What do/did mathematics exams look like on your college (engieering departments)?

[Real_PhillBert]

4 minutes ago, MyName13 said:

I'm not sure what it's like in other fields, I'm talking about electrical (and mechanical) engineering.For example, how many engineers are going to calculate limits by hand or by using the epsilon delta definition or solve inf/inf or 0/0 limits without using Lhopital's rule?Who is going to calculate derivatives and integrals by definition?

Honest answer, no one. It's not about sitting at your desk and finding a limit, it's about understanding the fundamental of how mathematics influences design. You'll understand a lot more of the impact when you get to specific design courses and differential equations.

 

6 minutes ago, MyName13 said:

When we covered integrals we haven't mentioned anything that involved the integration symbol, instead we went through large amounts of theory that was somehow supposed to explain how it all works (which is impossible to cover in a short amount of time so no one understood anything).

Welcome to university. Dont worry, further classes will explain how it all ties together. I had a very real mind blown moment one day in differential equations. 

[MyName13]

2 minutes ago, Real_PhillBert said:

Honest answer, no one. It's not about sitting at your desk and finding a limit, it's about understanding the fundamental of how mathematics influences design. You'll understand a lot more of the impact when you get to specific design courses and differential equations.

 

Welcome to university. Dont worry, further classes will explain how it all ties together. I had a very real mind blown moment one day in differential equations. 

Serious question, does anyone even remember all of these lower level things?If not, how is it helping anyone "understand the fundamentals of mathematical influence on design"?

[Real_PhillBert]

3 minutes ago, MyName13 said:

1)What?

Just like drafters, mathematicians really aren't a thing. You can major in Mathematics, but you'd better get another related degree if you expect to get a job. 

 

4 minutes ago, MyName13 said:

2)How is understanding of mathematics giving you the knowledge of how something in that particular field works (how does it tell anything about that field anyway?Does mathematics teach you about materials used in that field, all the processes etc.)?

Here's an easy example; damping. Springs and dampers are extremely common machines, how do you figure out what the proper damper is for a specific application? - Differential equations is how. But you need the lower level calculus courses in order to understand what's happening in differential equations. 

 

6 minutes ago, MyName13 said:

If everything was proven from scratch then no one would do anything.For example, should one prove why and how Coulomb's law, Ohm's law, Kirchoff's laws etc. work?

You have a fundamental misunderstanding of what's happening. The goal of proving mathematical formulas is not so that you know it's true, but so that you understand the process. No one is ever going to ask you to prove any mathematical formula after college. 

[bimmerman]

4 minutes ago, Real_PhillBert said:

Honest answer, no one. It's not about sitting at your desk and finding a limit, it's about understanding the fundamental of how mathematics influences design. You'll understand a lot more of the impact when you get to specific design courses and differential equations.

 

Welcome to university. Dont worry, further classes will explain how it all ties together. I had a very real mind blown moment one day in differential equations. 

This.

 

Mathematicians, in the sense of people who are researching math and do proofs all day, are 99.9% in academia.

 

In industry, engineers, physicists, and chemists are the "mathematicians", because literally everything is rooted in math. You need to have a solid understanding of how calculus actually works to be able to use it, for lack of a better term, 'conversationally' in your other subjects.

 

I haven't done proofs since high school/college math, but I can do them and have done them, and understand that aspect of math still very well. That might sound like a lot of words that says nothing, so here's an example.

 

You can represent any function by a sum of infinite polynomial series-- you probably have seen Taylor/Maclaurin series at some point. Great, who cares. Well, signal processing as a field is all about taking gibberish signal and finding meaning in it. One way to do that is to literally fit polynomial series to the data to find what the underlying function is, and to then be able to draw meaningful information from it. Also, once you get to infinite series and derivatives/integrals of them, you understand fundamentally why and how sin, cos, e, etc are all interrelated.

