MTH 220 Spring 2008 Midterm 2 Study Sheet, Exams of Discrete Structures and Graph Theory

Download MTH 220 Spring 2008 Midterm 2 Study Sheet and more Exams Discrete Structures and Graph Theory in PDF only on Docsity! 04/07/2008 MTH 220-201 Spring 2008 STUDY SHEET for MIDTERM #2 (Monday, April 14) - Ch. 3 (3.5) - Ch. 4 (4.1, 4.2, 4.4, 4.5, 4.6) - Ch. 5 (5.1, 5.2, 5.3) The best way to prepare to the exam is to read the book and to do the homework exercises. Please, take time to go over the material. Here is what you have to have an idea about: 1. Recurrence Relations (Section 3.5). a) Backtracking method to solve a recurrence relation. b) Examples: compound interest, Fibonacci sequence, Tower of Hanoi. c) How to solve a linear homogeneous relation of order 2. Characteristic Equation. 2. Product Sets and Partitions (Section 4.1). a) Ordered pair. b) Product set or Cartesian product. c) Partition or quotient set. Blocks of a partition. 3. Relations and Digraphs (Section 4.2). a) A relation R from A to B. b) A relation on A. c) Sets arising from relations: domain, range, R-relative sets. d) The matrix of a relation. e) The digraph of a relation: vertices, edges, in-degree, out-degree. 4. Properties of Relations (Section 4.4). a) Reflexive and irreflexive relations. b) Symmetric, asymmetric, and antisymmetric relations. c) Transitive relations. 5. Equivalence Relations (Section 4.5). a) Equivalence relations. b) Equivalence relations and partitions. c) Equivalence classes. 6. Computer Representation of Relations and Digraphs (Section 4.6). a) Linked list, storage cell, pointer. b) START, TAIL, HEAD, NEXT method. c) VERT, TAIL, HEAD, NEXT method. 7. Functions (Section 5.1). a) Definition of a function. An argument and the value of a function. b) Identity function. c) Everywhere defined, onto, and one-to-one functions. d) One-to-one correspondence. e) Invertible functions and its properties. 8. Functions in Computer Science (Section 5.2). a) Characteristic function. b) Mod-n function. c) Floor function. d) Ceiling function. e) Polynomial functions. f) Exponential functions. g) Logarithmic functions. h) Boolean function. i) Hashing functions. 9. Growth of functions (Section 5.3). a) Big-O definition. b) Same order functions. c) Lower order function. d) Big-theta relation.