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Mathematician vs Engineer

  • #1

Main Question or Discussion Point

So I'm a high school senior at the moment, and i LOVE mathematics, i love studying it, especially difficult and challenging problems, most of the stuff i breeze through but every now and then i run into problems that are tricky or challenging, i love these problems because to figure them out i literally have to take my brain, rip it apart and put it back together again to understand the problem and to come up with a solution and my brain works in a funny sort of way, its like soft clay I noticed that i am very good at problem solving, if someone gives me an interesting or challenging problem to solve, i have this ability to be able to figure it out, sometimes it takes a few minutes, sometimes it takes hours or even days, but if say 5 days later someone gives me a similar problem i will have forgotten quite a bit of what i learned a few days ago and will have to refer back to my notes. In other words I just solve problems after challenging problems but for some reason i don't RETAIN them, i just sort of forget about them a bit, like my brain just molds like clay but doesn't dry out and hold a shape..

anyway that was just a bit of background and I wanted to become a mathematician since thats what i like and im good at it, i like how it just kind of grabs hold of me and hours will pass by without me even realizing it, like i'm taken to another world, and ill finish all my work and realize sheesh 6 hours just passed by, but then i read somewhere on these forums someone saying "The difference between a mathematician(with a phd) and a large pizza is that a large pizza can feed a family of four" I also read that a lot of mathematicians end up working in finance or on wall street, i dont like this trend(i disdain finance/wall street to be honest like they take someone beautiful like mathematics and twist it and manipulate it for very selfish reasons) so i figured I'll go into engineering since there is a lot of mathematics involved and physics and chemistry etc...which wont be much different from going into just strictly mathematics, in essence ill get to do the same thing but the difference will be ill make decent money and wont have to worry about barely scratching a living as a mathematician, what do you guys think? do mathematicians starve? Do they barely scratch a living?

Whats the difference between going into an engineering program as opposed to a strictly mathematics program?(In the long run because if i were to go into a mathematics program i would probably go in it for the long run and want a phd)

I actually get pleasure out of studying mathematics, and the more interesting and challenging the problems, the better :)
(I know that makes me a dork :P)

Also I like the idea of creating something REAL, i dont like that there are so many people out there working in finance etc, making things up out of thin air, i like the idea of creating things that have intrinsic value in and of itself, (for example a stock broker touting a new financial product, things like that i dont like) i do like the idea of creating something tangible and real, something that does something, and contributes to the world, like i can dream it up and create it and grab it with my hands

by the way i apologize for the wall of text
 
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Answers and Replies

  • #2
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There is a HUGE difference between mathematics and engineering. The courses in first year will probably be very alike, but after that it diverges very fast.

An engineer will only learn math that he wants to apply to some real-world problem. This will entail calculus and linear algebra, but probably not much else. (correct me if I'm wrong about this!) They probably won't care about the beauty of the mathematics or the "why"-questions. However, engineers get to do things which are actually useful, something that mathematics often lacks.

Mathematicians on the other hand want to know 'why' the math works and want to generalize the mathematics. They are very much into proofs. They will carefully prove anything they do, and they care for the elegance of their arguments. For the mathematicians, the math is not just a tool, but a field worth to study, even if there are no applications what-so-ever (in the real world).

You must ask yourself: which one of the previous do you prefer: do you like mathematics because it let's you solve problems in the real world, or because it is beautiful in it's own right. This should tell you whether you would do engineering or mathematics.

Also ask yourself: what do you want to do after your studies. This is a very important questions. But don't worry, mathematicians do get a job! Engineers will find a job more quickly, but mathematicians don't end up living on the streets either!

And there are a lot of things you can do with mathematics: finance, teaching, computer programming, statistics,...

Don't worry about it to much! If you really can't choose, then maybe you can start with engineering, if you like the math in the first year, you can always tranfer to mathematics flawlessly!! Also, consider a double major, this might also what you are looking for (although it might be much work)
 
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  • #3
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There are Engineering Mathematics programs out there, you might want to look those up.
 
  • #4
There are Engineering Mathematics programs out there, you might want to look those up.
yes but then I'd be going into a mathematics program, because it is non engineering( in other words they fall under physical science/mathematics program and not under the faculty of engineering)
 
  • #5
gb7nash
Homework Helper
805
1
Mathematics is a very broad subject, and that's what's great about it. You could honestly get a job in almost anything that has the term "analyst" in it. Financial analyst, operations research analyst, cryptologist, mathematician, etc.. As you'll learn when entering the work force, most companies give you more specialized training to get you up to pace with everyone else.