 

Another example-- diff eq and laplace transforms. Proofs of how these work suck, but diff eq is second only to trig for utility and necessity. Nearly everything can be represented or simplified into a second order diff eq-- mass-spring-damper, RLC circuits (resistor + inductor + capacitor, there's your kirchoff's law), etc. Then once you have a system of multiple of these, how do you solve them? Linear algebra. How do you know how to solve them computationally efficiently? By doing it the shitty way first so that you understand and appreciate what the better methods are doing. How do you quickly solve diff eqs? Laplace transforms. How do these work? Well, time to go back to proofs so that you understand.

 

Final example: statistics. If you don't know how the underlying principles and math work, how can you trust anything you read or are told? Do you fundamentally understand the difference between a population and a sample, std dev of each, and when to use them? No? Back to proofs and exercises until you do.

 

You're in college to learn, not be told what to do. You need to learn the math not just be told 'do this and this and it works, don't ask questions'.

[bimmerman]

17 minutes ago, MyName13 said:

Serious question, does anyone even remember all of these lower level things?If not, how is it helping anyone "understand the fundamentals of mathematical influence on design"?

~85% of it, yes. More importantly I know where to look in my textbooks when I'm rusty. To expand on that, everything builds on the math. With a solid math foundation the higher level "low level" stuff is simple and intuitive since everything is based in first principles. Then simmer and add seasoning and you're doing mechatronics.

 

Seriously, knowing trig, calc, statistics, and F=m*d2x/dt2, you're golden.....once you realize how everything else builds from those first principles.

 

source: am a mechanical PE.

[Sauron]

29 minutes ago, MyName13 said:

 

Shouldn't engineers just take the knowledge (instead of learning how and why everything works at the low level) from mathematics (and other sciences) and make / design things instead of learning all mathematics in depth?

I'm sorry, how is "taking the knowledge and designing things" separate from "learning in depth"? Trying to apply random formulas without understanding what they mean is a recipe for failure. And don't worry, there's PLENTY they don't teach you in engineering courses about mathematics - we already get the watered down version. There's a reason there are entire degrees on mathematics while we only get 4-5 courses.

12 minutes ago, MyName13 said:

For example, how many engineers are going to calculate limits by hand or by using the epsilon delta definition or solve inf/inf or 0/0 limits without using Lhopital's rule?

It doesn't matter - to use a tool effectively you need to have some idea of how it works. Nobody remembers everything by heart, but learning it once allows you to remember the important parts with just a glance to the wikipedia page.

17 minutes ago, MyName13 said:

When we covered integrals we haven't mentioned anything that involved the integration symbol, instead we went through large amounts of theory that was somehow supposed to explain how it all works (which is impossible to cover in a short amount of time so no one understood anything).

That's university for you; you're expected to learn large amounts of information in short periods of time. It's not just the math courses.

37 minutes ago, JoeyDM said:

There aren't typically mathematicians in engineering firms doing the math for engineers

 

Although there are mathematicians who work as engineers in some situations...

41 minutes ago, MyName13 said:

What separates engineers from mathematicians then?

Specialization. A mathematician is typically more suited for research in the field of, you guessed it, mathematics (of which there are several sub fields, of course). An engineer is specialized in research and design in their own field, electronics for example. A mathematician won't know (at least, not thanks to their degree) how a CMOS works, just like an engineer won't be taught advanced topology.

 

But to be honest, mathematicians and engineers have a lot in common on a base level - they're (supposed to be) good at solving hard problems.

[MyName13]

25 minutes ago, Real_PhillBert said:

Just like drafters, mathematicians really aren't a thing. You can major in Mathematics, but you'd better get another related degree if you expect to get a job. 

 

Here's an easy example; damping. Springs and dampers are extremely common machines, how do you figure out what the proper damper is for a specific application? - Differential equations is how. But you need the lower level calculus courses in order to understand what's happening in differential equations. 

 

You have a fundamental misunderstanding of what's happening. The goal of proving mathematical formulas is not so that you know it's true, but so that you understand the process. No one is ever going to ask you to prove any mathematical formula after college. 

1)I'm pretty sure these are the only ones who teach us mathematics (there is no such thing as majors and minors here so you can't study several fields).

