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Daily Daily Announcements Announcements CS/APMA 202 CS/APMA 202 Spring 2005 Spring 2005 Aaron Bloomfield Aaron Bloomfield

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Page 1: Daily announcements slides

Daily AnnouncementsDaily Announcements

CS/APMA 202CS/APMA 202

Spring 2005Spring 2005

Aaron BloomfieldAaron Bloomfield

Page 2: Daily announcements slides

Tuesday, 25 January 2005Tuesday, 25 January 2005

HW 1: assigned today, due next Tue (1 Feb)HW 1: assigned today, due next Tue (1 Feb) Rosen, section 1.1: 18, 48, 60Rosen, section 1.1: 18, 48, 60

HW 2: assigned Thu, due following Thu (3 Feb)HW 2: assigned Thu, due following Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalencesMust answer 19 by both truth tables and logical equivalences

TA office hours will be posted on the websiteTA 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 018Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018Friday 10:00-noon in Olsson 018

My Thursday office hours are changing, but I’m not sure My Thursday office hours are changing, but I’m not sure what to yetwhat to yet

Page 3: Daily announcements slides

Thursday, 27 January 2005Thursday, 27 January 2005

HW 1: assigned last time, due next Tue (1 Feb)HW 1: assigned last time, due next Tue (1 Feb) Rosen, section 1.1: 18, 48, 60Rosen, section 1.1: 18, 48, 60

HW 2: assigned today, due next Thu (3 Feb)HW 2: assigned today, due next Thu (3 Feb) Rosen, section 1.2: 19, 35, 39, 50Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalencesMust answer 19 by both truth tables and logical equivalences

TA office hours:TA office hours: Monday afternoon/evening (a homework review session)Monday afternoon/evening (a homework review session) Wednesday 3:30-5:30 in Olsson 018Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018Friday 10:00-noon in Olsson 018

About the grade requirement for CS 216About the grade requirement for CS 216 And about doing well in this class…And about doing well in this class…

Reading for Tuesday: 1.3Reading for Tuesday: 1.3 Ideally, should have read 1.1, 1.2, and 10.3 by nowIdeally, should have read 1.1, 1.2, and 10.3 by now

My Thursday office hoursMy Thursday office hoursProof methodsProof methods

Page 4: Daily announcements slides

Proof methods learned so farProof methods learned so far

Logical equivalencesLogical equivalences via truth tablesvia truth tables via logical equivalencesvia logical equivalences

Set equivalencesSet equivalences via membership tablesvia membership tables via set identitiesvia set identities via mutual subset proofvia mutual subset proof via set builder notation and via set builder notation and

logical equivalenceslogical equivalencesRules of inferenceRules of inference

for propositionsfor propositions for quantified statementsfor quantified statements

Pigeonhole principlePigeonhole principleCombinatorial proofsCombinatorial proofs

Ten proof methods in section 1.5:Ten proof methods in section 1.5: Direct proofsDirect proofs Indirect proofsIndirect proofs Vacuous proofsVacuous proofs Trivial proofsTrivial proofs Proof by contradictionProof by contradiction Proof by casesProof by cases Proofs of equivalenceProofs of equivalence Existence proofsExistence proofs

ConstructiveConstructiveNon-constructiveNon-constructive

Uniqueness proofsUniqueness proofs CounterexamplesCounterexamples

InductionInduction Weak mathematical inductionWeak mathematical induction Strong mathematical inductionStrong mathematical induction Structural inductionStructural induction

Page 5: Daily announcements slides

Tuesday, 1 February 2005Tuesday, 1 February 2005HW 1: due todayHW 1: due today

Rosen, section 1.1: 18, 48, 60Rosen, section 1.1: 18, 48, 60HW 2: due Thu (3 Feb)HW 2: due Thu (3 Feb)

Rosen, section 1.2: 19, 35, 39, 50Rosen, section 1.2: 19, 35, 39, 50 Must answer 19 by both truth tables and logical equivalencesMust answer 19 by both truth tables and logical equivalences

HW 3: due Tue (8 Feb)HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9Rosen, section 10.3: 3, 4, 5, 9

TA office hours: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 018Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018Friday 10:00-noon in Olsson 018

Reading for Tuesday: 1.6/1.7Reading for Tuesday: 1.6/1.7My Thursday office hours: now 10:30-noonMy Thursday office hours: now 10:30-noonRescheduling the homework review session (so as not to conflict with CS Rescheduling the homework review session (so as not to conflict with CS 201 labs)?201 labs)?Terminology: disjunction and conjunction (and question 1.2 # 35)Terminology: disjunction and conjunction (and question 1.2 # 35)Logic gates: not on test, but on HW 3Logic gates: not on test, but on HW 3

Page 6: Daily announcements slides

Are all of their statements true?Are all of their statements true?Show values for s, b, and f such Show values for s, b, and f such

that the equation is truethat the equation is trueOriginal 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 ANDTsbf

Tsbffbfs ))(()()(

Tsbffbfs ))(()()(

Tsbffbfs )()(

Tsbfbffs )()(

Tsbfbfs )()(

Tbssfbf )()(

Tsfbf )(

Tsfbf )(

Tsffbf )()(

TsFbf )(

Tsbf )(

Page 7: Daily announcements slides

Thursday, 3 February 2005Thursday, 3 February 2005

HW 2: due todayHW 2: due today Rosen, section 1.2: 19, 35, 39, 50Rosen, section 1.2: 19, 35, 39, 50

