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

[MyName13]

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)?

[79wjd]

It depends entirely on the course and professor. 

 

My Calc 3, linear algebra, and DIFFEQ exams were a mix of complicated and conceptual problems. Calc 2 was a mix of the above and multiple choice. Meanwhile Stat and the remaining dozen or so math classes were all heavy theory classes and my exams looked more like essays than math.

[MyName13]

18 hours ago, 79wjd said:

My Calc 3, linear algebra, and DIFFEQ exams were a mix of complicated and conceptual problems. Calc 2 was a mix of the above and multiple choice.

For example?Were you supposed to solve some limits, derivations and integrals when you covered these in calculus or was it application of these concepts?

[79wjd]

35 minutes ago, MyName13 said:

For example?Were you supposed to solve some limits, derivations and integrals when you covered these in calculus or was it application of these concepts?

Both.

[wasab]

I am not a math major so my required math courses are all applied mathematics so mostly word problems and very little focus on theories. 

[spwath]

Yeah, for calc 2, 3, differential equations, and statistics, its problems and applications. Kind of like any other math test.

[Sauron]

Here's an example of the kind of exam I did for calculus 1 (I have a bachelor's degree in "software, electronics and telecom engineering"):

Spoiler

It's in Italian, but here's a translation of the questions:

 

Exercise 1. Find the solutions z,w ∈ ℂ  of the following system of equations

 

Exercise 2. Let S(x)=[series]

(a) Determine the values of x∈[0,2] for which the series converges and work out its sum S(x)

(b) Determine the values of k∈ ℝ  for which the equation S(x)=k has a solution

 

Exercise 3. Let f(x)=[function]

(a) Determine the Taylor polynomial of f with center in x₀=0 up to the first non null term

(b) If it exists, find the value of [limit]

 

Exercise 4. If it exists, find the value of [integral]

 

There was also an oral part of the exam which consisted in presenting the proof of a few theorems and, in order to access the exam above, a shorter multiple choice test also had to be completed with a decent result. Differential equations were also part of the program, they aren't present in this exam by pure chance.

 

Calculus 2 was pretty much this but in multiple dimensions. I also had a dedicated geometry course (matrices, vectors, the works) and some signal theory (lots of probability distributions and fourier transforms) as well as an introductory course to control theory (laplace transforms, zeta transforms, nyquist diagrams).

 

If you want more examples you can find them (as well as the solutions and a lot more material for various courses) on my friend's website: http://johnwhite.it/university/

Much of it is in Italian, but google translate should get you through most exams. Calculus is "analisi" in Italian.

 

Of course, exactly what is required of you will depend on your university.

[Real_PhillBert]

On 12/8/2018 at 7:56 AM, 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)?

Yes you will be tested on limits, derivatives and integrals, in my university, you were expected to know the theory, and were tested on the application. 

 

When I went to college, Calc 1 and calc 2 were used as weed out courses, and very tough. In my calc 1 class at the end of the semester the class average was something like 38%, but it was curved so 38% was a "C". They did this to get rid of the students who didn't really want to be there, and to look for students doing significantly above the average to pluck out for mathematics majors. 

 

I never had a multiple choice exam in any mathematics class in college. 

 

Once you made it to multivariate calculus and differential equations you pretty well had things down. 

 

I have a Bachelors of Science in Mechanical Engineering. 

[Rodinski]

Engineering = hard mode calculus (adding to that, your teacher doesn't explain the entire lesson, horrible penmanship, and doesn't speak your native language)

 

Everyone else = easy mode (sometimes mathematics might bump the difficulty up to normal mode, but mostly it's easy.  Adding to that, your teacher is an actual teacher)

[Rakanoth]

On 12/8/2018 at 2:56 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)?

Quite similar to the homework questions on this page:

http://math.jacobs-university.de/petrat/teaching/2018_fall_advanced_calculus/

 

[MyName13]

20 hours ago, Real_PhillBert said:

When I went to college, Calc 1 and calc 2 were used as weed out courses

Same thing.Why does anyone need to be weeded out anyway by using mathematics as a filter (add bad teaching to that and you're expected to learn everything yourself...).Biggest problem on my university is that engineers study mathematics too deeply (makes me wonder if they consider us mathematicians or engineers).

[Real_PhillBert]

2 minutes ago, MyName13 said:

Same thing.Why does anyone need to be weeded out anyway by using mathematics as a filter (add bad teaching to that and you're expected to learn everything yourself...).Biggest problem on my university is that engineers study mathematics too deeply (makes me wonder if they consider us mathematicians or engineers).

Where I went, there was only one class substitution between an ME and an ME with a mathematics minor, and only two additional courses for an ME to double major in ME and Mathematics. 

 

Engineering is really just applied mathematics so it makes sense that the two follow so closely. 

[Blasteque]

On 12/8/2018 at 5:56 AM, 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)?

Where I went the majority of the calculus instruction was math classes from the math department.  Thus, they were much like any other math class: a mix of practical and theoretical.

 

Once in the aerospace engineering program there was a dedicated math class that served to remind undergrads of what they had learned (potentially several years earlier) and provide additional focus on certain functions just for aerospace.  For instance: in fluid mechanics and structures there are several 2nd order partial differentials that are important, so that class went over that.  I don't know how common such department specific such classes are.

