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MAT133: Calculus and Linear Algebra for Commerce

Project #4 – 2021

Instructions Booklet

Introduction

This project is based on course content discussed in Modules L - M. There are three main pieces to it: the individual problems, the pod project, and the reflective questions. This document outlines the instructions for accessing and submitting each part.

Each part of the project is to be submitted on gradescope.ca. You should have received an invite to log into Gradescope to your official UofT email address; please use the link contained within in this invite to log in for the first time. Do not submit from a non-UofT email address. Note that you may re-submit or change your submission as many times as you like before the submission deadline. No late submissions will be accepted.

Caution: Please be sure to always use gradescope.ca for this class and not gradescope.com. If you type “gradescope” into Google, the first result will be gradescope.com and not gradescope.ca.

You will also create a presentation based on your pod project. Instructions for the presentation will be posted in a separate document.

1 Individual Submission

As part of your first submission, you’ll need to include an academic integrity statement along with your own solutions to the individual problems.

1.1 The Code and the OK List

UofT upholds high standards of academic integrity. It is your responsibility to read and understand the Code of Behaviour on Academic Matters and to adhere to the list of “OK” resources below.

The OK List

This OK list is a closed list of allowed resources, not just a list of examples. If you are unsure of what you are allowed to use, do not hesitate to ask on Piazza.

OK: Collaboration with other members of your pod and hive – this is encouraged for all parts of this project and required for the Pod Project portion.

OK: Anything that can be found on the MAT133 Quercus page

OK: Your own and your hive member’s previous MAT133 work, including any projects, tests, or homework

OK: Your own and your hive members’ notes from this course and your other courses

OK: Any other textbook (online or physical) you have access to

OK: Online learning videos (e.g. Khan Academy)

OK: Data sources including, but not limited to, those listed in Appendix A

OK: General advice on the MAT133 Piazza page (e.g. “Can someone please help me understand RREF?”)

OK: wolframalpha.com, desmos.com, any calculator

OK: Anything else declared as OK in a written announcement by the course coordinator

Examples of Not OK Things

Here are some examples of things that are not OK. These are just examples. Unless something is on the OK list, it is not OK.

NO: Communicating about the project with anyone not in your hive. This means, for example, that you must not use group chats to share project content if these group chats involve anyone who is not in your hive.

NO: Asking for answers on Piazza (e.g. “how do you solve Question 2...”)

NO: Accessing or posting on so-called “tutoring websites” like chegg.com or Easy 4.0

NO: Using online forums like stackexchange

NO: Entering the question text into a search engine

An important note on group chats: If you have administration privileges for any online chat that involves anyone not on your team and in which assignment content is shared, you must delete any non-authorized content from that group chat as soon as you see it (if this is technologically possible on that platform). Otherwise, you are considered to have helped someone cheat and therefore committed an academic offence.

1.2 Your Statement

As part of your individual project submission, you’ll include an abbreviated statement to Gradescope that implies the following.

In submitting this assessment ...	In short
... I confirm that my conduct during this take-home exam adheres   to the Code of Behaviour on Academic Matters.	I know the Code.
... I confirm that I have not acted in such a way that would consti-   tute cheating, misrepresentation, or unfairness, including but not   limited to, using unauthorized aids and assistance, impersonating   another person, and committing plagiarism.	I didn’t cheat.
... I confirm that the work I am submitting in my name is my   own work. The work submitted for the pod project is the work of   myself and my pod.	This is my work.
... I confirm that I have only used the aids marked as approved   in the “OK List”.	I only used “OK” aids.

On the front page of your individual submission, you’ll be asked handwrite and sign the abbreviated academic integrity statement, as follows:

“I have read the project instructions. I know the Code. I didn’t cheat. This is my work. I only used “OK” aids. I pledge upon my honour that I have not violated the Code during this assessment.”

Include your student ID number, the date, and your signature at the bottom. Here is an example:

1.3 Submission Instructions

The individual problems are to be completed by each student individually. You are allowed and encouraged to discuss these problems with other members of your hive, but you must write your own solution for submission.

Please note the following general policies for the individual problems:

• You must handwrite directly into the problem template, using either a tablet or printer and scanner, just as you did for the written parts of the tests. You should see the boxes in your submission roughly line up with the boxes the template when you submit to Gradescope.

• Your solutions should written clearly and concisely in a linear fashion. Do not submit messy scrapwork.

• Explain all your steps. Your solution should be easy to understand by any other student in the class.

• When applicable, please state your final answer in the form of a sentence, including units.

The individual problems will be accessed and submitted on gradescope.ca. (They will be posted shortly.)

2 Pod Project: Measuring Inequality

Collaboration Instructions: This part of the project is to be completed in your pods. You should collaborate as a group on all parts of this project and you may organize the work however you’d like. However, for the first three parts we recommend everyone work through the calculations together, then designating one person (as usual) to be primarily responsible for the write-up on each part.

