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Abstract Algebra and Number Theory.

SAT Score Range

•

16 sessions

•

+4

This series ended on July 20, 2023. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

This is a course on Abstract Algebra and Number Theory for the curious minds. Ideally learners enrolled in this series would have some experience with some basic proof writing, otherwise understanding the proofs will be tough. The goal here is to introduce learners into the vast world of both Abstract Algebra and Number Theory and most importantly, being able to see connections between the two subjects!

Tutored by

Lucas S 🇦🇺

Certified in 19 topics

View Profile

Hello! I am Lucas, and I am a university student studying pure math.

Schedule

✋ ATTENDANCE POLICY

This series has lots of material to cover, so learners that happen to miss sessions will possibly fall behind. If this does happen then I strongly suggest to message me either privately or publicly so that I can either sort out a catch up session or direct learners to external materials.

SESSION 1

3

Jul

SESSION 1

Orientation

Orientation

Mon 12:00 AM - 1:30 AM UTCJul 3, 12:00 AM - 1:30 AM UTC

Let's get to know each other! We will also go over some basic proof writing for anyone that needs a reminder. Attendance here is not needed if you feel okay with proof writing!
SESSION 2

4

Jul

SESSION 2

Orientation

Orientation

Tue 12:00 AM - 1:30 AM UTCJul 4, 12:00 AM - 1:30 AM UTC

Let's get to know each other! We will go over some basic proof writing for anyone that needs a reminder. Attendance is not needed here if you feel okay with proof writing!
SESSION 3

5

Jul

SESSION 3

Other Topics

Other Topics

Wed 12:00 AM - 2:00 AM UTCJul 5, 12:00 AM - 2:00 AM UTC

We'll cover some basic facts about divisibility. In particular, we will learn how to precisely state what it means for two integers to divide into each other and some of the properties that come with it! After this, we will investigate a really important result known as the Division Algorithm. This allows us to generalise the idea of divisibility to have division with remainder! A big part of this session is to prove this algorithm. We'll also look at the Well-Ordering Principle and the greatest common divisor.
SESSION 4

6

Jul

SESSION 4

Other Topics

Other Topics

Thu 12:00 AM - 2:00 AM UTCJul 6, 12:00 AM - 2:00 AM UTC

We will discover when a linear diophantine equation has a solution over the integers. This will quickly lead us into the Euclidean Algorithm and the Extended Euclidean Algorithm. We will also look at primes and some basic properties that primes have!
SESSION 5

7

Jul

SESSION 5

Other Topics

Other Topics

Fri 12:00 AM - 2:00 AM UTCJul 7, 12:00 AM - 2:00 AM UTC

We will continue looking at properties that primes have. Another big milestone will be looking at the Fundamental Theorem of Arithmetic and its proof. Alongside this big theorem we will look at a result by Euclid from over 2000 years ago that there are infinitely many primes. At the end, we may get to look at the distribution of primes by looking at the Prime Number Theorem. We will not provide a proof here. The proof is well and truely outside the scope of this series!
SESSION 6

8

Jul

SESSION 6

Other Topics

Other Topics

Sat 12:00 AM - 1:30 AM UTCJul 8, 12:00 AM - 1:30 AM UTC

We will continue our work on semi-groups and later move on to looking at groups! We will look at some basic examples of groups, followed by a nice result that will help us in our next bit of study on Number Theory. Afterwards, we dive back into Number Theory!
SESSION 7

10

Jul

SESSION 7

Other Topics

Other Topics

Mon 12:00 AM - 1:30 AM UTCJul 10, 12:00 AM - 1:30 AM UTC

We will continue with investigating some Number Theory and see some of the connections it has with Algebra! We will also look at the Chinese Remainder Theorem.
SESSION 8

11

Jul

SESSION 8

Review

Review

Tue 12:00 AM - 1:30 AM UTCJul 11, 12:00 AM - 1:30 AM UTC

We will provide a review of what we have done so far and answer any questions you may have! Note that this session is not important to attend if you are okay with the content so far.
SESSION 9

12

Jul

SESSION 9

Other Topics

Other Topics

Wed 12:00 AM - 1:30 AM UTCJul 12, 12:00 AM - 1:30 AM UTC

We know look at the group of integers modulo n and the algebraic properties that this group has. From this we can define a new group, known as the group of units (or the multiplicative group of integers modulo n).
SESSION 10

13

Jul

SESSION 10

Other Topics

Other Topics

Thu 12:00 AM - 1:30 AM UTCJul 13, 12:00 AM - 1:30 AM UTC

A big day, we look at the Chinese Remainder Theorem! This is a really big theorem in Number Theory. After this, we will move back to group theory looking at some more basic results to do with groups.
SESSION 11

14

Jul

SESSION 11

Other Topics

Other Topics

Fri 12:00 AM - 1:30 AM UTCJul 14, 12:00 AM - 1:30 AM UTC

We will go through a quiz that covers the content that we have done so far! Hopefully this will be a useful review and also a fun activity to do. After this, we will move on to look at a special family of groups known as the Symmetric groups (along with another special class of groups known as the Dihedral Groups) and subgroups.
SESSION 12

15

Jul

SESSION 12

Other Topics

Other Topics

Sat 12:00 AM - 1:30 AM UTCJul 15, 12:00 AM - 1:30 AM UTC

We will now look at the Dihedral Group and subgroups. The Dihedral Group will act as another example of an important type of group. We will also look at criterions for subgroups (the Subgroup Test).
SESSION 13

16

Jul

SESSION 13

Other Topics

Other Topics

Sun 12:00 AM - 1:30 AM UTCJul 16, 12:00 AM - 1:30 AM UTC

We will look at what the order of an element is in a group and cyclic groups. This will prove useful for our later studies in Number Theory!
SESSION 14

17

Jul

SESSION 14

Other Topics

Other Topics

Mon 12:00 AM - 1:30 AM UTCJul 17, 12:00 AM - 1:30 AM UTC

We will look at Group Homomorphisms and Group Isomorphisms. These are important maps between groups.
SESSION 15

19

Jul

SESSION 15

Other Topics

Other Topics

Wed 12:00 AM - 1:30 AM UTCJul 19, 12:00 AM - 1:30 AM UTC

We will look back at some Number Theory. In particular, we will look at Euler's Totient Function and some classic theorems that come along with it!
SESSION 16

20

Jul

SESSION 16

Other Topics

Other Topics

Thu 12:00 AM - 1:30 AM UTCJul 20, 12:00 AM - 1:30 AM UTC

This session will be a review of everything that we have covered so far. As well as a chance to go over the final quiz of the series! This is also the last session of the series.

Public Discussion

Please log in to see discussion on this series.

Jul 3 - Jul 20

3 weeks

90 - 120 mins

/ session

SCHEDULE

Mondays

12:00AM

Tuesdays

12:00AM

Wednesdays

12:00AM

Thursdays

12:00AM

Fridays

12:00AM

Saturdays

12:00AM