Mathematician Chat V.floor(π) - General

[QUOTE=Number-41;44879302]Have a good understanding of epsilon-delta proofs? I don't know if you really need "preparation", i.e. any preparation just coincides with a part of the course itself. So preparing would just be spoiling the course I think :v: In my case, the courses started really from the bottom. You could (in principle) walk in with the knowledge of just basic arithmetic and no idea what a matrix is and you would have no holes in your knowledge in either analysis or linear algebra. It would be tough because some concepts you have to get comfortable with, like epsilon-delta proofs and the idea of an abstract vector space. I struggled a lot with those when I heard of them for the first time. In retrospect, one thing that could help with both analysis and linear algebra is imho some basic set theory (morphisms, relations, ...), at least the theoretical parts. Just look at the first chapters of the courses you'll take and maybe delve deeper into things that seem difficult or that you are not familiar with.[/QUOTE] Spoiling the courses would just be a good thing, wouldn't it? Because then I would get more comfortable with stuff before I actually do them. I'm [b]think[/b] that I pretty much understand epsilon-delta proofs. The theoretical parts of set theory is really interesting to me, and I've read about a bunch of it. I know what relations, morphisms, etc are.

[QUOTE=Number-41;44879302]basic set theory[/QUOTE] [QUOTE=Number-41;44879302]morphisms[/QUOTE] wut [editline]22nd May 2014[/editline] maybe it's different where you are, the term "morphism" (outside the context of "isomorphism," "homomorphism", etc.) doesn't get thrown around here until category theory, which you might get an introduction to in algebraic topology or so [editline]22nd May 2014[/editline] [QUOTE=ArgvCompany;44879584]Spoiling the courses would just be a good thing, wouldn't it? Because then I would get more comfortable with stuff before I actually do them. I'm [b]think[/b] that I pretty much understand epsilon-delta proofs. The theoretical parts of set theory is really interesting to me, and I've read about a bunch of it. I know what relations, morphisms, etc are.[/QUOTE] If you're pretty decent at epsilon-delta proofs your analysis class should be fine. Practicing them is really the best thing you could probably do to prepare.

[QUOTE=JohnnyMo1;44879680]wut [editline]22nd May 2014[/editline] maybe it's different where you are, the term "morphism" (outside the context of "isomorphism," "homomorphism", etc.) doesn't get thrown around here until category theory, which you might get an introduction to in algebraic topology or so [editline]22nd May 2014[/editline] If you're pretty decent at epsilon-delta proofs your analysis class should be fine. Practicing them is really the best thing you could probably do to prepare.[/QUOTE] Sounds really promising! Are you referring to the single-variable one or both?

[QUOTE=ArgvCompany;44879858]Sounds really promising! Are you referring to the single-variable one or both?[/QUOTE] Single variable for sure. Have you taken any non-analysis multivariable calc? I think epsilon-delta proofs will probably be less prominent in the multivariable part, at least they were in my real analysis class.

[QUOTE=JohnnyMo1;44879923]Single variable for sure. Have you taken any non-analysis multivariable calc? I think epsilon-delta proofs will probably be less prominent in the multivariable part, at least they were in my real analysis class.[/QUOTE] I have not taken any such course. I get a feeling that there is supposed to be a sharp line between calculus and analysis, but I'm not sure where it goes. Kind of everything in that area of study is called analysis in my country (I live in Sweden, my flag is incorrect :v:). This makes me unsure if we speak about the same analysis.

[QUOTE=ArgvCompany;44880039]I have not taken any such course. I get a feeling that there is supposed to be a sharp line between calculus and analysis, but I'm not sure where it goes. Kind of everything in that area of study is called analysis in my country.[/QUOTE] Oh. You might (in fact, probably if it's engineering) not need to know anything about epsilon-delta proofs in that case. If you just go in with a strong background in algebra you'll be fine. [editline]22nd May 2014[/editline] You say you've seen epsilon-delta proofs before? In what context?

[QUOTE=JohnnyMo1;44880051]Oh. You might (in fact, probably if it's engineering) not need to know anything about epsilon-delta proofs in that case. If you just go in with a strong background in algebra you'll be fine.[/QUOTE] It's engineering (though this engineering program is known to be the most theoretical one). I have taken all math courses in our equivalent to high school, so I guess I am supposed to be fine. I'm just worried since a lot of people have told me that university math will, in general, hit me like a brick wall. Also, I'm curious. What are you currently studying, yourself? (if you do study something)

[QUOTE=ArgvCompany;44880104]It's engineering (though this engineering program is known to be the most theoretical one). I have taken all math courses in our equivalent to high school, so I guess I am supposed to be fine. I'm just worried since a lot of people have told me that university math will, in general, hit me like a brick wall.[/QUOTE] Probably not, honestly. If you've done a decent job in all the math you've taken so far, you should be fine. I've never run into any class in the normal progression that was disproportionately horrible. [editline]22nd May 2014[/editline] I just finished a physics and math degree.

[QUOTE=JohnnyMo1;44880128]Probably not, honestly. If you've done a decent job in all the math you've taken so far, you should be fine. I've never run into any class in the normal progression that was disproportionately horrible. [editline]22nd May 2014[/editline] I just finished a physics and math degree.[/QUOTE] Just to be clear, a "physics and math degree" is not the same thing as an engineering degree "in those subjects", right? I get a feeling that what is called an engineering degree over here is a lot more general in some way, and that a physics engineering degree could be similar to the kind of degree you just finished. Just some speculations on my part.

