Construction of our Basic Number Systems.
SAT Score Range
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5 sessions
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NN
JD
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
If the timings of the sessions do not suit you, then please send me a message either directly or through the series chat.
I plan for this to be a conversational series where we investigate how one actually goes about constructing the number systems we use throughout Calculus.
In this series, I plan to construct the natural numbers, integers, rational numbers and (possibly) the real numbers. The real numbers are fairly complicated to understand. Consequently, I will only cover this construction if there is any demand for it and how strong the audience is in mathematical maturity.
I expect that the audience has some familiarity with basic proof writing. Though if needed, I can quickly cover this at the beginning of the series. That's it, bye for now!
Schedule
✋ ATTENDANCE POLICY
Try not to miss sessions for the reason that sessions are highly dependent on previous ones.
If you cannot make a session, please notify me about it in either the series chat, or a private chat. This way I can plan a catchup session before the next one.
SESSION 1
10
Jul
SESSION 1
Orientation
Orientation
Mon 3:00 AM - 4:30 AM UTCJul 10, 3:00 AM - 4:30 AM UTC
Let's get to know each other! We will cover basic logic and proof writing needed for this series. If you feel okay with proof writing then this session can be skipped.
SESSION 2
14
Jul
SESSION 2
Other Topics
Other Topics
Fri 2:00 AM - 3:30 AM UTCJul 14, 2:00 AM - 3:30 AM UTC
Now that we have a basic idea on how the natural numbers are made, we are in a position to discover some basic properties that the natural numbers have!
SESSION 3
17
Jul
SESSION 3
Other Topics
Other Topics
Mon 3:00 AM - 4:30 AM UTCJul 17, 3:00 AM - 4:30 AM UTC
Here we talk about the need for such constructions and get some basic scaffolding built so we can get a footing on how the natural numbers are constructed! In order for this to happen, we must try to forget everything we know about numbers. This is rather a difficult task to do! Only allow our intuition to take over and not let any advanced tricks such as the rules of algebra take over our thinking!
SESSION 4
19
Jul
SESSION 4
Other Topics
Other Topics
Wed 3:00 AM - 4:30 AM UTCJul 19, 3:00 AM - 4:30 AM UTC
We will continue looking at multiplication of natural numbers and look at exponentiation as well. From there, we will move on to the construction of the integers. This will be done by introducing subtraction as an operation on the integers.
SESSION 5
20
Jul
SESSION 5
Other Topics
Other Topics
Thu 3:00 AM - 4:30 AM UTCJul 20, 3:00 AM - 4:30 AM UTC
We will finish our discussion of the integers and then move onto the rational numbers.