Math Self-Study: Build a Strong Foundation for AI PhD

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Hi, I'm embarking on a mission to self-study math, and would like some recommendations on any missing books or ones that should be replaced in my repertoire.

The goal is to build a strong mathematical foundation. My naive idea of what that means is something like an undergraduate math major, so I have googled a bit to get an idea of the relevant areas, and searched amazon for the best books on those topics, this is what I have so far:

Savov - No Bull**** Guide to Math and Physics
Velleman - How to Prove it
Spivak - Calculus
Axler - Linear Algebra Done Right
Mendelson - Introduction to Topology
Kleene - Mathematical Logic
Graham - Concrete Mathematics
Ghorpade - Course in Multivariable Calculus and Analysis
Rudin - Principles of Mathematical Analysis
Pinter - Abstract Algebra
Farlow - PDE for Scientists and Engineers

My long-LONG term goal is a PhD in CS, specifically AI. So please advice me! Keep in mind that I'm really starting from basics here, as I'm currently only 7/10 through Khan Academy and nothing more.

 

[Dr. Courtney]

Most students arrive at college with weak algebra and trig skills.

Don't waste your time with those books before you have completed the ALEKS pre-calculus course (online) to make sure you are ready.

 

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My idea was to master the World of Math mission on Khan Academy [0] before starting books. That program includes pre/calculus, so if I can complete it, that would indicate that I'm ready to start some of those books, don't you agree?

[0] https://www.khanacademy.org/math

 

[KiggenPig]

I'm not entirely sure it would, to be honest. Khan academy doesn't have enough practice questions, and the ones it does have aren't very challenging.

Plus, I don't believe video lectures replace learning straight out of a textbook at all. You're not always going to have Khan to hold your hand throughout difficult concepts. Especially if Michael Spivak is going to be your first exposure to calculus.

 

[Dr. Courtney]

I also think you need a lot of practice and validated assessments of learning. ALEKS has that.

A lot of math departments have validated and confirmed that ALEKS pre-calc ensures readiness for calculus.

 

[bubblescript]

I'm not entirely sure it would, to be honest. Khan academy doesn't have enough practice questions, and the ones it does have aren't very challenging.

Plus, I don't believe video lectures replace learning straight out of a textbook at all. You're not always going to have Khan to hold your hand throughout difficult concepts. Especially if Michael Spivak is going to be your first exposure to calculus.

What do you mean by not enough practice questions? As in variety, or difficulty? Because KA keeps generating new questions forever until the student gets it right enough times.

And in my plan Spivak would not be the first exposure, I was thinking KA -> Savov No BS Guide -> Velleman Proofs -> Spivak.

But please tell me bluntly if this is a bad idea, because I'm here to find advice for the best learning path!

 

[lordianed]

Hello, I'm currently working myself through Spivak, and that was after I've worked through most of "Book of Proof"; even then Spivak proved to be exceedingly tough. It is really a whole other ball game compared to anything you may have learned in school. I'm not sure about the "No BS Guide" since I've never heard of it, but I strongly suggest you follow Dr Courtney's advice, you need to be very good at Algebra and Trig, I learned that the hard way by trying to overcome rigorous Math without said skills. If you would like a book instead of using ALEKS you could try Mathematics: The Core Course for A-level

 

[bubblescript]

Hello, I'm currently working myself through Spivak, and that was after I've worked through most of "Book of Proof"; even then Spivak proved to be exceedingly tough. It is really a whole other ball game compared to anything you may have learned in school. I'm not sure about the "No BS Guide" since I've never heard of it, but I strongly suggest you follow Dr Courtney's advice, you need to be very good at Algebra and Trig, I learned that the hard way by trying to overcome rigorous Math without said skills. If you would like a book instead of using ALEKS you could try Mathematics: The Core Course for A-level

Thanks, I will take your advice under consideration, and add the book to my list of potential study material.

I think the "No BS Guide" seems good since it supposedly takes the reader from high school math to calculus, and everyone on amazon is singing high praise in the reviews, so if they are honest reviews then it seems like a good book to start with.