Course Announcements

Welcome to Week 1: Critical Thinking, Problem Solving, and Reasoning

Great Students,

Greetings to everyone.
Welcome to Module 1.

What is Critical Thinking?
Why is it important to everyone?

What is Problem Solving?
Why do you think it is important in Mathematics?
Why is teaching problem solving an important part of​ mathematics?
Describe George Polya's Four Step Problem Solving Process.
Describe the​ Understand-Solve-Explain approach to problem​ solving, giving examples of things that should be considered in each step.

What is Logic?
Explain how logic can be useful.
Logic is the study of the methods and principles of reasoning.
It can be useful in providing strong support for​ conclusions, and to help identify errors in​ reasoning, or fallacies.

What is Reasoning?
Use reasoning to solve this problem.

A magic square is a square array of numbers arranged so that the numbers in: all​ rows, all​ columns, and the two diagonals have the same sum.
Find a​ 3-by-3 magic square using the numbers 2​, 5​, 8​, 12​, 15​, 18​, 22​, 25​, and 28.



Welcome to Critical Thinking, Problem Solving, and Reasoning.

May you please:
(1.) Click the Week 1 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 1 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 2: Mathematical Logic

Great Students,

Greetings to everyone.
Welcome to Module 2.

In the previous module, we defined Logic as the study of the methods and principles of reasoning.
We briefly studied the concept of logic, reasoning, and arguments.
In this module, we shall discuss logic extensively.
Further, we shall use several methods in logic to determine whether an argument is valid or invalid.
May I introduce this topic by telling you a story? Yes, I tell stories too 😊

A family of Dad, Mom, and two children: a boy and a girl
Mom: Please go outside and observe the sky.
The two children run outside, spend some time, and come back inside.

Girl: Mom, the sky is blue.
Boy: Mom, the sky is not blue.
Girl: It is blue.
Boy: It is not blue.
Dad: Okay, let's say we do not want to get in trouble.
Let's say we want to be safe and say the truth.
Girl: Then, believe me Dad. Go ahead and take a look. It is blue.
Mom: Alright my princess, we want to accommodate what your brother said.
We want to accommodate what you said and what your brother said.
And still say the truth to be on the safe side...
Can you make a true statement in that regard?
Girl: I do not understand, Mom.
Please explain.
Dad: How do you join the two simple statements: the one you said, and the one your brother said; into one true compound statement?

Pause.
This is a question for you before you continue.
You do not want to say that the sky is blue to avoid offending the boy.
You do not want to say that the sky is not blue so you do not offend the girl.
What would you say to accommodate their statements?
Write only one statement that accommodates the girl's statement and the boy's statement without a contradiction.
Note students' responses, and advise accordingly.

You may finish reading the rest of the story.

Welcome to Mathematical Logic.

May you please:
(1.) Click the Week 2 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 2 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 3: Set Theory

Great Students,

Greetings to everyone.
Welcome to Module 3.

Recall that in the previous module:
(1.) We used logical connectives to connect simple propositions.
Just as we connect simple propositions using logical connectives, we can perform operations on sets using set operators.
Let us look at one of the comparisons of Logic and Set Theory.
The meaning of the term in Logic is applicable to the meaning of the corresponding term in Set Theory.

(2.) We determined the validity or invalidity of arguments using several methods including Euler diagrams and Venn diagrams.
In Set Theory, we shall use Venn diagrams to represent sets and set operations, and perform set calculations.

Welcome to Set Theory.

May you please:
(1.) Click the Week 3 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 3 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 4: Measurements and Units

Great Students,

Greetings to everyone.
Welcome to Module 4.

Last week, we used variables in Venn Diagrams and Formulas to do set calculations.
This week, we shall use variables in Proportional Reasoning method to solve calculations involving measurements and units.
The use of variables in the other method: Unity Fraction method is optional.

Let us do some activity.
Look around you.
Do you see any container such as containers of food, drinks, soap, paint, lotion?
Bring out a piece of paper and take note.
Look at the entire container. Do you see any measurements? units?
How many measurements (values) do you see?
How many units do you see?
Most likely, you saw at least two different measurements and two different units?

Questions for Thought: 1st Set
(1.) Which unit is the United States/Customary unit?
(2.) Which unit is the International/Metric unit?
(3.) Why are there at least two different measurements and two different units?
(Hint: If an American company that produces food in containers wants to sell them in Mexico, is it not appropriate for the company to use the unit that Mexico uses for the measurement of food?
Similarly, If a Mexican company that produces food in containers wants to sell them in America, is it not appropriate for the company to use the unit that America uses for the measurement of food?)
(4.) Is it possible to have errors in measurements?
What are the errors in measurements?
If two or more people measure the length of a desk, would they obtain the same measurement to the: nearest integer, tenth, hundredth, ..., unit?
...and so on and so forth.

