Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield.

Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield

Tuesday, 25 January 2005 HW 1: assigned today, due next Tue (1 Feb) Rosen, section 1.1: 18, 48, 60 Rosen, section 1.1: 18, 48, 60 HW 2: assigned Thu, due following Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalences Must answer 19 by both truth tables and logical equivalences TA office hours will be posted on the website Monday afternoon/evening (a homework review session) Monday afternoon/evening (a homework review session) Wednesday 3:30-5:30 in Olsson 018 Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 Friday 10:00-noon in Olsson 018 My Thursday office hours are changing, but I’m not sure what to yet

Thursday, 27 January 2005 HW 1: assigned last time, due next Tue (1 Feb) Rosen, section 1.1: 18, 48, 60 Rosen, section 1.1: 18, 48, 60 HW 2: assigned today, due next Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalences Must answer 19 by both truth tables and logical equivalences TA office hours: Monday afternoon/evening (a homework review session) Monday afternoon/evening (a homework review session) Wednesday 3:30-5:30 in Olsson 018 Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 Friday 10:00-noon in Olsson 018 About the grade requirement for CS 216 And about doing well in this class… And about doing well in this class… Reading for Tuesday: 1.3 Ideally, should have read 1.1, 1.2, and 10.3 by now Ideally, should have read 1.1, 1.2, and 10.3 by now My Thursday office hours Proof methods

Proof methods learned so far Logical equivalences via truth tables via truth tables via logical equivalences via logical equivalences Set equivalences via membership tables via membership tables via set identities via set identities via mutual subset proof via mutual subset proof via set builder notation and logical equivalences via set builder notation and logical equivalences Rules of inference for propositions for propositions for quantified statements for quantified statements Pigeonhole principle Combinatorial proofs Ten proof methods in section 1.5: Direct proofs Direct proofs Indirect proofs Indirect proofs Vacuous proofs Vacuous proofs Trivial proofs Trivial proofs Proof by contradiction Proof by contradiction Proof by cases Proof by cases Proofs of equivalence Proofs of equivalence Existence proofs Existence proofsConstructiveNon-constructive Uniqueness proofs Uniqueness proofs Counterexamples CounterexamplesInduction Weak mathematical induction Weak mathematical induction Strong mathematical induction Strong mathematical induction Structural induction Structural induction

Tuesday, 1 February 2005 HW 1: due today Rosen, section 1.1: 18, 48, 60 Rosen, section 1.1: 18, 48, 60 HW 2: due Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalences Must answer 19 by both truth tables and logical equivalences HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9 Rosen, section 10.3: 3, 4, 5, 9 TA office hours: Monday 5:00-7:00 (a homework review session) Monday 5:00-7:00 (a homework review session) Wednesday 3:30-5:30 in Olsson 018 Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 Friday 10:00-noon in Olsson 018 Reading for Tuesday: 1.6/1.7 My Thursday office hours: now 10:30-noon Rescheduling the homework review session (so as not to conflict with CS 201 labs)? Terminology: disjunction and conjunction (and question 1.2 # 35) Logic gates: not on test, but on HW 3

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

Thursday, 3 February 2005 HW 2: due today Rosen, section 1.2: 19, 35, 39, 50 Rosen, section 1.2: 19, 35, 39, 50 HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9 Rosen, section 10.3: 3, 4, 5, 9 HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43 Rosen, section 1.7: 10, 16, 22, 34, 43 TA office hours: Monday 5:00-7:00 (a homework review session) Monday 5:00-7:00 (a homework review session) Wednesday 3:30-5:30 in Olsson 018 Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 Friday 10:00-noon in Olsson 018 Reading for Tuesday: 1.3/1.4 That crane picture sequence…

A bit of humor…

Quick survey The amount of time the homeworks are taking: The amount of time the homeworks are taking: a) Very little b) About right c) A lot d) Way to much

Quick survey How hard have the homeworks been so far? How hard have the homeworks been so far? a) Way too hard b) Somewhat hard c) About right d) Very easy

Tuesday, 8 February 2005 HW 3: due today Rosen, section 10.3: 3, 4, 5, 9 Rosen, section 10.3: 3, 4, 5, 9 HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43 Rosen, section 1.7: 10, 16, 22, 34, 43 HW 5: due Tue (15 Feb) Rosen, section 1.3: 15, 20, 24, 41 Rosen, section 1.3: 15, 20, 24, 41 HW 6: Due Thu (17 Feb) Rosen, section 1.4: 12, 22, 33, 40 Rosen, section 1.4: 12, 22, 33, 40 Reading for Thursday: 1.5 Exam: two weeks from this Thursday Last semester’s exam will be posted on the website Last semester’s exam will be posted on the website Would people use forums if I set them up?

