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 HW 2: assigned Thu, due following Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 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) Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 My Thursday office hours are changing, but Im 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 HW 2: assigned today, due next Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalences TA office hours: Monday afternoon/evening (a homework review session) Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018 About the grade requirement for CS 216 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 My Thursday office hours Proof methods Proof methods learned so far Logical equivalences

via truth tables via logical equivalences Set equivalences via membership tables via set identities via mutual subset proof via set builder notation and logical equivalences Ten proof methods in section 1.5: Constructive Non-constructive Rules of inference for propositions

for quantified statements Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs Uniqueness proofs Counterexamples Induction Pigeonhole principle Combinatorial proofs Weak mathematical induction Strong mathematical induction Structural induction Tuesday, 1 February 2005 HW 1: due today Rosen, section 1.1: 18, 48, 60

HW 2: due Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalences HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9 TA office hours: Monday 5:00-7:00 (a homework review session) Wednesday 3:30-5:30 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 ( s f ) ( b f ) ( f ( b s )) T ( s f ) (b f ) ( f ( b s )) T s f (b f ) f ( b s ) T

s f f (b f ) ( b s ) T s f (b f ) ( b s ) T f (b f ) s ( s b) T f (b f ) s T f (b f ) s T ( f b) ( f f ) s T ( f b) F s T ( f b) s T f b s T 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

HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9 HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43 TA office hours: Monday 5:00-7:00 (a homework review session) Wednesday 3:30-5:30 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 a) b) c) d) The amount of time the homeworks are taking: Very little

About right A lot Way to much Quick survey a) b) c) d) How hard have the homeworks been so far? Way too hard Somewhat hard About right Very easy Proof methods learned so far Logical equivalences via truth tables via logical equivalences Set equivalences via membership tables via set identities

via mutual subset proof via set builder notation and logical equivalences Ten proof methods in section 1.5: Constructive Non-constructive Rules of inference for propositions for quantified statements Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs

Uniqueness proofs Counterexamples Induction Pigeonhole principle Combinatorial proofs Weak mathematical induction Strong mathematical induction Structural induction Tuesday, 8 February 2005 HW 3: due today Rosen, section 10.3: 3, 4, 5, 9 HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43 HW 5: due Tue (15 Feb) Rosen, section 1.3: 15, 20, 24, 41 HW 6: Due Thu (17 Feb)

Rosen, section 1.4: 12, 22, 33, 40 Reading for Thursday: 1.5 Exam: two weeks from this Thursday Last semesters 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 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 4: due today Rosen, section 1.7: 10, 16, 22, 34, 43 HW 5: due Tue (15 Feb) Rosen, section 1.3: 15, 20, 24, 41

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 semesters exam will be posted on the website Quick survey a) b) c) d) The amount of time the homeworks are taking: Very little About right A lot Way to much Quick survey a) b) c) d) How hard have the homeworks been so far? Way too hard

Somewhat hard About right Very easy Tuesday, 15 February 2005 Homeworks HW 4 returned today Solutions and grading guidelines will be posted shortly HW 5: due today Rosen, section 1.3: 15, 20, 24, 41 HW 6: Due Thu (17 Feb) Rosen, section 1.4: 12, 22, 33, 40 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 Regrades for homeworks

Form is on the website 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) Last semesters 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: Average 82.3 A lot of missing HW 3s check your grades on Toolkit 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 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 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) What is not on the reference sheet: Universal/existential generalization/instantiation Last semesters 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 n3+5 is odd, then n is even Rephrased: If n3+5 is odd, then n is even Thus, p is n3+5 is odd, q is n is even Assume p and q Assume that n3+5 is odd, and n is odd Since n is odd:

n=2k+1 for some integer k (definition of odd numbers) n3+5 = (2k+1)3+5 = 8k3+12k2+6k+6 = 2(4k3+6k2+3k+3) As n = 2(4k3+6k2+3k+3) is 2 times an integer, n must be even Thus, we have concluded q Contradiction! 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 A note on that problem Rosen, section 1.5, question 21 Prove that if n is an integer and n3+5 is odd, then n is even Here, our implication is: If n3+5 is odd, then n is even The indirect proof proved the contrapositive: q p

