Alternate paths to careers in mathematics

[gosper]

I have a dilemma that I don't know how to solve, and I'm hoping for advice. My dilemma is that I simultaneously love mathematics and hate school. If you just want to get to the point, skip to the last paragraph, but if you want the details, read on. To elaborate, I have dropped out of college twice now, and am dropping out for a third time at the end of this semester. Any time I have not been in school, I have found myself drawn back to mathematics and studying it in my free time. I taught myself trig after high school, and later calculus. I find number theory incredibly interesting and am very interested in cryptography and data compression. However, every time I go back to school I find myself laying in bed every morning dreading the day ahead. I find the lectures long and boring, the course material shallow and vapid, and the emphasis more on student's work output and memorization and mindless application of equations rather than on intuitive understanding of the course material. One of my calculus professors once said that the work load in the course was as heavy as it was because there were "so many possible variations, and you have to know what to do when you encounter them." My question to him, if I actually understand what is going on intuitively, then shouldn't I know how to applying that understanding to any variation of a problem? Isn't it impossible to teach an algorithmic process for solving EVERY possible problem? (He didn't seem to like that line of questioning much)

I feel I have to add that I'm not one of these "I'm really smart, but I have a 2.2 GPA" people, either. I do well in my classes when I am taking them. I currently have a 3.87 GPA and the only reason it isn't a 4.0 is that I was passing kidney stones during finals week one semester and didn't do so well on a few of the tests. But I hate it. I hate dragging myself to class every day. I hate sitting in a classroom and listening to someone lecture on material that I know I could read in half the time and understand twice as well. I hate doing the mindless assignments and stupid tests and jumping through all the academic hoops so I can get the GPA that is dangled in front of me every semester. Add on to this that the way the economy is, it's really incredibly doubtful that I'm actually going to get a decent job in a field that I want after graduation anyway, which makes me wonder what the hell I'm putting myself through this for.

I seriously feel like my brain is rotting and oozing slowly out of my ears. If I continued school, at this point I would have 2 1/2 more years until graduation, and the thought of pushing myself through that makes me want to shoot myself. I can't put myself through another semester, and I don't want to keep going with this stupid cycle of "enroll, complete a semester or two, drop out, repeat" because I don't see it getting me anywhere in the end.

So my question is this: what other options are there available to me? Work is difficult to come by right now, but I've considering joining the military and just studying on my own in my free time. But could I actually go anywhere doing this? Is there some sort of field for people with an aptitude for and interest in mathematics who are willing to study the subject, but not willing to go to school? I can't imagine the only path available to me is the typical school -> internship -> office job, but it is the only path that I know.

Thank you to anyone who actually read through all of this.

 

[chiro]

Hey gosper and welcome to the forums.

In terms of finding work involving mathematics without the need to get formal training (i.e. university), the only one that I am familiar with is the actuarial profession.

If you can pass the actuarial exams (you take them with your associated actuarial society), you could get an entry level job and then by passing your exams you can become a qualified actuary.

But in saying the above, the exams themselves are very hard. They are harder than your standard university science-type exams and they require a lot of dedication and discipline to pass. If you can pass these exams without having to get a major in mathematics or statistics, then by all means go for it. You can see what to expect by going to your actuarial society website.

With regards to lectures being boring and assignments being pointless, you should realize that most jobs do become routine and boring after a while, and for the jobs that are very diverse, they will require you to get a lot of training before someone will allow you to have the responsibility to do those kinds of tasks.

Have you ever worked any part-time or full-time jobs in the past? If you have you should realize that working in an office in front of a computer running simulations or writing a report can easily beat the hell out of working in a factory, or busting your arse out in the sun doing manual labour.

The military might be good for you to build character and certainly it would be a good idea if you find your current life 'boring'. A lot of people enter the military for that reason: they want a new set of challenges.

The only thing however is that many military experiences don't necessarily have an application in the civilian sector. Some do, but others do not. If you do end up going this route, I would suggest you pick a civilian type trade like an electrician or an electronics technician or something of that sort.

Also it seems like you are putting all of your attention into your school. Maybe you could find a new hobby or something that breaks up your day.

For me its playing the guitar and writing songs, reading insightful posts here at PF, spending an hour or two on online games, or allocating time to my own research.

