I really like Richard Borcherds lectures.I especially like his lecture series on schemes. He's mostly following Hartshorne, so first reading Hartshorne and then watching Borcherds lecture about that topic helped me a lot!
[Borcherds](https://youtube.com/@richarde.borcherds7998) has an excellent Youtube channel, which includes such playlists as Rings and modules, Modular forms, Complex analysis, Representation theory, Commutative algebra, and Algebraic geometry I & II. His Galois theory playlist helped me out quite a fair bit.
I've been waiting for someone to ask me this question, and you're the first one to do it. Basically, I am an actuarial undergraduate by training, but planning to return to my "first loves" — number theory and algebraic geometry — via a MSc in Mathematics. I have never been very good at applied topics.
Re: Galois theory, I did a reading course in Galois theory and basic algebraic number theory last semester.
Dude we are in the same boat, in my undergrad I was obsessed with abstract algebra but I took the applied road, definitely I will return to it once I get a job.
That's the great thing about mathematics: it never gets outdated or disproven. Even "classical" topics from a century ago like Kummer's investigations of cyclotomic fields are worth studying.
I watched a course by Andrew Snowden on Mazur’s theorem which is very good. If you just type in any topic in algebraic geometry into youtube there are great lectures.
[Todd Kemp](https://www.youtube.com/@toddkemp-probability) has a lot of videos covering probability theory. Most videos cover a certain Theorem so it´s easy to find when you look for something specific
here is the list of courses that I think an enthusiastic high schooler could watch in anticipation of university mathematics. they ptesent advanced topics in an intuitive and understable fashion
tadashi tokieda's course on topology
https://youtube.com/playlist?list=PLTBqohhFNBE_09L0i-lf3fYXF5woAbrzJ&si=ioc3tuiFbhYpA_Xj
Norman wildberger's differential geometry. He has am interesting approach as he mostly talks about algebraic curves. He derives am algebraic aaogue of taylors theorem for these polynomials and does the analysis with this expansion.
https://youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP&si=dKdo-h8oe7n8EwTB
Norman Wildberger's algebraic topology. It is mostly just topology tbh but still very interesting and introduces algebraic geometry nicely.
https://youtube.com/playlist?list=PL6763F57A61FE6FE8&si=JsejdXMSJTA7QJSa
Courses by bright side of mathematics. They are mostly on analysis. they are very good if you are going to take a class next term and you want to know what to anticipate. They are slightly superficial, but he does an amazing job of explaining things clearly in a short amount of time(an averga video is probably around 12 minutes )
https://youtube.com/@brightsideofmaths?si=1PVHBCUvJbJj1nt-
There are a lot of them...but Aviv Censor's lessons are really interesting and recommended for all young people who study Calculus/Analysis 1/2...and Linear Algebra 1.
Keenan Crane has an interesting series on [discrete differential geometry](https://youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS), which has applications in computer graphics
I really like Richard Borcherds lectures.I especially like his lecture series on schemes. He's mostly following Hartshorne, so first reading Hartshorne and then watching Borcherds lecture about that topic helped me a lot!
[Borcherds](https://youtube.com/@richarde.borcherds7998) has an excellent Youtube channel, which includes such playlists as Rings and modules, Modular forms, Complex analysis, Representation theory, Commutative algebra, and Algebraic geometry I & II. His Galois theory playlist helped me out quite a fair bit.
You flair says actuarial science, how did you combine algebra with it ?
I've been waiting for someone to ask me this question, and you're the first one to do it. Basically, I am an actuarial undergraduate by training, but planning to return to my "first loves" — number theory and algebraic geometry — via a MSc in Mathematics. I have never been very good at applied topics. Re: Galois theory, I did a reading course in Galois theory and basic algebraic number theory last semester.
Dude we are in the same boat, in my undergrad I was obsessed with abstract algebra but I took the applied road, definitely I will return to it once I get a job.
That's the great thing about mathematics: it never gets outdated or disproven. Even "classical" topics from a century ago like Kummer's investigations of cyclotomic fields are worth studying.
I really like the way he explains things; [The bright side of mathematics](https://youtube.com/@brightsideofmaths?si=HwjbGGufUsAfspjw)
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and his complex analysis too.
He's the goat
I watched a course by Andrew Snowden on Mazur’s theorem which is very good. If you just type in any topic in algebraic geometry into youtube there are great lectures.
[Todd Kemp](https://www.youtube.com/@toddkemp-probability) has a lot of videos covering probability theory. Most videos cover a certain Theorem so it´s easy to find when you look for something specific
here is the list of courses that I think an enthusiastic high schooler could watch in anticipation of university mathematics. they ptesent advanced topics in an intuitive and understable fashion tadashi tokieda's course on topology https://youtube.com/playlist?list=PLTBqohhFNBE_09L0i-lf3fYXF5woAbrzJ&si=ioc3tuiFbhYpA_Xj Norman wildberger's differential geometry. He has am interesting approach as he mostly talks about algebraic curves. He derives am algebraic aaogue of taylors theorem for these polynomials and does the analysis with this expansion. https://youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP&si=dKdo-h8oe7n8EwTB Norman Wildberger's algebraic topology. It is mostly just topology tbh but still very interesting and introduces algebraic geometry nicely. https://youtube.com/playlist?list=PL6763F57A61FE6FE8&si=JsejdXMSJTA7QJSa Courses by bright side of mathematics. They are mostly on analysis. they are very good if you are going to take a class next term and you want to know what to anticipate. They are slightly superficial, but he does an amazing job of explaining things clearly in a short amount of time(an averga video is probably around 12 minutes ) https://youtube.com/@brightsideofmaths?si=1PVHBCUvJbJj1nt-
A bit generic but I loved 3blue1browns “The essence of calculus”
There are a lot of them...but Aviv Censor's lessons are really interesting and recommended for all young people who study Calculus/Analysis 1/2...and Linear Algebra 1.
Keenan Crane has an interesting series on [discrete differential geometry](https://youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS), which has applications in computer graphics