Should I Become a Mathematician?

[daudaudaudau]

That is being very sensitive. I too am so sick of those lame comments every time someone mentions the defence industry.

 

[atyy]

mathwonk's comment was not lame at all, nor was it necessarily against the defence industry. War is perhaps sometimes necessary, and it makes sense to be prepared to wage it - but only in the very last resort, and it is certainly never "cool".

 

[Tickitata]

Although I agree with mathwonk that there are much better avenues to which one can apply their intelligence than a glorification of war, I'd have to agree with russ in the sense that the original post was not asking for an ethical argument but instead asked a simple directed question regarding employability.

That being said, it'd be a damn shame to let that be the cause for one of the most prominent and influential PF members to leave.

 

[PhysicalAnomaly]

Awww. His angry comment that I shouldn't find Munkres easy was great motivation. For that I will be always thankful. <3 :(

 

[qspeechc]

Is there anything we can do to change your mind and get you to stay mathwonk?

 

[lisab]

I understand your point, mathwonk, but I wish you'd reconsider. You make a tremendous contribution to PF.

 

[Hurkyl]

We have a politics forum to cater to those times when people want to talk about politics; the academic guidance forum is not the place for it. (And mathwonk's comment completely derailed the thread before it could even get started)

 

[kfmfe04]

I'm sure that "cool" OP made a lot of people's blood boil... ...but it's best to just try to not pay attention to these people on the Web.

mathwonk, please do come back!

I've learned SO MUCH from reading this thread (my main reason for coming to this forum) and all the posts have been extremely informative and inspirational.

 

[jgg]

If it's okay to butt in and ask a question, has anyone here attended http://www.hcssim.org/"? If so, what did you think of it?

EDIT: Or related summer math program.

 

[mathgeek2]

what jobs are there for mathematicians other than teaching profession. can u be specific.

 

[tgt]

what jobs are there for mathematicians other than teaching profession. can u be specific.

Many. One easy way to tell is to look at job ads where they specify i.e Target qualifications with mathematics in it. Common ones are in commerce and technology/computing jobs.

 

[Chewy0087]

Reminds me of that Good Will Hunting rant where he answers 'Why not work for the NSA?' =P

Ontopic though, I'm starting to enjoy math more and more and hopefully will be taking it forward to some level (alongside physics!)

 

[Wisey]

Is it possible for me to learn mathematics on my own as a hobby? I wasn't really into it in high school, mainly because from middle school I was shoved with a bunch of formulae and asked to solve a horde of similar looking problems that did nothing to help me think in different directions, or heck, even give me a clue that such a fascinating world of mathematics existed. Indeed, mathematics to me meant rigidity rather than creativity for a lot of years. Because of my limited concept of it, I actually struggled a bit when some creativity was needed in my course, it took me a while to get used to it as it had come as a surprise, all I had done in mathematics till then was learn how to put values into equations to get results, and some methods on how to solve things without an actual explanation of those methods.

All that started changing in the past year or so, my last year of high school, after having found a good teacher that did a little more than explain how to solve problems that are going to come in examinations. I started gaining more interest in the subject, and at the present am quite enthusiastic about learning more about it.

Right now I will probably be going into electrical engineering(a result of my interest in physics and whatever little I have heard about engineering) having already almost joined a college, but I still want to learn mathematics as well, maybe not as much as in a pure course, but as much as I can on my own anyway.

Would it be possible for me to learn stuff on my own doing self-study, using the internet as a resource? I can't afford to spend much on books, as I will be spending a lot on doing my actual college study anyway, hence the internet, so are there quality resources on the net that I can effectively use to learn on my own? If so, can someone please guide me to those resources? I would prefer to start from the basics covering the theory, even stuff that I already know, as I really wasn't taught a lot of them very well, so that I can get them right in my head before proceeding to more advanced topics.

