Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield
Tuesday, 25 January 2005 <ul><li>HW 1: assigned today, due next Tue (1 Feb) </li></ul><ul><ul><li>Rosen, section 1.1: 18, ...
Thursday, 27 January 2005 <ul><li>HW 1: assigned last time, due next Tue (1 Feb) </li></ul><ul><ul><li>Rosen, section 1.1:...
Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><l...
Tuesday, 1 February 2005 <ul><li>HW 1: due today </li></ul><ul><ul><li>Rosen, section 1.1: 18, 48, 60 </li></ul></ul><ul><...
Are all of their statements true? Show values for s, b, and f such that the equation is true Original statement Definition...
Thursday, 3 February 2005 <ul><li>HW 2: due today </li></ul><ul><ul><li>Rosen, section 1.2: 19, 35, 39, 50 </li></ul></ul>...
A bit of humor…
Quick survey <ul><li>The amount of time the homeworks are taking: </li></ul><ul><li>Very little </li></ul><ul><li>About ri...
Quick survey <ul><li>How hard have the homeworks been so far? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat ha...
Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><l...
Tuesday, 8 February 2005 <ul><li>HW 3: due today </li></ul><ul><ul><li>Rosen, section 10.3: 3, 4, 5, 9 </li></ul></ul><ul>...
Thursday, 10 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HWs 1 and 2 returned today </li></ul></ul><ul><ul><ul><...
Quick survey <ul><li>The amount of time the homeworks are taking: </li></ul><ul><li>Very little </li></ul><ul><li>About ri...
Quick survey <ul><li>How hard have the homeworks been so far? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat ha...
Tuesday, 15 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 4 returned today </li></ul></ul><ul><ul><ul><li>Solut...
Thursday, 15 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 3 returned today </li></ul></ul><ul><ul><ul><li>HW 3...
Proof by contradiction example 2 <ul><li>Rosen, section 1.5, question 21 (b) </li></ul><ul><ul><li>Prove that if n is an i...
A note on that problem… <ul><li>Rosen, section 1.5, question 21 </li></ul><ul><ul><li>Prove that if n is an integer and n ...
How the book explains  proof by contradiction <ul><li>A very poor explanation, IMHO </li></ul><ul><li>Suppose q is a contr...
Tuesday, 22 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 7: Due today </li></ul></ul><ul><ul><li>HW 8: Due nex...
Tuesday, 1 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 8: Due today (Rosen, section 1.8: 17, 36, 61, 64) </li></...
Quick survey <ul><li>How hard was the exam? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat hard </li></ul><ul><...
Thursday, 3 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 8: Due last Tuesday, can hand it in today  </li></ul></u...
Tuesday, 15 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 10: Due today: Rosen, section 2.6, question 46 and 47 (s...
Thursday, 17 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 10: Due today: Rosen, section 2.6, question 46 and 47 (...
Tuesday, 22 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34 </li></u...
Thursday, 24 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 12: due today: Rosen, section 2.2: 10, 14, 17, 20  </li...
Third induction again: what if your inductive hypothesis was wrong? <ul><li>Show: </li></ul><ul><li>Base case:  n  = 1: </...
Third induction again: what if your inductive hypothesis was wrong? <ul><li>Inductive step: show  </li></ul>
Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><l...
Tuesday, 29 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 </li></ul...
Thursday, 31 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 </li></u...
Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><l...
Comments from the surveys <ul><li>53 surveys received </li></ul><ul><li>Biggest complaint: textbook (12 negative responses...
Tuesday, 5 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 15: due today: Rosen, section 3.4: 11, 27, 44, 59 </li></...
About the second midterm <ul><li>Sections 2.1, 2.2, 2.4, 2.6 (the RSA part), 3.1-3.4, and 4.1, as well as the talk about N...
New homework grading scheme <ul><li>Homeworks will now be graded on a 10-point scale </li></ul><ul><li>Each problem is wor...
Thursday, 7 April 2005 <ul><li>Test today! </li></ul><ul><ul><li>In case you forgot… </li></ul></ul><ul><li>Homeworks </li...
Tuesday, 12 April 2005 <ul><li>Tests returned today… </li></ul><ul><ul><li>Average: 78.9 (without extra credit) </li></ul>...
Thursday, 14 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 </li><...
Tuesday, 19 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 18: due today: Rosen, section 4.4: 7, 15, 30* </li></ul>...
Thursday, 21 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35 </li>...
Tuesday, 26 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45 </li><...
Thursday, 28 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, ...
Course objectives <ul><li>Logic </li></ul><ul><ul><li>Introduce a formal system (propositional and predicate logic) which ...
The End <ul><li>Homeworks </li></ul><ul><ul><li>HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26 </li></ul></ul><ul><u...