Questions for Thought: 2nd Set
(1.) Are you familiar with the unit: meter (m)?
(2.) What quantity is measured in meters?
(3.) Are you familiar with the unit: square meter (m²)?
(4.) What quantity is measured in square meters?
(5.) Are you familiar with the unit: cubic meter (m³)?
(6.) What quantity is measured in cubic meters?
(7.) Which of these quantities and units is a linear measure?
(8.) Which of these quantities and units is a quadratic (square) measure?
(9.) Which of these quantities and units is a cubic measure?

Welcome to Measurements and Units.

May you please:
(1.) Click the Week 4 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 4 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 5: Fractions, Decimals, and Percents

Great Students,

Greetings to everyone.
Welcome to Module 5.

We discussed the topic of Measurements and Units in the previous module.
The measurements are the values. They are numbers.
In this module, we shall study some forms of numbers: fractions, decimals, and percents.
For this announcement, let us focus on fractions.

Why do we have fractions?
Why do we need fractions?
Why do we study fractions?
Let us review some scenarios where we have used fractions.

Scenario 1
Pizzaiolo: How do you want your pizza after I finish making it: round-cut or square-cut?
Client: There's five of us. So, please divide it into 5 parts either way.

$ \dfrac{part}{whole} = \dfrac{1}{5} \\[5ex] $ This implies that each person gets a part.

Scenario 2
The United States comprises 50 states.
48 states are conterminous states.
49 states are continental states.
(Source: USGS: What constitutes the United States? What are the official definitions? )
This implies that 48 out of the 50 states are conterminous (contiguous) states while 49 states out of the 50 states are continental states.
This implies that:
(a.) The fraction of the U.S states that are conterminous are:

$ \dfrac{part}{whole} = \dfrac{48}{50} = \dfrac{24}{25} \\[5ex] $ (b.) The fraction of the U.S states that are continental are:

$ \dfrac{part}{whole} = \dfrac{49}{50} \\[5ex] $ Scenario 3
Nine out of 10 Nigerians say at least “some” public officials are corrupt.
(Source: Afrobarometer Dispatch No. 187: Page 2: Corruption in Nigeria)

$ \dfrac{part}{whole} = \dfrac{9}{10} \\[5ex] $ ...among many other examples/scenarios.

Welcome to Fractions, Decimals, and Percents.

May you please:
(1.) Click the Week 5 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 5 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 6: Index Numbers

Great Students,

Greetings to everyone.
Welcome to Module 6.

Last week, we discussed forms of numbers: Fractions, Decimals, and Percents.
We converted one number from one form to another form.
This week, we shall discuss a number: Index Number, which is a ratio (fraction), typically expressed as a decimal, but can also be expressed as a percent.
An index number provides a simple way to compare measurements made at different times or in different places.

(1.) Why is the cost of college so high when politicians spend millions of dollars attacking one another with political ads?
Those dollars could be put to good use to fund education/tuition and fees for students.
Hey Dad, how much did it cost you to get your first degree?
Can you imagine what it costs now?
Compare: Average cost to get a four-year degree in 2023 than in 1993 (30 years ago).
Comparing the same quantity at different times.

(2.) As at:
01/30/23, the average price of a gallon of gas in the U.S was $3.489
02/06/23, the average price of a gallon of gas in the U.S was $3.444
02/13/23, the average price of a gallon of gas in the U.S was $3.390
Source: (Gasoline and Diesel Fuel Update by U.S Energy Information Administration)

Compare: Average cost of a gallon of gasoline per week (Weekly average gas prices) in the U.S.
Comparing the same quantity at different times.

(3.) How much does a K12 Teacher make in the United States?
The average K12 Teacher salary in the United States is $58,547 as of January 26, 2023, but the salary range typically falls between $48,895 and $71,398.
(Source: K12 Teacher Salary in the United States https://www.salary.com/research/salary/posting/k12-teacher-salary by salary.com)
How does the salary vary by state?
Compare: K12 Teacher Salary by State in 2023
Comparing the same quantity at different places.
...among other comparisons.

Welcome to Index Numbers.

May you please:
(1.) Click the Week 6 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 6 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 7: The Mathematics of Finance: Part I

Great Students,

Greetings to everyone.
Welcome to Module 7.

Let us begin with this classroom discussion.
Classroom Discussion
For Educational Purposes only (I do not teach any religion in the classroom):
Psalm 15:5 (Christians) and Quran 2:276 (Muslims) and Torah: Exodus 22:25 (Jews) talks against lending money with interest.
So, why do we charge interest on money borrowed?
Why do we lend money with interest?

