PPT-22C:19 Discrete Math

Discrete Probability Fall 2011 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. 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.. Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . Sequence and Sums. 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.. 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 . 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 . 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 . Induction and Recursion. Fall . 2011. Sukumar Ghosh. What is mathematical induction?. It is a method of proving that something holds.. Suppose we have an . infinite ladder. , and we want to know. if we . 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. Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. 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 . 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. 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 .