[bold]Math Lovers - How to choose Math major vs Engineering?[/bold]
Ok, there are no right or wrong answers here. I'm just trying to solicit some hints and insights.
One of our kids is a gifted mathematician who briefly considered switching from Engineering (undecided) to Math major. My husband and I and many of our friends are engineers, so we know a lot about Engineering careers. The Math discussions made me realize how little we know about Math careers.
Other families are likely having similar Math vs Engineering discussions. In some cases it may be a factor in the college choice. (Engineering schools usually do offer math majors. But schools with Math may not have engineering, especially if more of a liberal arts college). So I decided to start this thread.
I don't know the answer, but I will be watching this thread! My son is very gifted mathematically, however he doesn't know anything about engineering, as his dad and I are more social science types. I have a hunch he'd be good at engineering, but how would he/we know?
We are thinking that a smaller school with engineering and math and liberal arts would suit him. Bucknell, Villanova, Lafayette, that sort of place.
I can't name a lot of careers off hand that demand a math major, but I am a big proponent of a broad liberal arts education - after all, many of the jobs our kids will have have not even been invented yet!
S1 is a very gifted math student. He will be graduating this spring with a triple major (yes, I am very proud of this!!!) in Actuarial Math, Economics and Statistics. He will be working as an Actuary for a large insurance company after he graduates. He received numerous job offers. There are ten exams that one has to pass to become an actuary. He has passed five already and will take the other five once he starts his job. You can research this on many websites - I'm not sure of the names. You have to be very gifted in math to succeed as an actuary. Engineering is math driven also, but I think there is a good bit of physics involved also.
This sort of relates (I hope.) Our son is especially gifted in math and sciences. His dad is an engineer. But he is choosing to major in physics rather than engineering at our state flagship because he wants to be able to have more variety in his classes. Engineering degree programs tend to have very little elective options in their courseload.
Ultimately, our son wants a PhD in nuclear engineering, but for undergraduate he will be a Physics major with a minor in nuclear engineering.
I would echo what michone says about acutarial math. We friends whose daughter has many job offers in that field as well. She just has to decide on which city to select.
I have two sons. One is a grad student in math (hopes to teach), absolutely zero interest in applied math or engineering. S2 is in his fourth year of a five year engineering program; he is an outstanding math student, but would never have considered a major in math. For them, this was never a question. Does your child have a gut feeling about it?
You might also look at "Dilbert - The Knack" on YouTube for clarity on this issue.
The training is different. A proper math degree should teach you how to think logically and how to make formal and rigorous proofs of arguments (or in math parlance, propositions, theorems, corollaries, and lemmas). An engineering degree should teach you how to solve problems in a specific area (e.g. civil, aerospace, mechanical, etc.) as well as how to solve problems in general.
As a first-year doctoral student taking econ courses, here's an illustration of the difference between a math major and an engineering major. (I was a business major, but I took math up to ordinary differential equations.) I recently had a problem on how to use the chain rule in taking derivatives of a matrix, as I wanted to derive an expression in my textbook.
I didn't know why the chain rule term was in the front, not the back. I was looking for a formula to use and keep in mind for future reference. But the two guys I asked for help were both math undergrads, and they responded differently: don't remember the formula, just check the dimension of the matrix, and you'll be fine.
Indeed, their answer reflects a training in logical thinking. If the chain rule term were in the back, then the matrix multiplication is not well-defined. So logically, it HAS to be in the front. To me, a guy who loves formulas, the answer is not "satisfying," but it is certainly correct.
Erin's DadPosts: 18,786Super ModeratorSenior Member
DD2 was never interested in Eng but was always interested in math. She is major in Math with a minor in Econ. My experience is you can get a job in just about any field with a math degree - actuary, cost estimating, lab stats, etc.
sunnyholidayPosts: 115Registered UserJunior Member
fabrizio--I have no idea what you just said lol (although I think it was really smart!).
1moremom--My son has no interest in engineering, but is wavering between a math major and a physics major. I have similar questions about how he will decide between those two.
In my experience there is a big difference between most high school math and being a college math major. I was good at math in HS and was a math major for a while - I ended up with a math minor. But most high school math is about learning how to solve problems. College level math, at least at the upper division level where majors will spend a lot of time, are about proving theorems. The aptitude and inclination for the one is neither necessary nor sufficient for the other.
