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Ralsei Learns You Some Things
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Posted: Mon, 20/09/2021 12:58 (3 Years ago)
Ralsei here, second year college student reporting for duty. Welcome to an idea I had for studying! This is a forum thread where I share/teach things that I learn in my classes or otherwise at college with you all! It will function sort of like a blog with the added bonuses of you learning cool things for free and me studying my topics.
First, a couple of classroom rules.
1. Please, PLEASE feel free to ask me questions! This will help me (and others!) further learn about the topics I'm presenting!
2. Please feel free to correct me if I get anything wrong! If you do it in an entitled or rude way, however, I might not receive it super well, so please be patient and kind.
3. Please feel free to request topics for me to cover! I would love to dig into something you're curious about or help you understand a subject in class!
4. Finally, while I welcome interaction, please don't spam the thread. This means repeatedly posting unrelated things.
Here are the classes/subjects/skills I'm familiar with or have taken in high school or later so that you have a general idea of what my experience/lack of experience is!
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Key:
Italicized - Currently taking
* - Have not taken recently but know well
** - Have not taken recently but know somewhat
Math
- Transition to Higher Mathematics
- Calculus I
- Pre-Calculus/Trigonometry
- Geometry
- Algebra II
- *Algebra I
- *Pre-Algebra
English
- Nobel Literature
- Creative Writing
- AP English (Lit)
- Worldviews
- American Literature
- *Movies as Literature
- Essay Writing
- Research Papers
- Formatting (MLA/APA)
Science
- Intro to Psychology
- Intro to Programming
- Computers I
- Physics
- Anatomy & Physiology
- Biology
- Chemistry
- **Geology
- **Astronomy
Theatre
- Intro to Theatre
- Technical Theatre
- Internship (Summer Camp)
Theology
- New Testament Studies
History
- Historical Perspectives
- AP World History
- US History I
- US History II
- *World History
- **NJ History
Other
- Mandarin I
- Human Learning and Development
- **French I
- **Latin I
- *Cake Decorating
- Western Culture
- Art I
- Clarinet (~7 years)
- *Recorder
- *Orchestra
- *Band
- Choir
- Swing Dancing
I will try to post at least once a week, but you might see a surge/lack of posts around exam times/break times, haha! Thanks for tuning in! Don't worry, I won't be taking attendance ;)
List of Covered Topics
Posted: Mon, 18/10/2021 12:57 (3 Years ago)
Welcome to the first class, woohoo! Today I will be learning you some math! The topic: Sets!
Sets are an important thing to understand in order to begin learning about why math does what it does and how math does what it does. It's a great way to express certain mathematical processes (for example, functions or relations like < or >) in a looser, easier to work with manner.
So, what is a set? In simple terms, a set is a collection of things, and an element of a set is a thing in that set. To write out a set, we use the fun { squiggly brackets to act like parentheses around the elements of the set. Here's a set for you:
A = {1, 2, 3}
This is the set A, and it has the elements 1, 2, and 3. Here's another set:
B = {a, b, c}
This set, B, has elements a, b, c. And here's a third set:
C = {97, rubber duck, %}
Yes, this is a set! A set doesn't need to have only numbers or letters as elements, nor do its elements have to be in any way related to each other (although in math, they usually are).
There is one important rule when working with sets that will help you identify whether something is or is not a set. See if you can guess which of these three is not a set:
D = {4, 76, 12, 8}
E = {2, 24, 2, 19}
F = {4, 8, 12, 76}
Which one do you think isn't a set? Well, it turns out that E is not a set. How come? Notice that in E, the element 2 appears twice. Sets are not allowed to repeat elements; that is, you cannot have two of the same element in one set.
Pretty fun, right? We can even have sets with sets as elements. For example,
G = {1, {2, 3}, {4}}
What are the elements of G? They are 1, {2,3} and {4}! Is 4 an element of G? Nope! {4} is not the same thing as 4. Take care when writing sets within sets and when using symbols within sets; remember, sets can have anything as an element! For example,
H = {odd integers, even integers}
I = {1, 2, 3, 4, 5...}
We use ellipses (...) within a set to indicate that it goes on forever. Two sets are equal if they have the exact same elements. Are H and I equal sets? Well, even though set I contains the odd integers and the even integers, the two sets aren't equal because the elements of H are "odd integers" and "even integers", not the numbers themselves.
One last thing about sets: how do we count the number of elements in a set? The number of elements in a set is called its cardinality, and is written like absolute value, for example |A|.
J = {1, 3, 5, 7, 9}
So, |J| or the cardinality of J is 5, because there are five elements in the set.
I hope this made sense and was easy to understand! Stay tuned for some more cool math things (and many more cool other things!)
- Rals