<p>Barium:</p>
<p>Just that. An infinite string of decimal digits. And while it is correct to say it agrees with the series’ partial sums of finite length, it requires proof for me to admit it is the same as the limit of the series. I could define the actual infinite series to be anything, but that doesn’t change the limit.</p>
<p>@AMT: An “infinite string of decimal digits” implies a series with the same number over 10^n, with n increasing, correct?</p>
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Wait, what?</p>
<p>Standard analysis does not deal with anything infinite. It only deals with finite approximations. One could define an infinite decimal expansion as a limit of a sequence of finite decimals, in standard analysis fashion. That’s what I did, but you rejected that construction. Can you provide a rigorous standard analysis definition of your notation? In particular, can you define it without using the word “infinite”?</p>
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<p>this is prob. the king of nitpicks, but that’s not a physics major test question. you don’t need to know lin. alg. that well for ugrad physics. you are definitely flattering yourself . . .</p>
<p>You don’t even need to know linear algebra that well as a math major.</p>
<p>they should understand the problem statement though, right?</p>
<p>that’s an important fact in lin. alg. (normal operators are diagonalizable)</p>
<p>I didn’t understand the problem statement. (normal operator? split polynomial?)</p>
<p>I know that self-adjoint operators are diagonalizable. That’s all I have ever needed.</p>
<p>oh. i guess some books/classes don’t talk about normal operators (ones where TT* = T*T). it really isn’t a more advanced topic though. it’s a larger class of operators, but it may not be one worth studying. hermitian operators are the ones that pop up a lot (e & m, quantum mechanics, more stuff i don’t know about . . .)</p>
<p>I guess normal is a little more general - I think Axler’s linear algebra book talks about normal operators and the complex spectral theorem, though it’s been a while.</p>
<p>Anyway, I have no idea how this stuff came up in this thread - I saw the beginning, the end, and probably won’t be checking the in between part :D</p>
<p>Did you notice how our little math discursions silenced the never-ending technical vs liberal arts discussions? The mods couldn’t have done that any better ;)</p>
<p>True. I was falling asleep reading through the math portion. However, the previous debate was engaging.</p>
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<p>I originally thought this was referring to me, but there was a physics major in the class - and a couple Econ majors too. That was probably one of the couple hardest problems on any of the homeworks. I doubt more than a couple people in the class solved it. Unfortunately about half of the final was of that difficulty level (or higher). It was definitely not a flattering experience.</p>
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<p>Yep, there’s a chapter on self-adjoint and normal operators</p>
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<p>Congrats, this thread has lived too long anyway.</p>
<p>LOL but don’t think you’re so smart…the liberal arts majors could have discussed the finer points of Latin poetry analysis and done the same thing.</p>
<p>But it WAS like reading a post in a foreign language! :D</p>
<p>higher level math and higher level analysis of literature are equally incomperhensible.</p>
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Isn’t math a liberal arts major?</p>
<p>You’re right, but I saw the math discussion, my eyes glazed over and my brain froze. :D</p>
<p>I should have said Classics majors or something.</p>
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<p>Although one can obtain both a BA and BSc in Math, as far as I know I dont think any universities consider math to a be a full blown liberal arts major. If you go way back in history, geometry and algebra were considered essential to a liberal arts education, but I think the curriculum has changed and mostly just focuses on the humanities and the arts, with a little encouragement to take a one or two math courses, which is probably entirely optional at most institutions.</p>
<p>st. john’s college (probably the most liberal arts school there is) has 4 years of math courses [St</a>. John’s College | Academic Program | The Mathematics Tutorial](<a href=“Liberal Arts College - Great Books Program | St. John's College”>Liberal Arts College - Great Books Program | St. John's College) , but it looks like they insist on studying the original papers and don’t learn much math. </p>
<p>Is there any benefit to reading original math/science papers that cover content in modern textbooks? My guess is no–modern texts cover the topics more elegantly (hindsight is 20/20, etc), and you don’t need to stumble over the language, but I could be wrong.</p>
<p>Yeah, but then you can’t say you studied the original papers.</p>