HW 3: due Tue (8 Feb)HW 3: due Tue (8 Feb) Rosen, section 10.3: 3, 4, 5, 9Rosen, section 10.3: 3, 4, 5, 9

HW 4: due Thu (10 Feb)HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43Rosen, section 1.7: 10, 16, 22, 34, 43

TA office hours: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 018Wednesday 3:30-5:30 in Olsson 018 Friday 10:00-noon in Olsson 018Friday 10:00-noon in Olsson 018

Reading for Tuesday: 1.3/1.4Reading for Tuesday: 1.3/1.4That crane picture sequence…That crane picture sequence…

Page 8: Daily announcements slides

A bit of humor…A bit of humor…

Page 9: Daily announcements slides

Quick surveyQuick survey

The amount of time the homeworks The amount of time the homeworks are taking:are taking:

a)a) Very littleVery little

b)b) About rightAbout right

c)c) A lotA lot

d)d) Way to muchWay to much

Page 10: Daily announcements slides

Quick surveyQuick survey

How hard have the homeworks How hard have the homeworks been so far?been so far?

a)a) Way too hardWay too hard

b)b) Somewhat hardSomewhat hard

c)c) About rightAbout right

d)d) Very easyVery easy

Page 11: Daily announcements slides

Proof methods learned so farProof methods learned so far

Logical equivalencesLogical equivalences via truth tablesvia truth tables via logical equivalencesvia logical equivalences

Set equivalencesSet equivalences via membership tablesvia membership tables via set identitiesvia set identities via mutual subset proofvia mutual subset proof via set builder notation and via set builder notation and

logical equivalenceslogical equivalencesRules of inferenceRules of inference

for propositionsfor propositions for quantified statementsfor quantified statements

Pigeonhole principlePigeonhole principleCombinatorial proofsCombinatorial proofs

Ten proof methods in section 1.5:Ten proof methods in section 1.5: Direct proofsDirect proofs Indirect proofsIndirect proofs Vacuous proofsVacuous proofs Trivial proofsTrivial proofs Proof by contradictionProof by contradiction Proof by casesProof by cases Proofs of equivalenceProofs of equivalence Existence proofsExistence proofs

ConstructiveConstructiveNon-constructiveNon-constructive

Uniqueness proofsUniqueness proofs CounterexamplesCounterexamples

InductionInduction Weak mathematical inductionWeak mathematical induction Strong mathematical inductionStrong mathematical induction Structural inductionStructural induction

Page 12: Daily announcements slides

Tuesday, 8 February 2005Tuesday, 8 February 2005

HW 3: due todayHW 3: due today Rosen, section 10.3: 3, 4, 5, 9Rosen, section 10.3: 3, 4, 5, 9

HW 4: due Thu (10 Feb)HW 4: due Thu (10 Feb) Rosen, section 1.7: 10, 16, 22, 34, 43Rosen, 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, 41Rosen, 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, 40Rosen, section 1.4: 12, 22, 33, 40

Reading for Thursday: 1.5Reading for Thursday: 1.5Exam: two weeks from this ThursdayExam: two weeks from this Thursday Last semester’s exam will be posted on the websiteLast semester’s exam will be posted on the website

Would people use forums if I set them up?Would people use forums if I set them up?

Page 13: Daily announcements slides

Thursday, 10 February 2005Thursday, 10 February 2005

HomeworksHomeworks HWs 1 and 2 returned todayHWs 1 and 2 returned today

HW 1: Average 80.3, standard deviation 20.0HW 1: Average 80.3, standard deviation 20.0HW 2: Average 85.0, standard deviation 18.4HW 2: Average 85.0, standard deviation 18.4Solutions and grading guidelines will be posted shortlySolutions and grading guidelines will be posted shortlyRegrades for homeworksRegrades for homeworks

HW 3: can turn in late…HW 3: can turn in late… HW 4: due todayHW 4: due today

Rosen, section 1.7: 10, 16, 22, 34, 43Rosen, 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, 41Rosen, 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, 40Rosen, section 1.4: 12, 22, 33, 40

Reading for today and next Tuesday: 1.5Reading for today and next Tuesday: 1.5Exam: two weeks from todayExam: two weeks from today

Last semester’s exam will be posted on the websiteLast semester’s exam will be posted on the website

Page 14: Daily announcements slides

Quick surveyQuick survey

The amount of time the homeworks The amount of time the homeworks are taking:are taking:

a)a) Very littleVery little

b)b) About rightAbout right

c)c) A lotA lot

d)d) Way to muchWay to much

Page 15: Daily announcements slides

Quick surveyQuick survey

How hard have the homeworks How hard have the homeworks been so far?been so far?

a)a) Way too hardWay too hard

b)b) Somewhat hardSomewhat hard

c)c) About rightAbout right

d)d) Very easyVery easy

Page 16: Daily announcements slides

Tuesday, 15 February 2005Tuesday, 15 February 2005HomeworksHomeworks

HW 4 returned todayHW 4 returned todaySolutions and grading guidelines will be posted shortlySolutions and grading guidelines will be posted shortly

