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CSE 260 Discrete Structures in Computer Science Course Intro

CSE 260 Discrete Structures in Computer Science Course Intro. 1. Discrete mathematics. From Wikipedia, the free encyclopedia: Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous . . . .

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CSE 260 Discrete Structures in Computer Science Course Intro

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  1. CSE 260Discrete Structures inComputer ScienceCourse Intro CSE 260, MSU 1

  2. Discrete mathematics • From Wikipedia, the free encyclopedia: • Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.. . . • Discrete mathematics has become popular in recent decades because of its applications to computer science. Current ABET CS accreditation requires a half year of math, but only Discrete Structures is specifically named. CSE 260, MSU

  3. Applications of discrete mathematics • Formal Languages (computer languages) • Compiler Design • Data Structures • Computability • Algorithm Design • Relational Database Theory • Complexity Theory (counting) • Security • Software Engineering & Formal Methods CSE 260, MSU

  4. PERT chart: 7 mo project (5 milestones, 6 activities) Some example uses CSE 260, MSU

  5. ASCII code (from “Wikipedia”) representing information for information-processing PERT chart: 7 mo project (5 milestones, 6 activities) Some example uses CSE 260, MSU

  6. ASCII code (from “Wikipedia”) representing information for information-processing PERT chart: 7 mo project (5 milestones, 6 activities) Some example uses error digit Finite State Automaton representing(unsigned) integers other Int OK Blank, delimiter, operator CSE 260, MSU

  7. Example: The Traveling Salesman Problem c1 • Important in • circuit design • many other CS problems _____________________ • Given: • n cities c1, c2, . . . , cn • the distance, dij, between city i and j • Find: the shortest “tour” 3 c2 1 2 2 5 c4 1 c3 1234: 3 + 5 + 1 = 9 CSE 260, MSU

  8. Example: The Traveling Salesman Problem c1 • Important in • circuit design • many other CS problems _____________________ • Given: • n cities c1, c2, . . . , cn • the distance, dij, between city i and j • Find: the shortest “tour” 3 c2 1 2 2 5 c4 1 c3 1234: 3 + 5 + 1 = 9 1243: 3 + 2 + 1 =6 CSE 260, MSU

  9. Example: The Traveling Salesman Problem c1 • Given a tour, how many additions, are needed to calculate the distance, in the case of: • 4 cities? • 5 cities? • 200 cities? • n cities? • How many possible tours are there in each case? • How many additions are done to solve this problem in each case? 3 c2 1 2 2 5 c4 1 c3 1234: 3 + 5 + 1 = 9 1243: 3 + 2 + 1 = 6 . . . CSE 260, MSU

  10. Example: The Traveling Salesman Problem c1 • Assume a very fast PC:1 flop = 1 nanosecond = 10-9 sec. = 1,000,000,000 ops/sec = 1 GHz. • If n=8 T(n) = 7•8! = 282,240 flops < 1/3 second. • If n=50 T(n) = 49•50! = 1.48 • 1066 flops = 4.73 • 1049 years. • There are some problems for which we don’t know if an efficient solutions exists! 3 c2 1 2 2 5 c4 1 c3 CSE 260, MSU

  11. Why mathematics? Abstraction: must emphasize properties and relations that are fundamental Notation: must document and describe the fundamentals (what kind of data is processed, what kind of operations, how do data items relate?) Correctness/completeness: by basing on known fundamentals, we know if our design will meet specs (imagine building a DBMS and then finding out that a particular kind of query can’t be asked) CSE 260, MSU

  12. Catalog Description • CSE 260:  Discrete Structures in Computer Science • Prerequisite: {MTH 126 (Survey of Calculus II) or MTH 133 (Calculus II) or MTH 153H (Honors Calculus II) or LBS 119 (Calculus II) } • Description: Propositional and first order logic. Equivalence, inference and method of proof. Mathematical induction, diagonalization principle. Basic counting. Set operations, relations, functions. Grammars and finite state automata. Boolean algebra. Truth tables and minimization of Boolean expressions. Applications to computer science and engineering. 12 CSE 260, MSU

  13. Course Motivation & Objectives • Motivation: • The role of discrete mathematics in the study of computer science is analogous to the role that calculus plays in physics or in the engineering disciplines • It allows us to define, describe and reason about complex systems. • Objectives: • Expose you to the mathematical concepts that form the basis for much of Computer Science. • Train you to analyze problems; think in a logical fashion; andcommunicate your reasoning in a clear and unambiguous manner. 13 CSE 260, MSU