 

[muppet]

The good news is that there's quite a lot on the internet. The first two places I'd look for maths are:
http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm#Mathematics
A huge list of free resources -Some of these will be better than others.
The hard parts will be 1) finding time to study such a broad and sometimes challenging subject in your spare time, and 2)working through things in a sensible order and sluicing out things you find interesting from things you don't without formal guidance.
My advice rearding the former would be to be prepared to work slowly- if math gets in the way of life rather than the other way round, you're probably doing something wrong. As for the latter, wikipedia might be able to help with giving you an overview of maths and a feel for individual topics; for some idea of a sensible order in which to study things, and a guide for what's important, have a look at a few university syllabuses.
Hope that helps!

 

[Bourbaki1123]

No one really tracks the math books torrent files as far as I know, so you could download "math complete"(google search it) without worry about getting in trouble. If you're worried about getting in trouble anyway, you can just get peer guardian 2. I think many of the books in the file are public domain, but many are not.

 

[Wisey]

Thank you for the replies!

Well I think I will find enough time to study math, right now I have 2 months of free time, and I will have sporadic periods of such joblessness anyway, so that won't be much of a problem. Even if I have to go slow, I would prefer it, I like to think upon things others consider basic and examine them to my satisfaction before letting go of them.

What I find intimidating(and exciting) is the sheer amount of resources from which I can study from.

 

[muppet]

No one really tracks the math books torrent files as far as I know, so you could download "math complete"(google search it) without worry about getting in trouble. If you're worried about getting in trouble anyway, you can just get peer guardian 2. I think many of the books in the file are public domain, but many are not.

I understood the point of that site to be that the works were all freely accessible?

 

[Bourbaki1123]

Not sure what you are asking. I was simply indicating that if you have the inclination to download something with questionable copyright status, the option was open and no one really would be keeping track. If that is contrary to your moral stance, ignore it.

 

[Dragonfall]

forgive me if i am over sensitive, but the following message was so insulting to me i decided to leave the forum

That's frakking BS! You helped me with my homework during my undergrad years more times than I can count. I hope you reconsider.

 

[wajed]

There are basically 3 branches of math, or maybe 4, algebra, topology, and analysis, or also maybe geometry and complex analysis.

1)why isn`t logic considered a branch?
2)does studying the history of mathematics help in understanding it? (this idea keeps popping up in my mind, and that is because I`m really trying to find my way to the very core of mathematics so that I can start and smoothly go up till the most modern mathematics topics/branches)
3) what do I need to read to start from the very core of mathematics?

The key thing to me is to want to understand and to do mathematics. When you have this goal, you should try to begin to solve as many problems as possible in all your books and courses, but also to find and make up new problems yourself.

I think solving many problems just get you used to the form of the problems and their proposed solutions... not that it really makes you understand what you are doing more..
but others say the otherwise..
I don`t have experience at all.. but that's what I see.. am I totally false?

 

[blerg]

1)why isn`t logic considered a branch?
2)does studying the history of mathematics help in understanding it? (this idea keeps popping up in my mind, and that is because I`m really trying to find my way to the very core of mathematics so that I can start and smoothly go up till the most modern mathematics topics/branches)
3) what do I need to read to start from the very core of mathematics?

1. Logic can also be considered a branch, but it is typically grouped more with computer science. The list of branches that was given is a very rough outline and different people will separate the branches of math differently, none of which are necessarily better than another

2. Studying math history can certainly help understand the motivation behind various mathematical topic. It is not completely necessary but it often helps. I never took a history of math course or anything like that, but have picked up a lot of it along the way. Some book actually include brief histories when beginning a new topic that is often helpful.

3. what do you mean by the very core of mathematics? arithmetic? calculus? logic? Where are you in your mathematical education?

I think solving many problems just get you used to the form of the problems and their proposed solutions... not that it really makes you understand what you are doing more..
but others say the otherwise..
I don`t have experience at all.. but that's what I see.. am I totally false?

Solving problems is the core of mathematics. You cannot truly understand and topic without emersing yourself in various problems. I don't know where you currently are in your education, but in higher level math there are very few "standard" type problems. Problems are solved by using a simple algorithm or formula. Instead you must rely on the base of knowledge you gained, creativity, and experience. You see the term "mathematical maturity" a lot. It is something hard to quantify, but it is definitely something only gained through constant practice.

