Should I Become a Mathematician?

[kramer733]

Marsden, vector analysis. I think it has Newton on its cover.

Is the rigor on par with spivak's calculus book?

 

[nucl34rgg]

Granted, it has been a while, but I used the 5th edition of Stewart's single variable and multivariable calculus books when I learned the majority of my calculus, and for what it's worth, I thought they were wonderful books ... not sure why they'd have a reputation of being bad.

Anyone who tells you "Stewart is bad" because it is handwavy is being a math snob. Yes, it lacks rigor. That doesn't matter. The point of the first course in calculus is to wrap your head around the fundamentals and teach you to calculate things. If you want rigor, there are better books that firmly set you up for more courses in analysis, such as Fitzpatrick, Rudin, or Wade. Honestly, I can't imagine skipping Stewart and simply starting Wade. I'm sure I'd be able to explain the theorems nicely, but I sure as hell wouldn't be able to solve any problems! :P I'm almost positive that everyone goes through something like Stewart first to become familiar with the computations of calculus.

 

[lurflurf]

^That is not true. Stewart is like many popular calculus books in that instead of actually teaching calculus it teaches one to solve trivial problems without any understanding like a defective calculus robot. It is true that many people enjoy and benefit from a first calculus book that is theoretical. Theorems are problems, so it is nonsense that there is some risk of understanding so much that one cannot solve trivial problems. Stewart is not a particularly good book of its type. There is not much to recommend it, even if cookbook calculus is desired.

 

[Dougggggg]

I used Stewart for Calculus, then Lay for Real Analysis. I liked Stewart for like nucl34rgg said, showed me what something was and how it worked in a way very pleasing to my intuition. Now that I am in Real Analysis, I'm appreciated that slight bit of Calculus intuition to help give me an idea of where to start trying to understand the actual foundations of it all. However, with the exception of Calc III, I had teachers that went through at least a watered down version of different theorems and their proofs. I still do use the Stewart text for reference whenever I am doing something else and I'm not 100% sure on something.

 

[Nano-Passion]

^That is not true. Stewart is like many popular calculus books in that instead of actually teaching calculus it teaches one to solve trivial problems without any understanding like a defective calculus robot. It is true that many people enjoy and benefit from a first calculus book that is theoretical. Theorems are problems, so it is nonsense that there is some risk of understanding so much that one cannot solve trivial problems. Stewart is not a particularly good book of its type. There is not much to recommend it, even if cookbook calculus is desired.

Stewart is a good introductory book. I think it has some pretty challenging problems [non plug and chug] in the book, you just have to look for them. I would personally recommend many to uses Stewart to grasp the basic concepts and problem solving and hit a more rigorous book such as Spivak, that seems like the best thing to do.

What I do is that as soon as I feel like that the plug-and-chug problems are too easy I will stop. Its practice to me so that I know that I won't mess up on the test, which is then followed by some harder problems that require thinking.

 

[Sina]

Is the rigor on par with spivak's calculus book?

I have not seen spivak's book but I wouldn't think that the level fo rigour on Marsdens book to be inadequate. But he also puts much importance to intuitevely and geometrically grasping the topics. That might be disturbing if you happen to develop good feelings toward Bourbaki

ps. just because it has Newton in its cover doesn't mean it is non-rigorous

 

[Sina]

Okay I will ask a question my self.

Is there any good books on functional analysis that goes parallel with application to quantum mechanics?

Remark:
1- I am already reading von neumann's book but ofcourse its scope is limited
2- I actually like von neumanns approach where he builds resolution of identity as a measure
so that approach would be a bouns
3- I know reed and simons book but I think it is mathematics first applications later right? I like it better when ideas are immedieatly applied to some physical problems.

Best wishes

 

[homeomorphic]

Okay I will ask a question my self.

Is there any good books on functional analysis that goes parallel with application to quantum mechanics?

Remark:
1- I am already reading von neumann's book but ofcourse its scope is limited
2- I actually like von neumanns approach where he builds resolution of identity as a measure
so that approach would be a bouns
3- I know reed and simons book but I think it is mathematics first applications later right? I like it better when ideas are immedieatly applied to some physical problems.

Best wishes

I'm not sure if this is what you want, but since no one else answered, I would recommend the last chapters of Robert Geroch's Mathematical Physics. Best intro to functional analysis I have ever seen by far. Despite the book's title, there isn't that much physics, though.