Thursday, 10 February 2005 Homeworks HWs 1 and 2 returned today HWs 1 and 2 returned today HW 1: Average 80.3, standard deviation 20.0 HW 2: Average 85.0, standard deviation 18.4 Solutions and grading guidelines will be posted shortly Regrades for homeworks HW 3: can turn in late… HW 3: can turn in late… HW 4: due today HW 4: due today Rosen, section 1.7: 10, 16, 22, 34, 43 HW 5: due Tue (15 Feb) HW 5: due Tue (15 Feb) Rosen, section 1.3: 15, 20, 24, 41 HW 6: Due Thu (17 Feb) HW 6: Due Thu (17 Feb) Rosen, section 1.4: 12, 22, 33, 40 Reading for today and next Tuesday: 1.5 Exam: two weeks from today Last semester’s exam will be posted on the website Last semester’s exam will be posted on the website

Quick survey The amount of time the homeworks are taking: The amount of time the homeworks are taking: a) Very little b) About right c) A lot d) Way to much

Quick survey How hard have the homeworks been so far? How hard have the homeworks been so far? a) Way too hard b) Somewhat hard c) About right d) Very easy

Tuesday, 15 February 2005 Homeworks HW 4 returned today HW 4 returned today Solutions and grading guidelines will be posted shortly HW 5: due today HW 5: due today Rosen, section 1.3: 15, 20, 24, 41 HW 6: Due Thu (17 Feb) HW 6: Due Thu (17 Feb) Rosen, section 1.4: 12, 22, 33, 40 HW 7: Due Tue (19 Feb) HW 7: Due Tue (19 Feb) Rosen, section 1.5: 10, 22, 34, 55 HW 8: Due Tue (26 Feb) HW 8: Due Tue (26 Feb) Rosen, section 1.8: 17, 36, 61, 64 Regrades for homeworks Form is on the website Form is on the website Must be within a week Must be within a week Reading for Thursday: 1.8 Exam: one week from this Thursday Will cover all of chapter 1 (sections 1.1-1.8) Will cover all of chapter 1 (sections 1.1-1.8) Last semester’s exam will be posted on the website Last semester’s exam will be posted on the website It only covered 1.1-1.7 And it was a 50 minute exam, not a 75 minute exam

Thursday, 15 February 2005 Homeworks HW 3 returned today HW 3 returned today HW 3: Average 82.3 A lot of missing HW 3’s – check your grades on Toolkit HW 6: Due today (Rosen, section 1.4: 12, 22, 33, 40) HW 6: Due today (Rosen, section 1.4: 12, 22, 33, 40) HW 7: Due Tue (19 Feb) (Rosen, section 1.5: 10, 22, 34, 55) HW 7: Due Tue (19 Feb) (Rosen, section 1.5: 10, 22, 34, 55) HW 8: Due Tue (26 Feb) (Rosen, section 1.8: 17, 36, 61, 64) HW 8: Due Tue (26 Feb) (Rosen, section 1.8: 17, 36, 61, 64) Regrades for homeworks Form is on the website, and I have copies on me Form is on the website, and I have copies on me Must be within a 10 days Must be within a 10 days Reading for Tuesday: 2.4 Review sessions: Tue from 9-11 p.m. and Wed from 7-10 p.m. Exam: one week from this Thursday Will cover all of chapter 1 (sections 1.1-1.8) Will cover all of chapter 1 (sections 1.1-1.8) What is not on the reference sheet: What is not on the reference sheet: Universal/existential generalization/instantiation Last semester’s exam is posted on the website Last semester’s exam is posted on the website It only covered 1.1-1.7 And it was a 50 minute exam, not a 75 minute exam