 

2)I still fail to see why an engineer needs to truly understand mathematics to the point where he reinvents mathematics instead of just taking it for granted and using it as a tool.If your goal is to do something you need, you're more interested in the end result and not in the specifics of why that tool lets you achieve that.Using the same logic, one should do the same for all subjects (why study programming languages if you can't make a computer first, why make a computer if you can't make logic circuits, why make logic circuits if you can't make electrical components, why make a CPU if you can't make a transistor etc...)

 

3)Ironically, these proofs are the reason nothing is understandable, I might simply be in a bad school.

15 minutes ago, bimmerman said:

not just be told 'do this and this and it works, don't ask questions'.

Same as above, why move into the field specifics if you don't understand chemistry, physics, then, for example, why learn electromagnetics / statics if you have no knowledge of quantum physics etc...

 

9 minutes ago, Sauron said:

 

That's university for you; you're expected to learn large amounts of information in short periods of time. It's not just the math courses.

 

 

Wouldn't it make more sense to simply make studies longer so that it's more realistic?

 

EDIT: I'm not sure how it's in other countries but where I'm from if you fail a certain subject, you can just carry it over into the next year so you're basically studying field specifics without passing mathematics (if one fails it).That doesn't make sense if you're supposed to use mathematical knowledge.

[Unhelpful]

12 minutes ago, Sauron said:

Although there are mathematicians who work as engineers in some situations...

Absolutely, I feel like that's what happens to 90% of math majors who don't go into education. 

[bimmerman]

I think you are misunderstanding-- the math competence required of engineers is orders of magnitude (ha!) less than that of a physicist, let alone a mathematician.

 

Math, for us, is the readers digest of easy mode-- we learn the first principles of useful math and that's it. We don't delve into set theory or more esoteric fields that even BS level mathematics majors study (a friend of mine did a math degree, I was out of my depth within a year).

 

You need to know the basics in any field before going down the rabbit hole. You may feel like you're at the bottom of the hole but you're very very very far from it. Just as physicists don't start with quantum, mechanical engineers don't start with system dynamics or fluid dynamics. First you need calc1-3, then statics, then dynamics, then diff eq and linear alg, and then you're ready to understand system / fluid dynamics. There is a reason the engineering curriculum across nearly all disciplines is identical for the first year or two, as all you're doing is learning the building blocks of math, physics, and chemistry. That's fully intentional.

 

I can also guarantee that true computer engineers DO study logic gates and how to build them, just not at first. Hell, we did in circuits for non-EEs. There is a certain level of background knowledge you need to have, and the math is a significant part of it. You need to start broad before going specialized. For math, the opposite is true, as you need to understand the building blocks before the interesting stuff makes sense. Otherwise, a derivative just seems like math made up on the spot.

 

It's the worst part, but once you're through you'll be like the other posters here, looking back, going "yea, those all nighters sucked but man, that ended up being useful"

[bimmerman]

1 minute ago, JoeyDM said:

Absolutely, I feel like that's what happens to 90% of math majors who don't go into education. 

Physicists too. A degree in math/physics can make you an excellent engineer with on the job training.

 

Which makes sense, since engineering is nothing but applied math and physics, with some chemistry thrown in on top.

[Sauron]

14 minutes ago, MyName13 said:

Wouldn't it make more sense to simply make studies longer so that it's more realistic?

It's not an unrealistic expectation, people graduate all the time. In most universities you can take as long as you like to finish a course (as long as you pay the fee or taxes), just don't expect to be employed with the same ease as someone who finished in time.

 

This sort of regime also gets you used to the environment you might face at your future job - a strict deadline and lots of new technologies to learn and integrate in your project.

 

It's not for everyone, that's for sure - but I'm convinced that, with enough effort, most people can get an engineering degree in time.

[bimmerman]

4-5 years is pretty normal for a bachelor.

 

1-2 years is pretty normal for a master. (post-BS)

 

5-6 years is pretty normal for a PhD. (post-BS, minus 1-2 for post-MS)

 

If you worked during school or had other circumstances, it can take longer, or shorter, but these are the trends.

