## MM250 Discrete Math Discussion

Set Theory as a Framework for Relational Databases
An Example of How Post Should Be Done is Attached
A set can be a collection of any type of object, ranging from people to places to things. Basic set theory includes the study of subsets, proper subsets, finite and infinite sets, and the logical operations on them. Set theory plays a foundational role in mathematical processes and ideas and also has connections to computer engineering, programming, and databases.
The relational database model, originally invented by computer scientist Edgar F. Codd in 1969, is based on ideas from set theory. A simple database is a collection of records stored in tables. A relational database also includes relationships stored across multiple tables. One can run queries on the relational database to request specific information with set theory operators, such as union and intersection.
Post 1: Initial Response
Imagine you are responsible for your organization’s analytic tasks, and you are currently brainstorming how to query a relational database of marketing information for the organization. You want to test your understanding of how you might relate the database tables with the use of set theory, and particularly subsets. To carry out your test, complete each of the following:
To define two sets, set A and set B, first conduct an online browsing trial, in which you spend 10–20 minutes looking at different websites, such as for national news, social media, sports, hobbies, recipes, etc. Let set A represent exactly three distinct company names from any online advertisements you saw during your browsing trial. Let set B represent at least three distinct company names for any online retailers you have purchased from in the past year.
To prepare to use your algorithm, answer the following questions:How many elements are in set A? This is what you will set as m = ___.
How many elements are in set B? This is what you will set as n = ___.
What are your first and last elements of A? Show these as a[1] = ____ and a[m] = ___.*
What are your first and last elements of B? Show these as b[1] = ____ and b[n] = ___.*

*Note: Recognize that there are other elements you will cycle through as you trace the algorithm. While you are not required to list all elements in this form, you will need to use them, in addition to the first and last elements, as you complete your trace.
Using your sets A and B along with what you just outlined to prepare, determine an algorithm that you can use to see whether A ⊆ B.
State the algorithm that you would use to compare these sets.
Based on your algorithm, did you find that A ⊆ B or that A ⊈ B? Explain. If A ⊈ B, how are they related (e.g., disjoint, intersecting)?

## Applied Mathematics Question

The testing session will be available between the dates of October 20-23, 2022.Please note that you should allow enough time to complete the testing session when you begin.If you wish to take the test later, you should save this email and the test link in a safe location so that they may be accessed when you are ready to take the tests. If your testing session is interrupted due to a power outage, computer crash, or any other incident, you can resume testing by clicking on the link provided in this email.The test is fully compatible with the latest version of Chrome, Edge, and Firefox. Safari users will have to follow the onscreen instructions after clicking the test link for enabling the auto-play function within the Safari browser. Please note, Microsoft is no longer supporting Internet Explorer thus the test may not be compatible with the Internet Explorer browser.

## Applied Mathematics Question

The testing session will be available between the dates of October 20-23, 2022.Please note that you should allow enough time to complete the testing session when you begin.If you wish to take the test later, you should save this email and the test link in a safe location so that they may be accessed when you are ready to take the tests. If your testing session is interrupted due to a power outage, computer crash, or any other incident, you can resume testing by clicking on the link provided in this email.The test is fully compatible with the latest version of Chrome, Edge, and Firefox. Safari users will have to follow the onscreen instructions after clicking the test link for enabling the auto-play function within the Safari browser. Please note, Microsoft is no longer supporting Internet Explorer thus the test may not be compatible with the Internet Explorer browser.

## Watch Video and complete Journal

Watch the week7 YouTube videos and take notes in the video journal (paper assignment).

Ch 6.2a The Empirical Rule (68 – 95 – 99.7)

Ch 6.3a The Sampling distribution of the sample means and the Central Limit Theorem

## Function question

Draw arrow diagrams to give an example in each of the following cases or explain why you cannot do that.
(a) A function that is surjective but not injective.
(b) Two functions f and g such that g◦f is bijective but both functions are not bijective.

## Discussion 2

A dart of mass 22g is travelling at 7ms-^1 when it strikes a board. How thick must the board be to prevent the point of the dart reaching the wall behind the board? Assume the resistive force exerted by the material of the board is constant and of value 20N.