Proof by contradiction example 2 Rosen, section 1.5, question 21 (b) Prove that if n is an integer and n 3 +5 is odd, then n is even Prove that if n is an integer and n 3 +5 is odd, then n is even Rephrased: If n 3 +5 is odd, then n is even Rephrased: If n 3 +5 is odd, then n is even Thus, p is “n 3 +5” is odd, q is “n is even” Assume p and  q Assume that n 3 +5 is odd, and n is odd Assume that n 3 +5 is odd, and n is odd Since n is odd: n=2k+1 for some integer k (definition of odd numbers) n=2k+1 for some integer k (definition of odd numbers) n 3 +5 = (2k+1) 3 +5 = 8k 3 +12k 2 +6k+6 = 2(4k 3 +6k 2 +3k+3) n 3 +5 = (2k+1) 3 +5 = 8k 3 +12k 2 +6k+6 = 2(4k 3 +6k 2 +3k+3) As n = 2(4k 3 +6k 2 +3k+3) is 2 times an integer, n must be even As n = 2(4k 3 +6k 2 +3k+3) is 2 times an integer, n must be even Thus, we have concluded q Thus, we have concluded qContradiction! We assumed q was false, and showed that this assumption implies that q must be true We assumed q was false, and showed that this assumption implies that q must be true As q cannot be both true and false, we have reached our contradiction As q cannot be both true and false, we have reached our contradiction

A note on that problem… Rosen, section 1.5, question 21 Prove that if n is an integer and n 3 +5 is odd, then n is even Prove that if n is an integer and n 3 +5 is odd, then n is even Here, our implication is: If n 3 +5 is odd, then n is even Here, our implication is: If n 3 +5 is odd, then n is even The indirect proof proved the contrapositive: ¬q → ¬p I.e., If n is odd, then n 3 +5 is even I.e., If n is odd, then n 3 +5 is even The proof by contradiction assumed that the implication was false, and showed that led to a contradiction If we assume p and ¬q, we can show that implies q If we assume p and ¬q, we can show that implies q The contradiction is q and ¬q The contradiction is q and ¬q Note that both used similar steps, but are different means of proving the implication

How the book explains proof by contradiction A very poor explanation, IMHO Suppose q is a contradiction (i.e. is always false) Show that ¬p→q is true Since the consequence is false, the antecedent must be false Since the consequence is false, the antecedent must be false Thus, p must be true Thus, p must be true Find a contradiction, such as (r  ¬r), to represent q Thus, you are showing that ¬p→(r  ¬r) Or that assuming p is false leads to a contradiction Or that assuming p is false leads to a contradiction

Tuesday, 22 February 2005 Homeworks HW 7: Due today HW 7: Due today HW 8: Due next Tue (1 Mar) (Rosen, section 1.8: 17, 36, 61, 64) HW 8: Due next Tue (1 Mar) (Rosen, section 1.8: 17, 36, 61, 64) HW 9: Due next Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) HW 9: Due next Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) Regrades for homeworks Form is on the website Form is on the website Must be within a 10 days Must be within a 10 days Reading for next Tuesday: 2.6 Review sessions: today from 9-11 p.m. and Wed from 7-10 p.m. Both are in Olsson 005 Both are in Olsson 005 Exam: this Thursday Will cover all of chapter 1 (sections 1.1-1.8) Will cover all of chapter 1 (sections 1.1-1.8) 3 proofs, 3 pages of short-answer What is not on the reference sheet: What is not on the reference sheet: Universal/existential generalization/instantiation Last semester’s exam is posted on the website Last semester’s exam is posted on the website It only covered 1.1-1.7 And it was a 50 minute exam, not a 75 minute exam About returning the exams (and posting of the grades) About returning the exams (and posting of the grades)

Tuesday, 1 March 2005 Homeworks HW 8: Due today (Rosen, section 1.8: 17, 36, 61, 64) HW 8: Due today (Rosen, section 1.8: 17, 36, 61, 64) Can hand it in Thursday, as the TA was not at office hours yesterday HW 9: Due this Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) HW 9: Due this Thu (3 Mar) (Rosen, section 2.4: 18, 34, 40, 52) HW 10: Rosen, section 2.6, question 46 and 47 (see note!) HW 10: Rosen, section 2.6, question 46 and 47 (see note!) For 46, encrypt "LEGEND" instead of "ATTACK“ For 47, the message to decrypt is 2268 2465 0565, instead of what's given 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) http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow Also, for question 47, d = 937 HW solutions and grading guidelines are now restricted to the virginia.edu domain Reading for Thursday: 2.1 & 2.2 Exams returned today Average: 86.5, standard deviation: 12.5, median: 90.5 Average: 86.5, standard deviation: 12.5, median: 90.5 There were six 100’s! There were six 100’s! Rough grade estimate based on the exam: A: 93+, B: 86+, C: 70+, D: 60+ A: 93+, B: 86+, C: 70+, D: 60+

