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Instructor: |
Mark Iwen |
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Time and Place: |
WF 11:45 AM - 1:00 PM in
Allen 318 |
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E-mail: |
markiwen@math.duke.edu |
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Office: |
Physics 015 |
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Office Phone: |
(919) 660-2871 |
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Office Hours: |
Mondays and Tuesdays from 3:00 PM until 4:00 PM. |
| Course Information: | Syllabus |
| The Book: | A Mathematical Introduction to Logic, Second Edition, by Herbert B. Enderton, Harcourt/Academic Press, San Diego, 2001. ISBN: 0-12-238452-0 |
| An Application: | Planning in artificial intelligence |
| LaTeX Examples: | See these zipped files. Both a .tex file and the resulting .pdf file are included.
|
| A list of LaTeX commands for the logical operators is here. | |
| Both the .tex and the resulting .pdf files for the WFF decomposition algorithm. | |
| Free LaTeX Compilers: | These programs compile .tex files into .pdf files. I recommend MiKTeX for windows, and MacTeX for Macs. |
| Homework Examples: | Page 19, 5.(b) as a pdf. The LaTeX file that created the pdf is here. |
| Page 34, 4 as a pdf. The LaTeX file that created the pdf is here. | |
| Page 99, 5 as a pdf. |
| Class Date |
Sections Covered |
Homework Assigned |
Homework Due |
| Wed, Aug 29 | 1.1, Pages 13--19 1.3, Pages 29--34 |
--Read Syllabus --Page 19: 1, 2 |
Wed, Sep 5 |
| Fri, Aug 31 | 1.1, 1.2, & 1.3 | --Prove that every wff has a unique ancestral tree (Hint: Reference Corollary 2.2 from class). --Page 34: 7 (Hint: Try to build a tree bottom up instead of top down. How can you distinguish connectives joining two atomic formulas from other connectives higher up the ancestral tree?) |
Wed, Sep 5 |
| Wed, Sep 5 | 1.2 & 1.3 | --Prove ((B ∨ A) → ((¬B) → A)) for all A,B in WFF. --Either do Page 27: 2, 4, 7, 12, OR, do Page 27: 4, 10 |
Type #4 in LaTeX for "proof workshop" held on Wed, Sep 12. Else due Wed, Sep 19. |
| Fri, Sep 7 | 1.5 & 1.3 | --Prove that {¬,→} is complete. --Page 52: 1, 3 |
Wed, Sep 19 |
| Wed, Sep 12 | Logic in AI, & Proof Workshop! |
--Read section 1.6 --Show that 2*(#blocks-1) move actions allow one to solve any solvable BLOCKS WORLD problem. |
Wed, Sep 19 |
| Fri, Sep 14 | Cardinality | --Read Chapter 0 pages 6 -- 10 --Prove that R3~R --Prove that R~P(N) by constructing two injective functions and then using the Schröder-Bernstein Theorem. |
Wed, Sep 19 |
| Wed, Sep 19 | 1.7 | --Page 65: 3, 6, 7 (Hint: #5 was done in Lecture 3. Consider repeatedly using #4 from page 27.) |
Wed, Sep 26 |
| Fri, Sep 21 | SAT & NP-completeness |
--Page 65: 11 | Wed, Sep 26 |
| Wed, Sep 26 | 2.1 & 2.2 | --Page 79: 1, 2, 4, 6 | Wed, Oct 3 |
| Fri, Sep 28 | 2.1, 1.4, & 2.3 | None! | Wed, Oct 3 |
| Wed, Oct 3 | 2.1, 2.2, & 2.3 | --Page 108: 2 | Wed, Oct 10 |
| Fri, Oct 5 | 2.2 | --Page 99: 1, 3, 4, 6 | Wed, Oct 10 |
| No Class Mon, Oct 8 |
Voter registration ends in 4 Days! |
Voter registration ends in 4 Days! |
Voter registration ends in 4 Days! |
| Wed, Oct 10 | 2.2 & 2.4 | --Page 129: #2 (Hint: A generalization of an axiom is still an axiom from the same group.), #3 (Hint: See page 114), and #4 |
Wed, Oct 17 |
| Fri, Oct 12 | 2.4 | --Page 130: 6, 8 | Wed, Oct 17 |
| Wed, Oct 17 | 2.4 & 2.5 | --Page 145: 2, 4 | Wed, Oct 24 |
| Fri, Oct 19 | 2.5 | --Study! | Wed, Oct 24 |
| Wed, Oct 24 | Class notes and HW through Oct 17th |
MIDTERM EXAM | Wed, Oct 24 |
| Fri, Oct 26 | 2.5 | --Prove that s̄(t)=t for all terms t, where s is the translation (w.r.t. the structure) defined on p. 137. --Page 146: 5, 7 |
Wed, Oct 31 |
| Wed, Oct 31 | 2.6 & 2.2 | --Page 101: 16 --Page 162: 1, 3 |
Wed, Nov 7 |
| Fri, Nov 2 | 2.6 | --Page 162: 2, 8 | Wed, Nov 7 |
| No Class Tues, Nov 6 |
Election Day! | Election Day! | Election Day! |
| Wed, Nov 7 | 3.1 & 2.6 | --Page 163: 5 --Page 193: 1, 4 |
Wed, Nov 14 |
| Fri, Nov 9 | 3.3 | --Page 223: 2 | Wed, Nov 14 |
| Wed, Nov 14 | 3.3 | --Page 223: 1 | Wed, Nov 28 |
| Fri, Nov 16 | 3.3 | --Page 223: 3, 4 | Wed, Nov 28 |
| Wed, Nov 21 | Thanksgiving | Thanksgiving break | Thanksgiving |
| Fri, Nov 23 | Thanksgiving | Thanksgiving break | Thanksgiving |
| Wed, Nov 28 | 3.4 & 3.3 | --Page 223: 5 (HINT: A number 'x' is a sequence number iff it's divisible by exactly the first y < x primes. You will need to use Thm 33I as well as items 2 (p. 217), 4 (p. 218), and 7 (p. 219).) |
Fri, Dec 7 |
| Fri, Nov 30 | 3.5, 3.4, & 3.3 | --Page 224: 9 (HINT: See the top of p. 220 for a related example.) |
Fri, Dec 7 |
| Wed, Dec 5 | 3.5 & 3.7 | None | N/A |
| Fri, Dec 7 | 3.7 | COME AND GET THE TAKE HOME FINAL! | Fri, Dec 14, 5:00 PM |
| Fri, Dec 14 | CUMULATIVE | FINAL EXAM | 2:00 PM - 5:00 PM |