## I have 4 matlab codes

Write a code to produce the Mandelbrot set and reproduce Fig 4.10 (hint: suppose that if |z|>2 then the orbit diverges to infinity).
Write a code to produce Julia sets and reproduce Fig 4.11.(a)
Write a code to compute the box counting dimension and compute it for the Hénon map. (Show your plot corresponding to Fig. 4.16 including the fitted line. To fit the line you can use polyfit in Matlab [An example to use polyfit can be found in this file: fit.m])
Write a code to compute the correlation dimension and compute it for the Hénon map. (show your plot of C(r) vs r and the fitted line)
Computer experiment 6.2 (p.238) [use many different ICs p to quantify the average rate of convergence for mn]
PAGE 168 FIG 4.10
PAGE 169 FIG 4.11
PAGE 179 FIG 4.16
NO PLAGIARISM
SEND ME ONE BY ONE WHEN IT’S DONE

## I have 4 matlab codes

Write a code to produce the Mandelbrot set and reproduce Fig 4.10 (hint: suppose that if |z|>2 then the orbit diverges to infinity).
Write a code to produce Julia sets and reproduce Fig 4.11.(a)
Write a code to compute the box counting dimension and compute it for the Hénon map. (Show your plot corresponding to Fig. 4.16 including the fitted line. To fit the line you can use polyfit in Matlab [An example to use polyfit can be found in this file: fit.m])
Write a code to compute the correlation dimension and compute it for the Hénon map. (show your plot of C(r) vs r and the fitted line)
Computer experiment 6.2 (p.238) [use many different ICs p to quantify the average rate of convergence for mn]
PAGE 168 FIG 4.10
PAGE 169 FIG 4.11
PAGE 179 FIG 4.16
NO PLAGIARISM
SEND ME ONE BY ONE WHEN IT’S DONE

## MathLab Question

I have 4 problems needs to be done on Matlab
– Please have all 4 codes in a pdf with the code and graph
INSTRUCTIONS
Write a code to produce the Mandelbrot set and reproduce Fig 4.10 (hint: suppose that if |z|>2 then the orbit diverges to infinity).
Write a code to produce Julia sets and reproduce Fig 4.11.
Write a code to compute the box-counting dimension and compute it for the Hénon map. (Show your plot corresponding to Fig. 4.16 including the fitted line. To fit the line you can use polyfit in Matlab [An example to use polyfit can be found in this file: fit.m])
Write a code to compute the correlation dimension and compute it for the Hénon map. (show your plot of C(r) vs r and the fitted line)
Extra/Grad Credit*: Computer experiment 6.2 (p.238) [use many different ICs p to quantify the average rate of convergence for mn ] Do please
Page 168 Fig. 4.10
Page169 Figure 4.11
Page 179 Fig. 4.16

## Simplify and explicit formula

1)
Simplify sum k = 0 to n of k^2 (n choose k).
2)
Find an explicit formula for a_n so that a_0 = 1, a_1 = 2, and a_{n 2} = 5a_{n 1}-3a_n.
3)
Find an explicit formula for the number of tilings of a 2xn grid with 1×2 and 2×1 and 2×2 tiles.
4)
Find all Fibonacci numbers that are divisible by 3.
Process and explanation required. Thanks

## Tutoring on the Normal Distribution

Scenario
Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course.
As Frank’s tutor, you need to provide Frank with guidance and instruction on a spreadsheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.
What to Submit
To complete this assignment, you must first download the spreadsheet, and then complete it by including the following items on the spreadsheet:
Deliverable 2 – Tutoring on the Normal Distribution.xlsx

Incorrect Answers – Correct any wrong answers. You must also explain the error performed in the problem in your own words.
Partially Finished Work – Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.
Blank Questions – Show how to complete any blank questions by providing step-by-step instructions including explanations.
Your step-by-step breakdown of the problems, including explanations and calculations performed, should be present within the Excel spreadsheet provide

## define the following terms Hamilton method Lowndes method Jefferson method webster method for each method give a short historical

define the following terms
Hamilton method
Lowndes method
Jefferson method
webster method

for each method give a short historical and/or current significance
example : where it was/is used, why/how it was developed, why/how it is different from other methods

provide complete and detailed instructions for each method being used.