Engineering requires a lot of problem solving. Some of the problem solving can be quite mathematically complex, but engineers generally don't derive proofs from first principles that a beam will hold a certain load or a circuit will work a certain way. They need to mathematically handy, but not necessarily mathematically original thinkers.
In the people I've seen, the engineering drive is a fairly clear desire to understand how things really work, how to build things, fix things, make things work better. Many mathematicians have little interest in how "things" actually work, as long as there's a beautiful proof.
ucbalumnusPosts: 35,558Registered UserSenior Member
A math major typically has enough free elective space to include some courses in some of the following:
computer science (e.g. algorithms and complexity, operating systems, networks, software engineering)
economics (e.g. intermediate micro and macro with math, finance)
statistics (e.g. junior level probability and statistics)
in addition to math courses. Including such courses can allow the math major to be have some preparation for jobs and careers in software development, actuarial science, and/or quantitative finance in case more pure math job, career, or graduate school do not pan out.
As others have said, junior and senior level math courses tend to be mostly proofs rather than problem solving. Honors freshman and sophomore level math, if offered, is likely to emphasize proofs more than the regular version.
colorado_momPosts: 6,051Registered UserSenior Member
Good comments. Thanks!
"Engineering is math driven also, but I think there is a good bit of physics involved also. " - Definitely. But a lot of that physics is intertwined with calculus. There is also chemistry required, with the amount depending on the specialty. And many other science-like courses, usually with mathematics based problem sets. (You can avoid biology totally if desired).
"engineering drive is a fairly clear desire to understand how things really work" - True. Some engineering students are disappointed that the academics are so intense, with less hand-on projects than expected. That depends a lot on the college and the program. For students that choose Engineering, I highly recommend joining a campus club such as Mini Baja (all terrain vehicle) or ChemCar or other project fun.
I agree that math would allow more course flexibility. I only had two free electives in college (plus many engineering electives). There were some humanities electives, but much fewer than other majors. If a student arrives with AP/IB credits, that can make space for more electives.
Yes, what is his gut feeling? My S1 is gifted in math, but never considered it as a major or a career. He'll graduate this May with a degree in aerospace engineering (and a math minor, but only because he added a few classes that he enjoyed). I think he enjoys the application of math principles in a broader discipline. S2, tho, is a math major. He loves theoretical math and is good at it (but I wouldn't say "gifted"). Never considered engineering or applied math. No idea of the long-term career prospects, but he's enjoying the studies, especially the liberal arts aspect of his college's requirements. Maybe he'll research & teach? Different personalities/different approaches to math-related careers.
D2 is gifted in math would like to go into research and teach at the college level. She is not remotely interested in how things work and probably couldn't find her way out of a box. She is very good at visualizing complex problems and seeing patterns/relationships. Most of the friends I have who are engineers were always interested in how things work, often taking apart cars, vacuum cleaners, toasters, etc. as kids. I think this innate curiosity is probably a requirement for good engineers.
A lot of info from diverse sources here. My son started with math or physics as his major (technically was undecided for a few years) and took both of the Honors sequences (started "over" with first semester calculus, 4 semester's math material in 3...)- this meant the proof based calculus courses. He eventually decided on math and has added comp sci. He has taken several grad level math courses as an undergrad by now.
It is best for an entering freshman to look at the available math courses. Most science/engineering students are best served by the regular/problem solving calculus sequence at son's school. A look at math major course requirements will also show differences based on whether abstract or applied math is desired. My son is about as abstract (and absent minded about practical things) as they come. I can't imagine him as an engineer, or majoring in applied math and engineering physics (AMEP). Statistics is a separate department at his highly math ranked school- I think it may be in the Comp Sci building.
My perusal of what math majors can do besides teaching at any level from Hs to college showed more possibilities than for a physics major. As always, there will be some overlap in what jobs different majors end up in. Still waiting regarding son, now that he decided to wait with grad school. I keep reminding my procrastinator he needs to be looking (hopefully he has been- won't tell us anything).
Statistics, including mathematical statistics, opens up a wide range of job opportunities.
