Are you a PhD student? And if so, are you aiming at a career in academic research? I'll offer my advice as a math professor, and as someone who supervises students.
If you want to get a strong foundation in physics, then reading Halliday + Resnick, and doing a large number of the exercises, would be one good way to go about it. (Look for used copies of previous editions on Amazon -- they'll be cheap.) There are plenty of other good suggestions in the blog post you linked, and also in this thread.
However, and I hate to throw water on such a noble aspiration, are you sure that this is what you want to do? Getting a "strong foundation" takes a lot of effort. If you want to invest this effort, then great! But you might consider investing that effort into learning something closer to your field, which would both be interesting and directly help in your research.
In my observation, it is common for graduate students and professors to learn about areas outside their research area, but they don't always worry so much about getting a "strong foundation". For example, when I was a PhD student, one of my fellow students enrolled in a graduate course in physics, without worrying too much about whether he satisfied the prerequisites. It was a great experience for him, and it's one that apparently helped him a great deal in his mathematics research career.
Myself, I have invested a fair amount of time learning algebraic geometry, which is a difficult area of mathematics, different from my specialty. The results have been ambiguous -- I still don't know the field nearly as well as I wish I did. In particular, I still have only a sketchy understanding of the foundations. But, happily, I know enough to talk to algebraic geometers. Indeed, I'm currently writing a paper with a colleague in the subject, which involves both his specialty and mine -- it's not one that either of us could have written on our own.
I personally really like the old (1960's) editions of Halliday and Resnick. I feel they are superior to the editions published today, and are available for very cheap.
I found in my undergrad I used both. Sometimes one would explain a specific topic better. Sometimes I just needed to hear the topic explained from a different voice. With the number of old editions and online copies floating around, I don't think it is bad to recommend both.
Are you a PhD student? And if so, are you aiming at a career in academic research? I'll offer my advice as a math professor, and as someone who supervises students.
If you want to get a strong foundation in physics, then reading Halliday + Resnick, and doing a large number of the exercises, would be one good way to go about it. (Look for used copies of previous editions on Amazon -- they'll be cheap.) There are plenty of other good suggestions in the blog post you linked, and also in this thread.
However, and I hate to throw water on such a noble aspiration, are you sure that this is what you want to do? Getting a "strong foundation" takes a lot of effort. If you want to invest this effort, then great! But you might consider investing that effort into learning something closer to your field, which would both be interesting and directly help in your research.
In my observation, it is common for graduate students and professors to learn about areas outside their research area, but they don't always worry so much about getting a "strong foundation". For example, when I was a PhD student, one of my fellow students enrolled in a graduate course in physics, without worrying too much about whether he satisfied the prerequisites. It was a great experience for him, and it's one that apparently helped him a great deal in his mathematics research career.
Myself, I have invested a fair amount of time learning algebraic geometry, which is a difficult area of mathematics, different from my specialty. The results have been ambiguous -- I still don't know the field nearly as well as I wish I did. In particular, I still have only a sketchy understanding of the foundations. But, happily, I know enough to talk to algebraic geometers. Indeed, I'm currently writing a paper with a colleague in the subject, which involves both his specialty and mine -- it's not one that either of us could have written on our own.
In any case, good luck and best wishes to you!