Discrete math matrices pdf

In the last lecture we introduced fast matrix multiplication, i. These materials are based on usqs tertiary preparation program. Discrete math cheat sheetstudy sheetstudy guide in pdf. Random matrices universality proof techniques random matrix models we will consider a number of random matrix models, which can be either discrete or continuous. To add or subtract two matrices of the same dimensions, we add or subtract the corresponding entries. Inverse functions i every bijection from set a to set b also has aninverse function i the inverse of bijection f, written f 1, is the function that assigns to b 2 b a unique element a 2 a such that fa b i observe. From a night class at fordham university, nyc, fall, 2008.

Browse other questions tagged discretemathematics matrices or. In general, an m n matrix has m rows and n columns and has mn entries. View notes discrete math lecture notes matrices from 1016 265 at rochester institute of technology. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, business, and the sciences. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields. Click here to download the full size worksheet pdf. This informative chapter offers a handy way to brush up on or learn something new about matrices in discrete math. At uga, our linear algebra class focuses on the geometric interpretations of vectors and matrices, while the discrete course focuses on things like logic, complexity, graph theory, and cryptography. Besides reading the book, students are strongly encouraged to do all the. Example here is a matrix of size 2 2 an order 2 square matrix. Matrices, vectors and discrete maths print materials to assist with any prerequisite mathematics required in usq courses. Discrete mathematics matrix additionsubtraction youtube. Computer science stack exchange is a question and answer site for students, researchers and practitioners of computer science. Discrete mathematics and its applications chapter 2 notes 2.

Here is a matrix of size 2 3 2 by 3, because it has 2 rows and 3 columns. Find each product, sum, andor difference, if possible, using the matrices below. The rows in a matrix are usually indexed 1 to m from top. Discrete mathematics overview conceptual categories, domains, and clusters number and quantity vector and matrix quantities c. Matrices and determinants the material in this chapter will be covered in your linear algebra class math 254 at mesa. Among the fields covered by discrete mathematics are graph and hypergraph theory, network theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. A matrix with m rows and n columns is called an m xn matrix. In many economic analysis, variables are assumed to be related by sets of linear equations. Matrices in discrete mathematics and its applications. Among the fields covered by discrete mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and. Perform operations on matrices and use matrices in applications algebra creating equations a.

Matrices in discrete math mathematics stack exchange. This is a course note on discrete mathematics as used in computer science. Cheat sheetstudy sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Matrices have many applications in discrete mathematics. Discrete mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. In this video we guide you through matrix addition and subtraction. Matrices a matrix is basically an organized box or array of numbers or other expressions. The numbers n and m are called the dimensions of the matrix. Browse other questions tagged matrices discretemathematics graphtheory or ask your own question. One innovation uses several major threads to help weave core topics into a cohesive whole. Transpose at switching the entries from rows to columns and columns to rows. Matrices in discrete mathematics and its applications slideshare.

Iid random matrices these are n n matrices a xij1 i. Matrix math equal matrices same order and each entry is equal question 16. Definition of matrix a matrix is a rectangular array of numbers. These active and wellknown authors have come together to create a fresh, innovative, and timely approach to discrete math. Discrete mathematics for computer science i university of. Suppose a fstudents in this math 42 class g and b fountriesc in the world other than the us g.

This booklet consists of problem sets for a typical undergraduate discrete mathematics course aimed at computer science students. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Free discrete mathematics books download ebooks online. Discrete math functions perform operations on integers, 2, 1, 0, 1, 2, or return discrete output as integers. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Matrices are used throughout discrete mathematics to express relationships between elements. The aim of this book is not to cover discrete mathematics in depth it should be clear from the description above that such a task would be illde.

Discrete mathematics and probability algebra 2 mathplanet. A square matrix is a matrix with the same number of rows as columns. Cantor developed the concept of the set during his study of the trigonometric series, which is now known as the limit point or the derived set operator. Sets, relations and functions, sequences, sums, cardinality of sets richard mayr university of edinburgh, uk.

Definition of matrix square matrix with example matrix operations matrix multiplication with example transposes and power matrices. A diagonal matrix is a square matrix whose entries o the main diagonal are zero. Model system defined by zeros and poles of discrete transfer function. Discrete was definitely easier, but they are so different that theres not enough overlap to.

A matrix with m rows and n columns is called an m n matrix. However, the rigorous treatment of sets happened only in the 19th century due to the german mathematician georg cantor. Notes on matrices matrices is the plural of matrix a matrix is a rectangular array of data. These problem may be used to supplement those in the course textbook. Sets, set operations, cardinality of sets, matrices. Number theory, probability, algorithms, and other stuff by j.

Richard johnsonbaugh is professor emeritus of computer science, telecommunications and information systems, depaul university, chicago. Johnsonbaugh, discrete mathematics, 8th edition pearson. A matrix with m rows and n columns is called an m x n matrix. Discrete math lecture notes matrices notes on matrices. Matrix algebra provides a clear and concise notation for the formulation and solution of such problems, many of which would be complicated in conventional algebraic notation. In this video we guide you through matrix order, which is a fancy way of saying matrix rows and columns click here to download the full size worksheet pdf. P kubelka equivalence relations a type of relation on athat is very important in many branches of mathematics is an equivalence relation. We call the individual numbers entriesof the matrix and refer to them by their row and column numbers. Discrete mathematics i fall 2014 identity matrix the identity matrix is a n n square matrix where the main diagonal consist of all ones and zeros elsewhere.

I this is why bijections are also calledinvertible functions instructor. He was solely responsible in ensuring that sets had a home in mathematics. Perform discretetime integration or accumulation of signal. The learner will use matrices and graphs to model relation ships and solve problems. You have probably encountered them in a precalculus course. Matrices in discrete mathematics and its applications 1. Prior to his 20year service at depaul university, he was a member and sometime chair of the mathematics departments at morehouse college and chicago state university. Among the fields covered by discrete mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic. If the product, sum, andor difference does not exist, state why it. An upper triangular matrix is a matrix having all the entries below the main diagonal equal to zero. Discrete mathematics and algorithms lecture 9 matrix.

Throughout the book the application of mathematical reasoning is emphasized to solve problems while the authors guide the student in thinking about, reading, and writing proofs in a. This page intentionally left blank university of belgrade. You can use these functions to factor large numbers, calculate factorials, find permutations and combinations, or find greatest common denominators. Chapter 18 out of 37 from discrete mathematics for neophytes. We will usually denote matrices with capital letters, like. We continue our investigation of discrete riemann surfaces with the discussion of the discrete analogs of period matrices, riemanns bilinear relations, exponential of constant argument, series and electrical moves.