A Deep Dive into Mathematics
SAT Score Range
•
9 sessions
•
BH
OL
MU
+7
This series ended on June 17, 2023. All 1:1 and group chats related to this series are disabled 7 days after the last session.
About
This series will be a dive into the fundamentals of algebra, where they come from and why we should care.
This is NOT a typical class, and should not be considered a replacement for an actual course in Algebra I! While we will cover some of the main topics and learn how to deal with them, this series will focus more on the WHY rather than the HOW.
As such, this will be a more interactive series where you are expected to have some knowledge of Algebra I. We may solve problems, but we will dedicate more time to discussing and debating the methods we use and why we use them in the first place. So while previous knowledge is not required, it will make following along much easier.
The complete series will cover more than just Algebra I, and the plan is to work all the way up to Calculus! But we will take quite some time to get there, so let's start simple.
Tutored by
Schedule
✋ ATTENDANCE POLICY
Since this is not a typical class, I won't mind if you skip any sessions. Although, I still would greatly appreciate it if you did the effort to attend as many sessions as you can!
SESSION 1
15
Apr
SESSION 1
Orientation
Orientation
Sat 5:00 PM - 6:00 PM UTCApr 15, 5:00 PM - 6:00 PM UTC
For this first session, we will cover a basic orientation of how the series will be structured and what to expect. After that, we will spend some time setting up and debating some questions about Algebra that will lay the foundations for the rest of the series. We will also talk about some of the history behind Algebra and why some things are the way they are (Examples: Where do all the letters come from? Why write equations? Who decided we would do math like this?)
SESSION 2
23
Apr
SESSION 2
Solving equations & inequalities
Solving equations & inequalities
Sun 5:00 PM - 6:00 PM UTCApr 23, 5:00 PM - 6:00 PM UTC
In the last session, we briefly talked about the place of variables and unknowns in Algebra. However, we didn't really talk about how to use them, just the why.
Today, we will talk about how to utilize these unknowns to solve equations and inequalities, and why they are important in the real world. We WILL solve some problems, unlike the first week, but it'll be mostly to understand the why rather to gain proficiency in these kinds of exercises.
SESSION 3
29
Apr
SESSION 3
Working with units
Working with units
Sat 5:00 PM - 6:00 PM UTCApr 29, 5:00 PM - 6:00 PM UTC
One of the main concepts in all math is the idea of abstraction. As we've discussed before, most of math is "made up", in the sense that we don't find many of the concepts in math anywhere in the real world. However, we still use math to describe reality, so we need something to link the two.
This is where units come in! Units are the system we came up with to relate numbers with real-life quantities. We will talk about where they come from, how the two most known systems (metric and imperial) came to be, and how to work with them.
SESSION 4
13
May
SESSION 4
Linear equations & graphs
Linear equations & graphs
Sat 5:00 PM - 6:00 PM UTCMay 13, 5:00 PM - 6:00 PM UTC
In previous sessions, we talked about unknowns and equations. Now, we will extend that idea into a more general form, introducing the notion of a graph and of linear equations with more than one unknown.
Once again, we will do some exercises, but most of our session time will be dedicated to talking about why we decided to come up with the idea of a linear equation and the idea of a graph, as well as how they can be useful in understanding these topics.
SESSION 5
20
May
SESSION 5
Systems of equations
Systems of equations
Sat 5:00 PM - 6:00 PM UTCMay 20, 5:00 PM - 6:00 PM UTC
Previously, we talked about linear equations. However, we saw that unlike regular equations, these don't have a single solution, at least not that we could find. Now, we will introduce the idea of systems of equations and find out how to make these linear equations have single solutions.
As always, we will talk about the why behind everything, as well as look into ways to better understand and deal with these concepts.
SESSION 6
27
May
SESSION 6
Inequalities (systems & graphs)
Inequalities (systems & graphs)
Sat 5:00 PM - 6:00 PM UTCMay 27, 5:00 PM - 6:00 PM UTC
We briefly touched on inequalities previously, but now we will dedicate more time to them, and apply the reasoning we have been seeing in our previous sessions in order to understand graphs and systems of linear inequalities.
SESSION 7
3
Jun
SESSION 7
Functions
Functions
Sat 5:00 PM - 6:00 PM UTCJun 3, 5:00 PM - 6:00 PM UTC
Equations and inequalities are all over mathematics. However, there is another concept found in math that you will see almost everywhere, one that you must get familiar with if you want to succeed on future math courses. The function.
We will see what a function is, how to understand its components, why such a concept was invented, and how it turns out to be useful even outside of mathematics.
SESSION 8
10
Jun
SESSION 8
Absolute value & piecewise functions
Absolute value & piecewise functions
Sat 5:00 PM - 6:00 PM UTCJun 10, 5:00 PM - 6:00 PM UTC
As we saw previously, functions are a kind of relationship that does not have to be expressed as an equation. Today, we will introduce one way in which functions can be defined that does not follow the pattern of everything we've seen up to this point: Piece-wise functions.
These may seem complicated at first glance, but we will go through all of their components, and even start with a simple function (the absolute value function) to comprehend why we should care.
SESSION 9
17
Jun
SESSION 9
Exponents & radicals
Exponents & radicals
Sat 5:00 PM - 6:00 PM UTCJun 17, 5:00 PM - 6:00 PM UTC
Today, we will introduce a new kind of operation that is essential to all sorts of math you'll see in the future: Exponents! (And by extension, radicals.)
In a nutshell, we can represent addition as repeated identity, and multiplication as repeated addition. Exponents are simply the next level in this chain; they're repeated multiplication! (There's more to it, but we'll discuss that in the session).
Unrelated, but this will actually be our last session for a while! I would like to continue, but will need to take a break due to outside circumstances. I don't know when I'll be available again, but I will be sure to let you know so we can finish up the last concepts in Algebra I!