  14. Course Topics (see syllabus for schedule) • Propositional Logic • Predicate Logic • Proof Methods • Set Theory • Number Theory • Recurrence Relations • Combinatorics, probabilities • Relations and their Representations • Languages and Grammars 14 CSE 260, MSU

  15. Class Procedures and Policies • Class exercises (attendance): 10% • Bi-weekly homework: 20% • Three quizzes: 15% • Two in-class exams: 30% • Final exam: 25% • Course Grade is based on straight scale; percentages are on total scores possible. 15 CSE 260, MSU

  16. Class Procedures …….. • Class notes and other course materials and resources will be available on the course website: http://www.cse.msu.edu/~cse260/ • Read the syllabus and get all questions answered tomorrow. • The syllabus contains the schedule of topics: try to read material before class and before exams. • Instructor information is on the syllabus. Between the instructor and one TA, there are 13 office hours/week that you can attend to get help. See website. 16 CSE 260, MSU

  17. Class Procedures … • Textbook:Discrete Mathematics and it's Applications by Kenneth H. Rosen, Seventh Edition, McGraw Hill. • We will assign regular reading and homework from this textbook. The textbook website also has a lot of exercises. The text has answers to odd numbered problems in the back. • The Engineering Library has a copy on reserve. (You will need to consult if you have the 6th edition.) 17 CSE 260, MSU

  18. Class Procedures … • We expect that you attend the class regularly; I will “take attendance” through daily class exercises. • Class exercises cannot be made up, but you will be given at least 2 “grace” exercises. • If you have to miss a quiz or exam for an approved MSU activity you must contact the instructor with sufficient lead time to make arrangements to take it in advance. • In case of illness or emergency, contact me as soon as possible, preferably in advance of missing class. • When possible, lecture slides will be posted by the time of lecture; otherwise, they will be posted later during the day. 18 CSE 260, MSU

  19. Class procedures … Bi-Weekly homework • Assignments are due on Mondays and Wednesdays • You may discuss homework with other students • Must do your own work (no copying) • Quizzes and exams are not collaborative • The lowest completed homework will be dropped (must be turned in) • Late assignments will be awarded half credit if turned in within one day. Later assignments will receive no credit (but must be turned in in order to be dropped). • Questions on the quizzes will be based on the problems assigned for homework; questions on exams may also contain questions outside that of the homework. • Solutions manuals for the textbook are on reserve in the Engineering library. CSE 260, MSU

  20. Class Procedures… • There will be daily in-class exercises • There will be no makeups for missed exercises • The two lowest scores will be dropped • You will grade your own exercises • Bring a red pen CSE 260, MSU

  21. Piazza • We will use Piazza for class communication. • You will receive an invitation to join in the first week of class. • You must join to receive course announcements. • http://piazza.com/class#spring2012/cse260/ CSE 260, MSU

  22. Class Procedures … • When attending the class, I ask you to observe a few simple rules meant to create a better learning environment. • Come to class on time. • Once class begins, please do not read the newspaper or talk, etc. Set your cell phones on vibrate. • Use laptops only for class slides – do not disturb others with other work or play. • If you have a question, do not hesitate to ask. • Others are likely to have the same question. • Do not be afraid to slow down the pace of the class. 22 CSE 260, MSU

  23. Class Procedure … • All students will have computer accounts on CSE machines. If your home account is under another domain, then it is your responsibility to have your mail forwarded. • Unless otherwise specified, exams will be closed-book and will cover material assigned from the texts, notes, handouts, and lectures. For exams only (NOT Quizzes) you are allowed to use one 8½ x 11 note sheet. You should utilize this to write down important formulae, proof techniques etc. • Being caught cheating on ANY aspect of the course is grounds for receiving a grade of 0.0 for the course. In addition, a report of any incident of cheating will be forwarded to the dean of your home college. 23 CSE 260, MSU

  24. Academic Integrity • Academic Integrity is very important in this class and in this university. In this class: • Students are permitted to discuss the homework problems with each other and to consult the solution manual, as needed. However, if you just copy answers or rely too heavily on your learning partner(s), you will not be able to perform well on the quizzes and exams. Practice is key to learning the material in this course! • No collaboration is permitted during examinations or quizzes. Students violating this policy will be dealt with according to the university policy. 24 CSE 260, MSU

  25. Honors Option • If you are interested, contact me in the first two weeks of class. 25 CSE 260, MSU

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