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TheWizardofCalculus

Career Information for Aspies: Math, Science, and Engineering

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TheWizardofCalculus

After talking with younger members of this forum, I felt it would be quite helpful to make things a bit clearer about what it is actually like to be in a "technical" career (As opposed to "artistic"; although I feel that the distinction is somewhat fake, as people in technical careers are often very creative and artists often have to be very technical, but I digress).  There are many technical careers.  I will take the ones that I think I know the most about and are the ones that most aspies, who want technical disciplines/careers, would be interested in.  Even then, it's not a very thorough list, as I miss many things.  Perhaps others will be willing to fill in those gaps for me.

 

 

I'll give a basic synopsis of what it actually means to be in the fields of mathematics, physics, and engineering.  I will speak very broadly, because sub-disciplines in these fields can be very different than what it's usually like to be in that field.  So take what I say loosely, but it is still reasonably accurately.  To be clear, I'm going to underline the key definitions/concepts that these groups tackle.  I'll describe them in the following way (N.B. Here I mean "to do research in" when I say "have a career" in these fields, and therefore these might not necessarily apply if you wanted to teach these disciplines):

 

 

1.) Mathematics.

 

Real math (research math) isn't like the maths that you're learning in high school or first year of undergraduate studies.  Mathematicians are fundamentally interested in studying and developing mathematical structures and studying in their applications.  As you develop a more sophisticated understanding of mathematics, it will basically split into two kinds of maths:

 

   A.) "Abstract Mathematics":  they have nothing to do with word problems or calculating numbers. This is the side of mathematics concerned with formally proving theorems, proving the existence of solutions to problems, and if possible, proving the uniqueness or non-uniqueness of these solutions.  They do this by developing "mathematical structures".  To be slightly more specific, a "mathematical structure" is a collection of objects, a collection of relations that "act" on the objects, and list of axioms that define properties of the objects and their relations.  This is, by definition, abstract, so let me take a concrete example: The collection of objects could be the real numbers, the relation could be addition, and the list of axioms that specify their properties could be the law of commutativity (i.e. "a+b = b + a") and the law of associativity (i.e. " (a+ B) + c = a + (b+c)").  An abstract mathematician would take these properties and derive theorems from them (e.g. "(a + B) +c = (a + c) + b") with rigorous logical inferences.  Abstract (or "pure") mathematicians are interested in creating mathematics structures, independent of their application or use.  They're interested in "true" statements, and the appeal of pure mathematics is in the logical deduction, the beauty of proofs, and the elegance of understanding the "bare" (abstract) mathematical structures that appear all over mathematics and the sciences.  There are usually two camps here, too, which are the "problem solvers" who are interested in solving specific problems (i.e. proving certain theorems) and the "theory builders" who are interested in constructing the theories behind mathematical structures (in other words, building up axioms around the mathematical theories rather than attacking a single problem within them).

 

   B.) "Applied Mathematics":  Applied mathematicians are more interested in using mathematical structures to calculate things.  So they will take the theorems that abstract mathematicians give them, and they will learn about efficient and robust ways to calculate solutions to problems.  They often work with scientists, engineers, computer scientists, etc, to help them solve their problems.  They are usually uninterested in the problem ("What does this solution to the Navier-Stokes equations mean for fluid dynamics?"), only in the use of mathematics to solve the problem ("What method do I use to solve the Navier-Stokes equations?  Is it robust and efficient?").  So they tend to divorce the physical intuition from the problem and hone in only on the underlying mathematical structures, where they know how to calculate things.

 

 

 

2.) Physics.