HW 5: due todayHW 5: due todayRosen, section 1.3: 15, 20, 24, 41Rosen, 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, 40Rosen, 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, 55Rosen, 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, 64Rosen, section 1.8: 17, 36, 61, 64

Regrades for homeworksRegrades for homeworks Form is on the websiteForm is on the website Must be within a weekMust be within a week

Reading for Thursday: 1.8Reading for Thursday: 1.8Exam: one week from this ThursdayExam: 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 websiteLast semester’s exam will be posted on the website

It only covered 1.1-1.7It only covered 1.1-1.7And it was a 50 minute exam, not a 75 minute examAnd it was a 50 minute exam, not a 75 minute exam

Page 17: Daily announcements slides

Thursday, 15 February 2005Thursday, 15 February 2005

HomeworksHomeworks HW 3 returned todayHW 3 returned today

HW 3: Average 82.3HW 3: Average 82.3A lot of missing HW 3’s – check your grades on ToolkitA 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 homeworksRegrades for homeworks Form is on the website, and I have copies on meForm is on the website, and I have copies on me Must be within a 10 daysMust be within a 10 days

Reading for Tuesday: 2.4Reading for Tuesday: 2.4Review sessions: Tue from 9-11 p.m. and Wed from 7-10 p.m.Review sessions: Tue from 9-11 p.m. and Wed from 7-10 p.m.Exam: one week from this ThursdayExam: 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/instantiationUniversal/existential generalization/instantiation Last semester’s exam is posted on the websiteLast semester’s exam is posted on the website

It only covered 1.1-1.7It only covered 1.1-1.7And it was a 50 minute exam, not a 75 minute examAnd it was a 50 minute exam, not a 75 minute exam

Page 18: Daily announcements slides

Proof by contradiction example 2Proof by contradiction example 2

Rosen, section 1.5, question 21 (b)Rosen, section 1.5, question 21 (b) Prove that if n is an integer and nProve that if n is an integer and n33+5 is odd, then n is even+5 is odd, then n is even Rephrased: If nRephrased: If n33+5 is odd, then n is even+5 is odd, then n is even

Thus, p is “nThus, p is “n33+5” is odd, q is “n is even”+5” is odd, q is “n is even”

Assume p and Assume p and qq Assume that nAssume that n33+5 is odd, and n is odd+5 is odd, and n is odd

Since 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) nn33+5 = (2k+1)+5 = (2k+1)33+5 = 8k+5 = 8k33+12k+12k22+6k+6 = 2(4k+6k+6 = 2(4k33+6k+6k22+3k+3)+3k+3) As n = 2(4kAs n = 2(4k33+6k+6k22+3k+3) is 2 times an integer, n must be even+3k+3) is 2 times an integer, n must be even Thus, we have concluded qThus, we have concluded q

Contradiction!Contradiction! We assumed q was false, and showed that this assumption implies that q must We assumed q was false, and showed that this assumption implies that q must

be truebe true As q cannot be both true and false, we have reached our contradictionAs q cannot be both true and false, we have reached our contradiction

Page 19: Daily announcements slides

A note on that problem…A note on that problem…

Rosen, section 1.5, question 21Rosen, section 1.5, question 21 Prove that if n is an integer and nProve that if n is an integer and n33+5 is odd, then n is even+5 is odd, then n is even Here, our implication is: If nHere, our implication is: If n33+5 is odd, then n is even+5 is odd, then n is even

The indirect proof proved the contrapositive: ¬q → ¬pThe indirect proof proved the contrapositive: ¬q → ¬p I.e., If n is odd, then nI.e., If n is odd, then n33+5 is even+5 is even

The proof by contradiction assumed that the implication The proof by contradiction assumed that the implication was false, and showed that led to a contradictionwas false, and showed that led to a contradiction

If we assume p and ¬q, we can show that implies qIf we assume p and ¬q, we can show that implies q The contradiction is q and ¬qThe contradiction is q and ¬q

Note that both used similar steps, but are different Note that both used similar steps, but are different means of proving the implicationmeans of proving the implication

Page 20: Daily announcements slides

How the book explains How the book explains proof by contradictionproof by contradiction

A very poor explanation, IMHOA very poor explanation, IMHO

Suppose q is a contradiction (i.e. is always false)Suppose q is a contradiction (i.e. is always false)

Show that ¬p→q is trueShow that ¬p→q is true Since the consequence is false, the antecedent must be Since the consequence is false, the antecedent must be

falsefalse Thus, p must be trueThus, p must be true

Find a contradiction, such as (rFind a contradiction, such as (r¬r), to represent q¬r), to represent q

Thus, you are showing that ¬p→(rThus, you are showing that ¬p→(r¬r)¬r) Or that assuming p is false leads to a contradictionOr that assuming p is false leads to a contradiction

Page 21: Daily announcements slides

Tuesday, 22 February 2005Tuesday, 22 February 2005HomeworksHomeworks

HW 7: Due todayHW 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 homeworksRegrades for homeworks Form is on the websiteForm is on the website Must be within a 10 daysMust be within a 10 days

Reading for next Tuesday: 2.6Reading for next Tuesday: 2.6Review sessions: today from 9-11 p.m. and Wed from 7-10 p.m.Review sessions: today from 9-11 p.m. and Wed from 7-10 p.m.

