My course recommendations for studying mathematics

[riccardoformenti]

As a Math undergrad, this is LITERALLY the best channel on YouTube right now; loving it!!

[mansurdaschaew]

I would say Topology is a must have! It helped me a lot to understand many fundamental concepts and their connections in between. Stuff like Optimazation or Numerics is cool too (if you are into aplied mathematics)

[Ean]

All channels like math scorcer are good channels I love channels that actively encourage learning through book recommendations, practice problems, or informative videos of such. You have earned my SUB, I hope to see more amazing videos in future. Would love to see videos doing certain problems if you have time to make such videos like solving specific integrals or teaching basic theorems or stuff.

[SteveRuprecht]

Thanks for the list! I'm considering going back to school to get a math degree and currently self studying but practically starting over from scratch because it's been so long. Been at it for a year and about to start calc I. Seeing the subjects planned out like this is very motivating.

[kristophamiller]

College Algebra
Pre- Calculus
Calculus 1, 2, 3
Differential Equations
Probability and stats
Discrete I, II
Linear Algebra
Real Analysis
Modern Algebra
Geometry
Topology
Optional( complex analysis, Number theory, Time series,

[notnotcharles]

'Linear Algebra Done Right' goes crazy hard. Was surprised to see you call it a textbook for advanced linear algebra since it requires no linear algebra background (and the first sub-chapter is literally on complex numbers). That explains why it hasn't helped me much in my first year uni linear algebra class lol.

[polymloth]

Interesting. In Finland the first year curriculum consists generally of:

Fall: Proofs, Calculus 1 & 2, Linear Algebra 1 (+ compulsory general studies like Finnish, Swedish & English)

Spring: Linear Algebra 2 & 3, Advanced Calculus (proof based Calc 1 & 2), Series

Spring Electives: Logic 1 & 2, Probability and Statistics, Applied Linear Algebra

Knowledge of trigonometry and elementary number theory is assumed.

[shabbos_goy]

I love this list, although it hurts not see any topology courses🥲

I personally had a much less consistent list of courses, since I picked most of my courses based on how much did the course sound interesting to me, and that way I found the topics that interested me the most, and I think I would recommend this way to every new student, of course after he took the basic courses that are necessary in basically every field in mathematics.

Great video!

[sharks]

Exactly what I've been looking for! Thanks for the upload 👍🏻

[mschuhler]

i can speak to recommending probability theory, it's crucial if you're intending to work in a field reliant on applied mathematics. knowing probability theory allows you to conceptualize how to approach problems people often face in these fields

[jh_esports]

It‘s interesting how different education systems are.
Here everything up to and usually including Calc3 is covered in school, university starts with Real Analysis, Linear Algebra and Differential Equations.

Which was actually kind of an issue for me because I started my degree 3 years after finishing school so I had to re-learn integration on my own while being asked to prove its underlying ideas in the Analysis class. The additional work was a struggle but I‘m glad I discovered my passion for math and theoretical physics. Better late than never.

[alexdotdash]

Thank you! I am planning to study mathematics in college and this gives me a great perspective!

[chin]

Thank you for the recommendations, this is very helpful

[GrifGrey]

Great! I will make sure to apply this in 5 years from now! :D

[YoungStudent]

Pls do from the start, I'm an 11 year old who wants to study it and I need it

[matt-gth]

If you are serious and have the opportunity, you should be completing calc 1-2 in high school. Ideally, you complete analysis in your freshman year. Putting serious proof based mathematics off til your junior year is a major waste of time. My hot take is that lin alg/difeq/calc 3 are all unmotivated and uninteresting until you have already done plenty of math.

[michaeltherandomperson]

What make this crazier is that some uni will have undergrad course covering a lot of these harder topics. My first discrete math course had number theory, probability theory, set theory, game theory, combinatorics, graph theory and logic and reasoning. so many things covered in a course.

[Salvador]

Interesante, gracias por las recomendaciones.

[SM_]

It's very strange, here in Germany (pure mathematics bachelor) we dont have Calculus 1, 2, 3 in university, everything is prove based and it starts with more advanced courses:

1 semester: Introduction to Real Analysis, Linear Algebra I
2 semester: Real Analysis, Linear Algebra II (which is advanced Linear Algebra)
3 semester: Measure and Integration Theory, Numerical Linear Algebra, Introduction to Probability Theory
4 semester: Introduction to abstract algebra and number theory, Complex Analysis and ODE, Numerical Analysis, Probability Theory
5 semester: Topology, Functional Analysis, Abstract Algebra, PDE
6 semester: 2 of the following:
Diff. Geometry, Alg. Topology, Alg. Geometry, Functional Analysis 2, Alg. number theory, advanced PDE, advanced numerical analysis

[divyanshlalwani]

I think Probability and Statistics should also be included in the undergraduate degree