GL
KC
Kindness C
Enrollment for this series has closed.
Series Details
About
We'll take a brief look at one of the first courses you will take in university if you would like to become a math major. We will begin with the fundamentals—learning some basic set theory, working with complex numbers, and setting the definitions of rings and fields. Then we'll prove some intuitive things that we know about number theory and modular arithmetic (i.e. working with remainders). From there we will generalize our methods to other areas, such as doing "number theory" and "modular arithmetic" with polynomials and much more!
No calculus knowledge is necessary for this series; however, high-school Algebra 1 and Algebra 2 are necessary.
BTW do you know that this series would be called "Algebra 1" in university?? 😂😜
(Note: This series has been recently restarted, so if you're looking to join us, you are still in a good position to do so!)
Tutor Qualifications
I am a math major really passionate about all things algebra!
✋ ATTENDANCE POLICY
Come to each session; it will be very difficult to catch up otherwise.
Dates
November 21 - January 2
Learners
24 / 30
Total Sessions
25
About the Tutor
GL
KC
Hi! I'm Kindness (aka Enci). As of 2024-25, I'm a junior year university student majoring in pure math! I graduated high school as part of the Class of 2023, and thanks to APs I skipped the freshman year of university. On Schoolhouse, I especially like to tutor in Enrichment as a study space host and advanced math tutor. I used to be quite active in tutoring the SAT, and I hope to return to doing that soon! In my free time (which I don't have much, lol), you can find me writing poems, playing the piano or violin, and scrapbooking.
View Kindness C's Profile
Upcoming Sessions
1
1
Jan
O
Session 25
Other
Just a reminder that our series won't end until we have covered finite fields, quotient rings, Lagrange's theorem, and all sorts of fun stuff!
Past Sessions
24
21
Nov
O
Session 1
Orientation
We'll introduce ourselves and dive into unions and intersections of sets. We'll prove a couple of results regarding sets and talk about proof techniques in general.
22
Nov
EM
Session 2
Even More Math
We'll talk about functions from one set to another. We'll distinguish between injective (one-to-on), surjective (onto) and bijective (both injective and surjective) functions.
EM
Session 3
Even More Math
We'll discuss function composition and inverses and talk about cardinality of sets. We'll introduce the Cantor-Bernstein theorem (my favorite theorem regarding this topic).
24
Nov
R
Session 4
Review
Review day! Any questions welcome :) I have some problems prepared!
27
Nov
EM
Session 5
Even More Math
We'll discuss the Cantor-Bernstein Theorem and prove some cool side results (e.g. proving that the "number" of rational numbers and the "number" of natural numbers are the same, but there are "more" real numbers than there are natural numbers).
28
Nov
EM
Session 6
Even More Math
We'll define an equivalence relation and make a quick run through complex numbers. If time permits, we'll introduce the definition of rings. (Session date TBD)
11
Dec
EM
Session 7
Even More Math
We'll look at some basic results of rings and look at some examples. We'll also define a field and look at some examples. (Session date TBD)
21
Dec
OT
Session 8
Other Topics
We will finish our short introduction to rings and fields (we'll talk about them a lot more later). Then we switch gears to the topic of basic number theory! This will be the springboard of more complicated stuff in the future. We'll begin the topic with divisibility and Bézout's lemma. If there is anything you should carry away from this session, be sure to carry away the logic of the proof for Bézout's lemma.
22
Dec
OT
Session 9
Other Topics
We will learn the Euclidean algorithm for finding greatest common factors and begin our discussion of prime numbers.
23
Dec
OT
Session 10
Other Topics
We will prove the Fundamental Theorem of Arithmetic and the infinitude of primes. (Credit given to Euclid!)
1
May
OT
Session 11
Other Topics
After a long break, we're ready to come back for some more algebra! Today's session is mainly a review of what we've looked at before the series wes suspended.
29
May
OT
Session 12
Other Topics
If we finish reviewing everything in our last session, we'll start looking at congruence relations as a very important example of equivalence relations. We'll also define cosets and get familiar with them. The next several sessions will all be centered around this topic.
5
Jun
OT
Session 13
Other Topics
Equivalence relations will be the big topic today. If there is time, we will do the definition of rings and fields as well.
12
Jun
OT
Session 14
Other Topics
Continuing the discussion about rings and fields. We'll prove some straightforward facts about them.
19
Jun
OT
Session 15
Other Topics
It's time to move on to some basic number theory, which will provide the motivation for a lot of more abstract work that we will do later. We will define divisibility and prove Bézout's lemma. Be sure to carry the proof of Bézout's lemma away!
26
Jun
OT
Session 16
Other Topics
We will introduce and prove the Euclidean algorithm for finding the greatest common factor. Perhaps we'll also introduce prime numbers.
3
Jul
OT
Session 17
Other Topics
We will prove the Fundamental Theorem of Arithmetic and the infinitude of primes.
10
Jul
OT
Session 18
Other Topics
Shift gears! We will proceed with introducing the set of rings Z/nZ (i.e. modular arithmetic) and discuss when this weird thing is a field.
17
Jul
OT
Session 19
Other Topics
TBD!
24
Jul
EM
Session 20
Even More Math
Whatever we get to!
7
Aug
EM
Session 21
Even More Math
Whatever we get to!
14
Aug
EM
Session 22
Even More Math
Whatever we get to!
28
Aug
EM
Session 23
Even More Math
I hope to cover the proof of Bezout's lemma today!
4
Sep
EM
Session 24
Even More Math
Wherever we get to—most likely basic properties of prime numbers.