My course recommendations for studying mathematics

Can you add book recommendations for each subject. That might be very useful if I want to self study. Thanks

I would say I wish I saw complex analysis sooner, it is absolutely beautiful and it is really helpful for studying modular forms which is a magical subject

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.

Bro really hates Topology. Otherwise, great list i really enjoy your videos°

Please bless us Oh Graduated One

Can you tell me about physics and chemistry

Yeah at ASU it’s called “Discreet Math” and it tore me a new one. I’ll never forget, though, there was a homeless guy that was auditing the class and he consistently was getting like 5% better scores than everyone on every exam

after reading topology i regret mathematics. But I love linear algebra

How does a bachelor in the US sum to a the first year of undergrad in europe... There must be some difference in what each course corresponds to...

I'm cs undergrad student and we did Introduction to Abstract Algebra course

I would recommend taking calc 3 if you are a chem major. I ended up dropping it a few weeks in, but think it would of been helpful. Usually just calc 1-2 are required.

Do you have any texts on the algebraic manipulations of sums, multiplications (capital pi), and other stuff that is not too readily taught in any course curriculums. I wish to start tackling MIT-level integrals and more advanced topics in math but need some texts to aid. Any suggestions on texts will be wonderfully appreciated.

Dont forget logic, specialy modell theory

What kind of pen are you using in this vid?

Galois Theory and Representation Theory were great classes for me in undergrad.

Thanks for the awesome information!

The disrespect tor topology

i was a biochemistry major and they us go up to calculus III. looking back at it, i wonder why

Absolutely! One needs a strong algebra background to undergo Calculus.

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

How do you go from college algebra to calculus? Wouldn't you need pre calc before?

Why do i have a fucking abstract algebra as a freshman in applied math bachelor?

bruh I'm taking abstract algebra and adv linear algebra sophomore year and I'm boutta fail finals ;( Axler is beating my ass

This made my brain hurt.

For all other business and biology chemistry degrees, math is really useful up to Calc AB-BC levels. After calc 2 (bc) math sort of becomes its own thing, unless you are doing physics.
Computer programming is also more math related depending on which branch you go.

In US we say mostly pre-calc not college calculus.
In UCLA there is a Pre-calc class and same in UCF and other places.
I assume college algebra 1 2 3 stands for Algebra 1 2 and Precalc…
The latter makes more sense. As there is usually one more course before Pre calc, that is geometry.
High schoolers usually finish Algebra 2 or Pre calc.
During highschool, the usual highest mathematics achievement is calculus 2.
Calculus 1 and 2 are named AB and BC in high school, which are great introductory to Calculus. Then in college they will take calc 3 4 and other math courses.

I'm study chemical engineering and i study algebra 3 and calculus 1, 2, 3 and ODE

You didn't talk much about differential geometry. Why was it?

what is that pen?

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

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

I would say that intro to point-set topology helps a lot with intro to analysis as you see everything generalized

Topology is also very important especially for those interested in Analysis at the graduate level.

Is this a pure math or applied math timeline? For the first half of your timeline.

I feel like Galois theory is missing

what do you think about taking discrete maths courses as soon as possible ?

which state are you from? you have a distinct accent

bro my community college had a placement test that if you scored high enough on it would automatically skip you straight to calculus. it was multiple choice and i just guessed for most of the questions bc i was very lost and i scored a 86 just from random educated guesses and now i’m taking this calculus class and i’m failing so hard bc i just don’t remember how to do algebra. i’m literally so fucked dude my parents are going to kill me idk how to tell them i got a 47 on my midterm

You forgot to add remedial algebra 1

what a great site!!!

I’m going to give my IGCSEs in November (if you don’t know, it’s what British curriculum students have to sit for at grade-10) and of course planning ahead and I want to do something in the field of mathematics and your videos make me feel like you are right in front of me talking and giving advices in a very chilled way which I just love about you!! Ty!! Keep going ✨

At my university (years ago), you can take exams prior to starting freshman year for College Algebra and Trigonometry. If you pass, you don't have to enrol for these subjects when the semester starts. You've received credits for them already. 

We also had Set Theory in college, though no Topology. Set Theory was usually taken along with Linear Algebra and Abstract Algebra (to help lift your overall GPA as Abstract Algebra can be tough - haha).

Finally, you cannot call yourself a "true" math undergrad unless you pass Vector Calculus, Abstract Algebra and Differential Equations (ODE, PDE). By this time, close to 60% of your cohort would have dropped out already.😄

Gracias

Love the video and your channel. As an older person (58) learning math as a hobby, I would love to see you match this list with the books you would use in order. The biggest problem I'm having is to choose which books to read with the limited time/money that I have. I'm also a book collector, which compounds the problem. So if you're on a desert island and want to learn math, what's your ideal list, with the caveat of stopping when you're ready for anything at the post-graduate level.

I was confused at first with the college algebra 1,2,3 but then you explained it can also be trig and then pre calculus and that made sense. At my college I did that; college algebra, trigonometry, and precalculus.

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

Do you guys not do any Topology, Differential Geometry, Representation Theory or Algebraic Geometry in America?
I would consider Topology and Algebraic Geometry a must have for anyone in Algebra or Geometry and Differential Geometry for anyone in Analysis and PDE's.

You are completely missing courses on point set topology and mathematical logic.

How many classes did you have to retake ?