Quick survey How hard was the exam? How hard was the exam? a) Way too hard b) Somewhat hard c) About right d) Very easy

Thursday, 3 March 2005 Homeworks HW 8: Due last Tuesday, can hand it in today HW 8: Due last Tuesday, can hand it in today HW 9: Due today (Rosen, section 2.4: 18, 34, 40, 52) HW 9: Due today (Rosen, section 2.4: 18, 34, 40, 52) HW 10: Due Tuesday, 15 Mar: Rosen, section 2.6, question 46 and 47 (see note!) HW 10: Due Tuesday, 15 Mar: Rosen, section 2.6, question 46 and 47 (see note!) For 46, encrypt "LEGEND" instead of "ATTACK“ For 47, the message to decrypt is 2268 2465 0565, instead of what's given 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) http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow Also, for question 47, d = 937 HW 11 will be posted shortly, due two weeks from today HW 11 will be posted shortly, due two weeks from today HW solutions and grading guidelines are now restricted to the virginia.edu domain Reading for Tuesday: 3.1 Exam regrades… No office hours tomorrow! Regrading of that question I used different ASCII code for the RSA questions for the HW

Tuesday, 15 March 2005 Homeworks HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) Can hand it in on Thursday No homework due Thursday No homework due Thursday As I didn’t get my act in gear in time HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 You MUST provide a Big-Oh estimate for each of your algorithms HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 HW solutions and grading guidelines are now restricted to the virginia.edu domain I’m all caught up on regrades, HW solutions, and grading guidelines (for homeworks and the midterm) Reading: read 3.1, 3.2 for Thursday Regrades 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) 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) All future regrades are due 10 days from when it is returned All future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (3 weeks from this Thursday) I would like to move it one week earlier (31 March). Thoughts? I would like to move it one week earlier (31 March). Thoughts? No office hours for me this Thursday! 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 Please submit that as a regrade Please submit that as a regrade

Thursday, 17 March 2005 Homeworks HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) HW 10: Due today: Rosen, section 2.6, question 46 and 47 (see note!) HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34 You MUST provide a Big-Oh estimate for each of your algorithms HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 HW 12: due next Thursday: Rosen, section 2.2: 10, 14, 17, 20 Reading: read 3.2, 3.3 for Tuesday Regrades 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) 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) All future regrades are due 10 days from when it is returned All future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (3 weeks from this Thursday) I would like to move it one week earlier (31 March). Thoughts? I would like to move it one week earlier (31 March). Thoughts? 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 Please submit that as a regrade Please submit that as a regrade

Tuesday, 22 March 2005 Homeworks HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34 HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34 You MUST provide a Big-Oh estimate for each of your algorithms HW 12: due Thursday: Rosen, section 2.2: 10, 14, 17, 20 HW 12: due Thursday: Rosen, section 2.2: 10, 14, 17, 20 HWs 13 & 14 will be on the website tonight HWs 13 & 14 will be on the website tonight Reading: read 3.3, 3.4 for Tuesday About office hours today… Regrades Am all caught up on regrades Am all caught up on regrades Regraded assignments are in the appropriate HW folder Grades are updated on Toolkit All regrades for HWs 1-7 and the first midterm are due one week from today (i.e. on 29 March) All regrades for HWs 1-7 and the first midterm are due one week from today (i.e. on 29 March) All future regrades are due 10 days from when it is returned All future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (2 weeks from this Thursday) The date won’t be changed The date won’t be changed

Thursday, 24 March 2005 Homeworks HW 12: due today: Rosen, section 2.2: 10, 14, 17, 20 HW 12: due today: Rosen, section 2.2: 10, 14, 17, 20 HW 13: due next Tuesday: Rosen, section 3.2: 8, 9, 23, 36 HW 13: due next Tuesday: Rosen, section 3.2: 8, 9, 23, 36 As I’m assigning it today, you can hand it in next Thursday as well HW 14: due next Thursday: Rosen, section 3.3: 12, 27, 29, 51 HW 14: due next Thursday: Rosen, section 3.3: 12, 27, 29, 51 Reading: 3.4 for today, 4.1 for Tuesday (although we might not get to it until Thursday) Regrades Am all caught up on regrades Am all caught up on regrades Regraded assignments are in the appropriate HW folder Grades are updated on Toolkit All regrades for HWs 1-7 and the first midterm are due next Tuesday (29 March) All regrades for HWs 1-7 and the first midterm are due next Tuesday (29 March) All future regrades are due 10 days from when it is returned All future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (2 weeks from today) The date won’t be changed The date won’t be changed

