Best Course Sequence For Math Majors

In this video I will give you the best sequence of courses to follow if you want to get a math degree. You can use this list as a guide to self study mathematics. Here are the books.
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************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course

Advanced Calculus Course

Calculus 1 Course

Calculus 2 Course

Calculus 3 Course

Calculus 1 Lectures with Assignments and a Final Exam

Calculus Integration Insanity

Differential Equations Course

Differential Equations Lectures Course (Includes Assignments + Final Exam)

College Algebra Course

How to Write Proofs with Sets Course

How to Write Proofs with Functions Course

Trigonometry 1 Course

Trigonometry 2 Course

Thank you:)

[martinhawrylkiewicz]

When learning mathematical analysis...I would not recommend Baby Rudin as your first book on the subject. It will test your wits and give you solid nightmares. Trust me.

[AVLife]

Interestingly enough, I never had to take a Trig course, neither in high school nor university. All of my experience with Trig came from what was taught in the Pre-Calc and high school geometry. That being said, I think the trig from precalc helped me understand justttt enough trig to make it through and do ok Physics I and Calc II (trig comes up a lot it seems). Curious if anyone else has a similar experience.

[martinhawrylkiewicz]

Great vid as always! I took Discrete Math in college and we used Susanna Epp textbook....in my option the best introduction to Logic and Set Theory I have seen (beginning chapters). Highly recommended.

[BarbaraPrice-sp]

I took PDEs my senior year. Took differential equations for the first time in grad school, no problem.

[misterthefreak]

It's also important to have a solid introduction to probability and stochastic processes

[douglasstrother]

"Discrete Mathematics and Its Applications" (4th ed) by Kenneth Rosen is a gem. (My copy is a Recycle Bin Rescue.) In addition to presenting Discrete Mathematics (aka, "Counting Gone Wild"), it details the tools needed to write proofs and think Mathematics like a Mathematician. There are also lots of examples and applications, so you can have good answers when your friends ask, "Why do you study this crazy Math Stuff?"

[abdullahmohammed]

literally, I thank you from the deepest point ever discovered in my heart for your existence.

[walterstevens]

That Mathematical Statistics book by Wackerly is THE ONE. I have about a dozen books on the topic, and this is the one that got me through math stat. I found that if I mostly tuned out the instructor and instead read the class text plus Wackerly, and worked problems in Wackerly, I understood the course much better. The solutions manual is a must, too.

[pinedelgado]

10:25 That linear algebra book came from my alma mater, Grossmont College (AS, Thank you lots for featuring THAT ♥♥♥♥♥ 🙂🙂🙂🙂🙂

[joshual]

In other universities outside the US, advanced calculus 1 and advanced calculus 2 are the prerequisites before you could take Real analysis and Complex analysis. Adv Calc 1-2 (Intro to Analysis) are like the stepping stones to further analysis courses.

[Eta_Carinae__]

Would it be alright if I made a request?

I'm trying to get some of the deeper theory behind AI in a nutshell, and I think I've identified some milestone topics I need to traverse:
- Phase transitions in statistical mechanics (only classical though), and the renormalisation group
- Bayesian Stats (up to the point where I'm comfortable with the theta parameter)
- Theoretical CS (akin to Sipser's book/MITOCW course)
- I guess I'll know that I'm good when I fully understand all the reasons the Gaussian is critical to statistical theory (at the moment I know about CLT, identity under FT, the relationship it has with the Frobenius norm)
- Information and Control Theory, particularly their combination. I understand there are four big asymptotic limiting theorems here, and I need to understand all of them. So far I have the Shannon-Nyquist limit down.
- Less important, Topois theory for the generalisation of classical logic, and Category theory for the foundations of mathematics (plus I like the commutative diagrams).

I was wondering if you have any recommended prerequisite material, maybe even a course structure like this video, where one could end up with the above points satisfied by the end of it all? Cheers.

[tarson-cmxs]

This is the best course sequence for everyone, not only math majors!

[РоманПивоваров-фш]

That's what i looking for! Thnank you very much!

[walterstevens]

That ODE by Ross is excellent. I used it in the mid 1970s for a summer class. It almost made the class fun. Almost. Had occasion to use it again within the last 10 years.

[jasperclement]

I think a mistake i made when taking mathematical stats is not understanding probability theory enough beforehand. it would be a good idea to read a book like a first course in probability before taking matematical statistics

[mysticpotato]

Great list! I’m a current math undergrad, and I love collecting older textbooks, so I’ll be on the look for these!

[medicisounds]

I took Calculus and got a D in it. But was somehow able to take Physics.
Physics was tough but it was much more interesting so the math seemed easier to tackle. I loved how Physics put a lot of Calculus into real world situations making it easier for me to grasp.
I am currently retaking Calculus 1 and taking Statics!
I'm studying 5+ hour everyday nowadays

[hotelmasternm]

My personal journey in lower level math at Riverside City College: 1) Intermediate algebra, 2) college algebra, 3) trigonometry, 4) precalculus, 5) calculus 1 and physics mechanics, 6) calculus 2 and physics electricity and magnetism, 7) calculus 3 and physics light heat and waves, 8) ordinary differential equations and statistics, 9) linear algebra

My thoughts: First become proficient in algebra with (1) and (2). Then become proficient in trigonometry with (3). Precalculus (4) is half algebra and half trigonometry, so it was a thorough review and a way to gain advanced proficiency. Calculus 1 and the first physics course just complement each other well; there's a section in calculus 1 with acceleration, velocity, position functions which are related with derivatives. These formulas are used in the physics of trajectories or 2D motion aka projectile motion of any object under only the influence of gravity aka when a mass is in a state of freefall. The (6) combo was very difficult because the tests in calculus 2 could be really hard with integration techniques unless you get nice test problems and physics of E&M (electricity and magnetism) is very difficult when compared to thermodynamics physics and modern physics that come after. If you can do well with both calc 2 and physics E&M then you are awesome, hit me up, I need smarter friends. Oddly, now for (7) calculus 3 is multivariable calc and repeats topics in Calc 1 and 2 and should be pretty easy but some topics will be more confusing in 3D or R3 which is the x, y, z-coordinate system. It was super interesting to make it up to differential equations while also taking Intro Stats. I knew more complex math and could also take a step back to the beginning where I'm mainly evaluating basic formulas or learning to use charts to find probabilities or areas under a curve. Differential equations is by far my favorite subject with instructions that all remain very similar throughout the entire course (they all ask you to solve the ODE, ordinary differential equation, just using different methods depending on the difficulty or form of the ODE). Lastly, linear algebra is about knowing math in a more generalized way. It starts by using matrices which is at first a way to organize a system of equations but because the solutions of a system of equations can be a set (as with infinitely many solutions), it opens up the subject to the properties of vector spaces (a vector space is a set of "vectors" in which the vectors can be matrices, ordered pairs, ordered triples, ordered tuples or any math object where all the values in each vector obey a list of rules or conditions). Matrix operations and notations should be learned in precalculus and learning more about them in linear algebra is a way to expand what you know and think more about sets (sets become more important in upper level math classes). Last thing is that in a differential equations course you may use matrices to solve a system of differential equations by using eigenvalues and eigenvectors; this is also done in linear algebra, so there is some important overlap.

[MajesticQT]

Honestly I don't know why most people recommend linear algebra so late. My uni had me take proof-based linear algebra at the same time as calc 2, and honestly as long as you have a little experience with proof writing you should be ok.

[Hwkman]

I saw a patient with a PhD is math. I said oh my grandfather also had a PhD in Mathematics. She asked what subject, so I answered, "Algebraic Topology." Her eyes got so big