2 1-Basic-math-students

# 2 1-Basic-math-students - fill-in animation only answer...

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1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M. A. Breuer 1 Some introductory mathematical concepts M. A. Breuer Ming Hsieh Department of Electrical Engineering Viterbi School of Engineering University of Southern California EE581 Fall 2007 fill-in animation only answer

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1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M. A. Breuer 2 Introductory material In this section we will review some basic material that most of you know already. If you do, then sit back and relax. If you do not, then go to some of the references at the end of this section and to the web and read up on those topics on which you are not sure about. The material to be covered in this section includes: Notation and concepts Logic Necessary and sufficient conditions Sets Relations and functions Complexity
1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M. A. Breuer 3 Functions The concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its "input") and the other as secondary (the value of the function, or "output"). A function then is a way to associate a unique output for each input of a specified type, for example, a real number or an element of a given set. A function is a mapping from a set of objects, called the domain, into a set of objects, called the range. Examples: 0 1 1 1 0 1 1 1 0 0 0 0 C B A 25 5 16 4 9 3 4 2 1 1 Y X C=A B Y=X 2 y=sin(x) F=ma

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1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M. A. Breuer 4 Monotonicity A function f ( n ) is monotonically increasing if m n implies that f ( m ) f ( n ), where all n and f(n) are real numbers. A monotonically decreasing function is defined similarly. A function is monotonic if it is either monotonically increasing or decreasing. For example, e x is a monotonically increasing function. Given a large logic design consisting of gates and their interconnections. Place a few gates of this design in partition A , the rest in partition B . In general, there will be interconnections between the two partitions. Remove a gate from partition B and place it in A , and then make sure all the connections between A and B are established. As gates are moved from partition B to A , in general the following are true. As new gates are added to partition A , the power dissipation associated with the logic in A is a monotonically increasing function As new gates are added to partition A , the number of I/O pins associated with partition A is not a monotonically increasing function .
1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M. A. Breuer 5 Questions Is “ sin ( x )” a monotonic function of x ? Is the human population of the world a monotonic function of the

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## This note was uploaded on 12/04/2009 for the course EE 581 at USC.

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2 1-Basic-math-students - fill-in animation only answer...

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