PPT-November 8, 2018 Applied Discrete Mathematics

November 8 2018 Applied Discrete Mathematics Week 9 Integer Properties 1 Induction The principle of mathematical induction is a useful tool for proving that a certain predicate is true for. 1 R is reflexive iff for all x A xx R ie xRx is true 2 R is symmetric iff for all x y A if x y R then y x R ie xRy o yRx is true 3 R is transitive iff for all x y z A if x y R and yz R then x z R ie xRy yRz o xRz is true Let R be a binary relatio Christian Yates. Centre for Mathematical Biology. Mathematical Institute. Who . am . I?. . Completed my . B.A. (Mathematics) and M.Sc. (Mathematical . M. odelling. and . S. cientific . C. omputing) at . Applied Discrete Mathematics Week 3: Algorithms. 1. Double Summations. Table 2 in . 4. th. Edition: Section 1.7. 5. th. Edition: Section 3.2. 6. th. . Applied Discrete Mathematics Week 11: Graphs. 1. Partial Orderings . In a poset the notation a  b denotes that (a, b)R.. Note that the symbol  is used to denote the relation in . Science and Industry Advance with Mathematics . International and Interdisciplinary . Members hail from . more than 100 countries . and work within industry, laboratories, government, and academia. . Applied Discrete Mathematics Week 5: Mathematical Reasoning. 1. Addition of Integers. Example:. Add a = (1110). 2. and b = (1011). 2. .. a. 0. + b. 0. = 0 + 1 = 02 + 1, so that c. Applied Discrete Mathematics Week 5: Mathematical Reasoning. 1. Identity Matrices. The . identity matrix of order n. is the nn matrix . I. n. = [. Introductory Lecture. What is Discrete Mathematics?. Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects.. Calculus deals with continuous objects and is not part of discrete mathematics. . Applied Discrete Mathematics Week 4: Number Theory. 1. Primes. A positive integer p greater than 1 is called prime if the only positive factors of p are 1 and p.. Applied Discrete Mathematics Week 5: Mathematical Reasoning. 1. Arguments. Just like a rule of inference, an . argument . consists of one or more hypotheses and a conclusion. . Applied Discrete Mathematics Week 1: Logic and Sets. 1. Welcome to. CS/MATH 320L – . Applied Discrete Mathematics. Spring . 207. . Instructor: Marc Pomplun. Applied Discrete Mathematics Week 14: Trees. 1. Representing Graphs. Definition:. Let G = (V, E) be a . directed graph. with |V| = n. Suppose that the vertices of G are listed in arbitrary order as v. Applied Discrete Mathematics Week 3: Algorithms. 1. The Growth of Functions. The growth of functions is usually described using the . big-O notation. .. Applied Discrete Mathematics Week 12: Equivalence Relations. 1. How About Some…. Relations. April 11, 2017. Applied Discrete Mathematics Week 12: Equivalence Relations.