GE141 - Course Introduction

Course Orientation

Dr Robert Batzinger
Instructor Emeritus

8/15/22

1 Introductions

Tell us about yourself

Who are you? Name, Home town, major
How do you like to be called?
What is your relationship to math?
What is your career goal?
What do you expect to be doing in 5 yrs?

1.1 Your Instructor

email: robert_b@payap.ac.th
Office: PC314 (Office hrs by appointment)

2 What Math skills do you need?

2.1 Math mistakes

1894, Indiana doctor Edward J. Goodwin announced a new way of calculating the area of circle
Taylor I. Record introduced a Bill to adopt this method being offered as a contribution to education free of cost.
The bill passed the lower house by people who trusted the presenters but could not understand the math
The State Senate never passed the bill because of international criticism $(\pi=3.2)$
However, some textbooks adopted the wrong value of $\pi$

The rotundra of the Indiana Statehouse was built around this time and has a leak that cannot be fixed.
The contractor used wrong value of $\pi$ then tried to cover the mistake by reshaping the foundation.
The rotundra is not circular causing weakness in the structure

2.2 Air Canada Flight 143

In July 1983, an Air Canada Boeing 767 flying from Ottawa to Edmonton with 69 passengers and crew had to crash-land after running out of fuel at 12,500 meters.
When the engines lost power, the airplane glided for 100 kilometers landing in Gimli, Manitoba.
Air Canada used the imperial system of measurement but was converting to the metric system, which this Boeing 767 already used.
Air Canada ground crews had used the imperial system when they refueled the airplane.
They measured the fuel in pounds instead of kilograms.
Since 1 kilogram equals 2.2 pounds, the airplane had only around half the amount of fuel it required.
The fuel gauge on the airplane was not working.

2.3 Mars Climate Orbiter

The Mars Climate Orbiter was a $125-million joint project between Lockheed Martin and NASA/JPL.
The orbiter crashed into Mars.
Lockheed Martin used the imperial measurements in the software
NASA used the metric system.
The conversion error was the cause of the crash.

2.4 Ariane 5 Rocket Explosion

On June 4, 1996, Ariane 5 rocket exploded 37 seconds after takeoff.
The accident was traced to an integer overflow error in the software used for launching the rocket.
The Ariane 5 was operating on 16-bit software capable of storing figures up to 32,767 thate had been used on Ariane 4 launches.
The Ariane 5 rocket generated data in excess of that the software limit causing the rocket to go rogue.
Ground control ordered it to self-destruct.

2.5 The Laufenberg Bridge Problem

Germany and Switzerland agreed to build a bridge over the Rhine between their cities on either side, both named Laufenburg.
Each country would started construction from their side of the river to meet in the middle.
The bridge was nearing completion in 2003, when it was discovered that one half of the bridge was higher than the other.
Germany uses the North Sea to define its sea level, while Switzerland prefers the Mediterranean sea.
There was a difference of 27 centimeters between the countries’ respective sea levels.
Althought Germany and Switzerland knew this, someone factored the disparity twice, causing one side of the bridge to be 54 centimeters higher.

3 Course Description

Fundamental mathematics and mathematics for everyday life, probability, analysis of fundamental mathematical and statistical data

3.1 Goals of this course

By the end of the course, students should be able to:

Employ fundamental mathematics and probability in various aspects for everyday life,
Analyze fundamental mathematical and statistical data
Solve application problems.

4 Lesson Plan: Part 1

Chapter 0: Introduce this course
Chapter 1: Whole Numbers
- To add and subtract whole numbers
- To multiply and divide whole numbers
- To solve applied problems involving the addition, subtraction, multiplication, and/or division of whole numbers

Chapter 2: Fractions
- To read or write fractions
- To find equivalent fractions
- To write a fraction in simplest form
- To compare fractions
- To add or subtract fractions
- To multiply or divide fractions

4.1 Lesson Plan: Part 2

Chapter 3: Decimals
1. To read or write decimals
2. To find fraction equivalent to a decimal
3. To compare decimals
4. To round decimals
5. To add and subtract decimals
6. To multiply and divide decimals
7. To solved applied problems involving decimals

MIDTERM EXAM
Chapter 4: Ratios and Rates
1. To write ratios in simplest form
2. To write rates in simplest form
3. To solve applied problems involving ratios and rates

4.2 Lesson Plan: Part 3

Chapter 5: Percents
1. To find the fraction or the decimal equivalent of a given percent
2. To find the percent equivalent of a given fraction or decimal

Chapter 6: Basic Statistics and Probability
1. To find the mean, median, and mode(s) of a set of numbers
2. To find the range of a set of numbers
3. To solve applied problems involving basic statistics
4. To calculate the probability of simple events
FINAL EXAM WEEK

4.3 Learning Outcome Assessment Plan

Class participation 10%
Quizzes 30%
Assignments 20%
Midterm exam 20%
Final exam 20%

4.4 Remark:

There is a quiz after each one or two chapters. The quizzes include review questions from previous chapters.
There is one midterm exam covering the contents of chapters 1 to 3, and one final exam covering all chapters with emphasis on the last three units.