Both are in Olsson 005Both are in Olsson 005Exam: this ThursdayExam: 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-answer3 proofs, 3 pages of short-answer

What is not on the reference sheet:What is not on the reference sheet:Universal/existential generalization/instantiationUniversal/existential generalization/instantiation

Last semester’s exam is posted on the websiteLast semester’s exam is posted on the websiteIt only covered 1.1-1.7It only covered 1.1-1.7And it was a 50 minute exam, not a 75 minute examAnd 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)

Page 22: Daily announcements slides

Tuesday, 1 March 2005Tuesday, 1 March 2005

HomeworksHomeworks 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 yesterdayCan 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 46, encrypt "LEGEND" instead of "ATTACK“For 47, the message to decrypt is 2268 2465 0565, instead of what's givenFor 47, the message to decrypt is 2268 2465 0565, instead of what's givenThe problems in section 2.6 will need to use the script at The problems in section 2.6 will need to use the script at http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpowhttp://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow to compute to compute nnee mod mod mm (or (or ccdd mod mod mm))Also, for question 47, Also, for question 47, dd = 937 = 937

HW solutions and grading guidelines are now restricted to the HW solutions and grading guidelines are now restricted to the virginia.edu domainvirginia.edu domainReading for Thursday: 2.1 & 2.2Reading for Thursday: 2.1 & 2.2Exams returned todayExams returned today

Average: 86.5, standard deviation: 12.5, median: 90.5Average: 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:Rough grade estimate based on the exam: A: 93+, B: 86+, C: 70+, D: 60+A: 93+, B: 86+, C: 70+, D: 60+

Page 23: Daily announcements slides

Quick surveyQuick survey

How hard was the exam?How hard was the exam?

a)a) Way too hardWay too hard

b)b) Somewhat hardSomewhat hard

c)c) About rightAbout right

d)d) Very easyVery easy

Page 24: Daily announcements slides

Thursday, 3 March 2005Thursday, 3 March 2005

HomeworksHomeworks 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 HW 10: Due Tuesday, 15 Mar: Rosen, section 2.6, question 46 and 47

(see note!)(see note!)For 46, encrypt "LEGEND" instead of "ATTACK“For 46, encrypt "LEGEND" instead of "ATTACK“For 47, the message to decrypt is 2268 2465 0565, instead of what's givenFor 47, the message to decrypt is 2268 2465 0565, instead of what's givenThe problems in section 2.6 will need to use the script at The problems in section 2.6 will need to use the script at http://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpowhttp://www.cs.virginia.edu/cgi-bin/cgiwrap/asb/modpow to compute to compute nnee mod mod mm (or (or ccdd mod mod mm))Also, for question 47, Also, for question 47, dd = 937 = 937

HW 11 will be posted shortly, due two weeks from todayHW 11 will be posted shortly, due two weeks from todayHW solutions and grading guidelines are now restricted to the HW solutions and grading guidelines are now restricted to the virginia.edu domainvirginia.edu domainReading for Tuesday: 3.1Reading for Tuesday: 3.1Exam regrades…Exam regrades…No office hours tomorrow!No office hours tomorrow!Regrading of that questionRegrading of that questionI used different ASCII code for the RSA questions for the HWI used different ASCII code for the RSA questions for the HW

Page 25: Daily announcements slides

Tuesday, 15 March 2005Tuesday, 15 March 2005HomeworksHomeworks

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 ThursdayCan hand it in on Thursday

No homework due ThursdayNo homework due ThursdayAs I didn’t get my act in gear in timeAs I didn’t get my act in gear in time

HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34You MUST provide a Big-Oh estimate for each of your algorithmsYou 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 domainHW solutions and grading guidelines are now restricted to the virginia.edu domainI’m all caught up on regrades, HW solutions, and grading guidelines (for homeworks I’m all caught up on regrades, HW solutions, and grading guidelines (for homeworks and the midterm)and the midterm)Reading: read 3.1, 3.2 for ThursdayReading: read 3.1, 3.2 for ThursdayRegradesRegrades

Let’s say all regrades for HWs 1-7 and the first midterm will be due two weeks from today 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)(i.e. on 29 March)

All future regrades are due 10 days from when it is returnedAll future regrades are due 10 days from when it is returned

Second midterm: Thursday, 7 April (3 weeks from this Thursday)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!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 Regrading of question 34 on HW 4: if you got points taken off because you did a truth table, you will get those points backtable, you will get those points back

Please submit that as a regradePlease submit that as a regrade

Page 26: Daily announcements slides

Thursday, 17 March 2005Thursday, 17 March 2005

HomeworksHomeworks 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, 34HW 11 due next Tuesday: Rosen, section 2.1: 9, 24, 26, 34

You MUST provide a Big-Oh estimate for each of your algorithmsYou 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 TuesdayReading: read 3.2, 3.3 for TuesdayRegradesRegrades

Let’s say all regrades for HWs 1-7 and the first midterm will be due two 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)weeks from last Tuesday (i.e. on 29 March)