 

[Mathguy15]

Hey guys! I'm new here, and I am strongly considering becoming a mathematician, but, like most people, I don't know if I am smart enough. I'm fifteen in the tenth grade, and I have taken tests like the AMC10 and 12, but I haven't done very well. I have dabbled some in abstract algebra and I have done some linear algebra(at least more than abstract algebra) and some number theory, but I'm not sure if I am smart enough. Are earlier posts in this thread going to be helpful?

 

[mathwonk]

Let me remind you that the voting is open in the PF lounge for awards. There is a math award, and I urge you to consider the very valuable work of those people who answer actual math questions day in and day out in the math forum for your vote.

 

[mathwonk]

To go out on a limb here, I want to suggest that for most of us there is such a thing as too much math. I.e. think about whether solving a famous problem is worth so much to you that you are happy to live like a hermit the rest of your life and only come out every few years for air, or whether you would rather be (if you are a guy) sort of a cross between a top math genius, brad pitt or jet li, segovia, umberto eco, david beckham, picasso, and the world's strongest man.

At some point in this journey you are at least going to want to know something about art, music, literature, politics, sports and psychology, even if only to get a date with someone other than "Watson". So take some courses in college that are not all math and science. I.e. there are skills courses and enrichment courses. Enrich your life a little, so you don't come across as a total nerd, like me. Note I have virtually never mentioned anything in this gargantuan thread except geeky stuff.

(Nonetheless, at least until recently, I could play pool fairly well, sing falsetto in the car, ride a bicycle, converse about wine, deal from the bottom of a deck, make an almost unguardable hookshot layup, a swan dive from a height slightly above my head, and the occasional three pointer. These accomplishments took years of dedicated practice mostly outside the library.)

Since a mathematician is also a person, and a happily adjusted person can actually do more math, becoming a mathematician includes these extra curricular topics too. Try not to become too narrow to relate to the rest of the society entirely. Just a suggestion.

 

[Sina]

no only take mathematics and physics courses while you still can you can read philosophy etc later

 

[Sina]

The small fonts were meant to signify that it was a joking statement :p

 

[mathwonk]

i logged back into delete my latest, and saw this. another thing about nerds, we never get the joke.

 

[Nano-Passion]

To go out on a limb here, I want to suggest that for most of us there is such a thing as too much math. I.e. think about whether solving a famous problem is worth so much to you that you are happy to live like a hermit the rest of your life and only come out every few years for air, or whether you would rather be (if you are a guy) sort of a cross between a top math genius, brad pitt or jet li, segovia, umberto eco, david beckham, picasso, and the world's strongest man.

At some point in this journey you are at least going to want to know something about art, music, literature, politics, sports and psychology, even if only to get a date with someone other than "Watson". So take some courses in college that are not all math and science. I.e. there are skills courses and enrichment courses. Enrich your life a little, so you don't come across as a total nerd, like me. Note I have virtually never mentioned anything in this gargantuan thread except geeky stuff.

(Nonetheless, at least until recently, I could play pool fairly well, sing falsetto in the car, ride a bicycle, converse about wine, deal from the bottom of a deck, make an almost unguardable hookshot layup, a swan dive from a height slightly above my head, and the occasional three pointer. These accomplishments took years of dedicated practice mostly outside the library.)

Since a mathematician is also a person, and a happily adjusted person can actually do more math, becoming a mathematician includes these extra curricular topics too. Try not to become too narrow to relate to the rest of the society entirely. Just a suggestion.

Top notch advice every time. You see the bigger picture of things mathwonk.

 

[lisab]

Top notch advice every time. You see the bigger picture of things mathwonk.

I agree, that was excellent advice.

I'm sometimes torn when I encounter a bright, ambitious young person seeking advice here. They're often so brilliant and willing to sacrifice to achieve their goals. Of course, I want to help them on their path - that's what PF is for.

But I also want to tell them, go hike in the woods! Learn to ski! Fall in love! There is more to life than academic achievement, and life is so short!

 

[eliya]

mathwonk is correct, of course, but it's not just that. I sometimes feel like people think that mathematicians sit in a study and work on mind boggling problems to a candle light. People have this very romantic (not in the sense of falling in love) view of mathematicians, or scientists in general. I think it's quite different than that. A lot of the time people are stuck on a problem and pull hairs out trying to figure it out. You need to vent and occupy your mind with other things every once in a while. You also want to be able to hang out with people, because human beings, whether you like it or not, are social animals. Living alone in an attic and doing math for fifty years will probably drive you insane. Do math, lots of it, but also know how to be a human being, because you are one.

 

[Nano-Passion]

I agree, that was excellent advice.

