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<h3>Incompleteness and Undecidability</h3>
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  <th width="30"> Number </th>
  <th width="93"> Lecture Date </th>
  <th width="241"> Subject </th>
  <th width="209"> Reading in Kleene's IM</th>
  <th width="88"> Homework</th>
</tr>
<td> 1 </td>
<td>  April 1 </td>
 <td> <a href="Lecture1Slides.pdf"> History and Introduction </a></td>
 <td> Chapters II and III </td>
 <td><a href="Assignment1.pdf">Assignment 1</a></td>
</tr>
<tr>
  <td> 2 </td>
  <td> April 3 </td>
  <td> <a href="Lecture2Slides.pdf"> Examples of First-order Theories </a></td>
  <td> Chapter IV </td>
  <td><a href="Assignment2.pdf">Assignment 2</a></td>
</tr>
<tr>
  <td> 3 </td>
  <td> April 8 </td>
  <td> <a href="Lecture3Slides.pdf"> Peano's Arithmetic, non-standard models, Skolem's paradox </a> <br>
  </td>
  <td> Chapter IV </td>
  <td> No assignment. </td>
</tr>
<tr>
  <td> 4 </td>
  <td> April 10 </td>
  <td> <a href="Lecture4Slides.pdf"> Primitive Recursive Functions</a></td>
  <td> Chapter IX, sections 43-46 and <br>
       Chapter XI, pages 270-274</td>
  <td><a href="Assignment4.pdf">Assignment 4</a></td>
</tr> 
<tr>
  <td> 5 </td>
  <td> April 15 </td>
  <td>  <a href="Lecture5Slides.pdf"> The Halting Problem</a> </td>
  <td> no reading in Kleene </td>
  <td><a href="Assignment5.pdf">Assignment 5</a></td>
  </tr>
<tr>
  <td> 6 </td>
<td> April 17 </td>
<td> <a href="Lecture6Slides.pdf">Turing Machines, Intro and examples</a> <br>
     <a href="https://www.youtube.com/watch?v=E3keLeMwfHY">Movie shown in class of a hobbyist's working Turing machine</a></td>
<td> Chapter XIII, sections 67 and 70
</td>
<td><a href="Assignment6.pdf">Assignment 6 </a></td>
</tr>
<tr>
  <td> 7 </td>
<td> April 22 </td>
<td><a href="Lecture7Slides.pdf"> Primitive recursion is Turing computable</a></td>
<td>no reading in Kleene                           </td>
<td><a href="Assignment7.pdf">Assignment 7 </a></td>
</tr>
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  <td> 8 </td>
<td> April 24 </td>
<td> <a href="Lecture8Slides.pdf">Computation by Turing Machines</a></td>
<td>no reading in Kleene  </td>
<td> <a href="Assignment8.pdf">Assignment 8 </a></td>
</tr>
   <td> 9 </td>
<td> April 29 </td>
<td>  <a href="Lecture9Slides.pdf">The recursion theorem</a> <br>
   <a href="Lecture9BSlides.pdf">The lambda calculus</a> </td>
<td>no reading in Kleene  </td>
<td> <a href="Assignment9.pdf">Assignment 9</a></td>
</tr>
<tr>
  <td> 10 </td>
<td> May 1 </td>
<td> <a href="Lecture10Slides.pdf"> Proof and Computation </a>  </td>
<td> Chapter VIII,sections 38-40 </td>
<td> <a href="Assignment10.pdf">Assignment 10 (revised) </a> </td>
</tr>
<tr>
  <td> 11 </td>
<td> May 6 </td>
<td><a href="Lecture11Slides.pdf">  Peano Arithmetic and Primitive Recursion</a></td>
<td> Chapter VIII,section 41 </td>
<td> <a href="Assignment11.pdf">Assignment 11 </a> </td>
</tr>
<tr>
  <td> 12 </td>
<td> May 8 </td>
<td><a href="Lecture12Slides.pdf"> Arithmetization of Syntax </a> </td>
<td> Chapter IX </td>
<td> <a href="Assignment12.pdf">Assignment 12 </a> </td>
</tr>
<tr>
  <td> 13 </td>
<td> May 13 </td>
<td><a href="Lecture13Slides.pdf">The First Incompleteness Theorem</a>    </td>
<td> Chapter VIII, section 42    </td>
<td> <a href="Assignment13.pdf">Assignment 13 </a> </td>
</tr>
<tr>
<tr>
  <td>  </td>
<td> May 15 </td>
<td>We worked on some problems from Assignment 11 in class  </td>
<td>    </td>
<td>   </a> </td>
</tr>
<tr>

<tr>
  <td> 14 </td>
<td> May 20 </td>
<td><a href="Lecture14Slides.pdf">Rosser's Theorem, the length of proofs, Robinson's Arithmetic, and Church's theorem</a></td>
<td> Section 42, Theorem 29 is Rosser's theorem <br>
   Section 76 for Church's theorem  </td>
<td> <a href="Assignment14.pdf">Assignment 14 </a> </td>
</tr>
<tr>
  <td> 15 </td>
<td> May 22 </td>
<td><a href="Lecture15Slides.pdf">The Second Incompleteness Theorem </a></td>
<td>Chapter VIII, Theorem 30</td>
<td> <a href="Assignment15.pdf"> Assignment 15 </a> </td>
</tr>
 
<tr>
  <td> 16 </td>
<td> May 27</td>
<td><a href="Lecture16Slides.pdf">Chaitin's work</a> </td>
<td> No reading in Kleene   </td>
<td> <a href="Assignment16.pdf"> Assignment 16 </a> </td>
</tr>
<tr>
  <td> 17 </td>
<td> May 29</td>
<td><a href="Lecture17Slides.pdf"> Discussion of incompleteness </a></td>
<td> No reading in Kleene   </td>
<td> No homework to turn in. <br>  Review old homework and bring any unresolved questions to class.</td>
</tr>
<tr>  
  <td> 18 </td>
<td> June 3</td>
<td>Loose ends; student questions; go over old homework <br>
   Here is the <a href="FinalExam.pdf">final exam</a>, due June 11 at noon.
 </td>
<td>  </td>
<td>All students earned A on the last homework assignment</td>
</tr>
  <td> 19 </td>
<td> We don't get here</td>
<td> Intuitionism </td>
<td>Chapter XV, section 81  </td>
<td>   </td>
</tr>
<tr>
  <td> 20 </td>
<td> We don't get here </td>
<td>Recursive Realizability </td>
<td> Chapter XV, section 82 </td>
<td>  </td>
</tr>
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