[QUOTE=ArgvCompany;44880158]Just to be clear, a "physics and math degree" is not the same thing as an engineering degree "in those subjects", right? I get a feeling that what is called an engineering degree over here is a lot more general in some way, and that a physics engineering degree could be similar to the kind of degree you just finished. Just some speculations on my part.[/QUOTE] I'm not sure I get what you mean

[QUOTE=JohnnyMo1;44880167]I'm not sure I get what you mean[/QUOTE] I think that what is named "physics engineering" over here is actually much like what you call a "physics and math degree".

[QUOTE=ArgvCompany;44880181]I think that what is named "physics engineering" over here is actually much like what you call a "physics and math degree".[/QUOTE] Physics and math are separate programs. I took a double major. I'm not sure what your physics engineering degree is like.

[QUOTE=ArgvCompany;44880181]I think that what is named "physics engineering" over here is actually much like what you call a "physics and math degree".[/QUOTE] No Johnny has two separate degrees, one in physics and one in mathematics. [editline]22nd May 2014[/editline] l8 m8

[QUOTE=Falubii;44880190]No Johnny has two separate degrees, one in physics and one in mathematics. [editline]22nd May 2014[/editline] l8 m8[/QUOTE] Yeah. Technically not separate degrees, but separate programs anyway. I was one credit away from getting two degrees, dammit! (though I doubt it changes much vs. a double major)

Oh, I see. How it works over here is that you can pick a special type of engineering program ("civilingenjör", [b]not[/b] the same as civil engineering). You then do three years of that program. Then you start your masters degree for the two last years of your education. At my chosen program, engineering physics, you can choose to get a masters degree in mathematics among others. I haven't really paid attention to this before but Sweden's and US' education systems have a lot of differences.

[QUOTE=ArgvCompany;44880215]Oh, I see. How it works over here is that you can pick a special type of engineering program ("civilingenjör", [b]not[/b] the same as civil engineering). You then do three years of that program. Then you start your masters degree for the two last years of your education. At my chosen program, engineering physics, you can choose to get a masters degree in mathematics among others. I haven't really paid attention to this before but Sweden's and US' education systems have a lot of differences.[/QUOTE] I'm not sure if that word is translating poorly, but he's not an engineer. It's much more theoretical than applied physics.

A little while ago I realized I hadn't ever seen the proof for the divergence of the harmonic series, so I found some hints online (namely the first lemma in the following document) and tried to come up with a proof myself. I would appreciate any comments and/or pointing out what is inevitably wrong in it. [url=https://dl.dropboxusercontent.com/u/128114072/harmoninen.pdf]Link[/url]

That proof is correct (as far as I can tell), but there are more still.

A good intuitive proof my professor gave me went like this: 1. He wrote out the harmonic series to a bunch of places (~30) 2. He started grouping terms together into some common value (I think it was 1/2) 3. He pretty much showed that you can always find some finite number of terms and group them to 1/2

[QUOTE=JohnnyMo1;44879680]wut [/QUOTE] yeah might've used that in the wrong way, I just mean some common mappings :v:

[QUOTE=Falubii;44880754]I'm not sure if that word is translating poorly, but he's not an engineer. It's much more theoretical than applied physics.[/QUOTE] I think the word does have the same meaning when referring to a job title, but I think it differs a little bit when referring to a type of education. My hypothesis is that an "engineering" education over here is a bit wider, more theoretical than in the US. In a way I think it is more like a middle ground between physics or math degree and what you refer to as an engineering degree. Might be wrong on this, but that is the feeling I get. I have asked multiple people and local forums for advice regarding what education to go with for someone interested in physics and math, and I have not gotten a single answer that does not say "civilingenjör". And maybe this is a bit off-topic :v:

Why is this true? [img]http://www4b.wolframalpha.com/Calculate/MSP/MSP8081e4e0d7ae5i6i046000068978f07634didie?MSPStoreType=image/gif&s=18&w=169.&h=28.[/img]

[QUOTE=Krinkels;44887772]Why is this true? [img]http://www4b.wolframalpha.com/Calculate/MSP/MSP8081e4e0d7ae5i6i046000068978f07634didie?MSPStoreType=image/gif&s=18&w=169.&h=28.[/img][/QUOTE] What is H?

Oh, right. H sub n is the nth harmonic number.

That is an interesting relation. I would expect the value to be negative, given that the first number is smaller. Am I reading those subscripts incorrectly?

Maybe. H(2n) = 1 + 1/2 + 1/3 + ... + 1/2n H(n+1) = 1 + 1/2 + 1/3 + ... + 1/(n+1) In fact, the first number is never smaller, and the difference is always positive.

Well, this is a half baked thought, but you might be able to tackle it with squeeze theorem. Relate the harmonic series to the natural log near equivalent and see where that takes you.

What was the relation? I just get a broken image link in Krinkels' original post.

[img]http://i.imgur.com/dPICgiO.png[/img] Rehosted. [editline]23rd May 2014[/editline] [QUOTE=Xeloras;44889270]Well, this is a half baked thought, but you might be able to tackle it with squeeze theorem. Relate the harmonic series to the natural log near equivalent and see where that takes you.[/QUOTE] It's very clear if you just replace the Hs with logs, but I'm not sure why that would be valid.

Well ln(n+1) < Hn <= 1 + ln(n) (n being only positive integers), so that's where I'm basing my reasoning. I'm not saying replace it with logs, but look at the logs surrounding it, and if they converge to a point as n approaches infinity, I think you've got a shot.