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  1. 1. Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield
  2. 2. Tuesday, 25 January 2005 <ul><li>HW 1: assigned today, due next Tue (1 Feb) </li></ul><ul><ul><li>Rosen, section 1.1: 18, 48, 60 </li></ul></ul><ul><li>HW 2: assigned Thu, due following Thu (3 Feb) </li></ul><ul><ul><li>Rosen, section 1.2: 19, 35, 39, 50 </li></ul></ul><ul><ul><li>Must answer 19 by both truth tables and logical equivalences </li></ul></ul><ul><li>TA office hours will be posted on the website </li></ul><ul><ul><li>Monday afternoon/evening (a homework review session) </li></ul></ul><ul><ul><li>Wednesday 3:30-5:30 in Olsson 018 </li></ul></ul><ul><ul><li>Friday 10:00-noon in Olsson 018 </li></ul></ul><ul><li>My Thursday office hours are changing, but I’m not sure what to yet </li></ul>
  3. 3. Thursday, 27 January 2005 <ul><li>HW 1: assigned last time, due next Tue (1 Feb) </li></ul><ul><ul><li>Rosen, section 1.1: 18, 48, 60 </li></ul></ul><ul><li>HW 2: assigned today, due next Thu (3 Feb) </li></ul><ul><ul><li>Rosen, section 1.2: 19, 35, 39, 50 </li></ul></ul><ul><ul><li>Must answer 19 by both truth tables and logical equivalences </li></ul></ul><ul><li>TA office hours: </li></ul><ul><ul><li>Monday afternoon/evening (a homework review session) </li></ul></ul><ul><ul><li>Wednesday 3:30-5:30 in Olsson 018 </li></ul></ul><ul><ul><li>Friday 10:00-noon in Olsson 018 </li></ul></ul><ul><li>About the grade requirement for CS 216 </li></ul><ul><ul><li>And about doing well in this class… </li></ul></ul><ul><li>Reading for Tuesday: 1.3 </li></ul><ul><ul><li>Ideally, should have read 1.1, 1.2, and 10.3 by now </li></ul></ul><ul><li>My Thursday office hours </li></ul><ul><li>Proof methods </li></ul>
  4. 4. Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><li>via logical equivalences </li></ul></ul><ul><li>Set equivalences </li></ul><ul><ul><li>via membership tables </li></ul></ul><ul><ul><li>via set identities </li></ul></ul><ul><ul><li>via mutual subset proof </li></ul></ul><ul><ul><li>via set builder notation and logical equivalences </li></ul></ul><ul><li>Rules of inference </li></ul><ul><ul><li>for propositions </li></ul></ul><ul><ul><li>for quantified statements </li></ul></ul><ul><li>Pigeonhole principle </li></ul><ul><li>Combinatorial proofs </li></ul><ul><li>Ten proof methods in section 1.5: </li></ul><ul><ul><li>Direct proofs </li></ul></ul><ul><ul><li>Indirect proofs </li></ul></ul><ul><ul><li>Vacuous proofs </li></ul></ul><ul><ul><li>Trivial proofs </li></ul></ul><ul><ul><li>Proof by contradiction </li></ul></ul><ul><ul><li>Proof by cases </li></ul></ul><ul><ul><li>Proofs of equivalence </li></ul></ul><ul><ul><li>Existence proofs </li></ul></ul><ul><ul><ul><li>Constructive </li></ul></ul></ul><ul><ul><ul><li>Non-constructive </li></ul></ul></ul><ul><ul><li>Uniqueness proofs </li></ul></ul><ul><ul><li>Counterexamples </li></ul></ul><ul><li>Induction </li></ul><ul><ul><li>Weak mathematical induction </li></ul></ul><ul><ul><li>Strong mathematical induction </li></ul></ul><ul><ul><li>Structural induction </li></ul></ul>
  5. 5. Tuesday, 1 February 2005 <ul><li>HW 1: due today </li></ul><ul><ul><li>Rosen, section 1.1: 18, 48, 60 </li></ul></ul><ul><li>HW 2: due Thu (3 Feb) </li></ul><ul><ul><li>Rosen, section 1.2: 19, 35, 39, 50 </li></ul></ul><ul><ul><li>Must answer 19 by both truth tables and logical equivalences </li></ul></ul><ul><li>HW 3: due Tue (8 Feb) </li></ul><ul><ul><li>Rosen, section 10.3: 3, 4, 5, 9 </li></ul></ul><ul><li>TA office hours: </li></ul><ul><ul><li>Monday 5:00-7:00 (a homework review session) </li></ul></ul><ul><ul><li>Wednesday 3:30-5:30 in Olsson 018 </li></ul></ul><ul><ul><li>Friday 10:00-noon in Olsson 018 </li></ul></ul><ul><li>Reading for Tuesday: 1.6/1.7 </li></ul><ul><li>My Thursday office hours: now 10:30-noon </li></ul><ul><li>Rescheduling the homework review session (so as not to conflict with CS 201 labs)? </li></ul><ul><li>Terminology: disjunction and conjunction (and question 1.2 # 35) </li></ul><ul><li>Logic gates: not on test, but on HW 3 </li></ul>
  6. 6. Are all of their statements true? Show values for s, b, and f such that the equation is true Original statement Definition of implication Associativity of AND Re-arranging Idempotent law Re-arranging Absorption law Re-arranging Distributive law Negation law Domination law Associativity of AND
  7. 7. Thursday, 3 February 2005 <ul><li>HW 2: due today </li></ul><ul><ul><li>Rosen, section 1.2: 19, 35, 39, 50 </li></ul></ul><ul><li>HW 3: due Tue (8 Feb) </li></ul><ul><ul><li>Rosen, section 10.3: 3, 4, 5, 9 </li></ul></ul><ul><li>HW 4: due Thu (10 Feb) </li></ul><ul><ul><li>Rosen, section 1.7: 10, 16, 22, 34, 43 </li></ul></ul><ul><li>TA office hours: </li></ul><ul><ul><li>Monday 5:00-7:00 (a homework review session) </li></ul></ul><ul><ul><li>Wednesday 3:30-5:30 in Olsson 018 </li></ul></ul><ul><ul><li>Friday 10:00-noon in Olsson 018 </li></ul></ul><ul><li>Reading for Tuesday: 1.3/1.4 </li></ul><ul><li>That crane picture sequence… </li></ul>
  8. 8. A bit of humor…
  9. 9. Quick survey <ul><li>The amount of time the homeworks are taking: </li></ul><ul><li>Very little </li></ul><ul><li>About right </li></ul><ul><li>A lot </li></ul><ul><li>Way to much </li></ul>
  10. 10. Quick survey <ul><li>How hard have the homeworks been so far? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat hard </li></ul><ul><li>About right </li></ul><ul><li>Very easy </li></ul>
