PPT-22C:19 Discrete Structures

Trees Spring 2014 Sukumar Ghosh What is a tree Rooted tree recursive definition Rooted tree terminology Rooted tree terminology A subtree Rooted tree terminology Important properties of trees. Integers and Modular Arithmetic . Spring 2014. Sukumar Ghosh. Preamble. Historically, . number theory . has been a beautiful area of . study in . pure mathematics. . However, in modern times, . number theory is very important in the . Surfaces. 2D/3D Shape Manipulation,. 3D Printing. CS 6501. Slides from Olga . Sorkine. , . Eitan. . Grinspun. Surfaces, Parametric Form. Continuous surface. Tangent plane at point . p. (. u,v. ). is spanned by. Introduction and . Scope. Propositions. Fall 2011. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . supporting . 1C. 1D. 2A. 2B. 2C. 2D. 3A. 3B. 3C. 3D. 4A. 4B. 4C. 4D. 5A. 5B. 5C. 6A. 6B. 6C. 7A. 7B. 7C. 8A. 8B. 8C. 9A. 9B. 9C. 10A. 10B. 10C. 11A. 11B. 11C. 12A. 12B. 12C. 13A. 13B. 13C. 14A. 14B. 14C. 15A. 15B. 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic .  . A Sampled or discrete time signal x[n] is just an ordered sequence of values corresponding to the index n that embodies the time history of the signal. A discrete signal is represented by a sequence of values x[n] ={1,2,. 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. . Logic and Proof. Fall 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . P(4) .  . A Sampled or discrete time signal x[n] is just an ordered sequence of values corresponding to the index n that embodies the time history of the signal. A discrete signal is represented by a sequence of values x[n] ={1,2,. Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . Relations. Spring. 2015. Sukumar Ghosh. What is a relation?. Let A, B be two sets. A . binary relation . R is a subset of A X B.. Example. Let A = {Alice, Bob, Claire, Dan) be a set students,. and B= {CS101, CS201, CS202) be a set of courses. Then,. Marek . Zrałek. University of Silesia, Katowice. Workshop on . Discrete Symmetries and Entanglement. 10. 06. 2017, . Kraków. Outline. Introduction. Discrete symmetries in Space Time and charge . c. Equations. Outline. • Discrete-time state equation from . solution of . continuous-time state equation.. • Expressions in terms of . constituent matrices. .. • Example.. 2. Solution of State Equation. Fall 2010. Sukumar Ghosh. Sample Space. DEFINITION. . The . sample space S . of an experiment is the set . of possible outcomes. An . event. . E. is a . subset. of the sample space.. What is probability?.