[MyName13]

6 minutes ago, Sauron said:

It's not an unrealistic expectation, people graduate all the time. In most universities you can take as long as you like to finish a course (as long as you pay the fee or taxes), just don't expect to be employed with the same ease as someone who finished in time.

 

This sort of regime also gets you used to the environment you might face at your future job - a strict deadline and lots of new technologies to learn and integrate in your project.

 

It's not for everyone, that's for sure - but I'm convinced that, with enough effort, most people can get an engineering degree in time.

Unless you have no use of the lectures and are supposed to learn all that yourself.

 

9 minutes ago, bimmerman said:

 

I can also guarantee that true computer engineers DO study logic gates and how to build them,

You could say that they should also have deep knowledge of physics and materials science, how deep is too deep before you might as well simply get someone from another field?

 

2 minutes ago, bimmerman said:

 

5-6 years is pretty normal for a PhD. (post-BS, minus 1-2 for post-MS)

 

 

 

Aren't PhD's 3 years long?

[bimmerman]

2 minutes ago, MyName13 said:

Unless you have no use of the lectures and are supposed to learn all that yourself.

It is on YOU to learn. Lectures aren't supposed to be enough.

 

2 minutes ago, MyName13 said:

You could say that they should also have deep knowledge of physics and materials science, how deep is too deep before you might as well simply get someone from another field?

Yes, at graduate level. Undergraduate level you don't need that level of knowledge, just a working knowledge, which does require some deep dives.

 

2 minutes ago, MyName13 said:

Aren't PhD's 3 years long?

After a master's, generally yes. If post BS that is exceedingly fast.

[MyName13]

4 minutes ago, bimmerman said:

It is on YOU to learn. Lectures aren't supposed to be enough.

 

In that case, what's the purpose of lectures?Add all the other subjects on that and you're basically learning the entire field yourself.

[bimmerman]

2 minutes ago, MyName13 said:

In that case, what's the purpose of lectures?Add all the other subjects on that and you're basically learning the entire field yourself.

Lectures are there to guide you through the material as you learn the subject on your own time, and provides an opportunity to ask an expert in the field when you have questions and/or are stumbling. Good lectures also teach you things, but the point of college is to learn how to learn.

[Sauron]

20 minutes ago, MyName13 said:

Unless you have no use of the lectures and are supposed to learn all that yourself.

Everyone has some bad teachers. Regardless, just attending the lectures is almost never enough.

[Unhelpful]

11 minutes ago, MyName13 said:

In that case, what's the purpose of lectures?Add all the other subjects on that and you're basically learning the entire field yourself.

You need to fix your mentality. If you want to be an engineer you need the desire to learn, including self-starting.

[MyName13]

11 minutes ago, bimmerman said:

Lectures are there to guide you through the material as you learn the subject on your own time, and provides an opportunity to ask an expert in the field when you have questions and/or are stumbling. Good lectures also teach you things, but the point of college is to learn how to learn.

That's where education in my country has completely failed, unfortunately.About learning on your own time, that's not feasible when you cover a lot of things in a day and cover the same amount the next day (we covered derivations in a single day, 3 classes 45 minutes long, by this pace we will cover integrals in the same amount of time).

 

4 minutes ago, JoeyDM said:

You need to fix your mentality. If you want to be an engineer you need the desire to learn, including self-starting.

It's not the desire that's the problem, but the fact that covering large amounts of cryptic information in a short amount of time, all by yourself, is nearly impossible.I'm saying this as someone who is studying a mixture of computer science and software engineering degree, I've learned some small amount of things by myself during high school but this is simply way beyond everything I've ever seen in my education so far.

[bimmerman]

1 hour ago, MyName13 said:

That's where education in my country has completely failed, unfortunately.About learning on your own time, that's not feasible when you cover a lot of things in a day and cover the same amount the next day (we covered derivations in a single day, 3 classes 45 minutes long, by this pace we will cover integrals in the same amount of time).

 

It's not the desire that's the problem, but the fact that covering large amounts of cryptic information in a short amount of time, all by yourself, is nearly impossible.I'm saying this as someone who is studying a mixture of computer science and software engineering degree, I've learned some small amount of things by myself during high school but this is simply way beyond everything I've ever seen in my education so far.

