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Discrete Math

Discrete math is the study of mathematical structures that are fundamentally discrete rather than continuous. The objects studied in discrete math include integers, graphs and statements in logic. These objects do not vary smoothly in this way but have distinct separated values. Therefore, discrete mathematics excludes topics in continuous mathematics such as calculus and analysis. Discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term discrete mathematics.

The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics which looks at finite sets; in particular, areas relevant to business. The concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography and software development.

Discrete math is an area of mathematics that is being increasingly used. It has many practical and relevant applications. Discrete math is so relevant because it is grounded in real-world problems. Many discrete math problems are simply stated and have few mathematical prerequisites.

Categories within Discrete Math

Discrete Optimization

Postings: 51

Discrete Optimization is a branch of optimization which embodies a significant area of combinatorics that deals with discrete values, such as integers.

Finite Element Method

Postings: 82

Finite element method is a numerical technique for finding approximate solutions to boundary value problems.

Excel Gradebook Project

1. Create an Excel spreadsheet that will be capable of calculating a student's final grade in a given course. Keep in mind that weighting is involved in determining the final grade. Your Excel spreadsheet should contain the following: □ The scores provided on the next page □ Category averages □ The weights used to de

Counting Problems

1) In how many ways can two married couples attending a concert be seated in a row of four seats if a) Each married couple is seated together? b) The members of each sex are seated together? 2) At a college library exhibition of faculty publications, four mathematics books, four social science books, and two biology books w

Graph Theory and Parse Tree

1. Path Analysis Here is a Question for you: For the diagram below find all the "simple paths" from A to F. A------------B------------C | | / | | | / | | | / | |D------------E------------F 2. Note a Hamiltonian circuit visits each

Discrete Math:Recursion

Discussion Questions 1. List all the steps used to search for 9 in the sequence 1,3, 4, 5, 6, 8, 9, 11 using a binary search. 2. Describe an induction process. How does induction process differ from a process of simple repetition? 3. Describe a favorite recreational activity in terms of its iterative components, such as sol

Automata Theory, Grammars and Languages

(1) A gate with three rotating arms at waist height is used to control access to a subway in New York city. Initially, the arms of the gate are locked preventing customers from passing through. Unlocking the arms requires depositing a token in a slot, which allows the arms to rotate to a complete turn which allows one customer t

Discrete math questions on relations and functions

Logic & Set Theory; Boolean Algebra; Relations & Functions 1. How do we distinguish relations from functions? 2. What sort of relation is friendship, using the human or sociological meaning of the word? Is it necessarily reflexive, symmetric, antisymmetric, or transitive? Explain why it is or is not any of these. What othe

Regression Analysis and Quarterly Compound Interest

1) For a five year period, Ken deposited $800 each quarter into an account paying 2.6% annual interest compounded quarterly. (Round your answers to the nearest cent.) (a) How much money was in the account at the end of 5 years? (b) How much interest was earned during the 5 year period? Ken then made no more deposits or w

Steps on solving 4 discrete math questions

Please see attached file with questions and provide ALL work so that I can understand how you arrived at the answers. Thank you. - 1. Let P (n) be the statement that 13+ 23+···+ n3 =(n(n+ 1)/2)2 for the positive integer n. a) What is the statement P (1)? b) Show that P (1) is true, completing the basis step of th

Discrete math questions

Looking for some answers to discrete math questions. Must show work so that I can understand how you achieved the results. See attached. 1. Note the contrapositive of the definition of one-to-one function given on of the text is: If a ≠ b then f(a) ≠ f(b). As we know, the contrapositive is equivalent to (another way o

Discrete Math Problems: Boolean Algebra

1. Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if xy + xy = 0. 2. a. How many rows are needed to construct the (function) table for a Boolean function of n variables? b. How many different Boolean functions of n variables are there? 3. Let g: B4 →B be defined by g(w, x, y, z) = (wz +

