Real Series

College and School of Mathematics

Math::Middle School Algebra::Grade VII::Real Numbers

From the first grade to the sixth grade, you learned so many kinds of numbers. In Grade 7, you will learn one more type of number: the Real numbers. Real numbers are all the numbers that you can do real arithmetic on.

The Real numbers are all the numbers that you've been learning in Arithmetic and Elementary Algebra. But you will have to include the negative decimals and the negative fractions because all numbers have their negative counterparts, just like positive integers have negative integers.

Solve the following questions on Real numbers.

a. 1 - 2 = ?
b. 3.04 + 5.06 = ?
c. 7 - (-8) = ?
d. 1/2 - 2/3 = ?
e. 5% + 7% = ?

John Sindayen

Math::Infinite Series::College Sophomore

A SERIES and an INFINITE SERIES is the same thing. Infinite series is just a redundant term since a series is already composed of INFINITE SEQUENCE of TERMS.

What is INFINITE? Infinite means it never ends like when you say "To infinity and beyond!"
What is a SEQUENCE? Sequence is something that comes one after another.
What is a TERM? Term means you are adding things up.

An infinite series uses the ellipsis (...) to mark that there are unnamed terms between two named terms or the terms just never ends.

The study of series is important. You cannot really add things up toward INFINITY, but you can add a sequence that is finite, in other words, a FINITE SERIES.

Now it's your turn to answer a question on finite series.
a. Find a formula to add the first 100 natural numbers from 1 to 100.

Math References:
http://mathworld.wolfram.com/Series.html
http://tutorial.math.lamar.edu/Classes/CalcII/Series_Basics.aspx

http://calculus.nipissingu.ca/tutorials/finiteseries.html

Name a TV series!

John Sindayen

C++ Inheritance

College of Information and Computer Science

Microsoft::Windows 7

Windows 7 is considered by most people to be the best Operating System in the 60 or so years since OSes were developed.

Reports in June 2016 states that Windows 7 are still used by around 50% of all users while Windows 10 by around 20% of all users.

Let's test your knowledge of Windows 7. Locate the following items in your OS.

1. Desktop
2. Taskbar
3. Navigation Pane
4. Notification Area
5. Control Panel

Microsoft References:
https://www.netmarketshare.com/operating-system-market-share.aspx?qprid=10&qpcustomd=0
http://www.thetoptens.com/best-operating-systems/
https://en.wikipedia.org/wiki/History_of_operating_systems

John Sindayen

Programming::C++

C++ supports multiple inheritance. You can use multiple inheritance in game programming. C++ is also the most used programming language to create computer games because it's fast and it's object-oriented.

Here is an example that demonstrates C++ multiple inheritance. The definitions of each class and implementations of methods are up to your imagination.

class Ninja
{
    int fight();
    int hide();
    int throw();
}

class Turtle
{
    int swim();
}

class Teenage_Mutant_Ninja_Turtle: public Ninja, public Turtle
{
}

Here's some C++ questions. Describe what the following keywords do.

1. private
2. virtual
3. public
4. friend
5. protected

C++ Reference:
https://www.quora.com/What-programming-language-is-the-most-used-to-make-video-games-Which-is-the-best

Cowabunga, dude!

John Sindayen

Politics

College and School of Arts and Sciences

Science::Physics::College Sophomore

Physics is the study of all matter. The general branches of physics along with their general descriptions are the following.

Classical Mechanics is about the movement of visible objects, including water.

Thermodynamics is about heat.

Electromagnetism is about the invisible to the naked eye objects called the entire length of the electromagnetic spectrum.

Quantum Mechanics is about the invisible to the naked eye objects called particles.

Relativity is about the comparison of two objects relative to each other.

Here's some physics questions. Give the general formula for the following.

1. Formula of Force
2. Formula of Energy
3. Formula of Work
4. Formula of Voltage
5. Formula of Pressure

Physics References:
http://www.explainthatstuff.com/electromagnetic-spectrum.html
https://en.wikipedia.org/wiki/Branches_of_physics
http://earthsky.org/space/what-is-the-electromagnetic-spectrum
https://www.quora.com/Is-electricity-an-electromagnetic-wave
http://science.howstuffworks.com/science-vs-myth/everyday-myths/what-is-relativity.htm

John Sindayen

Art::Political Science::Presidential Election

This year, 2016, is the year for the United States citizens to vote for another president to (I was going to say represent them, but it's false since there is no organization higher than the presidency) lead them.

The fact of the matter, however, is that the Electoral College is the organization that is going to vote the president. The electoral votes has precedence over the popular votes, which is the vote of the people.

In the election year of 2000, Al Gore, Bill Clinton's vice president had the most popular votes over his Republic opponent. But Al Gore did not become president because the electoral votes voted for his rival. Why? It's all political.

Political Science References:
https://www.usa.gov/election
http://www.urbandictionary.com/define.php?term=vote%20for%20pedro

Vote for Pedro!

John Sindayen

Trigonometry

College and School of Mathematics

Math::Elementary Algebra::Grade VI::Integers

Just when you think you know everything about numbers comes along negative numbers. "Negative numbers?!," you might say. How can numbers be negative?

Well, negative numbers do exist. They are part of the Integer numbers.

If you draw a number line, the right part of the line goes to positive infinity while the left part of the line goes to negative infinity. From 0 to negative infinity are the negative integers, -1, -2, -3, and so on.