I.e., If n is odd, then n3+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 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 pq is true Since the consequence is false, the antecedent must be false Thus, p must be true Find a contradiction, such as (rr), to represent q Thus, you are showing that p(rr) Or that assuming p is false leads to a contradiction Tuesday, 22 February 2005 Homeworks

HW 7: Due today 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) Regrades for homeworks Form is on the website 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 Exam: this Thursday 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: Universal/existential generalization/instantiation Last semesters 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) Tuesday, 1 March 2005 Homeworks 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 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 ne mod m (or cd mod m) 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 There were six 100s!

Rough grade estimate based on the exam: A: 93+, B: 86+, C: 70+, D: 60+ Quick survey a) b) c) d) How hard was the exam? Way too hard Somewhat hard About right Very easy Thursday, 3 March 2005 Homeworks HW 8: Due last Tuesday, can hand it in today 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!) 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 ne mod m (or cd mod m) Also, for question 47, d = 937

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!) Can hand it in on Thursday No homework due Thursday As I didnt get my act in gear in time 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 solutions and grading guidelines are now restricted to the virginia.edu domain Im all caught up on regrades, HW solutions, and grading guidelines (for homeworks

and the midterm) Reading: read 3.1, 3.2 for Thursday Regrades Lets 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 Second midterm: Thursday, 7 April (3 weeks from this Thursday) 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 Thursday, 17 March 2005 Homeworks 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 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

Reading: read 3.2, 3.3 for Tuesday Regrades Lets 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 Second midterm: Thursday, 7 April (3 weeks from this Thursday) 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 Tuesday, 22 March 2005 Homeworks 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 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 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 future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (2 weeks from this Thursday) The date wont be changed Thursday, 24 March 2005 Homeworks 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 As Im 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

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 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 future regrades are due 10 days from when it is returned Second midterm: Thursday, 7 April (2 weeks from today) The date wont be changed Third induction again: what if your inductive hypothesis was wrong? Show: i 2 n(n 1)(2n 2) 6 n i 1 Base case: n = 1: 1 1(1 1)(2 2)

2 i 6 i 1 7 2 1 6 7 1 6 But lets continue anyway Inductive hypothesis: assume k k (k 1)(2k 2) i 6 i 1 2 Third induction again: what if your inductive hypothesis was wrong? Inductive step: show k 1 k 1 (k 1)((k 1) 1)(2(k 1) 2) i

6 i 1 2 (k 1)((k 1) 1)(2(k 1) 2) i 6 i 1 k 2 ( k 1)(k 2)(2k 4) (k 1) i 6 i 1 2 2 k (k 1)(2k 2) (k 1)(k 2)(2k 4) (k 1) 6 6 2 6(k 1) 2 k (k 1)(2k 2) (k 1)(k 2)(2k 4) k 2k 10k 14k 6 2k 10k 16k 8 i 2 3 2

3 2 i 1 k (k 1)(2k 2) 6 Proof methods learned so far Logical equivalences via truth tables via logical equivalences Set equivalences via membership tables via set identities via mutual subset proof via set builder notation and logical equivalences Ten proof methods in section 1.5:

Constructive Non-constructive Rules of inference for propositions for quantified statements Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs Uniqueness proofs Counterexamples Induction Pigeonhole principle Combinatorial proofs

Weak mathematical induction Strong mathematical induction Structural induction Tuesday, 29 March 2005 Homeworks 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 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 No homework due next Thursday (as its the midterm) Reading: read 4.1 for Thursday Second midterm: Thursday, 7 April (1 week from this Thursday) The date wont be changed Last semesters exam (and solutions) is on the website Will cover through section 4.1 All that material will be presented this week