I'm sometimes torn when I encounter a bright, ambitious young person seeking advice here. They're often so brilliant and willing to sacrifice to achieve their goals. Of course, I want to help them on their path - that's what PF is for.

But I also want to tell them, go hike in the woods! Learn to ski! Fall in love! There is more to life than academic achievement, and life is so short!

This really influenced me actually.

Edit: Especially because I'm kind of a 'romantic' and love all the things you listed above.

 

[homeomorphic]

I wonder if my "well-roundedness" just makes me even more of a nerd, though.

I play piano, but that just makes me a music nerd, on top of a math and physics nerd (though it does impress people). I learned a lot about biology, but that, of course, just makes me a biology nerd, on top of all the other kinds of nerd I am. Playing go. Also kind of nerdy. It does help me connect with different types of nerds, though. Philosophy also just makes you more nerdy.

Of course, I do some other things that aren't so nerdy, like playing soccer and running, too.

The fact is, cultures can be somewhat anti-intellectual, and no one should try too hard to fit into them.

One thing that would probably go a long way towards fitting in is watching TV, but I find it a challenge to enjoy most things on TV. I believe this has significant consequences for my social life, but it's hard to do make myself do things I am not the least bit interested in, just so I can fit in more. I suppose, to some extent, that means I am doomed, socially. But I think it's worth the price I pay.

 

[kramer733]

I`m no math nerd at all .. althought i wish i was. I do brazilian jiu jitsu and mma recreationally. I also started doing salsa recreationally as well. I feel like math is more of a recreational activity for me as well. I don`t know where i`m going at in my life at all now. Everything i do feels so recreational.

I`ll probably end up joining the air force.

 

[mathwonk]

we should not ignore the spiritual side of life either. tonight while watching "the man who knew too little". I was rewarded with reassurance that the universe loves me, when i dropped my cheese cracker on the floor and it fell cheese side up.

i.e. math guys can love movies too.

 

[deckoff9]

Everything i do feels so recreational.

Isnt this a really good thing?

 

[Functor97]

I agree, that was excellent advice.

I'm sometimes torn when I encounter a bright, ambitious young person seeking advice here. They're often so brilliant and willing to sacrifice to achieve their goals. Of course, I want to help them on their path - that's what PF is for.

But I also want to tell them, go hike in the woods! Learn to ski! Fall in love! There is more to life than academic achievement, and life is so short!

It is kinda hard for people to fall in love with you when you major in pure mathematics. Most people i tell my major to reply "why would you want to do that?" or "What job are you going to get with that?", what is more these people are generally of above average intelligence (history, literature, engineering, economics majors). Why a football player is a more worthy mate than a mathematician is beyond me

 

[chiro]

It is kinda hard for people to fall in love with you when you major in pure mathematics. Most people i tell my major to reply "why would you want to do that?" or "What job are you going to get with that?", what is more these people are generally of above average intelligence (history, literature, engineering, economics majors). Why a football player is a more worthy mate than a mathematician is beyond me

If this is the case for you, you need to meet other people.

I spent a lot of time growing up in the country and I was the only person that found computer programming "cool" and to a large extent mathematics "cool".

Then you end up going to a university or doing a diploma course and you realize that in this environment your "average" or more likely, "less than average". The best thing though, is that you don't have to hide who you are, your quirks, and all the rest of that because this is normal.

Having said that, mathwonks advice is very important. Even if you want to dedicate a lot of your time to math (even when measured with respect to other scientists/mathematicians), sometimes you need to break up the day by doing something else.

Also with regards to the opposite sex, again that's just meeting different people. The argument is exactly the same as above.

 

[kramer733]

Isnt this a really good thing?

No it's because i felt like I've never had true passion in life. I don't want to live in a life without passion. I feel like I'm going nowhere.

 

[Nano-Passion]

No it's because i felt like I've never had true passion in life. I don't want to live in a life without passion. I feel like I'm going nowhere.

Life without passion is life without breath, without motivation. My passions help define who I am, and give me the motivation to live. Of course though, it is part of happiness and you can easily live through life without liking anything particularly deeply. But as for my case, I like having the intellectual stimulation. ^.^ Passion doesn't just include studying though, sometimes it could mean staring into the river or something else that is beautiful.

If you want a passion, go look for it. Passion is a fuzzy term, its all psychology. Your thoughts stem from your psychology. You can influence your own psychology, go for it.. think about it for a bit.

 

[deckoff9]

It is kinda hard for people to fall in love with you when you major in pure mathematics.

Lol. Here's a hint. No one is going to fall in love with you or not based on your major.