All future regrades are due 10 days from when it is returnedAll future regrades are due 10 days from when it is returnedSecond midterm: Thursday, 7 April (3 weeks from this Thursday)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 Regrading of question 34 on HW 4: if you got points taken off because you did a truth table, you will get those points backbecause you did a truth table, you will get those points back

Please submit that as a regradePlease submit that as a regrade

Page 27: Daily announcements slides

Tuesday, 22 March 2005Tuesday, 22 March 2005

HomeworksHomeworks HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34HW 11 due today: Rosen, section 2.1: 9, 24, 26, 34

You MUST provide a Big-Oh estimate for each of your algorithmsYou 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 tonightHWs 13 & 14 will be on the website tonight

Reading: read 3.3, 3.4 for TuesdayReading: read 3.3, 3.4 for TuesdayAbout office hours today…About office hours today…RegradesRegrades

Am all caught up on regradesAm all caught up on regradesRegraded assignments are in the appropriate HW folderRegraded assignments are in the appropriate HW folderGrades are updated on ToolkitGrades are updated on Toolkit

All regrades for HWs 1-7 and the first midterm are due one week from All regrades for HWs 1-7 and the first midterm are due one week from today (i.e. on 29 March)today (i.e. on 29 March)

All future regrades are due 10 days from when it is returnedAll future regrades are due 10 days from when it is returnedSecond midterm: Thursday, 7 April (2 weeks from this Thursday)Second midterm: Thursday, 7 April (2 weeks from this Thursday)

The date won’t be changedThe date won’t be changed

Page 28: Daily announcements slides

Thursday, 24 March 2005Thursday, 24 March 2005

HomeworksHomeworks 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, 36HW 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 wellAs 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, 51HW 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 Reading: 3.4 for today, 4.1 for Tuesday (although we might not get to it until Thursday) to it until Thursday) RegradesRegrades

Am all caught up on regradesAm all caught up on regradesRegraded assignments are in the appropriate HW folderRegraded assignments are in the appropriate HW folderGrades are updated on ToolkitGrades are updated on Toolkit

All regrades for HWs 1-7 and the first midterm are due next Tuesday All regrades for HWs 1-7 and the first midterm are due next Tuesday (29 March)(29 March)

All future regrades are due 10 days from when it is returnedAll future regrades are due 10 days from when it is returnedSecond midterm: Thursday, 7 April (2 weeks from today)Second midterm: Thursday, 7 April (2 weeks from today)

The date won’t be changedThe date won’t be changed

Page 29: Daily announcements slides

Third induction again: what if your Third induction again: what if your inductive hypothesis was wrong?inductive hypothesis was wrong?Show:Show:

Base case: Base case: nn = 1: = 1:

But let’s continue anyway…But let’s continue anyway…Inductive hypothesis: assume Inductive hypothesis: assume

6

)22)(1(

1

2

nnni

n

i

6

71

6

71

6

)22)(11(1

2

1

1

2

i

i

6

)22)(1(

1

2

kkki

k

i

Page 30: Daily announcements slides

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

6

)2)1(2)(1)1)((1(1

1

2

kkki

k

i

6

)42)(2)(1()1(

1

22

kkkik

k

i

816102614102 2323 kkkkkk

)42)(2)(1()22)(1()1(6 2 kkkkkkk

6

)42)(2)(1(

6

)22)(1()1( 2

kkkkkk

k

6

)2)1(2)(1)1)((1(1

1

2

kkki

k

i

6

)22)(1(

1

2

kkki

k

i

Page 31: Daily announcements slides

Proof methods learned so farProof methods learned so far

Logical equivalencesLogical equivalences via truth tablesvia truth tables via logical equivalencesvia logical equivalences

Set equivalencesSet equivalences via membership tablesvia membership tables via set identitiesvia set identities via mutual subset proofvia mutual subset proof via set builder notation and via set builder notation and

logical equivalenceslogical equivalencesRules of inferenceRules of inference

for propositionsfor propositions for quantified statementsfor quantified statements

Pigeonhole principlePigeonhole principleCombinatorial proofsCombinatorial proofs

Ten proof methods in section 1.5:Ten proof methods in section 1.5: Direct proofsDirect proofs Indirect proofsIndirect proofs Vacuous proofsVacuous proofs Trivial proofsTrivial proofs Proof by contradictionProof by contradiction Proof by casesProof by cases Proofs of equivalenceProofs of equivalence Existence proofsExistence proofs

ConstructiveConstructiveNon-constructiveNon-constructive

Uniqueness proofsUniqueness proofs CounterexamplesCounterexamples

InductionInduction Weak mathematical inductionWeak mathematical induction Strong mathematical inductionStrong mathematical induction Structural inductionStructural induction

Page 32: Daily announcements slides

Tuesday, 29 March 2005Tuesday, 29 March 2005

HomeworksHomeworks HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 14: due Thursday: Rosen, section 3.3: 12, 27, 29, 51HW 14: due Thursday: Rosen, section 3.3: 12, 27, 29, 51 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59HW 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 ThursdayReading: read 4.1 for ThursdaySecond midterm: Thursday, 7 April (1 week from this Thursday)Second midterm: Thursday, 7 April (1 week from this Thursday)

