SL
KC
Kindness C
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?? 😂😜)
Tutor Qualifications
I am taking abstract algebra in university right now and approaching the end of the course.
✋ ATTENDANCE POLICY
Come to each session; it will be very difficult to catch up otherwise.
Dates
November 21 - January 2
Learners
15 / 20
Total Sessions
14
About the Tutor
SL
KC
Hi! I'm Kindness (aka Enci). As of 2023-24, I'm a first-year university student with sophomore standing, and I'm majoring in pure math and minoring in computer science (I'm considering changing my minor, so if you have advice please give some). I love to share whatever I know, and when Schoolhouse offered me the opportunity, I jumped at it. In my free time, you can find me writing poems, playing the piano or violin, and scrapbooking.
View Kindness C's Profile
Upcoming Sessions
3
22
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.
29
May
OT
Session 13
Other Topics
TBD!
1
Jan
O
Session 14
Other
Just a reminder that our series won't end until we have covered finite fields, quotient rings, and all sorts of fun stuff!
Past Sessions
11
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.