Teacher: Why would an individual or the financial institution charge the extra money (interest) on the loans they give to an individual or business?
Student: Because they traded with your money.
Teacher: Partly, yes. But not fully.
Student: Why not fully?
What are the other reasons?
Teacher: Assume someone, say your friend asks you to lend him some money.
Assume you wanted to use that money to purchase land.
But you realize that your friend's need for your money is probably a higher priority
You decide to lend him the money if he promises to pay back within a month
This is because you really wanted to purchase that land because it was listed for a reasonable price you could afford
Your friend did not pay back the money in a month.
Did not pay back in two, three, four, five, ..., ten months.
He pays you back the money in a year
You found out that the land you wanted to purchase has appreciated in value, and hence was listed at a higher price
Would you be happy if your friend pays you the exact amount he borrowed from you?
Student: Not really.
Teacher: Why?
Student: Because I can no longer purchase the land for the amount I loaned him...due to Inflation.
We just covered the topic of Index Numbers...remember?
Rarely have we had deflation. It's always been inflation and the inflation rate has been increasing for the most part.
Teacher: Makes sense.
But, what if you could still purchase the land for that amount or for a lesser amount?

As you can see, we have made the connection of last week's topic: Index Numbers to an concept of this week's topics: Interest.
Specifically, we shall discuss:
Finance Literacy
Simple Interest
Compound Interest
Continuous Compound Interest
Annual Percentage Yield (APY)

Welcome to The Mathematics of Finance: Part I.

May you please:
(1.) Click the Week 7 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 7 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 8: The Mathematics of Finance: Part II

Great Students,

Greetings to everyone.
Welcome to Module 8.

This week, we shall continue our study on the Mathematics of Finance that we started last week.
Specifically, we shall discuss:
Investments for Retirement
Ordinary Annuity
Amortization
Income Taxes

Welcome to The Mathematics of Finance: Part II.

May you please:
(1.) Click the Week 8 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 8 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 9: Introductory Statistics

Great Students,

Greetings to everyone.
Welcome to Module 9.

For the past two weeks, we discussed a branch of Mathematics known as the Mathematics of Finance, also known as Financial Mathematics.
This week, we shall begin another branch of Mathematics known as Statistics.
Let us begin with Introductory Statistics.

Questions for Thought:
(1.) Did you register for this course?
( Of course...Mr. C, what kind of question is that?
How did I have access to the Canvas course if I did not register for it? )
Are you familiar with any of these?
Name:
Date of Birth:
Age:
Address:
...among others
All of the information you submitted when you enrolled in BRCC or any other academic institution is known as Data.
You provided these data to BRCC.
Have you ever wondered: what does BRCC do with these data?

(2.) Some of you are on social media platforms: YouTube, Facebook, Twitter, TikTok, Instagram, Snapchat among others.
You gave these platforms your data when you registered for their services.
Have you asked yourself: what do these platforms do with my data?

(3.) In your daily conversation/interaction/communication with people, have you discussed: race, gender, color, age, religion, temperature, height, weight, number of people, number of something, etc.? You have discussed data.

Statistics is all about data:
Data Collection: How do you collect data?
Data Organization: What do you do with the raw data? Is it not better to organize it before you use it?
Data Presentation: What are the several tools to present this data so that it is meaningful?
Data Analysis: How do we analyze this data? What evidence/information/results can we get by analyzing the data? How do we use the results of the analysis?
Data Interpretation: After analyzing the data, do we need to use our results to make the right decision and the right conclusion?

Welcome to Introductory Statistics.

May you please:
(1.) Click the Week 9 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 9 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 10: Correlation and Regression

Great Students,

Greetings to everyone.
Welcome to Module 10.

In Module 9, we began our study on Introductory Statistics.
After collecting the data, we organize the data in classes.
After organizing the data, we use several data presentation tools to present the data.
Statistics has several data presentation tools including: line graph, bar chart (bar graph), Pareto chart, pie chart (circle graph), histogram, pictogram (pictograph), dotplot, stem-and-leaf plot (stemplot), box-and-whisker plot (boxplot) and scatter plot (scatter diagram) among others.
Given that we have different types of variables and data sets, what tool is best suited for representing a specific data?
What are the merits and demerits of using each tool?

We shall extend our discussion in this module by using one of the tools (scatter diagram) to show the relationship between two variables.
A relationship between two variables implies that there is an association between the two variables.

Do you agree or disagree?
It is okay to disagree. You just have to support your disagreement with facts. 😊

That association may or may not be causal.
So, we note these terms: relationship, association, causation
For example:
Old Age and Osteoarthritis
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2818253/
Osteoarthritis is a multi-factorial condition for which aging is the major risk factor. (Anderson, A.S., & Loeser, R.F.; 2010, February)
Arthritis is associated with old age.
However, does old age cause arthritis?

This leads us to the topic of Correlation and Regression, which is not covered entirely in this course.
However, some courses in Statistics and Psychology discuss it in detail.

Welcome to Correlation and Regression.

May you please:
(1.) Click the Week 10 module.
(2.) Review the Overview and Objectives.
(3.) Review the Readings/Assessments.
(4.) Complete the assessments initially due this week.
(5.) Participate in the Week 10 Discussion.
(6.) Attend the Live Sessions/Student Engagement Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success