Anyone who has a major in mathematics has mastered logic. In your job, you may not use a lot of the higher mathematics that you've learned, but when companies look around, they want people who can think out of the box and do something for them. Having a math degree and being able to create good proofs develops your mind and makes you a much better thinker, and shows you have an understand of "why" something works instead of "how".

As far as engineering goes, if you want to be that guy who designs that next airplane or building, this might be for you. It all depends what you want to do.
 
  • #6
Mathematics is a very broad subject, and that's what's great about it. You could honestly get a job in almost anything that has the term "analyst" in it. Financial analyst, operations research analyst, cryptologist, mathematician, etc.. As you'll learn when entering the work force, most companies give you more specialized training to get you up to pace with everyone else.

Anyone who has a major in mathematics has mastered logic. In your job, you may not use a lot of the higher mathematics that you've learned, but when companies look around, they want people who can think out of the box and do something for them. Having a math degree and being able to create good proofs develops your mind and makes you a much better thinker, and shows you have an understand of "why" something works instead of "how".

As far as engineering goes, if you want to be that guy who designs that next airplane or building, this might be for you. It all depends what you want to do.
hm...you make it sound as though engineers do the exciting stuff? (Although this is what the u of t rep told me, she said they do some incredible and amazing stuff in the engineering programs)
 
  • #7
gb7nash
Homework Helper
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hm...you make it sound as though engineers do the exciting stuff? (Although this is what the u of t rep told me, she said they do some incredible and amazing stuff in the engineering programs)
Depends what you consider exciting. :tongue:

If designing the best ________ sounds more exciting, then you answered your own question.
 
  • #8
Depends what you consider exciting. :tongue:

If designing the best ________ sounds more exciting, then you answered your own question.
haha, i suppose your right, thanks :P
 
  • #9
901
2
I was at U of T today, but for something separate. The campus is HUGE!
 
  • #10
and thats just one campus, they have 2 others as i suspect you know
 
  • #11
You could probably double major in mathematics and engineering. I've looked into a couple programs. One requires twelve extra classes, another requires eight extra classes for the double major program. I think it's completely in the realm of possibility of uniting engineering and mathematics into one superengineer -- but make no mistake, you'll be an engineer first and a mathematician second. If you are interested in design using theoretical mathematical principles, then engineering is a career for you.

Also, someone above said that engineering just uses basic calculus and linear algebra. That's not entirely true. Depending on the field, extensive knowledge of differential equations (partial and ordinary) is essential. I, for instance, will be taking courses on PDE's because my field of interest involves lots and lots of fluid flow.
 
  • #12
901
2
Chemical Engineering, Aerospace Engineering?
 
  • #13
I'm a third year Space Systems Eng.

First thing I will say is don't take engineering because you want the money. Money is nice but to be honest engineering on its own has the same number of courses as a double major and the stress will not be worth it if you don't like the program. Something I think everyone in engineering will tell you is that it takes dedication.

Second thing is that you will learn to write. As terrible as it is yes you will write more documents and papers than an arts student. This however isn't a bad thing since communication skills is what employers want more than anything.

Now to the math. You will probably learn single and multivariate calculus, differential equations, mathematical methods(for those nasty PDEs), and linear algebra. Oh and stats but lets not talk about stats. These are generally in classes geared toward engineering and physics students so the questions will be more practical than theoretical in nature. The nice thing about these math courses are that you can in general focus on the method or the theory depending on your preference. To tell you the truth I'm not much of a mathematician, and I never bothered to memorize theories and proofs just the method, but I passed those courses with A- and B+ easily enough. I have friends who did the opposite and can prove pretty much anything but that entirely preference.

As a side note once you start getting to more design based courses you will see a tendency towards the "cheap method" of math. This of course being numerical methods which are used to solve non linear systems, complex integrals, and other such problems using a computer and accepting a certain degree of inherent error.

I can also perhaps suggest Engineering Physics which is one of the more theory and math based disciplines. Space systems is pretty cool as well with a little bit of everything including electronics, structures, aerodynamics, and propulsion.

So as a summary if you want to work with your hands so that you have (grease, solder burns, metal powder, or concrete) on them as often as pen marks engineering might be for you. But don't do it if you don't enjoy the idea of creating things as such. I personally think that engineering is an amazing degree that bridges the gap between pure science and actually being useful.
 
  • #14
I'm a third year Space Systems Eng.