You need to learn the material, and to stop pointing the blame finger elsewhere. Yes there are obstacles, figure out how to overcome them or don't and fail. The prime mistake you're making is the "all by yourself" -- don't do that.

 

When you have questions or are struggling, do you go to:

-Professor office hours?

-teaching assistant office hours?

-study group with fellow students? (if not, form one!)

-Professors or classmates you have a good relationship with who know the subject?

-Mentor of some sort?

-find/hire a tutor?

 

How about working extra problems with a solution guide (amazon!)?

Find a different textbook or resource to augment your studies?

Does the prof post solutions to the homework/projects/exams after the fact? Have you gone back through the assignments with the solutions to see where you went wrong?

etc etc.

 

How much time outside of school do you spend on school? What else do you do during a day that isn't directly related to your studies / affording your studies / consuming sustenance? How much time do you spend on non-essential areas (gaming, movies/Netflix/tv, etc), and how much can you cut back on those without losing your sanity? For me, prioritizing and affording school meant minimal hobby time, like 2-3 hours a week or less. YMMV.

 

It is on you to learn the subject and to make it happen. You aren't the first to have issues with teachers and classes-- I had a heat transfer professor that was terrible and where lectures were rather useless. What I and others did was find other books, other problem sets, go to office hours, discuss with the TA and classmates, and eventually form study groups so that we learned the material on our own. What do you know, we did well and survived, and absolutely would not have if we had sat passively in the lecture hall listening to the material and doing the homeworks. I didn't sleep much that semester and had zero time for gaming, but I nailed it in that class. That study group was the best thing to come out of that class, as we also got each other through the rest of that year's backbreaking curriculum (mech e junior year...for yall who survived).

[captain_to_fire]

Not an engineer but this is what my math courses are:

 

1st year: Algebra, Trigonometry

2nd year: Differential Calculus, Integral Calculus

3rd year: Biostatistics 

 

On 12/8/2018 at 9:56 PM, MyName13 said:

Do you have any examples of your tests?I assume you covered limits and calculus, were you supposed to solve some convoluted limits, derivations and integrals or was it something else (theory or some easy to medium hard problems)?

I think you have those questions at the end of each chapter in your textbooks. That's how I did it back in the day because studying math requires practice, not memorization. 

[captain_to_fire]

20 hours ago, MyName13 said:

How is understanding of mathematics giving you the knowledge of how something in that particular field works (how does it tell anything about that field anyway?Does mathematics teach you about materials used in that field, all the processes etc.)

The applications in the real world made me appreciate math especially in industry made me appreciate math. Also, math is inevitable. Heck, even doctors have to use math.

[Bouzoo]

20 hours ago, MyName13 said:

In that case, what's the purpose of lectures?Add all the other subjects on that and you're basically learning the entire field yourself.

Here is the thing. Lectures alone are not enough, but they can make life oh so easier. Something that your teacher may explain in 5 min may take you literal hours of figuring out, and I can say that from experience (math bachelor, currently on computer science, so I've seen my fair share of math). I am a person that almost never goes to lectures, but boy can they be a life saver. And for many courses, the best way is to study from the class notes, so to figure those out, attending classes does help a lot. Lectures are introduction, it's up to you to figure everything.

A couple of my close buddies graduated in engineering (robotics, aviation and can't remember the last one), it's the same thing. 

 

[Bouzoo]

8 minutes ago, captain_to_fire said:

math requires practice, not memorization. 

For solving problems yeah, but when it comes to theory, where most of the math is, memorization has a huge part, with logical thinking of course. 

[captain_to_fire]

Just now, Bouzoo said:

For solving problems yeah, but when it comes to theory, where most of the math is, memorization has a huge part, with logical thinking of course. 

I don't think one can learn how to solve a quadratic equation simply by staring at the quadratic equation or at the difference of two squares. It requires practicing sample questions typically provided by textbooks or by the professor. In fact, the best way to memorize a formula or a theorem is by practicing like how can the quadratic equation be derived from ax² + bx + c = 0?