PPT-CS100: Discrete structures

Lecture 7 Counting Lecture Overview 61 The Basics of Counting THE PRODUCT RULE THE SUM RULE THE SUBTRACTION RULE THE DIVISION RULE 62 The Pigeonhole Principle 63 Permutations and Combinations. A1Masoud 1 ShihYu Chu 2 Tarunraj Singh a School of Engineering SUNY at Buffalo Buffalo New York 14260 Abstract The primary objective of this work is to investigate lin ear time invariant systems undergoing rest to rest ma neuvers in a finite time us By Pigeonhole Principal out of 1 integers at least 2 are congruent modulo b Among any 64257ve points with integer coordinates in the plane there are two such that the center of the line segment that connects them also has integer coordinates Soluti 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 . 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 . Variational. Time Integrators. Ari Stern. Mathieu . Desbrun. Geometric, . Variational. Integrators for Computer Animation. L. . Kharevych. Weiwei. Y. Tong. E. . Kanso. J. E. Marsden. P. . Schr. ö. Logic and Proof. Spring 2015. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). .  . 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. . Chapter 1. CISC 2315 Discrete Structures. Professor William G. Tanner, Jr.. Fall 2010. Slides created by James L. Hein. , . author of. Discrete Structures, Logic, and Computability. , 2010, 3rd Edition, Jones & Bartlett Computer Science, . Instructor: Kecheng Yang. yangk@cs.unc.edu. We meet . at FB 009, 1:15 PM – 2:45 PM, . MoTuWeThFr. Course Homepage. : . http://cs.unc.edu/~. yangk/comp283/home.html. About Me. I am a fourth-year (fifth-year next fall) Ph.D. student.. & . Information Communication Technology, Ahmadu Bello University, Zaria.. DCS104-Discrete Structures II. By. Aliyu Garba (galiyu@abu.edu.ng. ). Mrs. . Esther . G.B (. ecekechukwu@abu.edu.ng). Discrete Structures II. Announcements:. HW . 4. . posted, . due Tues May 8 at 4:30pm. . No late HWs as solutions will be available immediately.. Midterm details on next page. HW . 5 will . be posted . Fri May 11. , . due . Xiliang Luo. 2014/11. 1. Block Diagram. Adder, Multiplier, Memory, Coefficient. 2. Example. 3. General Case. 4. Direct Form 1. Rearrangement. 5. Rearrangement. 6. Zeros 1. st. . Poles 1. st. . Canonic Form. . . Feng Luo . . Rutgers University. D. Gu (Stony Brook), J. Sun (Tsinghua Univ.), and T. Wu (Courant). Oct. 12, 2017. Geometric Analysis, . Roscoff. , France.