D's best high school friend is graduating this year as an engineer, but decided to go to grad school in statistics.
Replies to: Math Lovers - How to choose Math major vs Engineering?
We are thinking that a smaller school with engineering and math and liberal arts would suit him. Bucknell, Villanova, Lafayette, that sort of place.
I can't name a lot of careers off hand that demand a math major, but I am a big proponent of a broad liberal arts education - after all, many of the jobs our kids will have have not even been invented yet!
Ultimately, our son wants a PhD in nuclear engineering, but for undergraduate he will be a Physics major with a minor in nuclear engineering.
I would echo what michone says about acutarial math. We friends whose daughter has many job offers in that field as well. She just has to decide on which city to select.
You might also look at "Dilbert - The Knack" on YouTube for clarity on this issue.
As a first-year doctoral student taking econ courses, here's an illustration of the difference between a math major and an engineering major. (I was a business major, but I took math up to ordinary differential equations.) I recently had a problem on how to use the chain rule in taking derivatives of a matrix, as I wanted to derive an expression in my textbook.
I didn't know why the chain rule term was in the front, not the back. I was looking for a formula to use and keep in mind for future reference. But the two guys I asked for help were both math undergrads, and they responded differently: don't remember the formula, just check the dimension of the matrix, and you'll be fine.
Indeed, their answer reflects a training in logical thinking. If the chain rule term were in the back, then the matrix multiplication is not well-defined. So logically, it HAS to be in the front. To me, a guy who loves formulas, the answer is not "satisfying," but it is certainly correct.
1moremom--My son has no interest in engineering, but is wavering between a math major and a physics major. I have similar questions about how he will decide between those two.
Engineering requires a lot of problem solving. Some of the problem solving can be quite mathematically complex, but engineers generally don't derive proofs from first principles that a beam will hold a certain load or a circuit will work a certain way. They need to mathematically handy, but not necessarily mathematically original thinkers.
In the people I've seen, the engineering drive is a fairly clear desire to understand how things really work, how to build things, fix things, make things work better. Many mathematicians have little interest in how "things" actually work, as long as there's a beautiful proof.
computer science (e.g. algorithms and complexity, operating systems, networks, software engineering)
economics (e.g. intermediate micro and macro with math, finance)
statistics (e.g. junior level probability and statistics)
in addition to math courses. Including such courses can allow the math major to be have some preparation for jobs and careers in software development, actuarial science, and/or quantitative finance in case more pure math job, career, or graduate school do not pan out.
As others have said, junior and senior level math courses tend to be mostly proofs rather than problem solving. Honors freshman and sophomore level math, if offered, is likely to emphasize proofs more than the regular version.
"Engineering is math driven also, but I think there is a good bit of physics involved also. " - Definitely. But a lot of that physics is intertwined with calculus. There is also chemistry required, with the amount depending on the specialty. And many other science-like courses, usually with mathematics based problem sets. (You can avoid biology totally if desired).
"engineering drive is a fairly clear desire to understand how things really work" - True. Some engineering students are disappointed that the academics are so intense, with less hand-on projects than expected. That depends a lot on the college and the program. For students that choose Engineering, I highly recommend joining a campus club such as Mini Baja (all terrain vehicle) or ChemCar or other project fun.
I agree that math would allow more course flexibility. I only had two free electives in college (plus many engineering electives). There were some humanities electives, but much fewer than other majors. If a student arrives with AP/IB credits, that can make space for more electives.
It is best for an entering freshman to look at the available math courses. Most science/engineering students are best served by the regular/problem solving calculus sequence at son's school. A look at math major course requirements will also show differences based on whether abstract or applied math is desired. My son is about as abstract (and absent minded about practical things) as they come. I can't imagine him as an engineer, or majoring in applied math and engineering physics (AMEP). Statistics is a separate department at his highly math ranked school- I think it may be in the Comp Sci building.
My perusal of what math majors can do besides teaching at any level from Hs to college showed more possibilities than for a physics major. As always, there will be some overlap in what jobs different majors end up in. Still waiting regarding son, now that he decided to wait with grad school. I keep reminding my procrastinator he needs to be looking (hopefully he has been- won't tell us anything).
D's best high school friend is graduating this year as an engineer, but decided to go to grad school in statistics.