PPT-22C:19 Discrete Math

Logic and Proof Fall 2011 Sukumar Ghosh Predicate Logic Propositional logic has limitations Consider this Is x gt 3 a proposition No it is a predicate Call it Px . http://www.ipracticemath.com iPracticeMath was an idea stemming from a group of innovative Engineers that were not only Masters of Science and Technology but possessed a passion to take their knowledge and make it accessible, understandable and fun for all ages, grades, and student’s skillsets. Sets and Functions. Fall . 2011. Sukumar Ghosh. What is a set?. Definition. . A set is an unordered collection of objects.. . S = {2, 4, 6, 8, …}. . COLOR = {red, blue, green, yellow}. Each object is called an element or a member of the set.. 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 . Introduction and . Scope. Propositions. Fall 2011. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . supporting . Dr. Feng Gu. Way to study a system. . Cited from Simulation, Modeling & Analysis (3/e) by Law and . Kelton. , 2000, p. 4, Figure 1.1. Model taxonomy. Modeling formalisms and their simulators . Discrete time model and their simulators . Integers and Modular Arithmetic . Fall 2010. 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 . 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. . Structures. Introduction and Scope:. Propositions. Spring 2015. Sukumar Ghosh. The Scope. Discrete . mathematics. . studies mathematical . structures that are . fundamentally . discrete. ,. . not . Fall . 2011. Sukumar Ghosh. The Product Rule. Example of Product Rule. Example of Product Rule. The Sum Rule. Example of Sum Rule. Example of Sum Rule. Wedding picture example. Counting subsets of a finite set. Fall 2010. Sukumar Ghosh. Boolean Algebra. In 1938, Shannon showed how the basic rules of logic. first given by George Boole in his 1854 publication . The Laws of Thought. , can be used to design circuits. Fall . 2011. Sukumar Ghosh. What is an algorithm. . A finite set (or sequence) of . precise instructions . for performing a computation. . . . Example: Maxima finding. . . procedure . max. (. 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?. Fall 2011. 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 . Fall 2011. Sukumar Ghosh. Sequence. A sequence is an . ordered. list of elements. . Examples of Sequence. Examples of Sequence. Examples of Sequence. Not all sequences are arithmetic or geometric sequences..