 

Physics also isn't like what you're learning now, but that's mostly for two distinct reasons (And is much closer to what classes you're doing now than the difference between your current math courses and being mathematician, for instance):  The first reason is that physics classes are fundamentally about things that are known to be true; physics research is about things that are not known to be true, and this makes the exercise of taking a physics course as being very different than actually having a career in physics (Obviously, this does not apply if you only wanted to teach physics, for instance, instead of doing research in physics).  So that is something that no one will tell you, but is something you should understand (This lesson applies, also, to both math and engineering, too, for the same reasons).  The second part is trivial, and that''s just the level of the material and the subject matters (We're not very interested in Newtonian mechanics, lol, for instance).  Physicists are fundamentally interested in using mathematical equations to write down the physical principles of Nature and then are interested in verifying, through the use of experiments, that these mathematical equations faithfully describe Nature.  In other words, physicists are concerned about mathematical structures in order to    Over the course of it's evolution, it has become convenient, also, for physicists to split into two camps:

 

A.) Theoretical physicists.  Theoretical physicists are interested in turning experimental results and physical intuitions into consistent physical theories that imply specific predictions (which can them be experimentally explored).  Theoretical physicists primarily dedicate their time to understanding applied mathematics, using math to define physical principles, and learning the skill of converting physical intuitions into mathematical equations.  In a certain sense, they would fall under the category of "applied mathematicians", because they're using mathematics to solve physical problems.  They don't care why the mathematics is true, only that it can be used to describe physical theories.  Theoretical physicists also fall into two sub-categories, often (but not always) called "formalists" and "phenomenologists". Formalists are interested in making sure that physical theories are internally self-consistent (both logically and with past experiments) and that the calculations are carefully and correctly done (This is what I do for a living).  Phenomenologists are interested in taking the predictions of a physical theory and converting it into precise numerical predictions (also called "observables") that can be directly compared with the results of an experiment.  But often theoretical physicists do a little of both during their careers.

 

B.) Experimental physicists.  Experimental physicists are interested in creating (engineering) apparatus that can explore Nature in order to test the predictions of physical theories.  Their day to day life is actually remarkably similar to that of engineers, only they are rarely concerned with mass production.  Their day-to-day lives involve constructing the experiments, performing experiments, and analyzing the results of their experiments.  For this reason, experimentalists (although usually every experimentalist has done both during their careers) are often primarily involved in either the construction of an experiment (designing sub-systems and constructing sub-systems) or in the data analysis of the results of an experiment (usually using computer programs).  It's also important to note the use of statistics and uncertainty in the scientific method; this occurs here.  Theoretical physics is largely deductive, but experimentalists (and phenomenological theoretical physicists) use statistics and inductive reasoning (often Bayesian or frequentist analysis) on their experiments.  (Science is not "exact", but subject to ever increasingly small error)

 

 

 

3.) Engineering.

 

 

Engineers are primarily concerned with taking physical theories (including both the theories from chemistry and physics, and in certain cases biology), applied mathematics, and experimental apparatus and converting these into usable (and in the modern age, that means "sellable") technologies.  I'm using technology in a very broad sense; from km long bridges to nanometer scale transistors.  Engineers are concerned with either developing these technologies and/or in the aspect of mass producing them.  Engineers do a lot of different things, actually, but largely they develop and design new technologies, test new technologies or improve old technologies, explore the applications of a physical theory, and explore methods of producing these technologies.  Generally, there are research engineers who work with the basic theories and industrial engineers who work on the side of mass producing these technologies, but again, often enough they'll work on both during their careers.  Also, it is important to understand that like physicists don't care why mathematics is true, engineers don't care why physical principles are true or what the connection between physical theories are.  Their goal is to use them to create new technologies.

 

 

There are many kinds of engineers.  A relatively robust list (but it's a long list so I'll skimp on descriptions) includes:

 

A.) Mechanical engineers.  They work, as the name suggests, on mechanical objects (like designing engines ).

B.) Chemical engineers.  They do a little bit of everything, but tend to focus on the use of the applications of chemistry in engineering.

C.) Civil engineers.  They design things with, as the name suggest, a "civil" applications (bridges, buildings, dams, etc).

D.) Biomedical engineers.  They engineer technologies for the use of medical applications.  (MRI machines, etc).

E.) Electrical Engineers.  They study the use of electromagnetism in modern technologies; a well-known sub-discipline is computer science.

 

It's harder to be more specific than this without doing a lot of research into the various disciplines of engineering, since engineering is such a huge field with many different kinds of technology --often centered on what basic science it is that they are using, such as electrical engineering (electromagnetism), material engineering (polymer science), chemical engineering (general chemistry and physics), and biomedical engineering (biochemistry, neuroscience, biology, and other sciences relevant for medicine).