Third induction again: what if your inductive hypothesis was wrong? Show: Base case: n = 1: But let’s continue anyway… Inductive hypothesis: assume

Third induction again: what if your inductive hypothesis was wrong? Inductive step: show

Tuesday, 29 March 2005 Homeworks HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 14: due Thursday: Rosen, section 3.3: 12, 27, 29, 51 HW 14: due Thursday: Rosen, section 3.3: 12, 27, 29, 51 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 No homework due next Thursday (as it’s the midterm) No homework due next Thursday (as it’s the midterm) Reading: read 4.1 for Thursday Second midterm: Thursday, 7 April (1 week from this Thursday) The date won’t be changed The date won’t be changed Last semester’s exam (and solutions) is on the website Last semester’s exam (and solutions) is on the website Will cover through section 4.1 Will cover through section 4.1 All that material will be presented this week 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 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 And of course material from sections 1.1-1.8 is fair game And of course material from sections 1.1-1.8 is fair game There will be review sessions next week (most likely Tue 9-11, Wed 7- 10) There will be review sessions next week (most likely Tue 9-11, Wed 7- 10)

Thursday, 31 March 2005 Homeworks HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 14: due today: Rosen, section 3.3: 12, 27, 29, 51 HW 14: due today: Rosen, section 3.3: 12, 27, 29, 51 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 No homework due next Thursday (as it’s the midterm) No homework due next Thursday (as it’s the midterm) Reading: read 4.2-4.4 for Tuesday Second midterm: Thursday, 7 April (1 week from this Thursday) Last semester’s exam (and solutions) is on the website Last semester’s exam (and solutions) is on the website Will cover through section 4.1 Will cover through section 4.1 All that material will be presented this week 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 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 And of course material from sections 1.1-1.8 is fair game And of course material from sections 1.1-1.8 is fair game There will be review sessions next week There will be review sessions next week Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005)

Comments from the surveys 53 surveys received Biggest complaint: textbook (12 negative responses) Comment was to make the course non-textbook based Comment was to make the course non-textbook based Second biggest complaint: errors in the slides Playing Enya in class: 3 positive responses, 7 negative Post slides earlier More/less example problems Have summaries of major topics available Humor asides… Cough drops Responding to surveys Post daily announcements on website Homework grading More KLAs Review difficult HW problems in class

Tuesday, 5 April 2005 Homeworks HW 15: due today: Rosen, section 3.4: 11, 27, 44, 59 HW 15: due today: Rosen, section 3.4: 11, 27, 44, 59 No homework due Thursday (as it’s the midterm) No homework due Thursday (as it’s the midterm) Homework due next Tue/Thu… Homework due next Tue/Thu… Reading: read 4.2-4.4 for Thursday Second midterm: this Thursday, 7 April Last semester’s exam (and solutions) is on the website Last semester’s exam (and solutions) is on the website Two review sessions Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005) Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005) Slide error checking…

About the second midterm 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 And of course material from sections 1.1- 1.8 is fair game The big proof method we’ve seen since the first midterm is induction About the problem database for sections 2.1 and 2.2

New homework grading scheme Homeworks will now be graded on a 10-point scale Each problem is worth 2.5 points: 2.5 points: If they got the problem completely right 2.5 points: If they got the problem completely right 2.0 points: If they got the problem right, but made a simple mistake somewhere (i.e. an arithmetic mistake) 2.0 points: If they got the problem right, but made a simple mistake somewhere (i.e. an arithmetic mistake) 1.5 points: If they might have had the right idea, but got it fairly wrong. 1.5 points: If they might have had the right idea, but got it fairly wrong. 1.0 points: If they got the problem totally wrong, but put in effort into the question 1.0 points: If they got the problem totally wrong, but put in effort into the question 0.5 points: If they got it totally wrong, and didn't put in much effort 0.5 points: If they got it totally wrong, and didn't put in much effort 0.0 points: If they left it blank, or obviously didn't try 0.0 points: If they left it blank, or obviously didn't try Grading will also be a bit more lenient

