Date  Materials  HW assignment 
04/26  topic: Chapter 11 Section 11.4 Spanning Trees (DFS and BFS) lecture slides: SpanningTrees  updated around 10:40pm on 04/26 practice: see lectures slides 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 19: due Wednesday, 05/03 pages 795796 / 3, 11(c,d), 16(for #13 only) 
04/24  topics: Chapter 11 Section 11.2 Applications of trees (Game trees) Section 11.3 Tree Traversal lecture slides: TreesTraversals practice: Section11.3Practice Hw 13 answers and solutions: CSI35_HW13_pages689690.pdf, CSI35_HW13_pages703704.pdf; Hw 14 answers and solutions: CSI35_HW14_page706.pdf, CSI35_HW14_pages716717.pdf; Hw 15 answers and solutions: CSI35_HW14_page706.pdf. 
HW 18: due Monday, 05/01 pages 783784 / 8, 11, 14, 16, 18, 22, 24 
04/20  topics: Chapter 11 Section 11.2 Applications of trees lecture slides: TreesApplications practice: see lecture slides 
HW 17: due Wednesday, 04/26 pages 769770 / 1, 3, 11, 19, 21, 23 
04/19  topics: Chapter 11 Section 11.1 Introduction to trees lecture slides: TreesIntro  updated on 04/19 at 6:30pm. practice: see lecture slides 
HW 16: due Monday, 04/24 pages 755756 / 1, 3, 5, 7, 9(b), 11, 19, 20, 27, 29, 36 Suggested reading: Examples 5, 6 on page 750; Prove Theorem 4 on page 753; exercise 23 on page 756. 
04/03  topics: Chapter 10 Section 10.8 Graph Coloring lecture slides: GraphColoring practice: pages 732733 / 4, 11, 18 Hw 13 answers and solutions: will be posted shortly Programming projects for extra credit: CSI35programmingProjects.pdf 
HW 15: due Wednesday, 04/19 page 733 / 3, 8, 9, 13, 15, 17 
04/03  topics: Chapter 10 Section 10.5 Euler and Hamilton Paths Section 10.6 ShortestPaths Problems lecture slides: HamiltonShortestPaths  updated on 04/19 at 6:30pm. practice: page 705 / 34, pages 716717 / 2, 26 Hw 12 answers and solutions: CSI35_HW12_pages 675677.pdf 
HW 14: due Wednesday, 04/05 pages 705  706 / 32, 33, 40, 47 (a,d), pages 716717 / 1, 3, 6, 25. Don't forget to explain your answers! Suggested reading: Example 8 on page 702 
03/29  topics: Chapter 10 Section 10.4 Connectivity (from page 687) Section 10.5 Euler and Hamilton Paths lecture slides: pathsIsomorphismEuler practice: page 703 / 2, 22, 26 Hw 11 answers and solutions: CSI35_HW11_pages 665666.pdf 
HW 13: due Monday, 04/03 pages 689691 / 1, 4, 11(a), 21, 23 pages 703  704 / 1, 7, 10, 13, 21, 27. Don't forget to explain your answers! Suggested reading: Example 3 on page 680 
03/27  topics: Chapter 10 Section 10.3 Representing Graphs and Graph Isomorphism Section 10.4 Connectivity (only up to page 683, including) lecture slides: GraphRepresentation_Connectivity practice: page 676 / 25, 30, 45, 57 (c) Hw 10 answers and solutions: CSI35_HW10_pages 650651.pdf 
HW 12: due Wednesday, 03/29 pages 675677 / 1, 3, 7, 9(c), 11, 15, 17, 21, 35, 41, 57 (a,b) Don't forget to explain your answers! Suggested reading: Example 3 on page 680 
03/22  topic: Chapter 10 Section 10.2 Graph terminology and special types of graphs lecture slides: GraphTerminology practice: page 665 / 2, 6, 8, draw K_{4,5}, and 22 
HW 11: due Monday, 03/27 pages 665666 / 3, 5, 9, 17, 20 (a,b,d,e,f), 21, 23, 27 Suggested reading: Some Applications of Special Types of Graphs (pages 661663 in the book). 
03/20  topic: Chapter 10 Section 10.1 Graphs and graph models lecture slides: GraphsAndGraphModels 
HW 10: due Wednesday, 03/22 pages 650651 / 3, 5, 7, 11, 13, 33 Suggested to look at: Biological Neworks(page 648, Examples 11 and 12) 
03/15  Midterm Exam The Midterm Grade will be composed of: Hws: 40% Midterm Exam: 60% 

03/13  Review Review all nine homeworks! Sample Midterm: CSI35MidtermExamSample.pdf (updated on Monday, 03/13 around 9:50am) Solutions/Answers: CSI35MidtermExamSampleSolutions.pdf Solutions to HW8: page 597 / 21, 27, 31 pages 615617 / 1, 3,9, 11, 21,23,41, 43, 1 Solutions to HW9: pages 630631: 1, 3, 5, 9, 15, 21, 33. 