 

 

Final Note 1

 

There are important caveats here.  For instance, string theorists in theoretical physics may often work on things that would be considered abstract mathematics (differential geometry and algebraic topology), and computer scientists can work on things that also might be considered abstract mathematics (e.g. the P = NP problem or the study of algorithms).  Likewise, engineers might work on basic physics theories (for instance engineers who work on Casimir forces), and experimental physicists might work on things that are manifestly technologies (e.g. most of condensed matter physics has direct engineering applications that an experimental physicist might work on).  The world of mathematics, science and engineering has a lot of interdisciplinary efforts.

 

 

Final Note 2:

 

Also, there's no "wrong" or "right" philosophy on what is important to understand.  Often times, each discipline gets very arrogant that they are the studying the "important" thing, but that's sort of a silly way of thinking about things, imo.  It is important that there are mathematicians who are proving that the maths that scientists and engineers use is correct and consistent.  It is important that we have basic scientists (physicists, chemists, and biologists) who create physical theories (often based on sound mathematical structures) and empirically verify them through experiments, because without these the engineers would create technologies at a very limited and a very slow pace, indeed.  And we need engineers to take the maths and science and turn it into useful technologies (that also means useful in conducting further mathematics and further science).  All of these disciplines play an essential role in the "technology pipeline", in advancing human knowledge, and in advancing what humans are capable of doing and experiencing.  Each discipline's role should be appreciated a bit more.

 

 

Final Note 3:

 

The list is, as I said, quite small.  I'm less comfortable talking about chemistry or biology (or their most-well known interdisciplinary efforts, biochemistry and neuroscience), but they, too, fall under the same category of physics as "basic science": being interested in understanding physical phenomena through experiments and physical theories.  Whereas medicine, engineering are considered "applied science."  Anyways, I hope this is helpful.

 

 

Final Note 4:

 

Being an aspie does not immediately correlate with being good at these fields.  However, the rigid thinking, desire to problem solve, and the increased ability to focus are often very helpful in being good at systematic and logical thinking, memorizing and intuiting concepts, mathematical acumen, etc, that is required to be good at these fields.  If you are young and think that these fields sound interesting, then start exposing yourself to these fields immediately.  No one will probably tell you to do this, so I will:  Take college classes, join topical clubs, read lots of Wikipedia articles about these subjects, take high school classes on them (or intro classes if you're in college), and go to forums with people who actually have careers in the field.  Find friends who you can study these things with (helpful if you take the classes or join clubs).  Being lone hunters, we tend to overlook or neglect the usefulness of that last suggestion, but it really is essential.  Try to learn to be curious; that's also essential.  Learn to write.  Technical people often hate learning to write, but it's an essential skill.  Learn to program; it's useful in everyone of these fields.  And lastly, take as many math courses as you can; this is also helpful in everyone of these fields.

 

 

=)

Edited by TheWizardofCalculus

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the strangest man

Second all your thoughts, even as a humble computer science specialist.

I'd emphasis the learning to write above just about everything. If you cannot communicate your findings no amount of outstanding research you do will have any meaning whatsoever.

Also don't jump too far ahead, get your basics right first. Einsteinean relativity may be fascinating, but you need to understand calculus beforehand.

Finally, if you do proceed to university watch out for the AS demon snaring you with its most deadly weapons boredom and over expectation. I expected university to be full of people there only to learn; oops what a mistake to make. If you're good enough head towards a top research university; Cambridge, Oxford, Imperial, Warwick etc find a group you're comfortable with and get your head down and work.

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TheWizardofCalculus

Second all your thoughts, even as a humble computer science specialist.

I'd emphasis the learning to write above just about everything. If you cannot communicate your findings no amount of outstanding research you do will have any meaning whatsoever.

Also don't jump too far ahead, get your basics right first. Einsteinean relativity may be fascinating, but you need to understand calculus beforehand.

Finally, if you do proceed to university watch out for the AS demon snaring you with its most deadly weapons boredom and over expectation. I expected university to be full of people there only to learn; oops what a mistake to make. If you're good enough head towards a top research university; Cambridge, Oxford, Imperial, Warwick etc find a group you're comfortable with and get your head down and work.

 

I'd like this post twice if I could.