 

[homeomorphic]

I don't blame the fact that I can't fall in love on my being a mathematician. I just don't have enough charisma, I guess. Plus, I am too shy, and I don't know how to get a date. More of a socially awkward thing than a mathematician thing. Being a mathematician may scare some people away, but when I asked around about it, it didn't seem to be a deal-breaker for most girls. It takes a certain kind of person to handle a relationship with a busy scientist or mathematician, though.

 

[homeomorphic]

math guys can love movies too.

I can do movies because people tend to put more effort into them. Just not most TV or at least only nerdy TV like the history channel or PBS or something.

 

[Cod]

What is the best way to prep for a Algebraic Structures course? Here is the course description: "An overview of algebraic structures. The aim is to construct mathematically correct and concise proofs. This course introduces techniques of proofs, set theory, and group theory, and the application of those techniques. An overview of groups, rings, integral domains, and fields; detailed study of several groups; and exploration of properties of integers and polynomials. Topics may include an introduction to computer algebra and Boolean algebra." Based on the pre-reqs and description, I'm thinking I need to go back over my Calc II and Linear Algebra notes. Any others? Also, of note, the course will probably not be very rigorous since its an online course through UMUC with teaching at the high school level in mind.

Any guidance is greatly appreciated.

EDIT: Text was just released. Its "An Introduction to Abstract Algebra with Notes to the Future Teacher" by Nicodemi (https://www.amazon.com/dp/0131019635/?tag=pfamazon01-20). Thanks again for any help!

 

[eliya]

I wonder if my "well-roundedness" just makes me even more of a nerd, though.

I play piano, but that just makes me a music nerd, on top of a math and physics nerd (though it does impress people).

I learned a lot about biology, but that, of course, just makes me a biology nerd, on top of all the other kinds of nerd I am.

Philosophy also just makes you more nerdy.

That doesn't make you a nerd. Unless your definition of a nerd is derived from 90's american teenage movies. Everyone can be regraded as nerd. People who are into football? They can be regarded as nerds too. Fantasy football is super "nerdy", especially if you go into all of the statistics behind it. The point is that everyone is nerdy. Everyone who has some sort of a passion is a nerd, and you don't want to date those who don't. Seriously, a nerd is just a term that dumb kids in high school invented.

You need to figure out the environments you want to hang out in, and how to present yourself. For instance, if you're not into sports, you won't go to a sports bar to hang out. Why? Because it's a different kind of nerds who hang out there. Don't expect to strike a conversation with someone at a sports bar in the midst of a football game by saying "I like math". That's not going to work. Also, I think that people don't want to hear too much about you when you just meet them. That is, if you tell someone you're a mathematician and they ask what it entails, don't start giving them details about the problem you're currently working on. They won't understand it. Explain to them what it generally means to be a mathematician and why you like it. The same way you won't talk about your ex-girlfriend the first time you meet someone. There's a time and a place for everything. If you tell someone that you like math/a mathematician and they look down at you and leave, then they're not worth your effort anyway.

One thing that would probably go a long way towards fitting in is watching TV, but I find it a challenge to enjoy most things on TV. I believe this has significant consequences for my social life, but it's hard to do make myself do things I am not the least bit interested in, just so I can fit in more. I suppose, to some extent, that means I am doomed, socially. But I think it's worth the price I pay.

There's a lot of bad TV, but there's also some good stuff on it. You just need to find what you like. I used to not watch TV at all and it never prevented me from fitting in. Now I do watch some shows, but only because I like them, not to fit in.

One last tip, drink when you go out. Don't get wasted, but a beer will help you loosen up a little bit. Ever watched Can't Hardly Wait? The nerdy guy drank at the party and became everyone's favorite.

Sorry I derailed the thread from talking about people's aspirations to becoming mathematicians to that. I'm just always a little upset when people complain about being too nerdy and not being able to socialize. To keep the thread on track - I like math and would like to keep doing it for a long time.

Playing go.

Now that's really nerdy.

 

[homeomorphic]

That doesn't make you a nerd. Unless your definition of a nerd is derived from 90's american teenage movies. Everyone can be regraded as nerd. People who are into football? They can be regarded as nerds too. Fantasy football is super "nerdy", especially if you go into all of the statistics behind it. The point is that everyone is nerdy. Everyone who has some sort of a passion is a nerd, and you don't want to date those who don't. Seriously, a nerd is just a term that dumb kids in high school invented.