## The project is adapted from the Chapter 4 Case Study dealing with North–South Airline In January 2012, Northern Airlines

The project is adapted from the Chapter 4 Case Study dealing with North–South Airline In
January 2012, Northern Airlines merged with Southeast Airlines to create the fourth largest U.S.
carrier. The new North–South Airline inherited both an aging fleet of Boeing 727-300 aircraft
and Stephen Ruth. Stephen was a tough former Secretary of the Navy who stepped in as new
president and chairman of the board.
Stephen’s first concern in creating a financially solid company was maintenance costs. It was
commonly surmised in the airline industry that maintenance costs rise with the age of the
aircraft. He quickly noticed that historically there had been a significant difference in the
reported B727-300 maintenance costs (from ATA Form 41s) in both the airframe and the engine
areas between Northern Airlines and Southeast Airlines, with Southeast having the newer fleet.
On February 12, 2012, Peg Jones, vice president for operations and maintenance, was called into
Stephen’s office and asked to study the issue. Specifically, Stephen wanted to know whether the
average fleet age was correlated to direct airframe maintenance costs and whether there was a
relationship between average fleet age and direct engine maintenance costs. Peg was to report
back by February 26 with the answer, along with quantitative and graphical descriiptions of the
relationship.
Peg’s first step was to have her staff construct the average age of the Northern and Southeast
B727-300 fleets, by quarter, since the introduction of that aircraft to service by each airline in
late 1993 and early 1994. The average age of each fleet was calculated by first multiplying the
total number of calendar days each aircraft had been in service at the pertinent point in time by
the average daily utilization of the respective fleet to determine the total fleet hours flown. The
total fleet hours flown was then divided by the number of aircraft in service at that time, giving
the age of the “average” aircraft in the fleet.
The average utilization was found by taking the actual total fleet hours flown on September 30,
2011, from Northern and Southeast data, and dividing by the total days in service for all aircraft
at that time. The average utilization for Southeast was 8.3 hours per day, and the average
utilization for Northern was 8.7 hours per day. Because the available cost data were calculated
for each yearly period ending at the end of the first quarter, average fleet age was calculated at
the same points in time. The fleet data are shown in the following table.
Airframe cost data and engine cost data are presented below (please note, I have altered the
number presented in the text so that online solutions cannot be used) paired with fleet average
age in that table.
The project is derived from a case study located at the end of chapter 4 dealing with regression
analysis. Please note, however that some of the numbers in the project tables in the text have
been changed so students should get their complete instructions from the Project area provided in
Getting Started section of the Table of Contents. Students should use the Data Analysis add-on
pack from the standard Microsoft Excel software available in every Microsoft Office software
since 2007. The project requirements are:
1. Prepare Excel Data Analysis Regression Tables demonstrating your excellence at
determining Northern and Southeast Costs to Average Age. Besides the data tables,
copied from the project instructions, four regression models are required each on a
separate tab. STUDENTS CANNOT USE MULTIPLE REGRESSION as this is not part
of Excel software. Place each regression model with supporting data labels, line fit plots,
and other required items on a separate worksheet tab.
2. On each worksheet tab (other than the data table tab) include:
a. a copy of your data entry screen (Use Alt Print Screen to copy picture of
Regression Data Entry from Data Analysis in Excel and paste on correct
worksheet tab).
b. The regression model derived from the data tables.
c. Line Fit Plot for each Worksheet tab.
d. Labels of the data included.
e. Highlight with yellow and label the following four items on each regression
model:
i. Coefficient of determination
ii. Coefficient of correlation or covariance
iii. Slope, and
iv. Beta or intercept
3. Finally prepare a formal response, using Microsoft Word, from Peg Jones’s to Stephen
Ruth explaining your numbers and calculations. Which costs are correlated with the
average age of the aircraft? What is the slope and beta? Explain the coefficient of
determination and covariance. Explain how this information benefits each airline. Finally,
Stephen wants to know:
a. If Northern’s average age gets to 20,000 hours how much will the Airframe and
Engine cost.
b. If Southeast’s average age gets to 12,000 hours how much will the Airframe and
Engine cost.
Submit your Excel Worksheet with five tabs (data, plus 4 tabs for the regressions) to the
assignment drop box. Also include your formal response in a Microsoft Word document. Late
work will not be accepted. The Excel worksheet and Word documents must be submitted
BEFORE then end of Unit 7. This project is worth 160 points.
Note: Dates and names of airlines and individuals have been changed in this case to maintain
confidentiality. The data and issues described here are real.
Northern Airline Data (numbers have been changed from text)
Airframe Cost Engine Cost Average Age
Year per Aircraft per Aircraft (Hours)
2001 61.80 33.49 6,512
2002 54.92 38.58 8,404
2003 69.70 51.48 11,077
2004 68.90 58.72 11,717
2005 63.72 45.47 13,275
2006 84.73 50.26 15,215
2007 78.74 80.60 18,390
Southeast Airline Data (numbers have been changed from text)
Airframe Cost Engine Cost Average Age
Year Per Aircraft per Aircraft (Hours)
2001 14.29 19.86 5,107
2002 25.15 31.55 8,145
2003 32.18 40.43 7,360
2004 31.78 22.10 5,773
2005 25.34 19.69 7,150
2006 32.78 32.58 9,364
2007 35.56 37.07 8,259

