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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.

## BrainMass Categories within Discrete Math

### Minimum-length cabling to connect computer-screen information

The management of a zoo wishes to place a computer-screen information system at the Entrance (E), and all the enclosures like the Tigers' enclosure (T), the Wolves' enclosure (W), the Lions' enclosure (L) and so on. These need to be connected to the main computer at the Entrance. For obvious reasons, the cables must run along th

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

### Discrete Math Problems: Set Operations, Counter Examples

Need solutions for the attached questions.

### 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

### History of Measurement in Non-Western Countries

Describe the historical development of measurement and measurement systems in non-Western cultures.

### Matrix operations and functions

Please show full work so that I can understand how you arrived at the answers.

### 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 +

### The solution gived detailed steps on solving various questions on the mathematical logic. All concepts are shown and explained.

if a*b = b*a is false then...

### The solution gived detailed steps on solving various questions on the linear system of equations. All formula and calcuations are shown and explained.

Solve linear system of equation x - 3y = -6 5x + 3y = 42

### Generating a code that detects errors

Construct a (7,3) code that detects 3 errors and do the following... a) Write the generator matrix b) Show by example that your code will detect 1 error, 2 errors, and 3 errors. c) Give an example where 4 errors are made in transmitting a message word, but your code does not detect any errors. d) How many errors are correcte

### Linear Programming - Optimal Assignment

An electronics firm produces electronic components, which it supplies to various electrical manufacturers. Quality control records indicate that different employees produce different numbers of defective items. The average number of defects produced by each employee for each of six components is given in the following table:

### 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

### Math: Combinations

1. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the department if at least one woman must be on the committee? 2. Find the value of C(16, 6). 3. How many different license plates can be created with 7 numbers if any di

### Mathematical Proof: Is the Argument Valid?

Determine whether the following argument is valid: P > Q (~P & R) > S ~Q :. ~R v S.

### 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)

### Runge-Kutta Method Errors

Question: How does this compare with the theoretical rate of convergence of 0(H2). Explain your result as best as you can? Data: We used the Runge-Kutta method to solve y'(x) = - y(x) + x^0.1[1.1 + x], y(0) = 0 whose solution is y(x) = x^1.1. We solved the equation on [0,5] and we printed the errors at x = 1,2,3,4,5. We u

### Makespan Scheduling Problem

A serial production line consists of two main workstations: an assembly workstation and a packaging workstation. The processing times for 11 jobs (in minutes) that must be processed on these two workstations are given below. There is plenty of space in between the workstations such that blocking does not occur. a) Find the o

### Set Sizes

Find the number of elements in A_1 [the union of] A_2 [the union of] A_3 if there are 100 elements in A_1, 1000 in A_2, and 10,000 in A_3 if: a) A_1 [is a subset of] A_s and A_2 [is a subset of] A_3. b) the sets are pairwise disjoint. c) there are two elements common to each pair of sets and one element in all three se

### One Dimensional Dirichlet

Consider the one-dimensional Dirichlet problem v_xx = f(x) on (0,1) v(0) = v(1) = 0 with f(x) = cos(x) and true solution v(x) = -f(x) + x*(f(1.0)-1.0)+1.0. Implement V-cycle multigrid algorithm to solve the above problem. On each level of multigrid use Gauss-Seidel algorithm to solve the system of equations. Use the f

### 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

### Discrete Math: Modular Arithmetic

Please provide an explanation of Modular Arithmetic. I find it very confusing and am having trouble understanding the definitions and applying them. If you could include some samples of some of the operations that might help.

### 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