Thats 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 There will be review sessions next week (most likely Tue 9-11, Wed 710) Thursday, 31 March 2005 Homeworks 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 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59 No homework due next Thursday (as its the midterm) Reading: read 4.2-4.4 for Tuesday Second midterm: Thursday, 7 April (1 week from this Thursday) Last semesters exam (and solutions) is on the website Will cover through section 4.1 All that material will be presented this week Thats 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 There will be review sessions next week Tue 9-11 and Wed 7-10 (both evening sessions and in Olsson 005) Proof methods learned so far Logical equivalences via truth tables via logical equivalences Set equivalences via membership tables via set identities via mutual subset proof via set builder notation and logical equivalences Ten proof methods in section 1.5: Constructive

Non-constructive Rules of inference for propositions for quantified statements Direct proofs Indirect proofs Vacuous proofs Trivial proofs Proof by contradiction Proof by cases Proofs of equivalence Existence proofs Uniqueness proofs Counterexamples Induction Pigeonhole principle Combinatorial proofs Weak mathematical induction Strong mathematical induction

Structural induction Comments from the surveys 53 surveys received Biggest complaint: textbook (12 negative responses) 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 No homework due Thursday (as its the midterm) Homework due next Tue/Thu Reading: read 4.2-4.4 for Thursday Second midterm: this Thursday, 7 April

Last semesters exam (and solutions) is on the website Two review sessions 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 1.11.8 is fair game The big proof method weve 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 2.0 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. 1.0 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 0.0 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 Homeworks 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 Reading: read 4.4, 5.1 for next Tuesday Tuesday, 12 April 2005

Tests returned today Average: 78.9 (without extra credit) Grade ranges: Homework average so far: 78.0 (HWs 1-12 and 14) A: 90 and above B: 80 and above C: 65 and above D: 50 and above About the oral exam Homeworks 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 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* 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 Holdem Thursday, 14 April 2005 Homeworks 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 18: due next Tuesday: Rosen, section 4.4: 7, 15, 30* 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 19: due Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45

If we dont 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 22: due Tuesday, 3 May: last homework, not yet assigned Am considering dropping the two lowest homework grades How to make the homework assignments less confusing next semester Exam 2 Grading guidelines are on the web 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 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 About matrices

Regrades All caught up on regrades 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) Final exam: Saturday, May 7, from 9 a.m. to noon Last semesters final is on the website Final layout will follow the course objectives (last semesters exam did as well) Thursday, 21 April 2005 Homeworks 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 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 22: due Tuesday, 3 May: last homework, not yet assigned Will drop the two lowest homework grades

Exam 2 Grading guidelines are on the web 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: 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 About matrices Regrades All caught up on regrades 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) Final exam:

Saturday, May 7, from 9 a.m. to noon Last semesters final is on the website Final layout will follow the course objectives (last semesters exam did as well) No office hours tomorrow! 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 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 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web 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 Last few classes will most likely cover 3.6 Final exam: Saturday, May 7, from 9 a.m. to noon Last semesters final is on the website Final layout will follow the course objectives (last semesters 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 Can hand it in today 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 Will drop the two lowest homework grades Exam 2 Grading guidelines are on the web

Reading: 7.1-7.6 for Tuesday The plan: Next 2 classes are on relations Last class will most likely cover 7.2 (*not* 3.6) Final exam: Saturday, May 7, from 9 a.m. to noon Am planning on having coffee but may be short on the coffee cups Last semesters final is on the website now (sorry!) Final layout will follow the course objectives (last semesters exam did as well) 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 Proofs

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 Counting 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 Structures 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 Applications Gain an understanding of some application areas of the material covered in the course. Sections 2.6, 7.2, 10.3 The End

Homeworks 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 Exam 2 Grading guidelines are on the web Final exam: Saturday, May 7, from 9 a.m. to noon Am planning on having coffee but may be short on the coffee cups Last semesters final is on the website Final layout will follow the course objectives (last semesters exam did as well) Review sessions One Wednesday, one Thursday Most likely 3:30-6:30 on Wednesday Exact info will be e-mailed out to everybody later today

Office hours this week Course evaluations Voting for the favorite demotivator