  11. 11. Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><li>via logical equivalences </li></ul></ul><ul><li>Set equivalences </li></ul><ul><ul><li>via membership tables </li></ul></ul><ul><ul><li>via set identities </li></ul></ul><ul><ul><li>via mutual subset proof </li></ul></ul><ul><ul><li>via set builder notation and logical equivalences </li></ul></ul><ul><li>Rules of inference </li></ul><ul><ul><li>for propositions </li></ul></ul><ul><ul><li>for quantified statements </li></ul></ul><ul><li>Pigeonhole principle </li></ul><ul><li>Combinatorial proofs </li></ul><ul><li>Ten proof methods in section 1.5: </li></ul><ul><ul><li>Direct proofs </li></ul></ul><ul><ul><li>Indirect proofs </li></ul></ul><ul><ul><li>Vacuous proofs </li></ul></ul><ul><ul><li>Trivial proofs </li></ul></ul><ul><ul><li>Proof by contradiction </li></ul></ul><ul><ul><li>Proof by cases </li></ul></ul><ul><ul><li>Proofs of equivalence </li></ul></ul><ul><ul><li>Existence proofs </li></ul></ul><ul><ul><ul><li>Constructive </li></ul></ul></ul><ul><ul><ul><li>Non-constructive </li></ul></ul></ul><ul><ul><li>Uniqueness proofs </li></ul></ul><ul><ul><li>Counterexamples </li></ul></ul><ul><li>Induction </li></ul><ul><ul><li>Weak mathematical induction </li></ul></ul><ul><ul><li>Strong mathematical induction </li></ul></ul><ul><ul><li>Structural induction </li></ul></ul>
  12. 12. Tuesday, 8 February 2005 <ul><li>HW 3: due today </li></ul><ul><ul><li>Rosen, section 10.3: 3, 4, 5, 9 </li></ul></ul><ul><li>HW 4: due Thu (10 Feb) </li></ul><ul><ul><li>Rosen, section 1.7: 10, 16, 22, 34, 43 </li></ul></ul><ul><li>HW 5: due Tue (15 Feb) </li></ul><ul><ul><li>Rosen, section 1.3: 15, 20, 24, 41 </li></ul></ul><ul><li>HW 6: Due Thu (17 Feb) </li></ul><ul><ul><li>Rosen, section 1.4: 12, 22, 33, 40 </li></ul></ul><ul><li>Reading for Thursday: 1.5 </li></ul><ul><li>Exam: two weeks from this Thursday </li></ul><ul><ul><li>Last semester’s exam will be posted on the website </li></ul></ul><ul><li>Would people use forums if I set them up? </li></ul>
  13. 13. Thursday, 10 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HWs 1 and 2 returned today </li></ul></ul><ul><ul><ul><li>HW 1: Average 80.3, standard deviation 20.0 </li></ul></ul></ul><ul><ul><ul><li>HW 2: Average 85.0, standard deviation 18.4 </li></ul></ul></ul><ul><ul><ul><li>Solutions and grading guidelines will be posted shortly </li></ul></ul></ul><ul><ul><ul><li>Regrades for homeworks </li></ul></ul></ul><ul><ul><li>HW 3: can turn in late… </li></ul></ul><ul><ul><li>HW 4: due today </li></ul></ul><ul><ul><ul><li>Rosen, section 1.7: 10, 16, 22, 34, 43 </li></ul></ul></ul><ul><ul><li>HW 5: due Tue (15 Feb) </li></ul></ul><ul><ul><ul><li>Rosen, section 1.3: 15, 20, 24, 41 </li></ul></ul></ul><ul><ul><li>HW 6: Due Thu (17 Feb) </li></ul></ul><ul><ul><ul><li>Rosen, section 1.4: 12, 22, 33, 40 </li></ul></ul></ul><ul><li>Reading for today and next Tuesday: 1.5 </li></ul><ul><li>Exam: two weeks from today </li></ul><ul><ul><li>Last semester’s exam will be posted on the website </li></ul></ul>
  14. 14. Quick survey <ul><li>The amount of time the homeworks are taking: </li></ul><ul><li>Very little </li></ul><ul><li>About right </li></ul><ul><li>A lot </li></ul><ul><li>Way to much </li></ul>
  15. 15. Quick survey <ul><li>How hard have the homeworks been so far? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat hard </li></ul><ul><li>About right </li></ul><ul><li>Very easy </li></ul>
  16. 16. Tuesday, 15 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 4 returned today </li></ul></ul><ul><ul><ul><li>Solutions and grading guidelines will be posted shortly </li></ul></ul></ul><ul><ul><li>HW 5: due today </li></ul></ul><ul><ul><ul><li>Rosen, section 1.3: 15, 20, 24, 41 </li></ul></ul></ul><ul><ul><li>HW 6: Due Thu (17 Feb) </li></ul></ul><ul><ul><ul><li>Rosen, section 1.4: 12, 22, 33, 40 </li></ul></ul></ul><ul><ul><li>HW 7: Due Tue (19 Feb) </li></ul></ul><ul><ul><ul><li>Rosen, section 1.5: 10, 22, 34, 55 </li></ul></ul></ul><ul><ul><li>HW 8: Due Tue (26 Feb) </li></ul></ul><ul><ul><ul><li>Rosen, section 1.8: 17, 36, 61, 64 </li></ul></ul></ul><ul><li>Regrades for homeworks </li></ul><ul><ul><li>Form is on the website </li></ul></ul><ul><ul><li>Must be within a week </li></ul></ul><ul><li>Reading for Thursday: 1.8 </li></ul><ul><li>Exam: one week from this Thursday </li></ul><ul><ul><li>Will cover all of chapter 1 (sections 1.1-1.8) </li></ul></ul><ul><ul><li>Last semester’s exam will be posted on the website </li></ul></ul><ul><ul><ul><li>It only covered 1.1-1.7 </li></ul></ul></ul><ul><ul><ul><li>And it was a 50 minute exam, not a 75 minute exam </li></ul></ul></ul>
  17. 17. Thursday, 15 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 3 returned today </li></ul></ul><ul><ul><ul><li>HW 3: Average 82.3 </li></ul></ul></ul><ul><ul><ul><li>A lot of missing HW 3’s – check your grades on Toolkit </li></ul></ul></ul><ul><ul><li>HW 6: Due today (Rosen, section 1.4: 12, 22, 33, 40) </li></ul></ul><ul><ul><li>HW 7: Due Tue (19 Feb) (Rosen, section 1.5: 10, 22, 34, 55) </li></ul></ul><ul><ul><li>HW 8: Due Tue (26 Feb) (Rosen, section 1.8: 17, 36, 61, 64) </li></ul></ul><ul><li>Regrades for homeworks </li></ul><ul><ul><li>Form is on the website, and I have copies on me </li></ul></ul><ul><ul><li>Must be within a 10 days </li></ul></ul><ul><li>Reading for Tuesday: 2.4 </li></ul><ul><li>Review sessions: Tue from 9-11 p.m. and Wed from 7-10 p.m. </li></ul><ul><li>Exam: one week from this Thursday </li></ul><ul><ul><li>Will cover all of chapter 1 (sections 1.1-1.8) </li></ul></ul><ul><ul><li>What is not on the reference sheet: </li></ul></ul><ul><ul><ul><li>Universal/existential generalization/instantiation </li></ul></ul></ul><ul><ul><li>Last semester’s exam is posted on the website </li></ul></ul><ul><ul><ul><li>It only covered 1.1-1.7 </li></ul></ul></ul><ul><ul><ul><li>And it was a 50 minute exam, not a 75 minute exam </li></ul></ul></ul>