Nerdiness, here, is basically referring to being into things that most people don't find interesting. What I have in mind is if you took a poll and saw what most people are interested in. Most people don't care that much about science, math, or philosophy. That's the point. What are the kind of lowest common denominator subjects that the man on the street is interested in?

You need to figure out the environments you want to hang out in, and how to present yourself.

I've been thinking about how to present myself since high school, and I have unable to come up with any answers. I just have a disability. I think I am mildly autistic.

For instance, if you're not into sports, you won't go to a sports bar to hang out. Why? Because it's a different kind of nerds who hang out there. Don't expect to strike a conversation with someone at a sports bar in the midst of a football game by saying "I like math". That's not going to work.

Of course not. I wouldn't try that. I don't bring up math for no reason. But, all they want to talk about is football, and I have no clue about football, so there's nothing for us to talk about. So, yes, I won't go there to hang out. The fact that there ARE sports bars tells you something. There are no philosophy bars or biology bars.

Also, I think that people don't want to hear too much about you when you just meet them. That is, if you tell someone you're a mathematician and they ask what it entails, don't start giving them details about the problem you're currently working on. They won't understand it. Explain to them what it generally means to be a mathematician and why you like it. The same way you won't talk about your ex-girlfriend the first time you meet someone. There's a time and a place for everything. If you tell someone that you like math/a mathematician and they look down at you and leave, then they're not worth your effort anyway.

It's not what I say. It's what I don't say. I don't have any good jokes. I don't know about anything that interests people. I have no charisma.

There's a lot of bad TV, but there's also some good stuff on it. You just need to find what you like. I used to not watch TV at all and it never prevented me from fitting in. Now I do watch some shows, but only because I like them, not to fit in.

Well, I have experienced an uncountable number of conversations that I had nothing to contribute to because I don't watch enough TV or movies.

One last tip, drink when you go out. Don't get wasted, but a beer will help you loosen up a little bit. Ever watched Can't Hardly Wait? The nerdy guy drank at the party and became everyone's favorite.

Well, I do drink alcohol on rare occasions, but I have never really been drunk. I really don't think it does anything for me. I am just the same awkward guy who doesn't know what to say.

I have a disability. I accepted long ago that I would never fit in anywhere or be a normal guy. There's just not much hope for me, socially. It's quite separate from being a mathematician. Other math grad students are not socially disabled like me. I don't even fit in among them.

Sorry I derailed the thread from talking about people's aspirations to becoming mathematicians to that. I'm just always a little upset when people complain about being too nerdy and not being able to socialize. To keep the thread on track - I like math and would like to keep doing it for a long time.

On another note, it looks like I am going to quit math (at least academia) because I am too slow at research, and I don't want to deal with student complaints that threaten my career all the time. No one wants the weird autistic prof who doesn't know how to communicate with ordinary people. Other grad students say teaching is easy for them. It's essentially impossible for me. Why try to force it? Even if I can get the students to shut up with their complaints, I don't want the pressure. So, it looks like I am going to go to industry and quit academic math. I have no publications, and a lousy teaching record.

Playing go.

Now that's really nerdy.

Hey, go is awesome.

 

[mathwonk]

The basic fact, that seems to take so long to grasp about social interactions, is that being popular is not about being fascinating oneself, but consists in finding other people fascinating. I told the story here before about the plane trip I took with a very boring woman seat mate, and another very likeable man seatmate, all of us in a 3 seat group.

At least I thought she was boring when I was talking to her, since she was not interested in my own hangups, and I thought him likeable since he listened to me skillfully and patiently while I talked about my passionate interests.

Then he began talking to her, and drew her out beautifully, at which point she became extremely fascinating to me as well. Then I realized, this man makes everyone seem interesting, because he genuinely takes an interest in them and the things they love.

He not only made friends of both of us, but he made us appreciate each other. I was very impressed. I confess I still have not mastered his gift. It takes a bit of work, but I have witnessed the wonderful potential it has.

Have you ever asked yourself: "how does that delightful woman find that turkey of a man attractive?" Then we watch them interact and we see that he loves her and appreciates her and thinks of her welfare and her interests, and she apparently would not give that up for anything.

 

[Reb]

There's also a different side to doing math. Reading from S. Ulam's "Adventures of a Mathematician":




"In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.) Yet one cannot be sure that this is the sole reason; for others, mathematics is what they can do better than anything else."

 

[mathwonk]

well that is true, but phrased in a somewhat negative way. it reminds me of a poem by a nobel prize winning author perhaps a czech, in the 1980's who wrote something like:

"I do not apologize for seeking out beautiful words, to me at least that seems better than killing and murdering."