# EE switching into Pure Math

I'm finishing up my second year in EE, but realizing that it may not be the right field for me. When I applied to colleges, I didn't really put much thought into what I wanted to study; my parents suggested engineering and I stuck with it. I've always been very strongly mathematically inclined, which is why they suggested engineering. For the first year, I was too overwhelmed with being in a new location to really make any changes to my curriculum; I took the standard freshman engineering curriculum. This year, however, I began to question whether EE really is what is best for me.

I've finished the math requirements for my degree, but I'm left with an even stronger desire to learn more about mathematics. On the contrary, my EE courses have not necessarily struck me as that interesting. Useful to the world, definitely, but ultimately not as interesting to me as mathematics. Ultimately, I think if I were to continue EE and land a job in the field, I would feel unsatisfied with my position.

This term, I took a course in proofs (basically, an intro to real mathematics), which has been very interesting. It made me realize what a disservice to myself it was to take the "engineering" calculus courses. I want to rectify that; I want to learn math the right way. I would much rather see myself in 5 years in grad school for mathematics, on a PhD track, than having an EE job that I may hate. Obviously, I wouldn't earn as comfortable of a living with Math, but I think it would be worth it over having a job that I don't like.

So, I've spoken with math advisors at my college, and they will let me into the honors mathematics track. Next year, I'd be taking Honors Analysis and Honors Combinatorics. The Analysis course is the one that some highly motivated incoming freshman take that covers their calculus and analysis requirements, but is also taken by juniors and seniors who opted to take standard calculus their freshman year.

My only concern is that I would feel "too old", however, I know this concern is ridiculous. I'm only 19, and will be 20 at the start of next year. I'm by no means "too old", but I for some reason cannot get this feeling out of my head. I get this notion that it's too late to switch; but it's not, is it?

Any form of guidance is appreciated. I just want someone to talk to; whenever I tell my friends they just tell me "do whatever you want" and obviously the Math and EE advisors push me into their respective fields. I just don't want to graduate in EE and get a job only to look back 5 years later, bored, and wonder why I didn't challenge myself with math.

I'm finishing up my second year in EE, but realizing that it may not be the right field for me. When I applied to colleges, I didn't really put much thought into what I wanted to study; my parents suggested engineering and I stuck with it. I've always been very strongly mathematically inclined, which is why they suggested engineering. For the first year, I was too overwhelmed with being in a new location to really make any changes to my curriculum; I took the standard freshman engineering curriculum. This year, however, I began to question whether EE really is what is best for me.

I've finished the math requirements for my degree, but I'm left with an even stronger desire to learn more about mathematics. On the contrary, my EE courses have not necessarily struck me as that interesting. Useful to the world, definitely, but ultimately not as interesting to me as mathematics. Ultimately, I think if I were to continue EE and land a job in the field, I would feel unsatisfied with my position.

This term, I took a course in proofs (basically, an intro to real mathematics), which has been very interesting. It made me realize what a disservice to myself it was to take the "engineering" calculus courses. I want to rectify that; I want to learn math the right way. I would much rather see myself in 5 years in grad school for mathematics, on a PhD track, than having an EE job that I may hate. Obviously, I wouldn't earn as comfortable of a living with Math, but I think it would be worth it over having a job that I don't like.

So, I've spoken with math advisors at my college, and they will let me into the honors mathematics track. Next year, I'd be taking Honors Analysis and Honors Combinatorics. The Analysis course is the one that some highly motivated incoming freshman take that covers their calculus and analysis requirements, but is also taken by juniors and seniors who opted to take standard calculus their freshman year.

My only concern is that I would feel "too old", however, I know this concern is ridiculous. I'm only 19, and will be 20 at the start of next year. I'm by no means "too old", but I for some reason cannot get this feeling out of my head. I get this notion that it's too late to switch; but it's not, is it?

Any form of guidance is appreciated. I just want someone to talk to; whenever I tell my friends they just tell me "do whatever you want" and obviously the Math and EE advisors push me into their respective fields. I just don't want to graduate in EE and get a job only to look back 5 years later, bored, and wonder why I didn't challenge myself with math.
I go to Georgia Tech and pretty much everyone starts off at Tech as some sort of engineering major. So, lots of the math majors have a similar story as yours. They thought that what they really like was engineering, so that's what they went after, then after taking calculus, they realise that they are really passionate about math.

