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Date  Materials  HW assignment 
12/19  FINAL EXAM 9:00 am  11:50 am at NI 203  
12/12  Sample Final Exam:
finalExam_CSI35Fall2018ZyBooks_Sample_.pdf Solutions: finalExam_CSI35Fall2018ZyBooks_Sample_answers.pdf 

12/10  Review  Chapter 14 Cheat sheet: ZyBooksFormulasSheetTrees.pdf, source file: ZyBooksFormulasSheetTrees.odg CSI35ZyBooksChapter14Review.pdf Answers/Solutions: CSI35ZyBooksChapter14Review_answers.pdf 
no hw assignment 
12/05  Review  Chapter 13 Cheat sheet: ZyBooksFormulasSheetGraphs.pdf, source file: ZyBooksFormulasSheetGraphs.odg CSI35ZyBooksChapter13Review.pdf Answers/Solutions: CSI35ZyBooksChapter13Review_answers.pdf 
no hw assignment 
12/03  no meeting, instead: The Bronx Community College is hosting a visit by a team of scientists, post docs and graduate students from Princeton University. LOCATION: NL 136 TIME: 10:20 – 11:30 AM The scheduled discussion's goal is to facilitate collaboration between BCC and Princeton University students and scientists from the Cooperative Institute for Climate Science (CICS) and their partners Atmospheric and Oceanic Sciences Program and NOAAGeophysical Fluid Dynamics Laboratory at Princeton University. Here is the flyer: Students Invite_Dec 3.pdf 
no hw assignment 
11/28  Review  Chapter 12 Cheat sheet: Chapter12 Formulas Sheet, source file: Chapter12FormulasSheet.odg Chapter12Review (no partitions, no restoration of equiv. relation from partitions, no SQL) Some answers and solutions: CSI35ZyBooksChapter12Review_answers.pdf 
no hw assignment 
11/26  Review  Chapter 11 Cheat sheet: Chapter11Cheat Sheet source file (Libre Office): Chapter11_cheatSheet.odg CSI35ZyBooksChapter11Review.pdf (no strong induction, no structural induction) We worked on questions 17, 13, 19, and 20 in class. Here are some answers/solutions to the reest of the questions: CSI35ZyBooksChapter11Review_q8.pdf, CSI35ZyBooksChapter11Review_q10.pdf, CSI35ZyBooksChapter11Review_someAnswers.pdf, CSI35ZyBooksChapter11Review_q9.pdf, CSI35ZyBooksChapter11Review_q171.pdf, CSI35ZyBooksChapter11Review_q172.pdf 
no hw assignment 
11/2223  College is closed. Thanksgiving Break. 