  18. 18. Proof by contradiction example 2 <ul><li>Rosen, section 1.5, question 21 (b) </li></ul><ul><ul><li>Prove that if n is an integer and n 3 +5 is odd, then n is even </li></ul></ul><ul><ul><li>Rephrased: If n 3 +5 is odd, then n is even </li></ul></ul><ul><ul><ul><li>Thus, p is “n 3 +5” is odd, q is “n is even” </li></ul></ul></ul><ul><li>Assume p and  q </li></ul><ul><ul><li>Assume that n 3 +5 is odd, and n is odd </li></ul></ul><ul><li>Since n is odd: </li></ul><ul><ul><li>n=2k+1 for some integer k (definition of odd numbers) </li></ul></ul><ul><ul><li>n 3 +5 = (2k+1) 3 +5 = 8k 3 +12k 2 +6k+6 = 2(4k 3 +6k 2 +3k+3) </li></ul></ul><ul><ul><li>As n = 2(4k 3 +6k 2 +3k+3) is 2 times an integer, n must be even </li></ul></ul><ul><ul><li>Thus, we have concluded q </li></ul></ul><ul><li>Contradiction! </li></ul><ul><ul><li>We assumed q was false, and showed that this assumption implies that q must be true </li></ul></ul><ul><ul><li>As q cannot be both true and false, we have reached our contradiction </li></ul></ul>
  19. 19. A note on that problem… <ul><li>Rosen, section 1.5, question 21 </li></ul><ul><ul><li>Prove that if n is an integer and n 3 +5 is odd, then n is even </li></ul></ul><ul><ul><li>Here, our implication is: If n 3 +5 is odd, then n is even </li></ul></ul><ul><li>The indirect proof proved the contrapositive: ¬q -> ¬p </li></ul><ul><ul><li>I.e., If n is odd, then n 3 +5 is even </li></ul></ul><ul><li>The proof by contradiction assumed that the implication was false, and showed that led to a contradiction </li></ul><ul><ul><li>If we assume p and ¬q, we can show that implies q </li></ul></ul><ul><ul><li>The contradiction is q and ¬q </li></ul></ul><ul><li>Note that both used similar steps, but are different means of proving the implication </li></ul>
  20. 20. How the book explains proof by contradiction <ul><li>A very poor explanation, IMHO </li></ul><ul><li>Suppose q is a contradiction (i.e. is always false) </li></ul><ul><li>Show that ¬p->q is true </li></ul><ul><ul><li>Since the consequence is false, the antecedent must be false </li></ul></ul><ul><ul><li>Thus, p must be true </li></ul></ul><ul><li>Find a contradiction, such as (r  ¬r), to represent q </li></ul><ul><li>Thus, you are showing that ¬p->(r  ¬r) </li></ul><ul><ul><li>Or that assuming p is false leads to a contradiction </li></ul></ul>
  21. 21. Tuesday, 22 February 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 7: Due today </li></ul></ul><ul><ul><li>HW 8: Due next Tue (1 Mar) (Rosen, section 1.8: 17, 36, 61, 64) </li></ul></ul><ul><ul><li>HW 9: Due next Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) </li></ul></ul><ul><li>Regrades for homeworks </li></ul><ul><ul><li>Form is on the website </li></ul></ul><ul><ul><li>Must be within a 10 days </li></ul></ul><ul><li>Reading for next Tuesday: 2.6 </li></ul><ul><li>Review sessions: today from 9-11 p.m. and Wed from 7-10 p.m. </li></ul><ul><ul><li>Both are in Olsson 005 </li></ul></ul><ul><li>Exam: this Thursday </li></ul><ul><ul><li>Will cover all of chapter 1 (sections 1.1-1.8) </li></ul></ul><ul><ul><ul><li>3 proofs, 3 pages of short-answer </li></ul></ul></ul><ul><ul><li>What is not on the reference sheet: </li></ul></ul><ul><ul><ul><li>Universal/existential generalization/instantiation </li></ul></ul></ul><ul><ul><li>Last semester’s exam is posted on the website </li></ul></ul><ul><ul><ul><li>It only covered 1.1-1.7 </li></ul></ul></ul><ul><ul><ul><li>And it was a 50 minute exam, not a 75 minute exam </li></ul></ul></ul><ul><ul><li>About returning the exams (and posting of the grades) </li></ul></ul>
  22. 22. Tuesday, 1 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 8: Due today (Rosen, section 1.8: 17, 36, 61, 64) </li></ul></ul><ul><ul><ul><li>Can hand it in Thursday, as the TA was not at office hours yesterday </li></ul></ul></ul><ul><ul><li>HW 9: Due this Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) </li></ul></ul><ul><ul><li>HW 10: Rosen, section 2.6, question 46 and 47 (see note!) </li></ul></ul><ul><ul><ul><li>For 46, encrypt &quot;LEGEND&quot; instead of &quot;ATTACK“ </li></ul></ul></ul><ul><ul><ul><li>For 47, the message to decrypt is 2268 2465 0565, instead of what's given </li></ul></ul></ul><ul><ul><ul><li>The problems in section 2.6 will need to use the script at http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow to compute n e mod m (or c d mod m ) </li></ul></ul></ul><ul><ul><ul><li>Also, for question 47, d = 937 </li></ul></ul></ul><ul><li>HW solutions and grading guidelines are now restricted to the virginia.edu domain </li></ul><ul><li>Reading for Thursday: 2.1 & 2.2 </li></ul><ul><li>Exams returned today </li></ul><ul><ul><li>Average: 86.5, standard deviation: 12.5, median: 90.5 </li></ul></ul><ul><ul><li>There were six 100’s! </li></ul></ul><ul><li>Rough grade estimate based on the exam: </li></ul><ul><ul><li>A: 93+, B: 86+, C: 70+, D: 60+ </li></ul></ul>
  23. 23. Quick survey <ul><li>How hard was the exam? </li></ul><ul><li>Way too hard </li></ul><ul><li>Somewhat hard </li></ul><ul><li>About right </li></ul><ul><li>Very easy </li></ul>
  24. 24. Thursday, 3 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 8: Due last Tuesday, can hand it in today </li></ul></ul><ul><ul><li>HW 9: Due today (Rosen, section 2.4: 18, 34, 40, 52) </li></ul></ul><ul><ul><li>HW 10: Due Tuesday, 15 Mar: Rosen, section 2.6, question 46 and 47 (see note!) </li></ul></ul><ul><ul><ul><li>For 46, encrypt &quot;LEGEND&quot; instead of &quot;ATTACK“ </li></ul></ul></ul><ul><ul><ul><li>For 47, the message to decrypt is 2268 2465 0565, instead of what's given </li></ul></ul></ul><ul><ul><ul><li>The problems in section 2.6 will need to use the script at http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow to compute n e mod m (or c d mod m ) </li></ul></ul></ul><ul><ul><ul><li>Also, for question 47, d = 937 </li></ul></ul></ul><ul><ul><li>HW 11 will be posted shortly, due two weeks from today </li></ul></ul><ul><li>HW solutions and grading guidelines are now restricted to the virginia.edu domain </li></ul><ul><li>Reading for Tuesday: 3.1 </li></ul><ul><li>Exam regrades… </li></ul><ul><li>No office hours tomorrow! </li></ul><ul><li>Regrading of that question </li></ul><ul><li>I used different ASCII code for the RSA questions for the HW </li></ul>