 

[wajed]

3. what do you mean by the very core of mathematics? arithmetic? calculus? logic? Where are you in your mathematical education?

Thats the question... where should I start?
I`m a 1st year engineering, finished CalcA and almost CalcB..
Gonna change to IT, so I`ll be studying Discrete mathematics.. but that will be not the next term, the one just after it..
I did move from egineering to IT because I can`t have enough time to study the mathematics and physics (and the other requirements) at the same time..I`ll dedicate most of my free time now to mathematics.. and when I finish my postgraduate studies I`ll be having enough abilities to get the physics I missed more easily and smoothly..


No.. solving more problems dosen`t make me feel like I have understood something..
I do solve more and more Integration problems.. that doesn`t mean I`ll ever understand what Integration really is (where did it come from, what is the exact definition, how to interpret that defintion in my mind and have it there like 1+1=2 and being convinced of it like "I should be" convinced that 1+1=2 -which I think will be easy to achieve if I study logic) by just solving more problems..


I know I need to be more into discrete mathematics and logic... but should I start with Number theory first? Well, I don`t know much about any of these, but the question that pops in mind is: which one depends more on the other? or simply just which one is more fundamental/basic?

Concerning calculus..I see these more fundamental thant calculus.. and understanding them will give easier/much better understanding of the definitions/proofs/concepts of calculus


PS: what ever you recommend me to start with, please recommend also a book to read on what you reocommend

 

[Jame]

I think "What is mathematics" by Richard Courant would be a terrific book for you.

 

[blerg]

I think "What is mathematics" by Richard Courant would be a terrific book for you.

I completely agree with this. Excellent book.

 

[muppet]

At the most basic level, solving problems cements connections in your mind as to the relationships between objects in the definitions, and helps you build an intuition as to what effect performing some operation (e.g. differentiation) actually has. Obviously, differentiating hundreds of powers of x will do little to improve your understanding of the theory of differentiation, but performing just a few differentiations explicitly from the definition gives you a much better lie of the land than just staring at the definition for 5 minutes. One thing you find in maths when studied as a subject in its own right is that the nature of the problems you undertake generally changes throughout your education- the balance shifts from "compute this" to "show that"; they become much more closely tied to the guts of the theory than the methodical plodding you do at school.

 

[Jame]

... performing just a few differentiations explicitly from the definition gives you a much better lie of the land than just staring at the definition for 5 minutes...

If you never try things for yourself, or do something in a very stupid way, there's no way you can appreciate the power and beauty of a general law. Jacobi once said something like "If your father had insisted on meeting every girl there is before marrying your mother, you would never exist.", the point being that it's worth trying things yourself even of someone has already done it before in a much smarter way.

This is easier said than done though, when learning something new it can feel very annoying to put a lot of work into trying for yourself before looking on the next page in the book. Nonetheless, the feeling of realizing that the idea you came up with yourself actually resembles that of the master, it's better than having sex with a beautiful woman, it's majestic.

 

[arshavin]

Reason: General Warning
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That's not a forum for editorializing or challenging people's motives. If you don't have anything useful to contribute, stay out.
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This infraction is worth 1 point(s) and may result in restricted access until it expires. Serious infractions will never expire.

Original Post:
https://www.physicsforums.com/showthread.php?p=2019454
creating bombs to kill people is cool? please think about your options. there might be something out there with a better impact on the world.

"If you don't have anything useful to contribute, stay out." This is pretty offensive. When someone posts something, its because they think its useful. And this is without mentioning the fact that Mathwonk is a great sage.

 

[cristo]

"If you don't have anything useful to contribute, stay out." This is pretty offensive. When someone posts something, its because they think its useful. And this is without mentioning the fact that Mathwonk is a great sage.

That's enough. This thread will not be derailed by discussions on specific infractions given to members. Such action is a breach of the PF rules, and any further posts on that topic will be dealt with accordingly.