The last thing I want to ask you to do is to be honest with yourself. The ultimate question I would ask is 'Why do you want to do mathematics?', 'What is the endgame?'

 

[jspenuk]

Unless you want to run your own business in some form or shape, not having a degree will severely limit your options. If I was you, I would finish the degree and then re-evaluate my options and priorities.

 

[hadsed]

Add on to this that the way the economy is, it's really incredibly doubtful that I'm actually going to get a decent job in a field that I want after graduation anyway, which makes me wonder what the hell I'm putting myself through this for.

Maybe, but without a degree you are much, much worse off.

What you really need to do is change your attitude. This is not taking a shot at you, but I know you feel from personal experience. I find school (or classes at least) to be highly irritating and I try to avoid them if at all possible. Of course this isn't something you can really fix, so you have to somehow change your state of thought and see the benefits of doing school. Don't focus on just the end results, think about how the classes are helping you instead of just how they're hurting you or annoying you. In general, people can't and won't do things they find to be a waste of time if they have a choice.

There are benefits to going to school. You have a structured place to learn the things you want without having to work, and it's built in a way that society finds acceptable. You have to think in relative terms; is going to school better than working construction while studying mathematics? It's doubtful that you'll be able to do the things you love if you do that. Think about the majority of other students who don't know what they love, and compare them to yourself. You know what you love, you know what you want to do and you're doing it, it's just not as flowery as it could be. So what, it'll never be like that. You could also try making the material harder on yourself. Finish the reading beforehand, do all the homeworks, then work on extra material. Ask your instructors if they will go over extra material with you. I can't imagine any professor who wouldn't be happy to see a bright young person showing such interest beyond the classroom. Doing the extra material will motivate you, because it's your choice and you're doing what you find useful and interesting.

Sometimes you just need to find a way.

 

[Sankaku]

I can't help you regarding Career, but this is an interesting comment:

...the emphasis more on student's work output and memorization and mindless application of equations rather than on intuitive understanding of the course material.

I hear your pain. In many universities, most of the math courses in the first year or two are aimed at computational skills. Calculus I,II,III, Matrix Algebra and ODEs (the way they are usually taught) are mostly number crunching. For someone going into Physics or Engineering, these skills are important. For many areas of pure mathematics, they don't matter quite as much as time goes on. For anything Analysis-related, you will still need to have your basic calculus skills honed, but for areas like Abstract Algebra you will be using different tools entirely.

I am assuming that you don't have access to honours-level courses that are more theoretical? The sad fact is that many departments want you to prove you can gut out the number crunching before the abstract stuff gets fun. If your school is decent, there should be early proof-based courses that could maintain your interest. If you are truly ahead of the game, ask for special permission to jump ahead to upper level classes. Some profs will let you sink or swim on your own skill if you want to bypass the official prerequisite system.

If not, it may be a cost-benefit measurement. Is the reward of doing the interesting stuff in mathematics worth the cost of boring computational courses? That is a question you will have to figure out yourself.

 

[Floid]

Part of life is playing the game and doing things you don't want to do/don't think are necessary. Sorry, that is just the way it is...

 

[gosper]

Hey gosper and welcome to the forums.

In terms of finding work involving mathematics without the need to get formal training (i.e. university), the only one that I am familiar with is the actuarial profession.

If you can pass the actuarial exams (you take them with your associated actuarial society), you could get an entry level job and then by passing your exams you can become a qualified actuary.

Thank you for the greeting. I've looked into the actuary thing before. From my understanding, there is a heavy emphasis on statistical analysis and business strategy which really doesn't interest me.

With regards to lectures being boring and assignments being pointless, you should realize that most jobs do become routine and boring after a while, and for the jobs that are very diverse, they will require you to get a lot of training before someone will allow you to have the responsibility to do those kinds of tasks.

Have you ever worked any part-time or full-time jobs in the past? If you have you should realize that working in an office in front of a computer running simulations or writing a report can easily beat the hell out of working in a factory, or busting your arse out in the sun doing manual labour.

The military might be good for you to build character and certainly it would be a good idea if you find your current life 'boring'. A lot of people enter the military for that reason: they want a new set of challenges.