Here are some integer questions. Solve the following questions.

1. Is 0 a positive integer?
2. -1 + 2 = ?
3. 3 - -4 = ?
4. 5 x -6 = ?
5. -100 + 100 = ?

John Sindayen

Math::Trigonometry::College Freshman

Trigonometry is the study of triangles and their angles. Sailors and mariners used trigonometry in the old days before computers were born, or rather invented. They take out their sextant, point to a star, then compute their location in the sea or ocean using trigonometry.

Learning trigonometry is easy, especially if you're going out to sea. But you need some basic facts about triangles and angles.

There are basically three types of triangles. There is the acute triangle, the obtuse triangle, and the most important right triangle.

There are also basically three types of angles: an acute angle, obtuse angle, and the most used one, the right angle which some people remember by being perpendicular.

Here some trig questions. Name the degrees and radians that apply to the following angles.

1. Acute
2. Right
3. Obtuse
4. Straight
5. No angle

Trigonometry Reference:
https://groups.google.com/forum/#!topic/soc.genealogy.britain/joeXUf4enag

Ship Ahoy!

John Sindayen

JavaScript

College of Information and Computer Science
Programming::JavaScript

It is hard to find a good JavaScript book that is informative and authoritative because most JavaScript books were not written by Computer Science professors. And this is mainly because JavaScript is not a programming language regularly taught in Computer Science courses. Computer Science is about C++ and sometimes Java.

Many JavaScript books in the market today can be full of errors. The probable reason for this is that authors were writing these books on the fly and without much forethought or they were written by ghostwriters.

Here is the correct way of using the JavaScript constructor Function, which is different from the JavaScript keyword function.

var a = new Function("b", "alert('Hello, ' + b + '!')");

a("John"); //calls the function.

John Sindayen

Microsoft::Excel

Microsoft Excel can be used as a database like Microsoft Access. But the main disadvantage is that you will not be able to write a query to create tables.

If your database consists only of a few records, probably less than 100, then Excel might just be able to do the job as well as Access. But if you need to create tables from your Excel database on a regular basis, writing these tables directly from the Excel file can be time consuming.

Nonetheless, Excel as a database is a good alternative to Microsoft Access.

Microsoft Reference:
http://www.pcworld.com/article/2462281/how-to-create-relational-databases-in-excel-2013.html

Excel in whatever you do!

John Sindayen

Fireworks

College and School of Arts and Sciences
Art::Psychology::Death

When famous people die, you hear about them. Here is my theory of why people die.

David Bowie, the punk rocker, and Karen Carpenter of "The Carpenters" died of natural causes.

The Prince, Michael Jackson, and Elvis Presley died from drugs.

Frank Sinatra and Bing Crosby died of old age.

And here's my theory.

People who die from natural causes have met all the goals they have established for themselves in life. People who die from drugs or like causes have no more challenges in life they want to take. People who die from old age have no more life to give in this world.

Psychology Reference:
http://www.usatoday.com/story/life/people/2016/06/03/princes-autopsy-stark-reminder-intersection-celebs-drugs-death/85318572/

John Sindayen

Science::Physics::Fireworks

Fireworks used for celebration today have their origin from China.

The Chinese invented gunpowder, the kind of stuff used in cannons. Cannons can be found in ships, like pirate ships. Those cannon balls from cannons go flying in the air because of gunpowder.

Fireworks are made using gunpowder. All those colorful fireworks were made by mixing gunpowder with different chemicals to make different colors.

Happy Independence Day!

Physics Reference:
https://en.wikipedia.org/wiki/Cannon
http://www.explainthatstuff.com/howfireworkswork.html
https://www.fireworks.com/fireworks-university/history-fireworks/

John Sindayen

Percentage

College and School of Mathematics
Math::Arithmetic::Grade V::Percentage

Percentages are special kind of numbers. They are special because when you write them in a fraction, their denominator is always 100.

The word "percent" itself gives you a clue as to what it is. Per means you have to divide it with something. And cent means one hundred.

So when you say 50%, you mean 50/100. After simplification, 50/100 becomes 1/2.

Now let's do some word problems.
1. What is 50% of 100?
2. What is 50% of 50?
3. What is 1% of 100?
4. If you cut a pizza in 8 slices, what is the percentage of each slice?
5. If you got 90% correct in a 20 questions test, how many answers did you got correct?

John Sindayen

Precalculus::Composite Function

Composite function or composition of functions is when you are working on two functions and one of them is the input of the other.

Let's say you have a function f(x) = 2x and another function g(x) = 3x.

Let's say you want to find the composite function (f * g)(x). Well (f * g)(x) = f(g(x)), which simply means that the input of the function f(x) is the output of the function g(x). In short, the input of function f(x) is the function g(x).

So now we have f(3x). Now, applying the input of function f(x), we now have f(3x) = 2(3x) = (2)(3)(x) = 6x.

Composite functions are used when something depend on another. Say, your monthly salary depends on the number of days of the month. So you have the composite function (monthlysalary * month)(days) = (monthlysalary(month(days)).

Now find the composite function of the following.
1. f(x) = 5x and g(x) = x + 1, what is (f * g)(x)?
2. f(x) = x + 1 and g(x) = 5x, what is (f * g)(x)?
3. f(x) = 5x and g(x) = x + 1, what is (g * f)(x)?

It's only math!

John Sindayen