 

[colonelcrayon]

A question for everyone here:

I have just finished my sophomore year in high school and along with it AP Calculus AB (I'll take BC next year). My math career up to this point has been pretty much the standard bemoaned in the first pages of this thread, albeit at a somewhat accelerated pace.

Math has always fascinated me - the vast realm of complex problems that can be solved with a pen and paper (though calculators and computers are rather handy). Being able to visualize a whole world of possibilities from math is exciting to me, and I want to continue with it. This leads me to my problem: as I start the college admissions process, I will need to think about my prospective major. So far, I am fascinated by the idea of an applied math major. It seems like the perfect combination of math and real world problem solving.

However, I don't know much about what math is really like beyond the standard school curriculum. Obviously I am nowhere near ready for more advanced math, but I would like a book that provides a good taste of the type of thinking required for a major in math and the careers that lie beyond. In other words, a book that focuses on higher-level proofs and problem solving without requiring completion of anything beyond AP Calc AB.

Several of the books mentioned early in this thread seem like good fits, but I'd be interested in more specific recommendations.

Thanks!

 

[thrill3rnit3]

A question for everyone here:

I have just finished my sophomore year in high school and along with it AP Calculus AB (I'll take BC next year). My math career up to this point has been pretty much the standard bemoaned in the first pages of this thread, albeit at a somewhat accelerated pace.

Math has always fascinated me - the vast realm of complex problems that can be solved with a pen and paper (though calculators and computers are rather handy). Being able to visualize a whole world of possibilities from math is exciting to me, and I want to continue with it. This leads me to my problem: as I start the college admissions process, I will need to think about my prospective major. So far, I am fascinated by the idea of an applied math major. It seems like the perfect combination of math and real world problem solving.

However, I don't know much about what math is really like beyond the standard school curriculum. Obviously I am nowhere near ready for more advanced math, but I would like a book that provides a good taste of the type of thinking required for a major in math and the careers that lie beyond. In other words, a book that focuses on higher-level proofs and problem solving without requiring completion of anything beyond AP Calc AB.

Several of the books mentioned early in this thread seem like good fits, but I'd be interested in more specific recommendations.

Thanks!

Try reading a more rigorous calculus textbook that focuses on theory more than methodology, it can serve as a beginner's text to analysis.

For beginners, Apostol's text would be a very good choice. I suggest you start from there.

 

[colonelcrayon]

^ Thanks. I'll look into that.

 

[thrill3rnit3]

What are good mathematics publications/magazines? I guess something that a high school student can appreciate...

 

[thrill3rnit3]

I guess we don't have any more mathematicians in here...

 

[blerg]

I guess we don't have any more mathematicians in here...

More like no more mathwonk.

 

[RJinkies]

tronter> Yeah, for example, if one self studies Analysis by an expert like Dieudonne/Simmons, he would probably be more prepared than one who is taught Analysis from a more contemporary text.

No i think you actually do good to study both the old and the new [aka contemporary[ texts.

There is something to be said for 'not' dismissing both the easy books and 'not' dismissing the 'not-quite-experts' writing books and merely picking the books of the 'masters'...

We shouldn't be worshipping merely the 'hard' texts, or the most 'famous' of writers. There are a lot of somewhat flawed texts (a few of the obscure dovers) that people might turn their nose up at, which with the right mindset are quite serviceable.

We could also make a similar argument for 'dismissing' merely older texts, or another for 'dismissing' newer texts as being not as polished or deep as some older classics, as well.

To me, its like saying the three star books the MAA recommends for a library are great, and all the 1 star books they'd recommend are crap.

One can get a lot of mileage out of the easy books 'not written for strongest mathematicians and minds' and by lesser lights. In fact, wouldn't an easy book on any mathematical subject be a good read before getting the 'rigorous' text? Nathan Grier Parke III used to speak about how a lot of math and physics/science textbooks where one needs the spiral approach, getting the 'baby calculus' text [JE and/or Sylvanius Thompson], or as Parke suggested C.O. Oakley's 'Barnes and Noble Introduction to Calculus from 1944] , before getting the Courant.

