@@VisualMath, thank you for that! It's amazing when you see something you've been familiar with for eons in an entirely new and beautifully simple way.
@@VisualMath, I'll share one of my favorites: the realization that the evolution of our number system from N to Z to Q to R to C can be seen as the composition of four quotient set constructions, each removing the obstruction to the inverse of addition, multiplication, and powers -- (Z yielding the inverse operation of subtraction, Q division, R logarithms, and C root extraction). This is such a lovely, simple, and unifying picture, and it makes the seemingly mysterious emergence of complex numbers perfectly logical and transparent, rather than feeling like they beamed in from Pluto.
Again a very good video. Emerging topics like this requires more attention. What a fabulous job you are doing !! The future is going to thank you immensely. May you shine and keep up illuminating the light of knowledge & wisdom.
Good question! When I started learning about CT I had basically the same background, just exchange stat & prob with topology. In other words, I think you are good to go. One really learns CT via the examples, and the examples that work for you depend on your taste and background. Here are some hints: A background in discrete math and algebra is very welcome since CT is basically a cleaned up version of these (very roughly speaking, of course). CT also plays a role in Stat & Prob, but the standard text won't cover examples. (See however golem.ph.utexas.edu/category/2020/06/statistics_for_category_theori.html) Since you do not have a background in topology (which is the classical field CT is applied to) I would recommend to ignore the examples coming from topology. Maybe try to get started with either of: www.cambridge.org/core/books/an-introduction-to-category-theory/38C6B02892C2FE7408F52975756AC88D www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf github.com/hmemcpy/milewski-ctfp-pdf Depending on your own taste, you might like one of these. The first two are kind of independent of previous knowledge, the last two take an approach that programmers might like. What I wouldn’t recommend, with the background you mention, are books such as MacLane. MacLane's book is an awesome book, but a lot of examples are topologically and geometrically motivated, so it might not be what would help you right now. I hope that helps!
Associativity as a natural topological feature is a beautiful way to look at it.
Yes, its one of my favorites as well ☺
@@VisualMath, thank you for that! It's amazing when you see something you've been familiar with for eons in an entirely new and beautifully simple way.
@@xyzct I felt exactly the same when I first saw this 😀
@@VisualMath, I'll share one of my favorites: the realization that the evolution of our number system from N to Z to Q to R to C can be seen as the composition of four quotient set constructions, each removing the obstruction to the inverse of addition, multiplication, and powers -- (Z yielding the inverse operation of subtraction, Q division, R logarithms, and C root extraction). This is such a lovely, simple, and unifying picture, and it makes the seemingly mysterious emergence of complex numbers perfectly logical and transparent, rather than feeling like they beamed in from Pluto.
@@xyzct Yes, that one is great as well!
Again a very good video. Emerging topics like this requires more attention. What a fabulous job you are doing !! The future is going to thank you immensely. May you shine and keep up illuminating the light of knowledge & wisdom.
Many many thanks - as usual I do not deserve your praise - I just do what I feel is nice and needs spotlight ;-)
Thanks for the video 😊
Thank you for the feedback, you are very welcome 😊 I hope you enjoy category theory!
@@VisualMath I’m total noob trying to understand the connection and differences between finite model theory and category theory. So this was helpful
@@Swangorapofficial You are welcome!
Many thanks for your videos. They help me a lot to understand CATs.😀. Wish you the best for 2024.
Excellent, I hope you will enjoy cats as much as I do 😚
And what a great start: yes, all the best for everyone for 2024 😘
I have a basic background in statistics & probability theory, discrete math, algebra & calculus. What should I do before jumping into category theory?
Good question!
When I started learning about CT I had basically the same background, just exchange stat & prob with topology. In other words, I think you are good to go.
One really learns CT via the examples, and the examples that work for you depend on your taste and background. Here are some hints:
A background in discrete math and algebra is very welcome since CT is basically a cleaned up version of these (very roughly speaking, of course). CT also plays a role in Stat & Prob, but the standard text won't cover examples.
(See however golem.ph.utexas.edu/category/2020/06/statistics_for_category_theori.html)
Since you do not have a background in topology (which is the classical field CT is applied to) I would recommend to ignore the examples coming from topology.
Maybe try to get started with either of:
www.cambridge.org/core/books/an-introduction-to-category-theory/38C6B02892C2FE7408F52975756AC88D
www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf
math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf
github.com/hmemcpy/milewski-ctfp-pdf
Depending on your own taste, you might like one of these. The first two are kind of independent of previous knowledge, the last two take an approach that programmers might like.
What I wouldn’t recommend, with the background you mention, are books such as MacLane. MacLane's book is an awesome book, but a lot of examples are topologically and geometrically motivated, so it might not be what would help you right now.
I hope that helps!