You are certainly not too old to switch. I started college when I was 21, I am not 26 and will be graduating in May. I am going to grad school and I won't get a Ph.D. before I'm 30. So, you are far ahead of me. And, as I said above, it seems most of the math majors at my college switched just like you did.

I disagree about the money thing, however.

Let's say you do the EE thing, according to the bls, the median salary for an EE is $89,000 (http://www.bls.gov/oes/current/oes172071.htm). This is cleary a good salary. Now, let's say you major in math, don't go to grad school, and become, say, an actuary (which is a popular choice, though it isn't easy.) Then the median is$87,650 (http://www.bls.gov/ooh/Math/Actuaries.htm) Now, this is a little lower than the EE, BUT, the actuary profession is growing faster than the EE, so it *might* be the case that in a few years these numbers will be switched. One other thing to consider is that actuaries usually are in the top of "job satisfaction" survys. Another important consideration is that there are many jobs one can get as a Math Major, not just actuary.

Now, let's say you get a Ph.D., then the median salary is $99000 (http://www.bls.gov/ooh/Math/Mathematicians.htm). So, in this case, you do better than if you get an EE. And, if you can work as a professor, you will have an almos stress free job (at least, this is what I am told.) I go to Georgia Tech and pretty much everyone starts off at Tech as some sort of engineering major. So, lots of the math majors have a similar story as yours. They thought that what they really like was engineering, so that's what they went after, then after taking calculus, they realise that they are really passionate about math. You are certainly not too old to switch. I started college when I was 21, I am not 26 and will be graduating in May. I am going to grad school and I won't get a Ph.D. before I'm 30. So, you are far ahead of me. And, as I said above, it seems most of the math majors at my college switched just like you did. That is comforting, I figured I was greatly overreacting to being "too late". I disagree about the money thing, however. Let's say you do the EE thing, according to the bls, the median salary for an EE is$89,000 (http://www.bls.gov/oes/current/oes172071.htm). This is cleary a good salary. Now, let's say you major in math, don't go to grad school, and become, say, an actuary (which is a popular choice, though it isn't easy.) Then the median is $87,650 (http://www.bls.gov/ooh/Math/Actuaries.htm) Now, this is a little lower than the EE, BUT, the actuary profession is growing faster than the EE, so it *might* be the case that in a few years these numbers will be switched. One other thing to consider is that actuaries usually are in the top of "job satisfaction" survys. Another important consideration is that there are many jobs one can get as a Math Major, not just actuary. Now, let's say you get a Ph.D., then the median salary is$99000 (http://www.bls.gov/ooh/Math/Mathematicians.htm). So, in this case, you do better than if you get an EE. And, if you can work as a professor, you will have an almos stress free job (at least, this is what I am told.)

That is true, as well. It's just that you normally hear that graduating in engineering is an almost guaranteed job, while in math it can be tough to find a job. Though, I always challenged the validity of these claims anyway.

Thanks for the response.

That is comforting, I figured I was greatly overreacting to being "too late".

That is true, as well. It's just that you normally hear that graduating in engineering is an almost guaranteed job, while in math it can be tough to find a job. Though, I always challenged the validity of these claims anyway.

Thanks for the response.

Yes, that is a sterotype with respect to the math major. But, to comfort you more, I read an article in Forbes that listed the three highest paying majors. They were: Engineering, Pharmacology and Math/CS.

Why not double major in EE and Math or minor in Math? You cover all of your bases that way. You could also try getting an EE internship or doing some EE research with an enginerring prof to see if you really like it or not.

Working in the field is a lot different than studying the field in college. It also helps to know you'll get a job when you graduate. The medians might be comparable but if you don't know the sample size or the job market they don't mean much.

Why not double major in EE and Math or minor in Math? You cover all of your bases that way. You could also try getting an EE internship or doing some EE research with an enginerring prof to see if you really like it or not.