Parke thought any 'introduction' to a subject in math or science had to have MAXIMUM intuition and MAXIMUM vigorousness, and that rigor when one genuinely FEELS a need, can come later.

A while back Cauchy's books were thought to be elegant and rigorous and top notch, he was one of those anal retentive experts that wanted analysis to be hardcore and rigourous and he didnt like to include a single diagram, preferring nothing but dense turgid notation. [assuming i recall the story correctly...]

and pretty much nothing of calculus or analysis books before 1880 passes the rigor test anymore... Horace Lamb's last Cambridge textbook [3rd edition 1919] might be the earliest one still useful - though it got the last correction to get rid of any errors was 1944] and Osgood's text - [Macmillan 1922] as well as Osgood's Advanced Calculus [Macmillan 1925] and Wilson's Advanced Calculus [Ginn 1912]

I think the old books are great, like Granville Longley Smith and Courant and so are some of the newer ones 'Spivak/Apostol].


now back on topic

tronter> Yeah, for example, if one self studies Analysis by an expert like Dieudonne/Simmons, he would probably be more prepared than one who is taught Analysis from a more contemporary text.

Depends on how 'exact' we define our subject here...

I wouldn't call EITHER Dieudonne or Simmons

'Elementary Real Analysis'

[actually i do wonder, but i don't think either would be a great - elementary first choice]

authors on that subject might be:

Apostol, Bartle, Binmore
Burkill, Kolmogorov, Rosenlicht
Ross, Royden, Rudin


and something on

'Advanced Real Analysis'

might be:

Boas, Carathrodory, Gelbaum
Halmos, Hewitt and Stromberg, Munkres
Polya, Stromberg, Angus Taylor


and we're omitting texts that blur Calculus and Analysis like:

- Apostol
- Bressoud
- Courant
- Courant and Fritz John
- Buck
- Hardy
- Kaplan

etc etc...

Dieudonne is a great author, maybe not the most approchable early on, but
he's a lot HARDER than
Binmore and Burkill which hold your hand nicely...

Rudin and Apostol are hard core but probably more approachable, but others would think that Dieudonne and Simmons both are more fun and alive than Rudin, but you can probably get students who like all three or hate all three, depending on taste, ability, what they are looking for in a book.

Royden would be more advanced, and maybe around that stage after reading some of the elementary analysis books, some of rudin or royden or bartle, yeah than you can tackle Dieudonne...


Simmons, that would be functional analysis and topology, a great book, great exposition, but not one's first step into analysis...


tronter> Or if one self studies Algebra by Hungerford/Lang, vs. someone who is taught algebra using Beachy/Blair etc..

Dunno, again it's recommending harder books good as second or third approaches to the subject, and dumping on the books that are for earlier parts of the 'spiral' when tackling a subject.

Lots of people, most all actually would say Dummit and Foote's book is way better than Hungerford and Lang for Abstract Algebra. And some would actually think that Dummit would be better for self-study on top of that.

Again, opinions are opinions, but there is something to be said for a terse book when you're studying on your own, and Dummit to some is better than Lang and Hungerford, but still an intimidating first text. I think that's because Dummit is a good second text, and Lang and Hungerford are good third texts, or at least that's my impression.

people think Beachy is fun to read, a gentle book, good for reading before you real Gallian's book and good to read with Gallian's book as well. People say that if you are looking for a RIGOROUS book in abstract algebra Gallian is not the book, but some think it's the most beautiful and fun, which i would think, makes one appreciate the 'rigor' later on when it's really really needed.

I like Beachy, Dieudonne and Simmons, and my abilities in math arent all that high, but my experience with good texts are way stronger...


tronter> I think self study forces you to develop your own perspectives of math rather than following a professor's.

Definately! and that's why i think Beachy stands out [for abstract algebra], it's a more basic textbook than the others, and a good one for self-study. Dieudonne stands out as a more advanced Analysis text, not so sure it would be a top 10 pick for basic texts, or top 10 for the next step up in analysis either, but it is a great book. Simmons as well, but teaches you higher up analysis as you're plunking into topology. [though there's a lot of simmons books, and two simmons if I'm not mistaken]