The only thing however is that many military experiences don't necessarily have an application in the civilian sector. Some do, but others do not. If you do end up going this route, I would suggest you pick a civilian type trade like an electrician or an electronics technician or something of that sort.

That's the thing that really scares me, to be perfectly honest. I don't want to drag myself through four miserable years of college to go on to an equally miserable job. I really have no interest in money, and I'd rather just get a job with little to no responsibility if that is going to be the case. I already live on next to nothing and I have no problem continuing to live that way. On top of that, I've talked with the heads of engineering, comp sci, and mathematics at my university and the job statistics are pathetic. Only something like 15% of students are actually offered positions in their field of study within a year of graduation. Personally, one of my friends graduated with a Civ. Engineering degree and ending up working at McDonalds and Subway for two years before he gave up and joined the army (to double the pain, he was stuck in an artillery unit so he isn't even using his education there either). Most of my other friends who graduated are in similar crappy situations and the few who got real jobs are working in IT or software dev, which I have absolutely no interest in getting into (well, back into to an extent). I think I would be able to swallow it for now if I thought there was a light at the end of the tunnel, but it just doesn't seem to be.

In terms of work, to be complete honest, I really prefer busting my *** in the sun to sitting behind a desk mindlessly enter code or numbers into a computer. I had a really well-paying job as a network admin assistant that I left because it was just miserable. I'd spend most of my day cramped up in a chair, reading through poorly written technical manuals to solve really stupid problems that other people created. I'd get home and I'd be exhausted from sheer boredom and my entire body would be killing me from lack of exercise. Honestly, as sad as it is, I've found working retail to be much more rewarding, and my short stint working construction was one of my happier periods. It was tough as hell, but I got some exercise everyday and interacted with other human beings on a regular basis.

I don't know how challenging the military would be. Really, I see it as somewhere where I can take my mind off my basic needs. I think I also hold an overly idealistic view that the military won't waste talent if they see it.

Also it seems like you are putting all of your attention into your school. Maybe you could find a new hobby or something that breaks up your day.

For me its playing the guitar and writing songs, reading insightful posts here at PF, spending an hour or two on online games, or allocating time to my own research.

The last thing I want to ask you to do is to be honest with yourself. The ultimate question I would ask is 'Why do you want to do mathematics?', 'What is the endgame?'

I wish I had the time. Unfortunately, when I'm not in class, I'm working. I consider myself lucky on the days that I get to cram two meals into my schedule. Even with financial aid and loans I still have a ridiculous number of expenses that aren't covered. And this is coming from a guy who doesn't spend money on ANYTHING. Seriously, I'm typing this up from a laptop that I bought for about $400 nearly 3 years ago.

To address the last point, I like puzzles and I like understanding how things work. That's one of the reasons why a career in mathematics interests me: I enjoy the study in itself. There doesn't have to be an endgame. I would happy scraping by on a crappy yearly wage if I could get a job that encouraged my studies and used the knowledge I had acquired in order to solve interesting problems. In fact, I would highly prefer it to a position that paid very well but in which I was just working in order to acquire money. I mean, I know no job is interesting 100% of the time, but as a general rule.

Maybe, but without a degree you are much, much worse off.

What you really need to do is change your attitude. This is not taking a shot at you, but I know you feel from personal experience. I find school (or classes at least) to be highly irritating and I try to avoid them if at all possible. Of course this isn't something you can really fix, so you have to somehow change your state of thought and see the benefits of doing school. Don't focus on just the end results, think about how the classes are helping you instead of just how they're hurting you or annoying you. In general, people can't and won't do things they find to be a waste of time if they have a choice.

There are benefits to going to school. You have a structured place to learn the things you want without having to work, and it's built in a way that society finds acceptable. You have to think in relative terms; is going to school better than working construction while studying mathematics? It's doubtful that you'll be able to do the things you love if you do that. Think about the majority of other students who don't know what they love, and compare them to yourself. You know what you love, you know what you want to do and you're doing it, it's just not as flowery as it could be. So what, it'll never be like that. You could also try making the material harder on yourself. Finish the reading beforehand, do all the homeworks, then work on extra material. Ask your instructors if they will go over extra material with you. I can't imagine any professor who wouldn't be happy to see a bright young person showing such interest beyond the classroom. Doing the extra material will motivate you, because it's your choice and you're doing what you find useful and interesting.