  25. 25. Tuesday, 15 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) </li></ul></ul><ul><ul><ul><li>Can hand it in on Thursday </li></ul></ul></ul><ul><ul><li>No homework due Thursday </li></ul></ul><ul><ul><ul><li>As I didn’t get my act in gear in time </li></ul></ul></ul><ul><ul><li>HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 </li></ul></ul><ul><ul><ul><li>You MUST provide a Big-Oh estimate for each of your algorithms </li></ul></ul></ul><ul><ul><li>HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 </li></ul></ul><ul><li>HW solutions and grading guidelines are now restricted to the virginia.edu domain </li></ul><ul><li>I’m all caught up on regrades, HW solutions, and grading guidelines (for homeworks and the midterm) </li></ul><ul><li>Reading: read 3.1, 3.2 for Thursday </li></ul><ul><li>Regrades </li></ul><ul><ul><li>Let’s say all regrades for HWs 1-7 and the first midterm will be due two weeks from today (i.e. on 29 March) </li></ul></ul><ul><ul><li>All future regrades are due 10 days from when it is returned </li></ul></ul><ul><li>Second midterm: Thursday, 7 April (3 weeks from this Thursday) </li></ul><ul><ul><li>I would like to move it one week earlier (31 March). Thoughts? </li></ul></ul><ul><li>No office hours for me this Thursday! </li></ul><ul><li>Regrading of question 34 on HW 4: if you got points taken off because you did a truth table, you will get those points back </li></ul><ul><ul><li>Please submit that as a regrade </li></ul></ul>
  26. 26. Thursday, 17 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) </li></ul></ul><ul><ul><li>HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 </li></ul></ul><ul><ul><ul><li>You MUST provide a Big-Oh estimate for each of your algorithms </li></ul></ul></ul><ul><ul><li>HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 </li></ul></ul><ul><li>Reading: read 3.2, 3.3 for Tuesday </li></ul><ul><li>Regrades </li></ul><ul><ul><li>Let’s say all regrades for HWs 1-7 and the first midterm will be due two weeks from last Tuesday (i.e. on 29 March) </li></ul></ul><ul><ul><li>All future regrades are due 10 days from when it is returned </li></ul></ul><ul><li>Second midterm: Thursday, 7 April (3 weeks from this Thursday) </li></ul><ul><ul><li>I would like to move it one week earlier (31 March). Thoughts? </li></ul></ul><ul><li>Regrading of question 34 on HW 4: if you got points taken off because you did a truth table, you will get those points back </li></ul><ul><ul><li>Please submit that as a regrade </li></ul></ul>
  27. 27. Tuesday, 22 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34 </li></ul></ul><ul><ul><ul><li>You MUST provide a Big-Oh estimate for each of your algorithms </li></ul></ul></ul><ul><ul><li>HW 12: due Thursday: Rosen, section 2.2: 10, 14, 17, 20 </li></ul></ul><ul><ul><li>HWs 13 & 14 will be on the website tonight </li></ul></ul><ul><li>Reading: read 3.3, 3.4 for Tuesday </li></ul><ul><li>About office hours today… </li></ul><ul><li>Regrades </li></ul><ul><ul><li>Am all caught up on regrades </li></ul></ul><ul><ul><ul><li>Regraded assignments are in the appropriate HW folder </li></ul></ul></ul><ul><ul><ul><li>Grades are updated on Toolkit </li></ul></ul></ul><ul><ul><li>All regrades for HWs 1-7 and the first midterm are due one week from today (i.e. on 29 March) </li></ul></ul><ul><ul><li>All future regrades are due 10 days from when it is returned </li></ul></ul><ul><li>Second midterm: Thursday, 7 April (2 weeks from this Thursday) </li></ul><ul><ul><li>The date won’t be changed </li></ul></ul>
  28. 28. Thursday, 24 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 12: due today: Rosen, section 2.2: 10, 14, 17, 20 </li></ul></ul><ul><ul><li>HW 13: due next Tuesday: Rosen, section 3.2: 8, 9, 23, 36 </li></ul></ul><ul><ul><ul><li>As I’m assigning it today, you can hand it in next Thursday as well </li></ul></ul></ul><ul><ul><li>HW 14: due next Thursday: Rosen, section 3.3: 12, 27, 29, 51 </li></ul></ul><ul><li>Reading: 3.4 for today, 4.1 for Tuesday (although we might not get to it until Thursday) </li></ul><ul><li>Regrades </li></ul><ul><ul><li>Am all caught up on regrades </li></ul></ul><ul><ul><ul><li>Regraded assignments are in the appropriate HW folder </li></ul></ul></ul><ul><ul><ul><li>Grades are updated on Toolkit </li></ul></ul></ul><ul><ul><li>All regrades for HWs 1-7 and the first midterm are due next Tuesday (29 March) </li></ul></ul><ul><ul><li>All future regrades are due 10 days from when it is returned </li></ul></ul><ul><li>Second midterm: Thursday, 7 April (2 weeks from today) </li></ul><ul><ul><li>The date won’t be changed </li></ul></ul>
  29. 29. Third induction again: what if your inductive hypothesis was wrong? <ul><li>Show: </li></ul><ul><li>Base case: n = 1: </li></ul><ul><li>But let’s continue anyway… </li></ul><ul><li>Inductive hypothesis: assume </li></ul>
  30. 30. Third induction again: what if your inductive hypothesis was wrong? <ul><li>Inductive step: show </li></ul>