First thing I will say is don't take engineering because you want the money. Money is nice but to be honest engineering on its own has the same number of courses as a double major and the stress will not be worth it if you don't like the program. Something I think everyone in engineering will tell you is that it takes dedication.

Second thing is that you will learn to write. As terrible as it is yes you will write more documents and papers than an arts student. This however isn't a bad thing since communication skills is what employers want more than anything.

Now to the math. You will probably learn single and multivariate calculus, differential equations, mathematical methods(for those nasty PDEs), and linear algebra. Oh and stats but lets not talk about stats. These are generally in classes geared toward engineering and physics students so the questions will be more practical than theoretical in nature. The nice thing about these math courses are that you can in general focus on the method or the theory depending on your preference. To tell you the truth I'm not much of a mathematician, and I never bothered to memorize theories and proofs just the method, but I passed those courses with A- and B+ easily enough. I have friends who did the opposite and can prove pretty much anything but that entirely preference.

As a side note once you start getting to more design based courses you will see a tendency towards the "cheap method" of math. This of course being numerical methods which are used to solve non linear systems, complex integrals, and other such problems using a computer and accepting a certain degree of inherent error.

I can also perhaps suggest Engineering Physics which is one of the more theory and math based disciplines. Space systems is pretty cool as well with a little bit of everything including electronics, structures, aerodynamics, and propulsion.

So as a summary if you want to work with your hands so that you have (grease, solder burns, metal powder, or concrete) on them as often as pen marks engineering might be for you. But don't do it if you don't enjoy the idea of creating things as such. I personally think that engineering is an amazing degree that bridges the gap between pure science and actually being useful.
Also i like mathematics but for some reason everyone says if you go on to a mathematics program(physical sciences faculty) the stuff will be pretty dry and to be honest I think engineering is where the exciting stuff is, others have agreed with that assessment(university faculty etc) so ill probably end up going into engineering:)
 
  • #15
Haha good luck to you then. It's worth every bit of the bad stuff for all the cool and fun stuff you do. If you aren't sure which one to go into many universities offer a general engineering first year (if the university doesn't however 90% of your courses will be the same so switching is easy).
 
  • #16
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Oh, the excitement of engineering! I, myself and Irene can hardly sleep at night after studying such exotic topics as sequential and combinational circuits.
 
  • #17
Oh, the excitement of engineering! I, myself and Irene can hardly sleep at night after studying such exotic topics as sequential and combinational circuits.
That's why you need to choose something cool like Space Systems Engineering or Nuclear Engineering
 
  • #18
Or space propulsion engineering. We work on plasma rockets!
 
  • #19
What about mechanical? Or chemical? I'm interested more in mechanical engineering, seems cooler to me(Also i hear its very similar and has overlapping curriculum with aerospace engineering)
 
  • #20
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0
You got to realize that as a ME you will not design the whole aircraft. Engineers will specify in a "technology" or part of the project.

It's better if you ask yourself, what do I want to work with ? Engines ? Processors?
 
  • #21
Being that I have an undergrad degree in engineering, and a PhD in mathematics I can share some light onto this topic.
As an engineer, you are challenged with 'problem set' meaning there is a set of problems that require physics and or mathematics to determine the most correct solution. However, there are many limitations to this, one being as an engineer your job will evolve with new found solutions to theoretical physics or mathematics. Mainly, engineers 'apply' math and physics topics.
Mathematicians, however consider a theory to be solved or proven wrong which utlimately leads to a scientific idea confirming one thing or diproving another. If the mathematical theory is valid, it can be tested to various applications and thus used as a tool for engineering. Example is Calculus the rigor proofs in both differential and integral calculus is a mathematical theory but the applications apply well to engineering.
Sure, you may not need to understand the theory or relativity or even string theory to be an engineer. Nevetheless, theories hold the possibility of having great applications to the world we live in. For example, turbulence is a greatest unsolved problem for both physics and math, but if a theory is valid and proven the implications of such can change engineering forever.
In the end as an engineer I felt limited and wanted to learn more and more about our world and try to understand from observations the great question of why? if your the same try learning more about mathematics, and physics.
 
  • #22
You got to realize that as a ME you will not design the whole aircraft. Engineers will specify in a "technology" or part of the project.

It's better if you ask yourself, what do I want to work with ? Engines ? Processors?
Engines, what kind of engineers work on that?
 
  • #23
AlephZero
Science Advisor
Homework Helper
6,994
291
Engines, what kind of engineers work on that?
Unless you were just being silly: Every kind, except Civil.
 

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