Explicit Runge-Kutta Method

Write a general purpose RK routine; here described in a matlab context (but feel free to re-interpret into and program in any language environment) [t_out,y_out,e_out] = rk ( ode_RHS, y_0, t_range, c, A, b1, b2 ) input parameters: ode_RHS= function handle to right side f of the ODE y'=f(t,y) y_0= initial value for ODE

Logic Problem - Death or freedom

Suppose a prisoner must make a choice between two doors. One door leads to freedom and the other door is booby-trapped so that it leads to death. The doors are labeled as follows: Door 1: This door leads to freedom and the other door leads to death. Door 2: One of these doors leads to freedom and the other of these doors le

Coding in Matlab - Dot, Cross, and Triple Products

See the attached file. The objective is to write MATLAB codes that calculate scalar, vector and triple (scalar) products of vectors. Example: the scalar product function is R^3 Copy and paste the following programme into the MATLAB editor and save the program as scalar_prod.m function z = scalar_prod(x,y)

Discrete Math Calculations

1) Three identical light beams are to be installed in the vertices of a hexagonal tower, ie., hexagonal cylinder, with 12 vertices. a) No other restriction applies? b) Only the top vertices are to be used? c) Only one beam goes at the top? 2) There are ten identical books, and one each of 10 different book

Build a LP Model and find the optimal solution.

A university needs to put together a committee to handle students' complaints. To ensure that all perspectives are represented, it is necessary to have a diverse committee by including at least one female, one male, one student, one administrator and one faculty member. Ten individuals have been nominated but since it is importa

Discrete Mathematical Definitions

Could you give me a "working" definition of each term and an example of how they are used if possible. Terms: - Image - Mapping - Range - Codomain - Domain - Surjective - Injective - Bijective - One to one.

Equivalence Relation vs. Equivalence Class

Concerning discrete math, I am very confused as to the relationship between an equivalence relation and an equivalence class. I would very much appreciate it if someone could explain this relationship and give examples of each such that the relationship (or difference) is clear.

Discrete Math - Counting

Please show these solutions in great detail with all steps explained as they will serve as a guide for future problems. 1. The integers 1 through 25 are arranged in a 5 x 5 array (we use each number from 1 to 25 exactly once). All that matters is which numbers are in each column and how they are arranged in the columns. It do

Discrete Math- Equivalence Relations

Please help with the following problem regarding discrete math. I need a clear explanation of what an equivalence relation is with an examples. Specifically given 5|(m-n), where m and n are integers, please verify if this is an equivalence relation. Please explain this clearly and in detail.

Set Theory and Counting

1. List the ordered pairs in the equivalence relations produced by these partitions of {0,1,2,3,4,5} a) {0}, {1,2}, {3,4,5} b) {0,1}, {2,3}, {4,5} c) {0,1,2}, {3,4,5} d) {0}, {1}, {2}, {3}, {4}, {5} 2. Which of these collections of subsets are partitions of the set of integers? a) the set of even integers and the set of

Counting and Set Theory

How many ways can n books be placed on k distinguishable shelves? a) if the books are indistinguishable copies of the same title? b) if no two books are the same, and the positions of the books on the shelves matter? How many ways are there to deal bands of five cards to each of six players from a deck containing 48 differe

Discrete math problems

1. A telephone number is a ten-digit number whose first digit cannot be a 0 or a 1. How many telephone numbers are possible? 2. A computer operating system allows files to be named using any combination of uppercase letters (A-Z) and digits (0-9), but the number of characters in the file name is at most eight (and there has t

Discrete Math: Integers

A US Social Security number is a nine-digit number. The first digit (or digits) may be zero. a) How many US Social Security numbers are available? b) How many US Social Security numbers are odd? c) How many US social security numbers read the same backward and forward (eg 350767053)? These 4-digit numbers cannot start wit

Discrete Math: Truth Tables

1) Construct the Truth Table for each of the following Boolean expressions: Are they equivalent expressions? Are they tautologies? Contradictions? 2) Find a Boolean expression involving x y which produces the following table: 3) Consider a statement of the form "if A then (B and C)". Assume you wish to disprove it. Th