  31. 31. Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><li>via logical equivalences </li></ul></ul><ul><li>Set equivalences </li></ul><ul><ul><li>via membership tables </li></ul></ul><ul><ul><li>via set identities </li></ul></ul><ul><ul><li>via mutual subset proof </li></ul></ul><ul><ul><li>via set builder notation and logical equivalences </li></ul></ul><ul><li>Rules of inference </li></ul><ul><ul><li>for propositions </li></ul></ul><ul><ul><li>for quantified statements </li></ul></ul><ul><li>Pigeonhole principle </li></ul><ul><li>Combinatorial proofs </li></ul><ul><li>Ten proof methods in section 1.5: </li></ul><ul><ul><li>Direct proofs </li></ul></ul><ul><ul><li>Indirect proofs </li></ul></ul><ul><ul><li>Vacuous proofs </li></ul></ul><ul><ul><li>Trivial proofs </li></ul></ul><ul><ul><li>Proof by contradiction </li></ul></ul><ul><ul><li>Proof by cases </li></ul></ul><ul><ul><li>Proofs of equivalence </li></ul></ul><ul><ul><li>Existence proofs </li></ul></ul><ul><ul><ul><li>Constructive </li></ul></ul></ul><ul><ul><ul><li>Non-constructive </li></ul></ul></ul><ul><ul><li>Uniqueness proofs </li></ul></ul><ul><ul><li>Counterexamples </li></ul></ul><ul><li>Induction </li></ul><ul><ul><li>Weak mathematical induction </li></ul></ul><ul><ul><li>Strong mathematical induction </li></ul></ul><ul><ul><li>Structural induction </li></ul></ul>
  32. 32. Tuesday, 29 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 </li></ul></ul><ul><ul><li>HW 14: due Thursday: Rosen, section 3.3: 12, 27, 29, 51 </li></ul></ul><ul><ul><li>HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 </li></ul></ul><ul><ul><li>No homework due next Thursday (as it’s the midterm) </li></ul></ul><ul><li>Reading: read 4.1 for Thursday </li></ul><ul><li>Second midterm: Thursday, 7 April (1 week from this Thursday) </li></ul><ul><ul><li>The date won’t be changed </li></ul></ul><ul><ul><li>Last semester’s exam (and solutions) is on the website </li></ul></ul><ul><ul><li>Will cover through section 4.1 </li></ul></ul><ul><ul><ul><li>All that material will be presented this week </li></ul></ul></ul><ul><ul><li>That’s sections 2.1, 2.2, 2.4, 2.6 (the RSA part), 3.1-3.4, and 4.1, as well as the talk about NP Completeness </li></ul></ul><ul><ul><li>And of course material from sections 1.1-1.8 is fair game </li></ul></ul><ul><ul><li>There will be review sessions next week (most likely Tue 9-11, Wed 7-10) </li></ul></ul>
  33. 33. Thursday, 31 March 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 </li></ul></ul><ul><ul><li>HW 14: due today: Rosen, section 3.3: 12, 27, 29, 51 </li></ul></ul><ul><ul><li>HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 </li></ul></ul><ul><ul><li>No homework due next Thursday (as it’s the midterm) </li></ul></ul><ul><li>Reading: read 4.2-4.4 for Tuesday </li></ul><ul><li>Second midterm: Thursday, 7 April (1 week from this Thursday) </li></ul><ul><ul><li>Last semester’s exam (and solutions) is on the website </li></ul></ul><ul><ul><li>Will cover through section 4.1 </li></ul></ul><ul><ul><ul><li>All that material will be presented this week </li></ul></ul></ul><ul><ul><li>That’s sections 2.1, 2.2, 2.4, 2.6 (the RSA part), 3.1-3.4, and 4.1, as well as the talk about NP Completeness </li></ul></ul><ul><ul><li>And of course material from sections 1.1-1.8 is fair game </li></ul></ul><ul><ul><li>There will be review sessions next week </li></ul></ul><ul><ul><ul><li>Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005) </li></ul></ul></ul>
  34. 34. Proof methods learned so far <ul><li>Logical equivalences </li></ul><ul><ul><li>via truth tables </li></ul></ul><ul><ul><li>via logical equivalences </li></ul></ul><ul><li>Set equivalences </li></ul><ul><ul><li>via membership tables </li></ul></ul><ul><ul><li>via set identities </li></ul></ul><ul><ul><li>via mutual subset proof </li></ul></ul><ul><ul><li>via set builder notation and logical equivalences </li></ul></ul><ul><li>Rules of inference </li></ul><ul><ul><li>for propositions </li></ul></ul><ul><ul><li>for quantified statements </li></ul></ul><ul><li>Pigeonhole principle </li></ul><ul><li>Combinatorial proofs </li></ul><ul><li>Ten proof methods in section 1.5: </li></ul><ul><ul><li>Direct proofs </li></ul></ul><ul><ul><li>Indirect proofs </li></ul></ul><ul><ul><li>Vacuous proofs </li></ul></ul><ul><ul><li>Trivial proofs </li></ul></ul><ul><ul><li>Proof by contradiction </li></ul></ul><ul><ul><li>Proof by cases </li></ul></ul><ul><ul><li>Proofs of equivalence </li></ul></ul><ul><ul><li>Existence proofs </li></ul></ul><ul><ul><ul><li>Constructive </li></ul></ul></ul><ul><ul><ul><li>Non-constructive </li></ul></ul></ul><ul><ul><li>Uniqueness proofs </li></ul></ul><ul><ul><li>Counterexamples </li></ul></ul><ul><li>Induction </li></ul><ul><ul><li>Weak mathematical induction </li></ul></ul><ul><ul><li>Strong mathematical induction </li></ul></ul><ul><ul><li>Structural induction </li></ul></ul>
  35. 35. Comments from the surveys <ul><li>53 surveys received </li></ul><ul><li>Biggest complaint: textbook (12 negative responses) </li></ul><ul><ul><li>Comment was to make the course non-textbook based </li></ul></ul><ul><li>Second biggest complaint: errors in the slides </li></ul><ul><li>Playing Enya in class: 3 positive responses, 7 negative </li></ul><ul><li>Post slides earlier </li></ul><ul><li>More/less example problems </li></ul><ul><li>Have summaries of major topics available </li></ul><ul><li>Humor asides… </li></ul><ul><li>Cough drops </li></ul><ul><li>Responding to surveys </li></ul><ul><li>Post daily announcements on website </li></ul><ul><li>Homework grading </li></ul><ul><li>More KLAs </li></ul><ul><li>Review difficult HW problems in class </li></ul>
  36. 36. Tuesday, 5 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 15: due today: Rosen, section 3.4: 11, 27, 44, 59 </li></ul></ul><ul><ul><li>No homework due Thursday (as it’s the midterm) </li></ul></ul><ul><ul><li>Homework due next Tue/Thu… </li></ul></ul><ul><li>Reading: read 4.2-4.4 for Thursday </li></ul><ul><li>Second midterm: this Thursday, 7 April </li></ul><ul><ul><li>Last semester’s exam (and solutions) is on the website </li></ul></ul><ul><li>Two review sessions </li></ul><ul><ul><li>Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005) </li></ul></ul><ul><li>Slide error checking… </li></ul>
