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Abstract Algebra Crash Course

SAT Score Range

•

24 sessions

•

+21

This series was cancelled by the tutor on January 1, 2025. We're very sorry–you can explore more Enrichment series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.

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!)

Tutored by

Kindness C 🇨🇦

Certified in 17 topics

View Profile

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.

Schedule

✋ ATTENDANCE POLICY

Come to each session; it will be very difficult to catch up otherwise.

SESSION 1

21

Nov

SESSION 1

Orientation

Orientation

Tue 1:00 AM - 1:30 AM UTCNov 21, 1:00 AM - 1:30 AM UTC

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.
SESSION 2

22

Nov

SESSION 2

Even More Math

Even More Math

Wed 12:00 AM - 12:30 AM UTCNov 22, 12:00 AM - 12:30 AM UTC

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.
SESSION 3

22

Nov

SESSION 3

Even More Math

Even More Math

Wed 11:00 PM - 11:50 PM UTCNov 22, 11:00 PM - 11:50 PM UTC

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).
SESSION 4

24

Nov

SESSION 4

Review

Review

Fri 11:00 PM - 11:50 PM UTCNov 24, 11:00 PM - 11:50 PM UTC

Review day! Any questions welcome :) I have some problems prepared!
SESSION 5

27

Nov

SESSION 5

Even More Math

Even More Math

Mon 11:00 PM - 11:50 PM UTCNov 27, 11:00 PM - 11:50 PM UTC

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).
SESSION 6

28

Nov

SESSION 6

Even More Math

Even More Math

Tue 11:00 PM - 11:50 PM UTCNov 28, 11:00 PM - 11:50 PM UTC

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)
SESSION 7

11

Dec

SESSION 7

Even More Math

Even More Math

Mon 11:00 PM - 11:50 PM UTCDec 11, 11:00 PM - 11:50 PM UTC

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)
SESSION 8

21

Dec

SESSION 8

Other Topics

Other Topics

Thu 11:00 PM - 11:50 PM UTCDec 21, 11:00 PM - 11:50 PM UTC

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.
SESSION 9

22

Dec

SESSION 9

Other Topics

Other Topics

Fri 11:00 PM - 11:50 PM UTCDec 22, 11:00 PM - 11:50 PM UTC

We will learn the Euclidean algorithm for finding greatest common factors and begin our discussion of prime numbers.
SESSION 10

23

Dec

SESSION 10

Other Topics

Other Topics

Sat 11:00 PM - 11:50 PM UTCDec 23, 11:00 PM - 11:50 PM UTC

We will prove the Fundamental Theorem of Arithmetic and the infinitude of primes. (Credit given to Euclid!)
SESSION 11

1

May

SESSION 11

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCMay 1, 10:00 PM - 10:40 PM UTC

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.
SESSION 12

29

May

SESSION 12

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCMay 29, 10:00 PM - 10:40 PM UTC

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.
SESSION 13

5

Jun

SESSION 13

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJun 5, 10:00 PM - 10:40 PM UTC

Equivalence relations will be the big topic today. If there is time, we will do the definition of rings and fields as well.
SESSION 14

12

Jun

SESSION 14

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJun 12, 10:00 PM - 10:40 PM UTC

Continuing the discussion about rings and fields. We'll prove some straightforward facts about them.
SESSION 15

19

Jun

SESSION 15

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJun 19, 10:00 PM - 10:40 PM UTC

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!
SESSION 16

26

Jun

SESSION 16

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJun 26, 10:00 PM - 10:40 PM UTC

We will introduce and prove the Euclidean algorithm for finding the greatest common factor. Perhaps we'll also introduce prime numbers.
SESSION 17

3

Jul

SESSION 17

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJul 3, 10:00 PM - 10:40 PM UTC

We will prove the Fundamental Theorem of Arithmetic and the infinitude of primes.
SESSION 18

10

Jul

SESSION 18

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJul 10, 10:00 PM - 10:40 PM UTC

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.
SESSION 19

17

Jul

SESSION 19

Other Topics

Other Topics

Wed 10:00 PM - 10:40 PM UTCJul 17, 10:00 PM - 10:40 PM UTC

TBD!
SESSION 20

24

Jul

SESSION 20

Even More Math

Even More Math

Wed 10:00 PM - 10:40 PM UTCJul 24, 10:00 PM - 10:40 PM UTC

Whatever we get to!
SESSION 21

7

Aug

SESSION 21

Even More Math

Even More Math

Wed 10:00 PM - 10:40 PM UTCAug 7, 10:00 PM - 10:40 PM UTC

Whatever we get to!
SESSION 22

14

Aug

SESSION 22

Even More Math

Even More Math

Wed 10:00 PM - 10:40 PM UTCAug 14, 10:00 PM - 10:40 PM UTC

Whatever we get to!
SESSION 23

28

Aug

SESSION 23

Even More Math

Even More Math

Wed 10:00 PM - 10:45 PM UTCAug 28, 10:00 PM - 10:45 PM UTC

I hope to cover the proof of Bezout's lemma today!
SESSION 24

4

Sep

SESSION 24

Even More Math

Even More Math

Wed 10:00 PM - 10:45 PM UTCSep 4, 10:00 PM - 10:45 PM UTC

Wherever we get to—most likely basic properties of prime numbers.

Public Discussion

Please log in to see discussion on this series.

Nov 21 - Sep 4

42 weeks

30 - 50 mins

/ session

SCHEDULE

Wednesdays

10:00PM