11/21  topic: Chapter 14 Section 14.6 Minimum Spanning Trees lecture slides: ZyBooksCSI35_Ch14Sect6.pdf practice: ZyBooksCSI35_Ch14Sect5Practice.pdf 
HW 19: due Tuesday, 11/27  last HW assignment ZyBooks, HW18: Chapter 14: Sections 14.6/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: page 796 / 23, page 802 / 1, 3, 7, 9 Answers: CSI35_pages 796802.pdf 
11/19  topic: Chapter 14 Section 14.5 Spanning trees and graph traversals (DFS and BFS) lecture slides: SpanningTrees practice: ZyBooksCSI35_Ch14Sect5Practice.pdf A short (~2mins) but very nice video of depth first search algorithm application: https://www.youtube.com/watch?v=mE_PCK0oFyo And BreadthFirst Search from the same person and using the same graph: https://www.youtube.com/watch?v=YYHeXhfwg3g The next two videos are for the graph that is used in our lecture slides: DepthFirstSearch BreadthFirst Search 
HW 18: due Saturday, 11/24, by 11:59pm ZyBooks, HW18: Chapter 14: Sections 14.5/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 795796 / 3, 11(c,d), 16(for #13 only), 17(b). Answers: CSI35_pages 795796.pdf 
11/14  topics: Chapter 14 Section 14.2 Tree application examples (more examples) Section 14.3 Properties of trees Section 14.4 Tree traversals lecture slides: TreesPropertiesAndTraversals practice: see lecture slides + ZyBooksCSI35_Ch14Sect4Practice.pdf 
HW 17: due Tuesday, 11/20, by 11:59pm ZyBooks, HW17: Chapter 14: Sections 14.3, 14.4/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 755756 / 19, 20, 27, 29, 36 Answers: CSI35_pages 755756.pdf pages 783784 / 8, 11, 14, 16, 18, 22, 24 Answers: CSI35_pages 783784.pdf 
11/12  topics: Chapter 14 Section 14.1 Introduction to trees Section 14.2 Tree application examples lecture slides: TreesIntro practice: ZyBooksCSI35_Ch14Sects12InClassPractice.pdf 
HW 16: due Saturday, 11/17, by 11:59pm ZyBooks, HW16: Chapter 14: Sections 14.1, 14.2/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 755756 / 1, 3, 5, 7, 9(b), 11 Answers: CSI35_pages 755756.pdf pages 769770 / 1, 3, 11, 19, 21, 23 Answers: CSI35_pages 769770.pdf 
11/07  topics: Chapter 13 Shortest Paths Problems lecture slides: ShortestPathsProblems practice: ZyBooksCSI35_Ch13AdditionPractice.pdf Chapter 13 overview (not finished): ZyBooksCSI35_Ch13Overview.pdf 
Extra practice (not graded, do not submit): Rosen book: page 716717 / 1, 3, 6, 25 Answers: CSI35_pages716717.pdf 
11/05  topics: Chapter 13 Section 13.8 Planar graphs Section 13.9 Graph coloring lecture slides: PlanarGraphsColoring (updated on 11/06) practice: ZyBooksCSI35_Ch13Sects89Practice.pdf 
HW 15: due Saturday, 11/10, by 11:59pm ZyBooks, HW15: Chapter 13: Sections 13.8, 13.9/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 733 / 3, 8, 9, 13, 15, 17 Answers: CSI35_pages 733734.pdf 
10/31  topics: Chapter 13 Section 13.6 Euler circuits and trails Section 13.7 Hamiltonian cycles and paths lecture slides: EulerCircuitsTrailsAndHamiltonianCyclesPaths EulerCircuitsAndPathsInDirectedGraphs Mohammed's scimitars: Rosen_697.pdf Grey Codes: Rosen_702703.pdf Terminology (ZyBooks > Rosen): walk > path circuit > simple circuit trail > simple path cycle > N/A path > N/A practice: ZyBooksCSI35_Ch13Sects67Practice.pdf 
HW 14: due Tuesday, 11/06, by 11:59pm ZyBooks, HW14: Chapter 13: Sections 13.6, 13.7/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 703  704 / 1, 7, 10, 13, 21, 2,. pages 705  706 / 32, 33, 34, 40, 47 (a,d), Answers: CSI35_pages703704.pdf, CSI35_page706.pdf 
10/29  topics: Chapter 13 Section 13.4 Walks, trails, circuits, paths, and cycles Section 13.5 Graph connectivity lecture slides: Connectivity practice: ZyBooksCSI35_Ch13Sects45Practice.pdf 
HW 13: due Saturday, 11/03, by 11:59pm ZyBooks, HW13: Chapter 13: Sections 13.4, 13.5/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 689691 / 1, 4, 11(a), 21, 23 Answers: CSI35_pages689690.pdf Suggested reading: Example 3 on page 680 
10/24  topic: Chapter 13 Section 13.2 Graph representations Section 13.3 Graph isomorphism lecture slides: ZyBooksCSI35_Ch13Sects2_3.pdf practice: see lecture slides 
HW 12: due Tuesday, 10/30, by 11:59pm ZyBooks, HW12: Chapter 13: Sections 13.213.3/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 665666 / 3, 5, 9, 17, 20 (a,b,d,e,f), 21, 23, 27 pages 675677 / 1, 3, 7, 9(c), 11, 15, 17, 21, 35, 41, 57 (a,b) Answers: CSI35_HW11_pages 665666.pdf, CSI35_pages 675677.pdf Suggested reading: Some Applications of Special Types of Graphs (pages 661663 in the book). 
10/22  topic: Chapter 13 Section 13.1 Graphs introduction lecture slides: GraphsGraphModelsGraphTerminology Formula/Cheat Sheet: ZyBooksFormulasSheetGraphs.pdf Practice: ZyBooksCSI35_Ch13Sect1_Practice.pdf 
HW 11: due Saturday, 10/27, by 11:59pm ZyBooks, HW11: Chapter 13: Section 13.1/ all participation and challenge activities as well as additional exercises Extra practice (not graded, do not submit): Rosen book: pages 650651 / 3, 5, 7, 11, 13, 33 Solutions: CSI35_pages 650651.pdf Suggested to look at: Biological Neworks(page 648, Examples 11 and 12) 
10/17  Midterm Exam The exam is closed book, closed notes, but you can use two pages of cheat sheets. will be based on material from Chapters 11 and 12 (Rosen Book: Chapters 5 and 9) The Midterm Grade will be composed of: Hws: 40% Midterm Exam: 60% 

10/15  Preparation for Midterm Exam Review questions are posted on the Midterm and Final Exam page. You can also find more information about the Midterm Exam there. 

