PPT-22C:19 Discrete Math

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 . 5 ME 360 35 ME 370 ME 320 ME 350 ME 390 HumSoc HumSoc ME 371 Free Elec Tech Elec MechSE Elec Statistics Tech Elec 46 Science Elec MechSE Elec Free Elec Eng 100 1415 hrs 1415 hrs 16 hrs 16 hrs 175 hrs 165 hrs 18 hrs 15 hrs ME 199 ME 199 ME 199 Freshma 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.. 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. ). . 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 . Counting. 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. Graphs. Fall . 2011. Sukumar Ghosh. Seven Bridges of . K. ⍥. nigsberg. Is it possible to walk along a route that cross . each bridge exactly once?. Seven Bridges of . K. ⍥. nigsberg. A Graph. What is a Graph. 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 . 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 . 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. 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?. �EJC� );:d)$N#)3S)ePG)[:P)f\))G)c')+0)H)c')N-22C,)E44/+/OC)g:)L6) !"#$%&'()V!%W)�&"�,"#1+#$&")+"'X&1)%=DD,1),Y�H+".,5)"CC4C4)/25 8BJ)/1)/*)E)3Q013QE+C)J-22C,)0,)/*)E 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 .