5 Grading Criterion

Scores	Grade	Numerical value	Meaning
80 - 100	A	4.0	Excellent
75 - 79	B+	3.5	Very Good
70 - 74	B	3.0	Good
65 - 69	C+	2.5	Fairly good
60 - 64	C	2.0	Fair
55 - 59	D+	1.5	Poor
50 - 54	D	1.0	Very Poor
0 - 49	F	0	Fail

5.1 Additional notes

Students are required to attend at least 80% of the classes to be eligible for the final exam.
If students fail to take the final exam, it shall be deemed as an incomplete evaluation. (F)

5.2 Teaching and Learning Resources

Main Texts and Teaching Materials
- Akst, Geoffrey and Bragg, Sadie. 2018. Basic College Mathematics through Applications. 6th Ed. Boston: Pearson. Lynn Marecek, MaryAnne
- Anthony-Smith, and Andrea Honeycutt Mathis, 2020. Pre-algebra. Open Stax Foundation. https://openstax.org/details/books/prealgebra-2e
Free Supplementary Resources:
- https://www.interactmath.com
- https://khanacademy.org

3.Graphing Calculator: https:/desmos.com

5.3 Course LMS

https://canvas.instructure.com/enroll/ADAGBH.
https://canvas.instructure.com/register
- Join code: ADAGBH

6 Example 1: Selling Trail Mix

Volume	Ingredient	Density	Cost
2 cups	Raisins	5.6 oz / 1cup	$9 / 13 oz
2 cups	Dry Roasted Peanuts	4.2 oz / cup	$16 / 16oz
2 cups	M&M Candy	5.6 oz / 1cup	$10.99 / 38 oz
1 cup	Shelled Sunflower Seeds	4.9oz / cup	$16 / 48oz

If you make one batch of trail mix and sell it for $5.00 profit over the cost of the ingredients used, what should the price be?

6.1 Example 1 Instructions

Meet up with the others in your group
Determine what the problem is.
Create strategy for solving the problem
Calculate the answer
Choose a spokes person to explain your approach and reveal your answer

6.2 Example 1 solution

\[Price = 5 + \sum_{i=1}^4 Volume_i \times Density_i \times Unit\_cost_i\] \[\begin{eqnarray}USD &=& USD + \sum_{i=1}^4 cup \times \frac{oz}{cup}\times \frac{USD}{oz}\\ &=& USD + \sum_{i=1}^4 {\fbox{cup}} \times \frac{\fbox{oz}}{\fbox{cup}}\times \frac{USD}{\fbox{oz}}\\ &=& USD + USD = USD\\ \end{eqnarray}\]

6.3 Calculation

\[Price = 5 + \sum_{i=1}^4 Volume_i \times Density_i \times Unit\_cost_i\] \[\begin{eqnarray} =&5 &+& 2 \times \frac{5.6}{1} \times \frac{9}{13} &+& 2 \times \frac{4.2}{1} \times \frac{16}{16}\\ & \quad &+& 2 \times \frac{5.6}{1} \times \frac{10.99}{38} &+& 1 \times \frac{4.9}{1} \times \frac{16}{48}\\ = & 5 &+&\quad 7.75 + 8.20 &+& \quad 1.62 + 1.63 &= 24.20\\ \end{eqnarray} \]

6.4 Example 2

A young boy has a brother who age is 5 times older.

In a couple of years the older brother is only 4 times older.

In a couple more years, the older brother is only 3 times older.

A few more years, the older brother is 2 times older.

6.5 Working on the solution

Gather in a group and work on a method to solve the problem
Determine a strategy to determine the possible ages of the boy and his older brother.
Calculate the length of time required to make the ages differ 5,4,3, and 2 times.
Consider how many other solutions there might be.
How long before the ages appear to be the same?
Summarize your discussion.

6.6

\[\begin{eqnarray} 5x &=& y\\ 4(x+a) &=& y+a\\ 3(x+b) &=& y + b\\ 2(x+c) &=& y + c\\ \end{eqnarray}\]

\[\begin{eqnarray} 5x &=& y & & & & \\ 4x+4a &=& 5x+a &\rightarrow& 3a = x &\rightarrow& a = \frac{x}{3}\\ 3x+3b &=& 5x + b &\rightarrow& 2b = 2x &\rightarrow& b =x\\ 2x+2c &=& 5x + c & \rightarrow& c =3x & &\\ \end{eqnarray}\]

6.7 Integer Solutions

\[\begin{matrix} x & y & a & (4x) & b (3x) & c & (2x) \\ 3 & 15 & 1 & (4,16) & 3 & (6,18) & 9 & (12,24) \\ 6 & 30 & 2 & (8,32) & 6 & (12,36) & 18 & (24,48) \\ 9 & 45 & 3 & (12,48) & 9 & (18,54) & 27 & (36,72) \\ 12 & 60 & 4 & (16,64) & 12 & (24,72) & 36 & (48,96) \\ \end{matrix}\]