10/10  topics: Chapter 12 Section 12.9 Equivalence relations Section 12.10 Nary relations and relational databases Practice: ZyBooksCSI35_Ch12Sect9_Practice.pdf lecture slides: ZyBooksCSI35_Ch12Sect9_10.pdf 
HW10: due Monday, 10/15, by 11:59pm ZyBooks, HW7: Chapter 12: Sections 12.912.10/ all participation and challenge activities as well as exercises 
10/08  Columbus Day College is closed 

10/03  topics: Chapter 12 Section 12.7 Partial orders Section 12.8 Strict orders and directed acyclic graphs lecture slides: PartialOrderStrictOrderDAGs 
HW9: due Tuesday, 10/09, by 11:59pm ZyBooks, HW7: Chapter 12: Sections 12.712.8/ all participation and challenge activities as well as exercises 
10/01  topic: Chapter 12 Section 12.5 Graph powers and the transitive closure, Section 12.6 Matrix multiplication and graph powers lecture slides: GraphPowersMatrices (corrected on 10/02 10:20 pm) inclass practice: will be posted 
HW8: due Saturday, 10/06, by 11:59pm ZyBooks, HW6: Chapter 12: Sections 12.512.6/ all participation and challenge activities as well as exercises 
09/26  topics: Chapter 12 Section 12.3 Directed graphs, paths, and cycles Section 12.4 Composition of relations lecture slides: DirectedGraphs_Composition (corrected on 09/26 4:15 pm) 
HW7: due Tuesday, 10/02, by 11:59pm ZyBooks, HW7: Chapter 12: Sections 12.312.4/ all participation and challenge activities as well as exercises 
09/24  topic: Chapter 12 Section 12.1 Introduction to binary relations, Section 12.2 Properties of binary relations lecture slides: RelationsIntro 
HW6: due Saturday, 09/29, by 11:59pm ZyBooks, HW6: Chapter 12: Sections 12.112.2/ all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): Rosen book: pages 581582 /1 (ad), 3, 7 (a, e, f), 18, 27, 35 (a,c,e,g) Solutions: CSI35_HW06_page 581N1.pdf, CSI35_HW06_page 581N3.pdf CSI35_HW06_page 581N7.pdf, CSI35_HW06_page 582N18_27.pdf, CSI35_HW06_page 582N35.pdf Suggested to look at: Examples 5 and 6 on pages 363364 
09/17  topic: Chapter 11 Section 11.10 Recursive algorithms Section 11.11 Induction and recursive algorithms the rest of the sections are optional lecture slides:Recursive algorithms practice: recAlgsPractice No classes are scheduled on Tuesday and Wednesday, September 1819th (Yom Kippur) 
HW5: due Sunday, 09/23, by 11:59 pm ZyBooks, HW5: Chapter 11: Sections 11.1011.11/ all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): Rosen book: pages 370371 / 3, 7, 11, 44 Solutions: CSI35_HW05_page370N3.pdf, CSI35_HW05_page370N7_11.pdf CSI35_HW05_page371N44.pdf Suggested to look at (not for grade): Examples 5 and 6 on pages 363364 
09/12  topic: Chapter 11 Section 11.7 Loops invariants Section 11.8 Recursive definitions Section 11.9 Structural induction lecture slides:Recursive definitions and structural induction practice: recDefsPractice Greek alphabet letters names: http://www.rapidtables.com/math/symbols/greek_alphabet.htm 
HW4: due Wednesday, 09/19, by 11:59 pm ZyBooks, HW4: Chapter 11: Sections 11.711.9/ all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): Rosen book: pages 357358 / 3 (c), 5(e), 7(c), 13, 25, 27 Solutions: CSI35_HW04_pages357_358N3_5_7.pdf, CSI35_HW04_page358N13.pdf, CSI35_HW04_page358N25.pdf, CSI35_HW04_page358N27.pdf Suggested to look at (not for grade): Ackermann's function: page 359 / 47, 48, 49, 51 
09/10  no classes (Rosh Hashanah)