The date won’t be changedThe date won’t be changed Last semester’s exam (and solutions) is on the websiteLast semester’s exam (and solutions) is on the website Will cover through section 4.1Will cover through section 4.1

All that material will be presented this weekAll 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 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 Completenesswell as the talk about NP Completeness And of course material from sections 1.1-1.8 is fair gameAnd 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-There will be review sessions next week (most likely Tue 9-11, Wed 7-

10)10)

Page 33: Daily announcements slides

Thursday, 31 March 2005Thursday, 31 March 2005

HomeworksHomeworks HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36HW 13 due today: Rosen, section 3.2: 8, 9, 23, 36 HW 14: due today: Rosen, section 3.3: 12, 27, 29, 51HW 14: due today: Rosen, section 3.3: 12, 27, 29, 51 HW 15: due next Tuesday: Rosen, section 3.4: 11, 27, 44, 59HW 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 TuesdayReading: read 4.2-4.4 for TuesdaySecond midterm: Thursday, 7 April (1 week from this Second midterm: Thursday, 7 April (1 week from this Thursday)Thursday)

Last semester’s exam (and solutions) is on the websiteLast semester’s exam (and solutions) is on the website Will cover through section 4.1Will cover through section 4.1

All that material will be presented this weekAll 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, 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 Completenessas well as the talk about NP Completeness And of course material from sections 1.1-1.8 is fair gameAnd of course material from sections 1.1-1.8 is fair game There will be review sessions next weekThere will be review sessions next week

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)

Page 34: Daily announcements slides

Proof methods learned so farProof methods learned so far

Logical equivalencesLogical equivalences via truth tablesvia truth tables via logical equivalencesvia logical equivalences

Set equivalencesSet equivalences via membership tablesvia membership tables via set identitiesvia set identities via mutual subset proofvia mutual subset proof via set builder notation and via set builder notation and

logical equivalenceslogical equivalencesRules of inferenceRules of inference

for propositionsfor propositions for quantified statementsfor quantified statements

Pigeonhole principlePigeonhole principleCombinatorial proofsCombinatorial proofs

Ten proof methods in section 1.5:Ten proof methods in section 1.5: Direct proofsDirect proofs Indirect proofsIndirect proofs Vacuous proofsVacuous proofs Trivial proofsTrivial proofs Proof by contradictionProof by contradiction Proof by casesProof by cases Proofs of equivalenceProofs of equivalence Existence proofsExistence proofs

ConstructiveConstructiveNon-constructiveNon-constructive

Uniqueness proofsUniqueness proofs CounterexamplesCounterexamples

InductionInduction Weak mathematical inductionWeak mathematical induction Strong mathematical inductionStrong mathematical induction Structural inductionStructural induction

Page 35: Daily announcements slides

Comments from the surveysComments from the surveys

53 surveys received53 surveys receivedBiggest complaint: textbook (12 negative responses)Biggest complaint: textbook (12 negative responses)

Comment was to make the course non-textbook basedComment was to make the course non-textbook basedSecond biggest complaint: errors in the slidesSecond biggest complaint: errors in the slidesPlaying Enya in class: 3 positive responses, 7 negativePlaying Enya in class: 3 positive responses, 7 negativePost slides earlierPost slides earlierMore/less example problemsMore/less example problemsHave summaries of major topics availableHave summaries of major topics availableHumor asides…Humor asides…Cough dropsCough dropsResponding to surveysResponding to surveysPost daily announcements on websitePost daily announcements on websiteHomework gradingHomework gradingMore KLAsMore KLAsReview difficult HW problems in classReview difficult HW problems in class

Page 36: Daily announcements slides

Tuesday, 5 April 2005Tuesday, 5 April 2005

HomeworksHomeworks HW 15: due today: Rosen, section 3.4: 11, 27, 44, 59HW 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 ThursdayReading: read 4.2-4.4 for ThursdaySecond midterm: this Thursday, 7 AprilSecond midterm: this Thursday, 7 April Last semester’s exam (and solutions) is on the Last semester’s exam (and solutions) is on the

websitewebsite

Two review sessionsTwo review sessions Tue 9-11 and Wed 7-10 (both evening sessions and Tue 9-11 and Wed 7-10 (both evening sessions and

in Olsson 005)in Olsson 005)

Slide error checking…Slide error checking…

Page 37: Daily announcements slides

About the second midtermAbout the second midterm

Sections 2.1, 2.2, 2.4, 2.6 (the RSA part), 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 3.1-3.4, and 4.1, as well as the talk about NP CompletenessNP Completeness

And of course material from sections 1.1-And of course material from sections 1.1-1.8 is fair game1.8 is fair game

The big proof method we’ve seen since The big proof method we’ve seen since the first midterm is inductionthe first midterm is induction

About the problem database for sections About the problem database for sections 2.1 and 2.22.1 and 2.2

Page 38: Daily announcements slides

New homework grading schemeNew homework grading scheme

Homeworks will now be graded on a 10-point scaleHomeworks will now be graded on a 10-point scaleEach problem is worth 2.5 points: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 2.0 points: If they got the problem right, but made a simple

mistake somewhere (i.e. an arithmetic mistake) mistake somewhere (i.e. an arithmetic mistake) 1.5 points: If they might have had the right idea, but got it fairly 1.5 points: If they might have had the right idea, but got it fairly

wrong. wrong. 1.0 points: If they got the problem totally wrong, but put in effort 1.0 points: If they got the problem totally wrong, but put in effort

into the question into the question 0.5 points: If they got it totally wrong, and didn't put in much 0.5 points: If they got it totally wrong, and didn't put in much

effort effort 0.0 points: If they left it blank, or obviously didn't try0.0 points: If they left it blank, or obviously didn't try