Thursday, 7 April 2005 Test today! In case you forgot… In case you forgot…Homeworks HW 16: due next Tuesday: Rosen, section 4.2: 7, 15, 29, 37 HW 16: due next Tuesday: Rosen, section 4.2: 7, 15, 29, 37 Can hand it in next Thursday as well HW 17: due next Thursday: Rosen, section 4.3: 14, 30, 37, 43 HW 17: due next Thursday: Rosen, section 4.3: 14, 30, 37, 43 Reading: read 4.4, 5.1 for next Tuesday

Tuesday, 12 April 2005 Tests returned today… Average: 78.9 (without extra credit) Average: 78.9 (without extra credit) Grade ranges: Homework average so far: 78.0 (HWs 1-12 and 14) Homework average so far: 78.0 (HWs 1-12 and 14) A: 90 and above A: 90 and above B: 80 and above B: 80 and above C: 65 and above C: 65 and above D: 50 and above D: 50 and above About the oral exam… Homeworks HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 Can hand it in Thursday as well HW 17: due Thursday: Rosen, section 4.3: 14, 30, 37, 43 HW 17: due Thursday: Rosen, section 4.3: 14, 30, 37, 43 HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 Reading: read 5.1 for Thursday Which game of chance should I go over? My preference: Texas Hold’em My preference: Texas Hold’em

Thursday, 14 April 2005 Homeworks HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37 Can hand it in Thursday as well HW 17: due today: Rosen, section 4.3: 14, 30, 37, 43 HW 17: due today: Rosen, section 4.3: 14, 30, 37, 43 HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35 Reading: read 5.1 for Thursday About P(52,5) vs. C(52,5) in the slides for the poker hands…

Tuesday, 19 April 2005 Homeworks HW 18: due today: Rosen, section 4.4: 7, 15, 30* HW 18: due today: Rosen, section 4.4: 7, 15, 30* HW 19: due Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 19: due Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 If we don’t get through much of the relations stuff, you can hand it in next Thursday Question 7.1 needs material from 7.3 to be answered – more on that in class HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: last homework, not yet assigned HW 22: due Tuesday, 3 May: last homework, not yet assigned Am considering dropping the two lowest homework grades Am considering dropping the two lowest homework grades How to make the homework assignments less confusing next semester How to make the homework assignments less confusing next semester Exam 2 Grading guidelines are on the web Grading guidelines are on the web I have regrade forms with me today I have regrade forms with me today Reading: read 7.1, 7.3 for Thursday The plan: Finish 5.1 today, go through relations next Finish 5.1 today, go through relations next Next 3 classes are on relations: Next 3 classes are on relations: This week and next week will cover sections 7.1, 7.3, 7.4, 7.5, and 7.6 Last few classes will most likely cover 3.6 Last few classes will most likely cover 3.6 About matrices… About matrices…Regrades All caught up on regrades All caught up on regrades All caught up on grade entry (through HW 17, but not HW 16 yet) All caught up on grade entry (through HW 17, but not HW 16 yet) All HW regrades must be submitted by the last Thursday of class (except pending HWs) All HW regrades must be submitted by the last Thursday of class (except pending HWs) Final exam: Saturday, May 7, from 9 a.m. to noon Saturday, May 7, from 9 a.m. to noon Last semester’s final is on the website Last semester’s final is on the website Final layout will follow the course objectives (last semester’s exam did as well) Final layout will follow the course objectives (last semester’s exam did as well)

Thursday, 21 April 2005 Homeworks HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35 HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45 Can hand it in next Thursday Question 7.1 needs material from 7.3 to be answered – more on that in class HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: last homework, not yet assigned HW 22: due Tuesday, 3 May: last homework, not yet assigned Will drop the two lowest homework grades Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web Grading guidelines are on the web I have regrade forms with me today I have regrade forms with me today Reading: read 7.1, 7.3, 7.4 for Tuesday The plan: Next 3 classes are on relations: Next 3 classes are on relations: This week and next week will cover sections 7.1, 7.3, 7.4, 7.5, and 7.6 Last few classes will most likely cover 3.6 Last few classes will most likely cover 3.6 About matrices… About matrices…Regrades All caught up on regrades All caught up on regrades All caught up on grade entry (through HW 17, but not HW 16 yet) All caught up on grade entry (through HW 17, but not HW 16 yet) All HW regrades must be submitted by the last Thursday of class (except pending HWs) All HW regrades must be submitted by the last Thursday of class (except pending HWs) Final exam: Saturday, May 7, from 9 a.m. to noon Saturday, May 7, from 9 a.m. to noon Last semester’s final is on the website Last semester’s final is on the website Final layout will follow the course objectives (last semester’s exam did as well) Final layout will follow the course objectives (last semester’s exam did as well) No office hours tomorrow! Brian will be quite drugged up from having his wisdom teeth removed Brian will be quite drugged up from having his wisdom teeth removed