Working in the field is a lot different than studying the field in college. It also helps to know you'll get a job when you graduate. The medians might be comparable but if you don't know the sample size or the job market they don't mean much.
The non-honors math courses at my school are a joke. Even the upper div courses like analysis and abstract algebra, etc. Which would be counter intuitive to the reasoning in me switching to math in the first place: I want to learn more. It seems like anyone can get an engineering degree, it's just a matter of working hard to do it. However, mathematics requires more intuition and creativity, which I've always felt that I've had, but never had the chance to really show in full. Also, probably math only draws those students that are very interested in the subject; while some are drawn to engineering mainly for the prospect of having a good career.

Switching into math means not looking back, which is fine with me. I don't have any real desire for engineering and only chose it because it was suggested by my parents. It's not like I had strong desires to get into engineering, but changed my mind once I was there. What I should have done is sat down and thought about what I wanted to do the summer before getting into college. But, I was so overwhelmed with the whole thing and have always been rather shy...it just didn't happen.

Thanks for the suggestion, though.

Going into math is great. But you got to know what you're starting. You will likely make less money than an engineer and you will have a bit more trouble finding a decent job (not that mathematicians are jobless and sleep in cardboard boxes, but engineers have it easier). Also, you need very decent grades to go into math grad school. Be sure to take all of this in account before making a final decision.

That said, if you find engineering boring, then it might not be something for you. But it is also very likely that you never had a decent math course before. Once you took analysis and algebra, then you know what math is like. Maybe you can take an analysis/abstract algebra over the summer and try to read it??

Also, let me remind you that pure math is not very applications oriented. So be prepared to talk about things that have nothing to do with the real world on first glance (I'd be inclined to say that all undergrad math is useful to the real world in some way, but this is often not very clear in math courses). If you want applications, then you should look in to applied math or physics. On the other hand, if you're interested in why math things are what they are, then pure math is the thing to do.

That's, um, for exploring bits of math that have already been discovered and drained dry, so it's possible to find all the formulae you need. If you're discovering something new, or not told what to do, there's a decent amount of creativity involved. Finding $\dfrac{\mathrm{d}x^x}{\mathrm{d}x}$ and $\displaystyle\int_0^{\frac\pi2}\left(\dfrac{\sin^n\left(x\right)}{\cos^n\left(x\right)+\sin^n\left(x\right)}\right)\cdot\mathrm{d}x$ I found quite creativity-requiring, but, then again, that was because I didn't look at the solution first.

If you think math doesn't involve creativity, I suggest you look into the Art of Problem Solving, taking courses you haven't already taken from other companies.

Very true. Problem solving in math requires lots of creativity. But that's only half of what math is about!! Basically, I feel that there are two branches in mathematics:

- Problem Solving
- Creating theory

Both require an extraordinary amount of creativity. Usually people prefer one over the other.

People that say or think that math is just about mindless calculations are extremely ignorant. Math is all about concepts and ideas. It's about seeing an idea applied many times and generalizing it to a broader concept. These abstraction steps are often quite hard for most people and take a while to get used to.

For example:
Step 1: In ancient times, people have always worked with basic things like lines and circles. For example, to divide acres of farmers, one needs to know about surface areas of things.

Step 2: The situation is abstracted by Euclid who introduces axioms for basic geometry and proves things from these basic axioms.

Step 3: The situation is abstracted by Descartes and Fermat who introduces algebraic manipulation as a means to work with geometry. For example, points/vectors are being identified with couples (x,y) and we can say that two vector (x,y) and (x',y') are perpendicular if xx'+yy'=0. This is abstracted by the dot product $\mathbf{x}\cdot \mathbf{y}=0$.

Step 4: The situation is abstracted by Hilbert and others who don't talk about lines and circles anymore, but merely about an abstract set H equipped with a dot product (called an inner product) $<\mathbf{x},\mathbf{y}>$ satisfying certain properties. In this form, this can be applied to a variety of very distinct topics. For example, one can say that two functions are perpendicular if

$$\int_a^b{ f(t)g(t)dt}=0$$

As an example: the sine and cosine function are perpendicular!! One can even prove Pythagoras' theorem for functions instead of just basic geometry!

This point-of-view may seem hopelessly abstract but is very important in applications. Applications give for example rise to Fourier series, Fourier transforms, quantum mechanics, signal processing, etc.