 

 

1.) Do not jump ahead.  Learn things correctly; this means that just because you read about string theory, General Relativity, or quantum mechanics, it does not you should try to learn these first.  The greatest tool you have as an aspie is to think logically and memorize a lot of stuff.  This means, work your way judiciously through all the material leading up to GR.  If you do, it means you will understand GR better than anyone else you know.  I use Special Relativity and General Relativity because relativity is one of my special interests, but I got obsessed with it  in the "right order".  I learned Newtonian (and Lagrangian and Hamiltonian) mechanics, electromagnetism, and Special Relativity before I tried GR.

 

2.) Expect to be bored a lot with the material and expect to have things, often enough, explained rather poorly.  Not everything is interesting, and not everything that is interesting is interesting immediately.  Be open to things.  Be willing to work hard on stuff you don't care about.  This was the greatest downfall that ended up hurting me the most when grad apps came do to get into my PhD program. (That and I can't take tests to save my life)

 

3.) University is not, contrary to popular belief, the place where only really smart and curious people go.  Most people, in fact, are just there to burn four years of their lives (and a whole lot of their parent's money) so they can get a bachelors and then "get a good job".  Most people are not open-minded, they are not curious, many times they don't like what they're studying very much, and their primary interest is in partying.  Don't get me wrong, have fun in college and definitely try to have a social life (it'll be much easier here --though still not easy-- than it was in high school).

Edited by TheWizardofCalculus

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Jale

I'd also say, if it is fun then learn "it" (whatever that might be, in any field), it may serve you somehow.

Take a break now and then if you feel like you need, because sometimes new ideas about solving a particular problem can pop in mind when you really don't pay attention to the that problem, but do this only when you are really stressed out, realize that your brain needs a rest and that you are not stupid.

 

I'm really interested in EECS.

Going to college this year.

I have bad grades at math. But I understand most of what "they" teach me, I just loose interested in it because it all seems so disconnected and I fell like something is missing

I should really do one pass over math and physics tho.

I want to start exploring what some people call Calculus :-), but I just don't have enough time now, maybe during summertime before college.

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lifeis

for someone thinking of going to uni, just how hard is the Math on a physics course. I'm good at algebra and working out complex equations, I'm just not good at remembering set answers and answering questions on the spot. I know that's a little contradictory but it's like I'm better than most people when it comes to understanding or working out how to solve problems but i hav'nt been interested enough to remember much of the base mathmatics until now. I'm good at science but as of yet don't know what area I want to go into, thats if I do go to uni and retake my A levels (had to drop out when I was younger).

Thanks

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the strangest man

Lifeis

Have a look at some of the Open University physics text books. They should give you a good understanding. You can buy them from the OU or there's normally plenty on EBay

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TheWizardofCalculus

I think that most early intro physics books are poor, but there's an out of print physics textbook that I was particularly fond of when I learned the early stuff.  It was an AP Princeton Review for an American AP test.  Sadly, I don't know where to find a digital copy of it, if one even exists.

 

 

Luke has alerted me to the existence of the following website, which seems interesting:

 

https://www.khanacademy.org/

 

You might look at the early physics courses.  In general, I would say it's better to know as much mathematics as possible than to know less mathematics.  It makes the physics problems harder, imo.  It doesn't mean you shy away from it, either, it just means that you should plan accordingly.

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Nesf

I wish I could have my life back again so I can do something productive and useful that I enjoy doing such as studying physics, which I was good at at school but dropped in order to study languages, instead of wasting my life on trying to do a dead-end job I'm no good at and don't enjoy. I can study languages at any time on my own, I didn't need to go to university to study them.

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Bruce

I'm sorry you feel that way, Nesf. (((Hugs)))

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lifeis

I wish I could have my life back again so I can do something productive and useful that I enjoy doing such as studying physics, which I was good at at school but dropped in order to study languages, instead of wasting my life on trying to do a dead-end job I'm no good at and don't enjoy. I can study languages at any time on my own, I didn't need to go to university to study them.

they do say it's never too late.

my dad got his phd when he was quite old (he also loves hitchhikers guide to the galaxy, I get that impression from the strangest man as well).

Edited by lifeis

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