Sometimes you just need to find a way.

Unfortunately, the reality of this is that I do have to work to feed myself. Also, I really would prefer to just work and study at my own pace on the side. That isn't so much a question as whether I can actually do anything with that later on. And I really don't have time to go over extra material on the side, not that it would matter as I've already studied far beyond what my class is going over at this point in time.

I can't help you regarding Career, but this is an interesting comment:I hear your pain. In many universities, most of the math courses in the first year or two are aimed at computational skills. Calculus I,II,III, Matrix Algebra and ODEs (the way they are usually taught) are mostly number crunching. For someone going into Physics or Engineering, these skills are important. For many areas of pure mathematics, they don't matter quite as much as time goes on. For anything Analysis-related, you will still need to have your basic calculus skills honed, but for areas like Abstract Algebra you will be using different tools entirely.

I am assuming that you don't have access to honours-level courses that are more theoretical? The sad fact is that many departments want you to prove you can gut out the number crunching before the abstract stuff gets fun. If your school is decent, there should be early proof-based courses that could maintain your interest. If you are truly ahead of the game, ask for special permission to jump ahead to upper level classes. Some profs will let you sink or swim on your own skill if you want to bypass the official prerequisite system.

If not, it may be a cost-benefit measurement. Is the reward of doing the interesting stuff in mathematics worth the cost of boring computational courses? That is a question you will have to figure out yourself.

That's really what it is. In my Calc course we have piece of paper covered front and back of obscure formulas that the instructor will provide for us if we need them on the test. It's the "these are the ones that I'm not requiring you to know" sheet. Beyond that, there are just an endless array of algorithmic procedures that we are required to memorize in order to solve esoteric problems that really don't test mathematical understanding as much as whether you've memorized a bunch of formulas. Sadly, I feel like this is really hurting my understanding of material that I already know. Instead of reinforcing knowledge that I had already obtained, I feel like I'm losing an actual understand of mathematics and replacing it with:

If problem is in form 4:
apply formula 87 to get problem in form 6
apply formula 23 to get answer
Else if problem is in form 6:
apply formula 23 to get answer

Actually, I've found most of my experience with college courses could be summed up as the above. We don't have any honors courses or proof-based courses. I tried convincing the mathematics department to let me test out of prerequisite course mathematics courses, but they would only let me test out of College Algebra, Pre-calc, and trig.

But beyond that, I really just don't see this changing in pace. Beyond what I'm taking now, I'm going to be paraded through another semester of calculus, physics, basics of computer programming, C programming (forget the fact that I could code around most of instructors, who have probably never written a practical program in their lives, I'm not allowed to test out of these courses either), basics of Computer Science, and a slew of other mindless "memorize these 10,000 things" courses. Even if the course work in mathematics classes became more interesting, I have no doubt it would be heavily overshadowed by other bull-crap that I would be forced to take.I guess what I'm really just looking for is an alternative to just working an studying as a hobby. But I think that the days are gone when some big company like AT&T will pick up kids with aptitude, and use their skills, wherever they may have come from.

Honestly, I'm really thinking the military option is the best thing for me unless anyone has any other suggestions. Considering cryptography is an interest of my anyway, that might be a decent place to go. At least I'll be freed of having to worry about any of my basic needs, even if my day-job is dreary. I think the lack of stress in that area would be an acceptable trade-off. Study in my free time, solve a few problems and make a few contributions and see if I can get anywhere with that.Thanks for the responses so far, and sorry for taking so long to respond. It got a little crazy in my neck of the woods the last couple of days.

 

[chiro]

I don't think you need to go to college or university to be successful or get a job that you like.

My advice to you if you don't want to go this route is think about an area and a particular skillset and work towards becoming the best (or really really good) in that domain.

It doesn't matter if its blue collar or white collar, intellectual or mechanical work, or any other variation inbetween. Find an area and speciality and spend a lot of time becoming the best.

The reason I'm studying mathematics and not running a business is because I really like mathematics. Its what I want to eventually become good at. The electricians, plumbers, chefs, and welders are probably going to make more money than me, especially if they have their own business and the ones that work to become the best in the business will probably make more money than a lot of the college/university graduates, and the reason they make the money is simple: they have a skillset that is very hard to find or obtain.