Tuesday, 26 April 2005 Homeworks HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45 HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45 Can hand it in Thursday Question 7.1 needs material from 7.3 to be answered – more on that in class HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 Will drop the two lowest homework grades Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web Grading guidelines are on the web I have regrade forms with me today I have regrade forms with me today Reading: read 7.1, 7.3-7.6 for Tuesday The plan: Next 2 classes are on relations Next 2 classes are on relations Last few classes will most likely cover 3.6 Last few classes will most likely cover 3.6 Final exam: Saturday, May 7, from 9 a.m. to noon Saturday, May 7, from 9 a.m. to noon Last semester’s final is on the website Last semester’s final is on the website Final layout will follow the course objectives (last semester’s exam did as well) Final layout will follow the course objectives (last semester’s exam did as well) Course evaluations…

Thursday, 28 April 2005 Homeworks HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, 31, 45 HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, 31, 45 Can hand it in today HW 21: due today: Rosen, section 7.3: 10, 13, 20, 33 HW 21: due today: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 Will drop the two lowest homework grades Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web Grading guidelines are on the web Reading: 7.1-7.6 for Tuesday The plan: Next 2 classes are on relations Next 2 classes are on relations Last class will most likely cover 7.2 (*not* 3.6) Last class will most likely cover 7.2 (*not* 3.6) Final exam: Saturday, May 7, from 9 a.m. to noon Saturday, May 7, from 9 a.m. to noon Am planning on having coffee – but may be short on the coffee cups… Am planning on having coffee – but may be short on the coffee cups… Last semester’s final is on the website now (sorry!) Last semester’s final is on the website now (sorry!) Final layout will follow the course objectives (last semester’s exam did as well) Final layout will follow the course objectives (last semester’s exam did as well) There will be review sessions, probably 2 There will be review sessions, probably 2 Course evaluations…

Course objectives Logic Introduce a formal system (propositional and predicate logic) which mathematical reasoning is based on Sections 1.1-1.4 Sections 1.1-1.4Proofs 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. 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. Sections 1.5, 3.1, 3.3, 3.4 Sections 1.5, 3.1, 3.3, 3.4Counting Introduce the basics of integer theory, combinatorics, and counting principles, including a brief introduction to discrete probability. Introduce the basics of integer theory, combinatorics, and counting principles, including a brief introduction to discrete probability. Sections 2.4, 4.1-4.4, 5.1 Sections 2.4, 4.1-4.4, 5.1Structures Introduce and work with important discrete data structures such as sets, relations, sequences, and discrete functions. Introduce and work with important discrete data structures such as sets, relations, sequences, and discrete functions. Sections 1.6-1.8, 2.7, 3.2, 7.1, 7.3-7.6 Sections 1.6-1.8, 2.7, 3.2, 7.1, 7.3-7.6Applications Gain an understanding of some application areas of the material covered in the course. Gain an understanding of some application areas of the material covered in the course. Sections 2.6, 7.2, 10.3 Sections 2.6, 7.2, 10.3

The End Homeworks HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26 HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26 Sorry 26 was so long! Will drop the two lowest homework grades Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web Grading guidelines are on the web Final exam: Saturday, May 7, from 9 a.m. to noon Saturday, May 7, from 9 a.m. to noon Am planning on having coffee – but may be short on the coffee cups… Am planning on having coffee – but may be short on the coffee cups… Last semester’s final is on the website Last semester’s final is on the website Final layout will follow the course objectives (last semester’s exam did as well) Final layout will follow the course objectives (last semester’s exam did as well) Review sessions One Wednesday, one Thursday One Wednesday, one Thursday Most likely 3:30-6:30 on Wednesday Most likely 3:30-6:30 on Wednesday Exact info will be e-mailed out to everybody later today Exact info will be e-mailed out to everybody later today Office hours this week… Course evaluations… Voting for the favorite demotivator

Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield.

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Daily Announcements CS/APMA 202 Spring 2005 Aaron Bloomfield.

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