For a basis:
Linear Algebra (really just affine functions)
Calculus
Optimization (specifically gradient methods)
Probability/statistics
Information theory
Numerical methods
For all of the above, you don't actually need to learn the entire field. You just need the subsets that apply to machine learning. The first two sections of the Goodfellow book give a good idea of the areas to focus on (don't bother with the third section, it's dated at this point).
www.deeplearningbook.org/For ML/AI:
Linear models (regressions, trees)
Bayesian methods
Unsupervised clustering
Dimensionality reduction (PCA, tSNE, UMAP)
Deep models (MLP, CNN, RNN/LSTM)
Modern architectures (resnets, transformers, etc)
Regularization
Generative models (images, text)
Outlier detection
I would go with Andrew Ng's course for traditional ML and
fast.ai for deep learning.
This will give you a decent base, but the place you need to get to if you want to get hired (especially with just a BS) is to be able to read, understand and implement papers fairly quickly. Also in terms of learning, actually coding stuff up is many times more valuable than reading about stuff.
>t. machine learning research scientist 