 

[Sankaku]

Gosper, I am a little worried that you say there are no proof courses. Surely there are some you get to eventually? Any math degree worth its salt should have at least some Discrete Math, Abstract Algebra, Analysis, Topology and Number Theory?

Beyond that, there are just an endless array of algorithmic procedures that we are required to memorize in order to solve esoteric problems that really don't test mathematical understanding as much as whether you've memorized a bunch of formulas.

I often worry that mathematics education, in many North American universities, is designed so that those who excel at computation will hit a wall when they get to proofs and those who have the imagination to do proofs never get through the endless computation.

That said, however, the basic skills you learn in Calculus I,II,III may seem esoteric now, but most of them will come up in many areas later on. Just because they don't teach you the theory, it doesn't mean you can't learn it on your own time. I would recommend "Understanding Analysis" by Abbott, if you want to see beneath the surface of the calculus you are doing. Ideally, if you understand what is going on, most of the "mindless" stuff should become pretty intuitive.

If it is too much all at once, take one less course and enjoy the process more.

 

[gosper]

Sorry, when I say there are no proofs courses, I mean there are no proofs courses that are available without prerequisite credits that I haven't obtained. At my university, you really can't take most of them until the junior level at the very least.

From my understanding, most places outside of the US general have course geared towards different majors. There is a guy from Brazil in one of my classes who said that the universities in his country will have, for instance, a calculus class for mathematics majors and a calculus class for engineers. This seems to make sense to me, because the focus is completely different. I'm expected to memorize tables of densities for liquids in my calculus class and tables of astronomical data and unit conversions in phyiscs for instance. I'm never going to use any of this outside of the class room, but it is heavily emphasized. I'm not an engineer student, or an astrophysics student. I really don't give a damn if I know how many inches are in a meter. The second I'm out of the classroom, I'm going to forget it anyway.

The problem with the last part lies in the fact that many of my instructors have required that problems be solved a certain way. I got marked off on one of my calculus tests on a question that involved finding the volume of an object by revolving a shape about an axis because I didn't find it using the specific method the instructor asked for. Granted, I could just say screw it and solve the problems how I see them and just take a C in the class, but that would beat the hell out of my GPA.

 

[ParticleGrl]

I really don't give a damn if I know how many inches are in a meter. The second I'm out of the classroom, I'm going to forget it anyway.

Have you really seen rulers that rarely? 1 ruler = 12 inches = 30.5 cm. Unit conversions for everyday units are useful for everyday living.

 

[gosper]

Have you really seen rulers that rarely? 1 ruler = 12 inches = 30.5 cm. Unit conversions for everyday units are useful for everyday living.

Please give me one example of where I will use this information in my everyday life. Better yet, give me one example of where knowing how many slugs are in a kilogram is going to come in handy. I'm still trying to figure that one out.

Besides, it was just a general example.

 

[ParticleGrl]

Please give me one example of where I will use this information in my everyday life.

Driving in another country, having a general idea of km vs miles is helpful. I recently bought a carpet for my sister's apartment, the carpet was sized in centimeters, and the dimensions of the room were given to me in square feet,etc.

 

[Sankaku]

While I agree that forcing someone to memorize conversions is completely unnecessary, they come up in real life all the time. Well, in North America at least.

Despite Canada being metric, I have to convert back and forth for the Baby-Boomers I work with. However, a metric conversion calculator costs a few bucks and can tell me that 4.26 hectares is 10.53 acres whenever I want (yes, I had to do that today). If the USA would finally switch over to metric, maybe our grandchildren could forget the prehistoric Imperial measurement system for good. ...Sorry, off topic.

 

[Sankaku]

Sorry, when I say there are no proofs courses, I mean there are no proofs courses that are available without prerequisite credits that I haven't obtained. At my university, you really can't take most of them until the junior level at the very least.

Here, some real Analysis for you:

http://www.youtube.com/playlist?list=PL0E754696F72137EC
http://www.math.hmc.edu/~su/math131/

Although he goes a little slow sometimes (depending on your experience level), they are very good.