To the OP: if you think this post was exciting, then you will like pure math

Going into math is great. But you got to know what you're starting. You will likely make less money than an engineer and you will have a bit more trouble finding a decent job (not that mathematicians are jobless and sleep in cardboard boxes, but engineers have it easier). Also, you need very decent grades to go into math grad school. Be sure to take all of this in account before making a final decision.

That said, if you find engineering boring, then it might not be something for you. But it is also very likely that you never had a decent math course before. Once you took analysis and algebra, then you know what math is like. Maybe you can take an analysis/abstract algebra over the summer and try to read it??

Also, let me remind you that pure math is not very applications oriented. So be prepared to talk about things that have nothing to do with the real world on first glance (I'd be inclined to say that all undergrad math is useful to the real world in some way, but this is often not very clear in math courses). If you want applications, then you should look in to applied math or physics. On the other hand, if you're interested in why math things are what they are, then pure math is the thing to do.
This is my plan; I have already started. I've bought a few books on Analysis and algebra and have been working through the analysis one on my own time. Most nights, I spend an hour or so reading from the Analysis book I bought (Understanding Analysis by Abbott) and have been really enjoying it. I think I have atleast some rough idea of what real mathematics consists of and it has substantially whetted my appetite to learn more about math.

OP: I majored in EE and let me tell you, certain sub-fields of EE can be quite math-heavy (such as signal processing) and if one was to
get their PhD in signal processing, one may even have to take graduate-level math classes (I know this from a friend who
did it). So some EE's who are especially mathematically inclined find certain subfields of EE satisy their "craving" for advanced
math.

However, I have read academic papers and done research (REU) in signal processing and while there is a lot of math,
there are not many proofs (formal proofs being less important in engineering than in pure math). So if you find what
you really love about math is proofs, such as you encountered in the "real" math class you took, you would probably
enjoy a career in math more than a career in EE.

And, if you can work as a professor, you will have an almos stress free job (at least, this is what I am told.)

Depends on where you are. It's usually very stressful, from what I've heard.

I want to learn more. It seems like anyone can get an engineering degree, it's just a matter of working hard to do it. However, mathematics requires more intuition and creativity, which I've always felt that I've had, but never had the chance to really show in full. Also, probably math only draws those students that are very interested in the subject; while some are drawn to engineering mainly for the prospect of having a good career.

My question to you then would be this. Do you love Math enough that you'd major in it even if it meant living in a shack for the rest of your life or working at McDonalds if you couldn't find a job?

It's great to be idealistic but nobody is going to care what your major was 10 years from now. However, you will if it means you can't provide for yourself or your family. The trick is finding the balance. IMO, once you reach a certain level of intelligence getting almost any degree is simply a matter of working hard and managing your time. Also, all science majors require a certain amount of intuition and creativity from those that pursue them who want to be successful. And really, if you don't have those things, you'll be mediocre at best no matter what your field.

My question to you then would be this. Do you love Math enough that you'd major in it even if it meant living in a shack for the rest of your life or working at McDonalds if you couldn't find a job?

That's not the actualy choice that he's presented. Mathematicians get very good jobs.

My question to you then would be this. Do you love Math enough that you'd major in it even if it meant living in a shack for the rest of your life or working at McDonalds if you couldn't find a job?

It's great to be idealistic but nobody is going to care what your major was 10 years from now. However, you will if it means you can't provide for yourself or your family. The trick is finding the balance. IMO, once you reach a certain level of intelligence getting almost any degree is simply a matter of working hard and managing your time. Also, all science majors require a certain amount of intuition and creativity from those that pursue them who want to be successful. And really, if you don't have those things, you'll be mediocre at best no matter what your field.

I invite you to read my first post in this thread (it is right after the OP.) In it, I listed the median salary of an actuary (which is a job many a math major has taken). It is around $87k/yr. I also listed the median salary for mathematicians at$90k/yr. These date were taken from the bls. Additionally, I mentioned an article I read in Forbes that said something (along the lines of) the three best money-producing majors are 1)Pharmacology 2)Engineering 3)Math/CS.

