I'm a junior year computer science undergrad just began to study machine learning a month ago. My aim is to start reading papers in my area of interest under Machine Learning and begin to do research in ML as an intern/independent project. I want to further go to grad school after a gap year and earn an MS + Ph.D. in machine learning.
I'm taking Prof. Andrew Ng's CS229 lectures online and side by side reading relevant chapters from Bishop's "Pattern Recognition and Machine Learning" book.
The mathematical problems/exercises given in both the problem sets of CS229 and PRML textbook are mathematically too sophisticated for me to solve on my own, although I can follow the solutions. How much of these exercises would an undergrad/masters student be expected to solve? And if I am considering a Ph.D., should I solve them or skip them at all?
Will only the mathematical knowledge and implementation of machine learning algorithms matter to start with research and later in grad school without spending time on these exercises?