## Determine the costs using FIFO and LIFO and Compute the gross margin for each method

The company uses a periodic inventory system.
a. Determine the costs assigned to ending inventory and to cost of goods sold using FIFO.b. Determine the costs assigned to ending inventory and to cost of goods sold using LIFO.c. Compute the gross margin for each method.
I need the answer in less than one hour

## Mathematical Survey

Prepare a brief questionnaire (15 questions: 5 nominal, 5 ordinal, 5 interval level variables) to study perceptions of crime near John Jay. Include questions asking respondents to describe a nearby area where they either are afraid to go after dark or think crime is a problem.
Operationalize each question/variable (list the attributes of the variable, aka answers). How you ask a question and operationalize it determines the level of measurement.
Indicate the codes you would utilize to input the data collected from administering these surveys into a statistical program like SPSS . So, numbers associated with the available responses.

## Write and post a linear equation in two variables and graph the linear equation using Desmos.com (Links to an

Write and post a linear equation in two variables and graph the linear equation using Desmos.com (Links to an external site.).

Please view this video on how to create and embed a graph using Desmos.com:
https://screencast-o-matic.com/watch/c3hXVsVrjgf

identify two points (written as ordered pairs) on the line and verify that they are true solutions. To do this, you need to plug both values into the equation and make sure that you get a true statement.

## Complete the Redistricter code to perform the following functions. Implement the MCMC process that iteratively produces candidate redistricting plans

Complete the Redistricter code to perform the following functions.

Implement the MCMC process that iteratively produces candidate redistricting plans and accepts or rejects these candidates based on the Metropolis criterion.
Run this process at least 1,000 times and record each run’s resulting plan.
Visualize the results of this simulation in a plot that displays the number of nodes in each district (3 districts => 2 dimensions required) and also a histogram of this information.
Produce a number of plan visualizations that illustrate the results
The data file which is given includes the adjacency matrix that is the connectivity of node, coordinates of node, the number of the nodes, and the population of the party.
The report should be written in complete sentences and structured with an appropriate introduction and conclusion. Its intended audience and tone should match the redistricting paper. Make sure to write in the words and do not plagiarize the other paper. The best way to do this is to write in several stages and not reference the original wording of the other paper after the first stage.
Build off of the work in Project 2 according to the following items. Write up your results in a well structured and organized report, using a similar tone and audience to the redistricting paper.

Basic geographical and demographic information about the map and initial plan.

Underlying theory of the MCMC algorithm that you’ve implemented.

Practical details of the MCMC algorithm (e.g. how many trials, how many samples, estimated runtime).

Equal population constraint implemented via Gibbs distribution: include information on how you tuned the beta parameter in order to achieve an appropriate constraint. You are permitted to allow relatively high variation in district population (even ±25% is OK with me) in order to allow your algorithm the flexibility to really explore the search space. Just make a choice for yourself and explain how you tuned the beta parameter to achieve this.

Resampling 1000 times to simulate uniform distribution after obtaining a Gibbs stationary distribution.

Analysis of electoral competitiveness of your sampled plans compared to the initial plan, visualized with a scatter plot.

Plan diagrams for notable plans in your analysis, together with commentary about what makes them notable.

Overall assessment of whether the initial plan exhibits partisan gerrymandering. If so, explain how this is observed and offer less biased alternatives. If not, explain how this is observed and exhibit some alternatives with a higher level of bias for comparison.

Important: the code needs to work in order to do this project properly. The codes need to succeed in performing the MCMC algorithm with an appropriate depth and breadth. Therefore, make sure to prototype the code by running it at small scales and identify any errors that may appear. If the code is working, it should never end prematurely with a Traceback.