  37. 37. About the second midterm <ul><li>Sections 2.1, 2.2, 2.4, 2.6 (the RSA part), 3.1-3.4, and 4.1, as well as the talk about NP Completeness </li></ul><ul><li>And of course material from sections 1.1-1.8 is fair game </li></ul><ul><li>The big proof method we’ve seen since the first midterm is induction </li></ul><ul><li>About the problem database for sections 2.1 and 2.2 </li></ul>
  38. 38. New homework grading scheme <ul><li>Homeworks will now be graded on a 10-point scale </li></ul><ul><li>Each problem is worth 2.5 points: </li></ul><ul><ul><li>2.5 points: If they got the problem completely right </li></ul></ul><ul><ul><li>2.0 points: If they got the problem right, but made a simple mistake somewhere (i.e. an arithmetic mistake) </li></ul></ul><ul><ul><li>1.5 points: If they might have had the right idea, but got it fairly wrong. </li></ul></ul><ul><ul><li>1.0 points: If they got the problem totally wrong, but put in effort into the question </li></ul></ul><ul><ul><li>0.5 points: If they got it totally wrong, and didn't put in much effort </li></ul></ul><ul><ul><li>0.0 points: If they left it blank, or obviously didn't try </li></ul></ul><ul><li>Grading will also be a bit more lenient </li></ul>
  39. 39. Thursday, 7 April 2005 <ul><li>Test today! </li></ul><ul><ul><li>In case you forgot… </li></ul></ul><ul><li>Homeworks </li></ul><ul><ul><li>HW 16: due next Tuesday: Rosen, section 4.2: 7, 15, 29, 37 </li></ul></ul><ul><ul><ul><li>Can hand it in next Thursday as well </li></ul></ul></ul><ul><ul><li>HW 17: due next Thursday: Rosen, section 4.3: 14, 30, 37, 43 </li></ul></ul><ul><li>Reading: read 4.4, 5.1 for next Tuesday </li></ul>
  40. 40. Tuesday, 12 April 2005 <ul><li>Tests returned today… </li></ul><ul><ul><li>Average: 78.9 (without extra credit) </li></ul></ul><ul><li>Grade ranges: </li></ul><ul><ul><li>Homework average so far: 78.0 (HWs 1-12 and 14) </li></ul></ul><ul><ul><li>A: 90 and above </li></ul></ul><ul><ul><li>B: 80 and above </li></ul></ul><ul><ul><li>C: 65 and above </li></ul></ul><ul><ul><li>D: 50 and above </li></ul></ul><ul><li>About the oral exam… </li></ul><ul><li>Homeworks </li></ul><ul><ul><li>HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 </li></ul></ul><ul><ul><ul><li>Can hand it in Thursday as well </li></ul></ul></ul><ul><ul><li>HW 17: due Thursday: Rosen, section 4.3: 14, 30, 37, 43 </li></ul></ul><ul><ul><li>HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* </li></ul></ul><ul><ul><li>HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 </li></ul></ul><ul><li>Reading: read 5.1 for Thursday </li></ul><ul><li>Which game of chance should I go over? </li></ul><ul><ul><li>My preference: Texas Hold’em </li></ul></ul>
  41. 41. Thursday, 14 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 </li></ul></ul><ul><ul><ul><li>Can hand it in Thursday as well </li></ul></ul></ul><ul><ul><li>HW 17: due today: Rosen, section 4.3: 14, 30, 37, 43 </li></ul></ul><ul><ul><li>HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* </li></ul></ul><ul><ul><li>HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 </li></ul></ul><ul><li>Reading: read 5.1 for Thursday </li></ul><ul><li>About P(52,5) vs. C(52,5) in the slides for the poker hands… </li></ul>
  42. 42. Tuesday, 19 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 18: due today: Rosen, section 4.4: 7, 15, 30* </li></ul></ul><ul><ul><li>HW 19: due Thursday: Rosen, section 5.1: 12, 17, 27, 35 </li></ul></ul><ul><ul><li>HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 </li></ul></ul><ul><ul><ul><li>If we don’t get through much of the relations stuff, you can hand it in next Thursday </li></ul></ul></ul><ul><ul><ul><li>Question 7.1 needs material from 7.3 to be answered – more on that in class </li></ul></ul></ul><ul><ul><li>HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 </li></ul></ul><ul><ul><li>HW 22: due Tuesday, 3 May: last homework, not yet assigned </li></ul></ul><ul><ul><li>Am considering dropping the two lowest homework grades </li></ul></ul><ul><ul><li>How to make the homework assignments less confusing next semester </li></ul></ul><ul><li>Exam 2 </li></ul><ul><ul><li>Grading guidelines are on the web </li></ul></ul><ul><ul><li>I have regrade forms with me today </li></ul></ul><ul><li>Reading: read 7.1, 7.3 for Thursday </li></ul><ul><li>The plan: </li></ul><ul><ul><li>Finish 5.1 today, go through relations next </li></ul></ul><ul><ul><li>Next 3 classes are on relations: </li></ul></ul><ul><ul><ul><li>This week and next week will cover sections 7.1, 7.3, 7.4, 7.5, and 7.6 </li></ul></ul></ul><ul><ul><li>Last few classes will most likely cover 3.6 </li></ul></ul><ul><ul><li>About matrices… </li></ul></ul><ul><li>Regrades </li></ul><ul><ul><li>All caught up on regrades </li></ul></ul><ul><ul><li>All caught up on grade entry (through HW 17, but not HW 16 yet) </li></ul></ul><ul><ul><li>All HW regrades must be submitted by the last Thursday of class (except pending HWs) </li></ul></ul><ul><li>Final exam: </li></ul><ul><ul><li>Saturday, May 7, from 9 a.m. to noon </li></ul></ul><ul><ul><li>Last semester’s final is on the website </li></ul></ul><ul><ul><li>Final layout will follow the course objectives (last semester’s exam did as well) </li></ul></ul>
