. | DUE:4-17. Brief report/paper on Video- How does Consistency prove Independence with models? |
| 13 | 4-15 1st Order Arithmetic | 4-171st Order Arithmetic | 4-19 Begin work on Formal Set Theory | H:5.4, 5.5
C:ch 6 Handout:SOS: 6,7,9 |
Due Monday: 4-29
H:5.2: 2,5,6 SOS: Ch.7:12-14,28 |
| 14 | 4-22 | 4-24 Axiom of Choice and The Continuum Hypothesis | 4-26 Formal arithmetic: Godel's Incompleteness Theorem (Introduction) | H: 5.5, 6.1,6.2,6.3
C: ch 4 |
|
| 15 | 4-29 Godel's Incompleteness Theorem.
Recursive functions and relations (Introduction) |
5-1Breath
More on Set Theory. |
5-3 Final exam distributed.More Set Theory. Zorn's Lemma | C: ch 5 | |
| 16 | 5-6 Cantor Bernstein. Start Turing Machines | 5-8 More Turing Machines | 5-10 A final look at the Continuum Hypothesis | ||
| 17 | 5-13 Final Exam Period | 5-15 Final Exam Period | 5-17 Final Examination
DUE by 5 pm! |