So, this notion that if you major in math you will be poor is one of the most incredibly ignorant ideas out there. Math, in it purest form, is an art, which is why the OP is drawn to it. At the same time, the result of this art can be incredibly useful to some people. Thus, if he majors in math, he will get to do this art for 4 years but he can actually take a (probably small) portion of this art and get paid rather well for knowing it.

EDIT:
Also, I currently don't have a degree; I'm still an undergrad. About 90% of the people I work with never went to college. Yet, somehow, we have all managed to avoid living in a cardboard shack or working at McDonald's. In fact, many live rather comfortable lives and manage to provide for their families. So, again, this notion that the choice is between engineering with a good job and majoring in math but, ultimatley having to live in a cardboard box is insanely absurd. It drives me completley insane. The math education people have received is already screwed up enough that it is a wonder that anyone wants to major in math in the first place, but spreading this falsehood that math majors are poor pretty much puts the last nail in the coffin for most (with respect to majoring in math.)

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That's not the actualy choice that he's presented. Mathematicians get very good jobs.

I'm not saying they don't. It's meant to be a gut check. To me, the OP sounds like someone who is caught up in the idealism of academia and is forgetting that life continues after your degree is finished. Getting a job in "science" generally seems to involve compromise. You find something to do that incorporates as much of what you like as possible and accept the reality that almost nobody is going to pay you to stay home and work on theory all day. If science isn't applied in some sense nobody can profit from it.

In it, I listed the median salary of an actuary (which is a job many a math major has taken). It is around $87k/yr. I also listed the median salary for mathematicians at$90k/yr. These date were taken from the bls. Additionally, I mentioned an article I read in Forbes that said something (along the lines of) the three best money-producing majors are 1)Pharmacology 2)Engineering 3)Math/CS. Yahoo.com?

So, this notion that if you major in math you will be poor is one of the most incredibly ignorant ideas out there. Keep it classy right.

Math, in it purest form, is an art, which is why the OP is drawn to it. All science is art. At the same time, the result of this art can be incredibly useful to some people. Thus, if he majors in math, he will get to do this art for 4 years but he can actually take a (probably small) portion of this art and get paid rather well for knowing it.

EDIT:
Also, I currently don't have a degree; I'm still an undergrad. QUOTE]

Take my undergrad major for example. The median salary for a chemist is 70K. I don't know anyone outside of academia that makes this much to be "just" a chemist and even profs aren't just chemists. Statistics are great until you're the one trying to find a job. People look at engineers differently than they do people with pure science degrees. There are jobs for mathematicians, but I'd bet the majority of them are applied, not theoretical, which sounds like it will be a problem for the OP.

Math, in it purest form, is an art, which is why the OP is drawn to it. All science is art. At the same time, the result of this art can be incredibly useful to some people. Thus, if he majors in math, he will get to do this art for 4 years but he can actually take a (probably small) portion of this art and get paid rather well for knowing it.

Just because you bold a sentence doesn't make it a fact. While I agree that some see math as an art I don't get that vibe in physics or CS; the only other sciences I know. They're mostly there to solve problems and figure out how the world works.

I agree that the overwhelmingly majority of jobs do not use pure math. I have many friends from a pure math background (bachelor's) and all of them except cryptography don't use much of what they learned in school. PhD's are another story. Because I worked in industry for a while before I went back to grad school I get to see my friends from undergrad finish their PhD's. Some of them are doing some very, very cool things and others entered the postdoc treadmill. I will say this, the ones that chose a field with some type of application seem to be doing much better than the "pure" field choices. Of course, who would have thought otherwise.

They're mostly there to solve problems and figure out how the world works.

Exactly. That's the art. Well, I wouldn't say they're there to solve problems.

Math, in it purest form, is an art.

Also what he was saying about science, in its purest form. Effectively, science is the art of taking observations about the world and formulating theories from that. If any observation goes against this theory, it's tossed out or modified. Any theory that does not yield any testable predictions is not disprovable, and, therefore, nonscientific. There we go. Science stripped down to its barest form.

Exactly. That's the art. Well, I wouldn't say they're there to solve problems.

Effectively, science is the art of taking observations about the world and formulating theories from that.