• If your pod has 3 members, then you may assign one member to write up each of parts (a), (b) and (c).

• If your pod has 4 members, then we recommend that two pod members work as a pair on writing up (a), while one person writes up (b) and another writes up (c).

• In either case, all pod members should be involved in part (d). Please work together and split up the writing as you see fit.

Important: Please be sure to also add all contributing pod members’ names to your Gradescope submission.

2.1 Description of Project Tasks

(a) Computing Gini Coefficients: Your pod will need to choose a country to study. Each pod must choose one country that is different from the countries chosen by other pods in their hive. You should start your report with a brief paragraph describing the country and explaining why your pod chose it to study.

In the Quercus module for Project 4, you’ll find income distribution data for each of the above countries. This data is taken from the World Inequality Database. The data set represents the Lorenz curve for your country by year. For each percentage x, the data set shows what percentage of the total country’s income is earned by the lowest-earning x% of the population.

Your pod’s task (a) is to estimate the Gini coefficient for your pod’s chosen country for four years: 1990, 2000, 2010 and 2020. (Hint: Use the definition that you found in the individual part of the project. Your definition should involve an integral. You should be calculating a Riemann sum to approximate this integral, in Excel. Ask for help if you’re not sure about your definition of the Gini coefficient.)

After your pod has finished their calculations, you should include a “snippet” of the first 10 rows and last 10 rows of your spreadsheet in your report to show your calculations. You should include any new calculated columns used in the calculation. Explain your calculations by showing in full detail how you calculated the Gini coefficient for 2020. Include a figure to supplement your explanation.

To summarize:

• Download the data set from Quercus.

• Each pod should choose a country to study and write a brief paragraph describing the country and explaining why your pod chose it to study.

• In the “Country info” tab in the data set, find the two-letter country code for your country.

• In the “Pivot” tab in the data set, enter your two-letter country code into cell B2. (If successful, the name of your country should appear in C2.)

• Copy the data for each year that you’re calculating the Gini coefficient into a new spreadsheet.

• In your report, include a snippet of your spreadsheet (first and last 10 rows) and a brief explanation your calculations in plain English so that the reader can understand how you calculated your Gini coefficients. Include a figure to supplement your explanation.

(b) Graphing the Gini Coefficient as a Function of Time: Extend the work your pod started in part (a) by calculating the Gini coefficient for more years (of your choice). Use your extended data set to create a graph of your country’s Gini coefficient as a function of time. Be sure that your graph is well-labelled. Write a short paragraph to interpret and discuss your results.

(c) Comparing Lorenz curves: While the Gini coefficient provides a useful summary of how inequality has changed in your country over time, it does not show the complete picture. Use your data from (a) to graph your country’s Lorenz curves for each of the four years. Be sure that your graphs are well-labelled. Write a short paragraph comparing the four graphs and interpreting your results.

(d) Explore Inequality Further: The Gini coefficient is a common measure of inequality, used around the world. In your pod, discuss with each other what countries and/or times you might be interested in finding the Gini coefficient for and why. (For example, are you interested in seeing whether the Gini coefficient has been increasing or decreasing in a certain country? Are you interested about comparing the Gini coefficients among certain countries? Why?) Then search the internet to see if you can find some interesting graphs or other data visualizations involving the Gini coefficient. (You may consider checking the OECD or World Bank websites as a start, but you are not limited to these sources.) Choose at least one graph or data visualization(s) that you find interesting.

In the report, include the following for Part (d):

• Screenshot(s) of the graph(s) or other data visualization(s) involving Gini coefficients that you found interesting;

• Cite the source(s), including links where applicable;

• Paragraphs explaining the following:

– the reason(s) why you are interested in the graph/visualization(s);

– what you learned from the graph/visualization(s);

– one aspect of the graph/visualisation(s) that helps to effectively communicate its results graphically;

– at least one further question that you’d like to investigate further after looking at this graph/visualization.

2.2 Presentation Instructions

In your presentation, please present your graphs/visualizations from part b, c, and d, as well as your discussion and further questions.

2.3 Report Instructions

• Please include a cover page that lists the names, student IDs and UofT email addresses of all group members.

• Be sure to include ALL pod members on your submission in Gradescope. All group members that appear on the cover page must appear in Gradescope. Penalties may apply to pods who do not follow these instructions.

• As usual, your submission must be in the form of a single pdf.

• IMPORTANT: Please make sure to pay special attention to your pod’s writing to ensure its quality and clarity. This includes integration of mathematics and figures into your paragraphs, ensuring all figures and graphs are well-labelled, and being mindful of the overall appearance of your submission.

3 Reflection Questions

These questions are generally intended to be a space for you to reflect on your experiences as a student and to give us feedback about the course. Your answers should typically be about 50-100 words long. There are no right or wrong answers. You are marked mainly on whether you put forth effort to address the questions posed and the length of your answer.

These will be submitted directly to Gradescope.