Grading will also be a bit more lenientGrading will also be a bit more lenient

Page 39: Daily announcements slides

Thursday, 7 April 2005Thursday, 7 April 2005

Test today!Test today! In case you forgot…In case you forgot…

HomeworksHomeworks HW 16: due next Tuesday: Rosen, section HW 16: due next Tuesday: Rosen, section

4.2: 7, 15, 29, 374.2: 7, 15, 29, 37Can hand it in next Thursday as wellCan hand it in next Thursday as well

HW 17: due next Thursday: Rosen, section HW 17: due next Thursday: Rosen, section 4.3: 14, 30, 37, 434.3: 14, 30, 37, 43

Reading: read 4.4, 5.1 for next TuesdayReading: read 4.4, 5.1 for next Tuesday

Page 40: Daily announcements slides

Tuesday, 12 April 2005Tuesday, 12 April 2005Tests returned today…Tests returned today…

Average: 78.9 (without extra credit)Average: 78.9 (without extra credit)Grade ranges: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 aboveA: 90 and above B: 80 and aboveB: 80 and above C: 65 and aboveC: 65 and above D: 50 and aboveD: 50 and above

About the oral exam…About the oral exam…HomeworksHomeworks

HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37Can hand it in Thursday as wellCan hand it in Thursday as well

HW 17: due Thursday: Rosen, section 4.3: 14, 30, 37, 43HW 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, 35HW 19: due next Thursday: Rosen, section 5.1: 12, 17, 27, 35

Reading: read 5.1 for ThursdayReading: read 5.1 for ThursdayWhich game of chance should I go over?Which game of chance should I go over?

My preference: Texas Hold’emMy preference: Texas Hold’em

Page 41: Daily announcements slides

Thursday, 14 April 2005Thursday, 14 April 2005

HomeworksHomeworks HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37HW 16: due today: Rosen, section 4.2: 7, 15, 29, 37

Can hand it in Thursday as wellCan hand it in Thursday as well HW 17: due today: Rosen, section 4.3: 14, 30, 37, 43HW 17: due today: Rosen, section 4.3: 14, 30, 37, 43 HW 18: due next Tuesday: Rosen, section 4.4: 7, 15, HW 18: due next Tuesday: Rosen, section 4.4: 7, 15,

30*30* HW 19: due next Thursday: Rosen, section 5.1: 12, HW 19: due next Thursday: Rosen, section 5.1: 12,

17, 27, 3517, 27, 35

Reading: read 5.1 for ThursdayReading: read 5.1 for Thursday

About P(52,5) vs. C(52,5) in the slides for the About P(52,5) vs. C(52,5) in the slides for the poker hands…poker hands…

Page 42: Daily announcements slides

Tuesday, 19 April 2005Tuesday, 19 April 2005HomeworksHomeworks

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, 35HW 19: due Thursday: Rosen, section 5.1: 12, 17, 27, 35 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45HW 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 ThursdayIf we don’t get through much of the relations stuff, you can hand it in next ThursdayQuestion 7.1 needs material from 7.3 to be answered – more on that in classQuestion 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, 33HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: last homework, not yet assignedHW 22: due Tuesday, 3 May: last homework, not yet assigned Am considering dropping the two lowest homework gradesAm considering dropping the two lowest homework grades How to make the homework assignments less confusing next semesterHow to make the homework assignments less confusing next semester

Exam 2Exam 2 Grading guidelines are on the webGrading guidelines are on the web I have regrade forms with me todayI have regrade forms with me today

Reading: read 7.1, 7.3 for ThursdayReading: read 7.1, 7.3 for ThursdayThe plan:The plan:

Finish 5.1 today, go through relations nextFinish 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 7.6This 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 3.6Last few classes will most likely cover 3.6 About matrices…About matrices…

RegradesRegrades 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:Final exam: Saturday, May 7, from 9 a.m. to noonSaturday, May 7, from 9 a.m. to noon Last semester’s final is on the websiteLast 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)

Page 43: Daily announcements slides

Thursday, 21 April 2005Thursday, 21 April 2005HomeworksHomeworks

HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35HW 19: due today: Rosen, section 5.1: 12, 17, 27, 35 HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45HW 20: due next Tuesday: Rosen, section 7.1: 22, 26, 31, 45

Can hand it in next ThursdayCan hand it in next ThursdayQuestion 7.1 needs material from 7.3 to be answered – more on that in classQuestion 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, 33HW 21: due next Thursday: Rosen, section 7.3: 10, 13, 20, 33 HW 22: due Tuesday, 3 May: last homework, not yet assignedHW 22: due Tuesday, 3 May: last homework, not yet assigned Will drop the two lowest homework gradesWill drop the two lowest homework grades

Exam 2Exam 2 Grading guidelines are on the webGrading guidelines are on the web I have regrade forms with me todayI have regrade forms with me today