## Have you ever watched Let’s Make a Deal? One of the games is based on a famous problem in

Have you ever watched Let’s Make a Deal? One of the games is based on a famous problem in probability. The game goes like this:

You have three doors. Under one door is a car and under two doors is a gag prize (known as a Zoink!)
You can choose one of the three doors (A, B, C).
Once you choose one of the three doors, the host (who knows where the prize is) closes one of the doors that does not contain the prize (so if you choose A, the host might close B if he/she knows the prize isn’t there).
You are prompted to keep the first door or switch to the remaining door?
Which option do you pick? How does this relate to conditional probability?

## Applied Mathematics Question

Your task in this assignment is to use polynomial functions to design a rollercoaster. To express your rollercoaster design you will create a piecewise function out of the polynomial functions. Your rollercoaster must meet certain criteria, and the questions below will guide you through this process. In the end, you will submit a written assignment, showing all of your calculations and ideas, to the dropbox. You can, and may find it very useful to, utilize graphing technology, such as Graph, to help you with this assignment. , BEWARE OF PLAIGRISM PLEASE
check file attached for instructions

## Math in Architecture Essay

Overview The Final Project is due by the close of Module 14, and comprises 15 percent of your course grade. Your instructor may or may not accept late work for a reduced grade. The Final Project is a stand-alone paper that you create, submit to Turnitin.com, and then post in the assignment topic by the due date. By “stand-alone” we mean that it is a complete product and requires no extra explanation. In other words, your assignment should not be a slideshow presentation that that you might use in support of a live presentation. Regardless of the subject, your Final Project should be in the format of an academic paper describing some research you undertook or a project that you completed on your own. Your file needs to be in .doc or .pdf format. Turnitin.com Instructors are not allowed to grade your assignment until you have submitted it to Turnitin.com. By now you should have a Turnitin.com account and have used it in this course in submitting your essays. However, there will be a topic dedicated to using Turrnitin.com for the Final Project in Module 14. Subject Choose a subject and project that furthers your understanding or skills in your major, or addresses your career goals. Some students will choose to complete a digital media-based project. In this case the digital product should be submitted, but still accompanied by an academic paper describing what you did and meeting all of the requirements described in the grading rubric. Alternatively, screen shots of digital work may be integrated into the text of your paper. Many practical projects can be documented with text and original images, whether photographs or computer-generated images. While images and graphics do not increase the page count of the paper, original images and graphics are one of the criteria on the grading rubric.. Of course, the central focus of the work should be quantitative and demonstrate the concepts and skills covered in this course. Quantitative literacy is often complex reasoning with simple math and graphics, involving the use of numbers in descriptions, analyses, organizing and analyzing data or works that have some quantitative component. Tips Start with an Introduction section. Explain what you did and why. Write your assignment to a general audience, who may or may not know much about the subject you chose. Particularly if you do some kind of practical project, include a section that explains the basic elements involved before launching into the project itself. Critical thinking, creativity, the generation of original material (text, photos, graphics, computergenerated or physical media of any kind), and the accuracy and clarity of quantitative communication are the most highly valued elements for this project. Regardless of your major, these skills are a contributing factor in navigating and succeeding in our highly digital and information-based world. Ideally, you will develops knowledge and skills in your major. This assignment could be the basic math and quantitative aspects to some project you are developing for your portfolio. See if you can get some guidance from instructors teaching courses in your major. Original charts, graphs, and images are valued in grading this assignment, but art skills are not a grading criterion. This is a Liberal Arts course, not a studio course. Your original images or graphs will be evaluated on their effectiveness in conveying quantitative information. Cite your images, even when they are your own. You can do this simply by creating a caption below the image with your name and the year.

*** Please, notify the customer about the subject you choose to write in the paper since they might need to share with you some images/screenshots according to these instructions:

“Choose a subject and project that furthers your understanding or skills in your major, or addresses your career goals. Some students will choose to complete a digital media-based project. In this case the digital product should be submitted, but still accompanied by an academic paper describing what you did and meeting all of the requirements described in the grading rubric. Alternatively, screen shots of digital work may be integrated into the text of your paper…… Quantitative literacy is often complex reasoning with simple math and graphics, involving the use of numbers in descriptions, analyses, organizing and analyzing data or works that have some quantitative component.”