Lol.. nice. This is the last I'll say about this because it's getting off topic and it's so subjective anyway but I've met many, many more mathematicians that view their field as an art than physicists. I guess writing this reply is the art of abstracting my thoughts into written communication, lol. =)

To Doppz, the EE's I've met are very good at physics and even pure math. The signal processing and logic kids fit the glove for doing higher level math later on. I know some EE's that went to grad school for physics or math. They usually took a couple upper level courses so they had more of an option to spread out into other fields in grad school.

Lol.. nice. This is the last I'll say about this because it's getting off topic and it's so subjective anyway but I've met many, many more mathematicians that view their field as an art than physicists. I guess writing this reply is the art of abstracting my thoughts into written communication, lol. =)

To Doppz, the EE's I've met are very good at physics and even pure math. The signal processing and logic kids fit the glove for doing higher level math later on. I know some EE's that went to grad school for physics or math. They usually took a couple upper level courses so they had more of an option to spread out into other fields in grad school.

That's true that those fields are math intensive, however it's more computational mathematics from what I can see. I want to learn more pure math, involving proofs and the like. If I were to go into an applied math-type field it would more along the lines of algorithms for computers, etc. I actually quite enjoy programming, my dad just highly discouraged me from going into it.

In it, I listed the median salary of an actuary (which is a job many a math major has taken). It is around $87k/yr. I also listed the median salary for mathematicians at$90k/yr. These date were taken from the bls. Additionally, I mentioned an article I read in Forbes that said something (along the lines of) the three best money-producing majors are 1)Pharmacology 2)Engineering 3)Math/CS. Yahoo.com?

So, this notion that if you major in math you will be poor is one of the most incredibly ignorant ideas out there. Keep it classy right.

Math, in it purest form, is an art, which is why the OP is drawn to it. All science is art. At the same time, the result of this art can be incredibly useful to some people. Thus, if he majors in math, he will get to do this art for 4 years but he can actually take a (probably small) portion of this art and get paid rather well for knowing it.

EDIT:
Also, I currently don't have a degree; I'm still an undergrad. QUOTE]

Take my undergrad major for example. The median salary for a chemist is 70K. I don't know anyone outside of academia that makes this much to be "just" a chemist and even profs aren't just chemists. Statistics are great until you're the one trying to find a job. People look at engineers differently than they do people with pure science degrees. There are jobs for mathematicians, but I'd bet the majority of them are applied, not theoretical, which sounds like it will be a problem for the OP.

A post with randomly bolded phrases!

What data (I'll even accept anecdotes) do you have to the contrary?

That's true that those fields are math intensive, however it's more computational mathematics from what I can see. I want to learn more pure math, involving proofs and the like. If I were to go into an applied math-type field it would more along the lines of algorithms for computers, etc. I actually quite enjoy programming, my dad just highly discouraged me from going into it.

CS definitely has it's share of proof-y topics, obviously nothing will compare to a math class. I see no reason why you couldn't do CS then take a bunch of math classes. If you intend on getting a PhD in math then I would say do math.

http://www.bls.gov/ooh/Math/Mathematicians.htm

3100 Mathematician jobs in 2010. There were almost 300 K EE jobs.

Apples and oranges. See, people like you think of college as being job training. You get a degree in X and then you take a job that has X somewhere in the title. So, since not many people are "mathematicians" in their job title, these aren't counted. For example, the data you listed (which I cited) probably does not include things like actuaries. Not to mention the fact that lots of math majors don't even go in a field that is math related. For example, I was offered a job in sales, though I did not take it. Was it \$80,000/year? No. But it was a good starting salary. The point is that many jobs are open to math people (and others, as well) that are not "mathematician."

People like me eh?

I look at it as return on investment. Why spend 25K to 100K of your own or your parent's money to get a piece of paper for something many people on this board could self study?According to the same site, there were just under 22K actuary jobs in 2010. Still nowhere close to the number of EE jobs if you sum the two.

Back to the original topic, the OP wanted an opinion and I gave mine. He wants to "do" pure math, not applied. That rules out all of the alternate careers you mentioned. My opinion would be to pursue something that will let you do high level math and earn a decent living at the same time without the hassle of competing for an extremely limited number of jobs as a "mathematician".

I guess you and the OP can get back to us when you graduate and let everyone know how the job search went.