03/08  topic: Chapter 9 Section 9.5 Equivalence relations (finishing up, from slide 81) Section 9.6 Partial orderings lecture slides: Relations3 (will start at slide 81), Relations4 practice: Section 9.5 Solutions to HW7: pages 589590 / 1, 5, 7, 13, 17, 19 page 596: 1, 3, 13 
HW9: due Monday, 03/13 pages 630631 / 1 (a,c,e), 3 (c,d), 5 (a,b), 9, 15, 21, 33. Suggested to look at: Lexicographical order (pages 620622) 
03/06  topic: Chapter 9 Section 9.3 Representing relations (using digraphs) Section 9.5 Equivalence relations lecture slides: Relations3 (we stopped at slide 81) practice: Section 9.3 (updated around 10:30 pm on 03/06), Section 9.5 Solutions to HW6: 1, 3, 7, 18, 27, 35 
HW8: due Wednesday, 03/08 page 597 / 21 (do only for a from #4), 27, 31, (due 03/08) pages 615  617 / 1(a,b,c), 3 (a,b,c), 9, 11, 21, 23, 41, 43 (a,b), 47 (c,d) (due 03/13) 
03/01  topics: Chapter 9 Section 9.2 nary relations Section 9.3 Representing relations (using matrices) lecture slides: Relations (updated around 4 pm on 03/07, binary multiplication of matrices if fixed) Solutions to HW5: 3, 7,11, 44 
HW7: due Monday, 03/06 pages 589590 /1, 5, 7, 13, 17, 19, page 596 / 1 (a,c), 3(c), 13 
02/27  topic: Chapter 9 Section 9.1 Relations and their properties lecture slides: RelationsIntro (updated on 02/27 around 6 pm) Solutions to HW4: 3,5,7, 13, 25, 27 
HW6: due Wednesday, 03/01 pages 581582 /1 (ad), 3, 7 (a, e, f), 18, 27, 35 (a,c,e,g) All the answers must be explained ! Answers without explanations get half credit. Suggested to look at (not for grade): Examples 5 and 6 on pages 363364 
02/22  topic: Chapter 5 Section 5.4 Recursive algorithms lecture slides:Recursive algorithms practice: recAlgsPractice Solutions to HW3: 33, 49, 77, 3, 11 
HW5: due Monday, 02/27 pages 370371 / 3, 7, 11, 44 Suggested to look at (not for grade): Examples 5 and 6 on pages 363364 
02/15 NI 211A 
topic: Chapter 5 Section 5.3 Recursive definitions and structural induction lecture slides:Recursive definitions and structural induction practice: recDefsPractice solutions to HW1: pages 15, page 6 solutions to HW2: 1 , 5, 11, 19, 23. I found two examples for using math. induction as proof technique for summations. Check 2) and 3) under 02/01 Greek alphabet letters names: http://www.rapidtables.com/math/symbols/greek_alphabet.htm There will be no classes on Monday, Februrary 20^{th} (President's Day) 
HW4: due Wednesday, 02/22 pages 357358 / 3 (c), 5(e), 7(c), 13, 25, 27 Suggested to look at (not for grade): Ackermann's function: page 359 / 47, 48, 49, 51 
02/13  no classes (Lincoln's birthday) Look through the: 1) practice, 2) suggested video proof 1), and 3) suggested example from our 02/08 meeting 

02/08 NI 211A 
topics: Chapter 5 Section 5.1 Mathematical induction (finishing up) Section 5.2 Strong induction and wellordering (most likely won't cover in class) lecture slides:Mathematical induction and Strong Induction practice: 3cent and 10cent stamps Warning: in homework submissions all work must be shown (otherwise no credit given) and no copying (both parties will get a grade of F without opportunity to redo the homework, upon the first occurence; and if it happens one more time, then the person who copied will be reported to the chairperson) There will be no classes on Monday, Februrary 13^{th} (Lincoln's Birthday), and Wednesday 02/15 will run on Monday's schedule. 
HW3: due Wednesday, 02/08 pages 329330 / exercises 33, 49, 77, pages 341342 / exercises 3, 11 Suggested video proofs for extra practice (not for grade, not for submission): 1) a proof that postage of 12 cents or more can be made with just 4c and 3c stamps (strong induction) 2) winning strategy for game NIM (~20 mins, for fun) Suggested examples from the book (not for grade, not for submission): 1) Example 2 (page 336) 
02/06  class is cancelled  
02/01 BL 104 
topics: Chapter 5 Section 5.1 Mathematical induction lecture slides:Mathematical induction, Part 1 (updated on 02/02) practice: Practice (Mathematical induction, Part 1) cheat sheet for Chapter 5 (to be completed later): Chapter5 Cheat Sheet (updated on 02/02) 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 Monday, 02/06^{} pages 329330 / exercises 1, 5, 11, 19, 23 
01/30 NI 211A 
Welcome to CSI35! topics: Chapter 5 Sequences and Summations lecture slides: Sequences and Summations (updated on 01/30 at 8pm) 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) First chapter of the book is available through ereserves: http://bcclibweb.bcc.cuny.edu/electroniccoursereserves/ Choose CSI35 from the dropdown menu 2) annual CUNY MATH CONTEST The contest begins online at 9:00 A.M. on Monday, February 15, 2016 more info: http://math.cisdd.org/ 
HW1: due Wednesday, 02/01 page1, page2, page3 (pdf files) Suggested guided exercises for practice (not for grade, 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 