That's like comparing a water-mellon to a grape. A person who has a PhD is bound to have much more research experience that guy with a Masters. A better comparison would be between guy with PhD in theoretical CS and a PhD in Physics.
Everyone knows that physicists are better and so there is a desire to teach the tools that they use. That's just a theory I have, nothing to back it up other than everyone knows how Einstein was and everybody has an idea who Hawking is and nobody knows who Turing was or Euler was or Galois
You're really clueless, aren't you? Popularity is absolutely no measure of how smart a person is, or how profound their work is. So just because Einstein is well known, doesn't make him the 'bestest' mathematician (physics and theoretical computer science are a subset of mathematics. So I'll call call the people who practice them just mathematicians). If you were to take a survey of people who understood the work of both Galois and Einstein, I think the results would surprise you. The insight that Galois had, and the profundity and extreme elegance of his work is one of the greatest achievements of contemporary mathematics. But this is getting tangential.
The link between linear algebra, abstract algebra and discrete math is pretty easy to see as you're doing it. The bridge between discrete and continuous math is a bit more complex but it's really undeniable when you see it.
Yes, the link of algebra to other subsets of algebra is obviously easy to see. The fun comes in when you try to use algebra the way it was meant to be used - i.e: as tool to study number theory (among other things). Study this link (that is: study arithmetic geometry and algebraic number theory) and tell me if this link is more or less complex than the "bridge between discrete and continuous math".
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