09/05 
Wednesday runs on Monday schedule! topics: Chapter 11 Section 11.5 Mathematical induction (finishing up) Section 11.6 Strong induction and wellordering (most likely won't cover in class) lecture slides: Mathematical induction and Strong Induction practice: 3cent and 10cent stamps Recommended additional resources (proofs): 1) Cardinality of a finite powerset (video) 2) a proof that postage of 12 cents or more can be made with just 4c and 3c stamps (strong induction) 3) winning strategy for game NIM (~20 mins, for fun) 
HW3: due Tuesday, 09/11, by 11:59 pm ZyBooks, HW3: Chapter 11: Sections 11.5 and 11.6/ all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): Rosen book: pages 329330 / exercises 33, 49, 77, pages 341342 / exercises 3, 11 Solutions: CSI35_HW03_page330N33.pdf, CSI35_HW03_page331N49page333N77.pdf, CSI35_HW03_page341N3.pdf, CSI35_HW03_page342N11.pdf 
09/03  College is closed. Labor Day! 

08/29 
topics: Chapter 11 Section 11.4 Mathematical induction lecture slides:Mathematical induction, Part 1 practice: Practice (Mathematical induction, Part 1) cheat sheet for Chapter 5 (to be completed later): Chapter5 Cheat Sheet Recommended additional resources (video/nonvideo links): 1) proof of summation 1+2+3+...+n = n(n+1)/2 (video) 2) proof of summation Σ^{n}_{i=1} (3i2)= n(3n1)/2 3) proof of summation Σ^{n}_{i=1} 1/(2i1)(2i+1)= n/(2n+1) 4) justification of geometric sequence partial sum formula (not using induction, worth checking out!) 
HW2: due Tuesday, 09/04, by 11:59 pm ZyBooks, HW2: Chapter 11: Section 11.4 / all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): Rosen book: pages 329330 / exercises 1, 5, 11, 19, 23 Solutions: CSI35_HW02_page326N1.pdf, CSI35_HW02_page329N5.pdf, CSI35_HW02_page330N11.pdf, CSI35_HW02_page330N19.pdf, CSI35_HW02_page330N23.pdf 
08/27 
Welcome to CSI35! topics: Chapter 11 11.1 Sequences 11.2 Recurrence relations 11.3 Summations lecture slides: Sequences and Summations practice: Practice Video resources from Khan Academy: 1) Sequences (a bunch of short videos and guided practices) note that you don't need to go over all videos, becuase they cover more than we did in class 2) Sigma notation and summations (a bunch of short videos and guided practices) note that it covers more than we did in class 3) geometric sequence sigma notation 4) Partial sums (consider only first two videos and a guided practice that follows them) Announcements: 1) The main book for our class is ZyBooks Discrete Mathematics (online book). The HW assignment will be given in this book. The price is $37. Here are the details on how to subscribe to it: 1. Sign in or create an account at learn.zybooks.com 2. Enter zyBook code: CUNYCSI35NovakFall2018 3. Subscribe (Subscriptions will last until Jan 12, 2019) You can also get the Discrete Mathematics and its Applications, Seventh Edition, by Kenneth H. Rosen, McGraw Hill, 2012 and use is as a suplementary textbook. First chapter of this book is available through ereserves: http://bcclibweb.bcc.cuny.edu/electroniccoursereserves/ choose CSI35 from the dropdown menu 2) Math and CS club meets on Thursdays, 121:50pm at CP 308 or ME 328 
HW1: due Sunday, 09/02, by 11:59 pm ZyBooks, HW1: Chapter 11: Sections 11.1  11.3 / all participation and challenge activities as well as exercises Extra practice (not graded, do not submit): page1, page2, page3 (pdf files) Solutions: CSI35_HW01_pages15.pdf, CSI35_HW01_page6.pdf Suggested guided exercises for practice (not graded, not for submission): 1) arithmetic sequences 2) arithmetic sequences 2 3) geometric sequences 4) geometric sequences 2 5) geometric sequences 3 6) sigma notation 7) summation (arithmetic series) 8) summation (geometric sequence) 9) general summation 