  43. 43. Thursday, 21 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35 </li></ul></ul><ul><ul><li>HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 </li></ul></ul><ul><ul><ul><li>Can hand it in next Thursday </li></ul></ul></ul><ul><ul><ul><li>Question 7.1 needs material from 7.3 to be answered – more on that in class </li></ul></ul></ul><ul><ul><li>HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 </li></ul></ul><ul><ul><li>HW 22: due Tuesday, 3 May: last homework, not yet assigned </li></ul></ul><ul><ul><li>Will drop the two lowest homework grades </li></ul></ul><ul><li>Exam 2 </li></ul><ul><ul><li>Grading guidelines are on the web </li></ul></ul><ul><ul><li>I have regrade forms with me today </li></ul></ul><ul><li>Reading: read 7.1, 7.3, 7.4 for Tuesday </li></ul><ul><li>The plan: </li></ul><ul><ul><li>Next 3 classes are on relations: </li></ul></ul><ul><ul><ul><li>This week and next week will cover sections 7.1, 7.3, 7.4, 7.5, and 7.6 </li></ul></ul></ul><ul><ul><li>Last few classes will most likely cover 3.6 </li></ul></ul><ul><ul><li>About matrices… </li></ul></ul><ul><li>Regrades </li></ul><ul><ul><li>All caught up on regrades </li></ul></ul><ul><ul><li>All caught up on grade entry (through HW 17, but not HW 16 yet) </li></ul></ul><ul><ul><li>All HW regrades must be submitted by the last Thursday of class (except pending HWs) </li></ul></ul><ul><li>Final exam: </li></ul><ul><ul><li>Saturday, May 7, from 9 a.m. to noon </li></ul></ul><ul><ul><li>Last semester’s final is on the website </li></ul></ul><ul><ul><li>Final layout will follow the course objectives (last semester’s exam did as well) </li></ul></ul><ul><li>No office hours tomorrow! </li></ul><ul><ul><li>Brian will be quite drugged up from having his wisdom teeth removed </li></ul></ul>
  44. 44. Tuesday, 26 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45 </li></ul></ul><ul><ul><ul><li>Can hand it in Thursday </li></ul></ul></ul><ul><ul><ul><li>Question 7.1 needs material from 7.3 to be answered – more on that in class </li></ul></ul></ul><ul><ul><li>HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 </li></ul></ul><ul><ul><li>HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 </li></ul></ul><ul><ul><li>Will drop the two lowest homework grades </li></ul></ul><ul><li>Exam 2 </li></ul><ul><ul><li>Grading guidelines are on the web </li></ul></ul><ul><ul><li>I have regrade forms with me today </li></ul></ul><ul><li>Reading: read 7.1, 7.3-7.6 for Tuesday </li></ul><ul><li>The plan: </li></ul><ul><ul><li>Next 2 classes are on relations </li></ul></ul><ul><ul><li>Last few classes will most likely cover 3.6 </li></ul></ul><ul><li>Final exam: </li></ul><ul><ul><li>Saturday, May 7, from 9 a.m. to noon </li></ul></ul><ul><ul><li>Last semester’s final is on the website </li></ul></ul><ul><ul><li>Final layout will follow the course objectives (last semester’s exam did as well) </li></ul></ul><ul><li>Course evaluations… </li></ul>
  45. 45. Thursday, 28 April 2005 <ul><li>Homeworks </li></ul><ul><ul><li>HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, 31, 45 </li></ul></ul><ul><ul><ul><li>Can hand it in today </li></ul></ul></ul><ul><ul><li>HW 21: due today: Rosen, section 7.3: 10, 13, 20, 33 </li></ul></ul><ul><ul><li>HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 </li></ul></ul><ul><ul><li>Will drop the two lowest homework grades </li></ul></ul><ul><li>Exam 2 </li></ul><ul><ul><li>Grading guidelines are on the web </li></ul></ul><ul><li>Reading: 7.1-7.6 for Tuesday </li></ul><ul><li>The plan: </li></ul><ul><ul><li>Next 2 classes are on relations </li></ul></ul><ul><ul><li>Last class will most likely cover 7.2 (*not* 3.6) </li></ul></ul><ul><li>Final exam: </li></ul><ul><ul><li>Saturday, May 7, from 9 a.m. to noon </li></ul></ul><ul><ul><li>Am planning on having coffee – but may be short on the coffee cups… </li></ul></ul><ul><ul><li>Last semester’s final is on the website now (sorry!) </li></ul></ul><ul><ul><li>Final layout will follow the course objectives (last semester’s exam did as well) </li></ul></ul><ul><ul><li>There will be review sessions, probably 2 </li></ul></ul><ul><li>Course evaluations… </li></ul>
  46. 46. Course objectives <ul><li>Logic </li></ul><ul><ul><li>Introduce a formal system (propositional and predicate logic) which mathematical reasoning is based on </li></ul></ul><ul><ul><li>Sections 1.1-1.4 </li></ul></ul><ul><li>Proofs </li></ul><ul><ul><li>Develop an understanding of how to read and construct valid mathematical arguments (proofs) and understand mathematical statements (theorems), including inductive proofs. Also, introduce and work with various problem solving strategies and techniques. </li></ul></ul><ul><ul><li>Sections 1.5, 3.1, 3.3, 3.4 </li></ul></ul><ul><li>Counting </li></ul><ul><ul><li>Introduce the basics of integer theory, combinatorics, and counting principles, including a brief introduction to discrete probability. </li></ul></ul><ul><ul><li>Sections 2.4, 4.1-4.4, 5.1 </li></ul></ul><ul><li>Structures </li></ul><ul><ul><li>Introduce and work with important discrete data structures such as sets, relations, sequences, and discrete functions. </li></ul></ul><ul><ul><li>Sections 1.6-1.8, 2.7, 3.2, 7.1, 7.3-7.6 </li></ul></ul><ul><li>Applications </li></ul><ul><ul><li>Gain an understanding of some application areas of the material covered in the course. </li></ul></ul><ul><ul><li>Sections 2.6, 7.2, 10.3 </li></ul></ul>
  47. 47. The End <ul><li>Homeworks </li></ul><ul><ul><li>HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26 </li></ul></ul><ul><ul><ul><li>Sorry 26 was so long! </li></ul></ul></ul><ul><ul><li>Will drop the two lowest homework grades </li></ul></ul><ul><li>Exam 2 </li></ul><ul><ul><li>Grading guidelines are on the web </li></ul></ul><ul><li>Final exam: </li></ul><ul><ul><li>Saturday, May 7, from 9 a.m. to noon </li></ul></ul><ul><ul><li>Am planning on having coffee – but may be short on the coffee cups… </li></ul></ul><ul><ul><li>Last semester’s final is on the website </li></ul></ul><ul><ul><li>Final layout will follow the course objectives (last semester’s exam did as well) </li></ul></ul><ul><li>Review sessions </li></ul><ul><ul><li>One Wednesday, one Thursday </li></ul></ul><ul><ul><li>Most likely 3:30-6:30 on Wednesday </li></ul></ul><ul><ul><li>Exact info will be e-mailed out to everybody later today </li></ul></ul><ul><li>Office hours this week… </li></ul><ul><li>Course evaluations… </li></ul><ul><li>Voting for the favorite demotivator </li></ul>
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