Reading: read 7.1, 7.3, 7.4 for TuesdayReading: read 7.1, 7.3, 7.4 for TuesdayThe plan: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 7.6This 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 3.6Last few classes will most likely cover 3.6 About matrices…About matrices…

RegradesRegrades 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:Final exam: Saturday, May 7, from 9 a.m. to noonSaturday, May 7, from 9 a.m. to noon Last semester’s final is on the websiteLast 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!No office hours tomorrow! Brian will be quite drugged up from having his wisdom teeth removedBrian will be quite drugged up from having his wisdom teeth removed

Page 44: Daily announcements slides

Tuesday, 26 April 2005Tuesday, 26 April 2005HomeworksHomeworks

HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45HW 20: due today: Rosen, section 7.1: 22, 26, 31, 45Can hand it in ThursdayCan hand it in ThursdayQuestion 7.1 needs material from 7.3 to be answered – more on that in classQuestion 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, 33HW 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, 26HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 Will drop the two lowest homework gradesWill drop the two lowest homework grades

Exam 2Exam 2 Grading guidelines are on the webGrading guidelines are on the web I have regrade forms with me todayI have regrade forms with me today

Reading: read 7.1, 7.3-7.6 for TuesdayReading: read 7.1, 7.3-7.6 for TuesdayThe plan:The plan:

Next 2 classes are on relationsNext 2 classes are on relations Last few classes will most likely cover 3.6Last few classes will most likely cover 3.6

Final exam:Final exam: Saturday, May 7, from 9 a.m. to noonSaturday, May 7, from 9 a.m. to noon Last semester’s final is on the websiteLast 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…Course evaluations…

Page 45: Daily announcements slides

Thursday, 28 April 2005Thursday, 28 April 2005HomeworksHomeworks

HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, 31, 45HW 20: due this past Tuesday: Rosen, section 7.1: 22, 26, 31, 45Can hand it in todayCan hand it in today

HW 21: due today: Rosen, section 7.3: 10, 13, 20, 33HW 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, 26HW 22: due Tuesday, 3 May: Rosen, section 7.4: 5-7, 9, 22, 26 Will drop the two lowest homework gradesWill drop the two lowest homework grades

Exam 2Exam 2 Grading guidelines are on the webGrading guidelines are on the web

Reading: 7.1-7.6 for TuesdayReading: 7.1-7.6 for TuesdayThe plan:The plan:

Next 2 classes are on relationsNext 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:Final exam: Saturday, May 7, from 9 a.m. to noonSaturday, 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 2There will be review sessions, probably 2

Course evaluations…Course evaluations…

Page 46: Daily announcements slides

Course objectivesCourse objectivesLogicLogic

Introduce a formal system (propositional and predicate logic) which mathematical Introduce a formal system (propositional and predicate logic) which mathematical reasoning is based onreasoning is based on

Sections 1.1-1.4Sections 1.1-1.4ProofsProofs

Develop an understanding of how to read and construct valid mathematical Develop an understanding of how to read and construct valid mathematical arguments (proofs) and understand mathematical statements (theorems), arguments (proofs) and understand mathematical statements (theorems), including inductive proofs. Also, introduce and work with various problem including inductive proofs. Also, introduce and work with various problem solving strategies and techniques.solving strategies and techniques.

Sections 1.5, 3.1, 3.3, 3.4Sections 1.5, 3.1, 3.3, 3.4CountingCounting

Introduce the basics of integer theory, combinatorics, and counting principles, Introduce the basics of integer theory, combinatorics, and counting principles, including a brief introduction to discrete probability.including a brief introduction to discrete probability.

Sections 2.4, 4.1-4.4, 5.1Sections 2.4, 4.1-4.4, 5.1StructuresStructures

Introduce and work with important discrete data structures such as sets, Introduce and work with important discrete data structures such as sets, relations, sequences, and discrete functions.relations, sequences, and discrete functions.

Sections 1.6-1.8, 2.7, 3.2, 7.1, 7.3-7.6Sections 1.6-1.8, 2.7, 3.2, 7.1, 7.3-7.6ApplicationsApplications

Gain an understanding of some application areas of the material covered in Gain an understanding of some application areas of the material covered in the course.the course.

Sections 2.6, 7.2, 10.3Sections 2.6, 7.2, 10.3

Page 47: Daily announcements slides

The EndThe EndHomeworksHomeworks

HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26HW 22: due today: Rosen, section 7.4: 5-7, 9, 22, 26Sorry 26 was so long!Sorry 26 was so long!

Will drop the two lowest homework gradesWill drop the two lowest homework gradesExam 2Exam 2

Grading guidelines are on the webGrading guidelines are on the webFinal exam:Final exam:

Saturday, May 7, from 9 a.m. to noonSaturday, 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 websiteLast 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 sessionsReview sessions One Wednesday, one ThursdayOne Wednesday, one Thursday Most likely 3:30-6:30 on WednesdayMost likely 3:30-6:30 on Wednesday Exact info will be e-mailed out to everybody later todayExact info will be e-mailed out to everybody later today

Office hours this week…Office hours this week…Course evaluations…Course evaluations…Voting for the favorite demotivatorVoting for the favorite demotivator