[Sauron]

3 hours ago, MyName13 said:

Same thing.Why does anyone need to be weeded out anyway by using mathematics as a filter (add bad teaching to that and you're expected to learn everything yourself...).Biggest problem on my university is that engineers study mathematics too deeply (makes me wonder if they consider us mathematicians or engineers).

Mathematics are useful for engineers - throwing it all out in harcore mode during the first couple of years ensures those who can't handle it don't sink too many years of their lives in a field they'll eventually get stuck in anyway.

[bimmerman]

You need to know the math cold to understand and apply the theory for the more interesting engineering subjects.

 

Chances are you won't need to do explicit multivariate calc or linear algebra frequently on the job, but you need to understand subjects like dynamics and multi-degree-of-freedom statics innately, which requires competence with the underlying math (calc, trig, lin alg) and physics. If you enjoy FEA and choose to specialize in it, guess what, that's all based on linear algebra. Say you model something in FEA, you still need to understand the math so that you can show why your FEA model is accurate and was worth your hours spent, by usually hand deriving backup calcs.

The math by itself might not be interesting, but what the math allows you to do is.

 

As for exams, we were not allowed to use calculators during any math exam nor was it open book. You could bring in one page of notes and a pencil, and that was really all you needed to do well.

[MyName13]

18 hours ago, Sauron said:

Mathematics are useful for engineers - throwing it all out in harcore mode during the first couple of years ensures those who can't handle it don't sink too many years of their lives in a field they'll eventually get stuck in anyway.

 

17 hours ago, bimmerman said:

You need to know the math cold to understand and apply the theory for the more interesting engineering subjects.

 

Chances are you won't need to do explicit multivariate calc or linear algebra frequently on the job, but you need to understand subjects like dynamics and multi-degree-of-freedom statics innately, which requires competence with the underlying math (calc, trig, lin alg) and physics. If you enjoy FEA and choose to specialize in it, guess what, that's all based on linear algebra. Say you model something in FEA, you still need to understand the math so that you can show why your FEA model is accurate and was worth your hours spent, by usually hand deriving backup calcs.

The math by itself might not be interesting, but what the math allows you to do is.

 

As for exams, we were not allowed to use calculators during any math exam nor was it open book. You could bring in one page of notes and a pencil, and that was really all you needed to do well.

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?On my university we're proving most of the things we work on.

[Unhelpful]

21 hours ago, MyName13 said:

Biggest problem on my university is that engineers study mathematics too deeply (makes me wonder if they consider us mathematicians or engineers).

Engineering is applied mathematics.

[Unhelpful]

5 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?On my university we're proving most of the things we work on.

No... No. That's a terrible idea. The engineers are the ones who understand how it works at the lowest level. You can't be trusted to design unless you have a true mastery of what you're working on, including the mathematics. If you are tired of the math, get out of engineering. This may not be the field for you.

[MyName13]

2 minutes ago, JoeyDM said:

Engineering is applied mathematics.

Obviously, but should engineers know mathematics in depth (by that I mean that they should really understand how any why everything they cover in mathematics works)?Shouldn't that be left to mathematicians?

1 minute ago, JoeyDM said:

No... No. That's a terrible idea. The engineers are the ones who understand how it works at the lowest level. You can't be trusted to design unless you have a true mastery of what you're working on, including the mathematics. If you are tired of the math, get out of engineering.

Isn't their area of engineering what they should understand at the lowest level instead of mathematics?What separates engineers from mathematicians then?

[Unhelpful]

2 minutes ago, MyName13 said:

Obviously, but should engineers know mathematics in depth (by that I mean that they should really understand how any why everything they cover in mathematics works)?Shouldn't that be left to mathematicians?

Yes, obviously. No... There aren't typically mathematicians in engineering firms doing the math for engineers, you're the math guy. Engineering is >90% math.

 

This isn't the field for you if you don't think engineers should 100% understand all of the math involved with what they're working on, or you think you won't be the one doing the math.

[MyName13]

2 minutes ago, JoeyDM said:

Yes, obviously. No... There aren't typically mathematicians in engineering firms, you're the math guy. Engineering is >90% math.

 

This isn't the field for you if you don't think engineers should 100% understand all of the math, or you think you won't be the one doing the math.

But for what reasons should an engineer understand mathematical tools as well as a mathematician?What does one gain from proving everything?For example, many software developers have no idea what happens at the low end (and they don't really need to).

[Unhelpful]

5 minutes ago, MyName13 said:

But for what reasons should an engineer understand mathematical tools as well as a mathematician?What does one gain from proving everything?

This is insane. What do you think engineers do? What field of engineering are you even talking about? Mechanical? Chemical? Electrical? Do you think they just play around with CNCs and motors, or chemicals all day? You do all of the work on paper, including the diagrams and (if applicable) mathematically proving your process... Then put it to somebody else for fabrication. 

 

And FYI - the shit you're learning is nowhere near the level of a mathematician, stop repeating that. You're learning engineer-level math, nothing more.

[Real_PhillBert]

12 minutes ago, MyName13 said:

Obviously, but should engineers know mathematics in depth (by that I mean that they should really understand how any why everything they cover in mathematics works)?

Of course they should, it's pretty fundamental to design.

 

13 minutes ago, MyName13 said:

Shouldn't that be left to mathematicians?

For all intents and purposes, mathematicians arent a thing. Engineers do their own math. 

 

14 minutes ago, MyName13 said:

Isn't their area of engineering what they should understand at the lowest level instead of mathematics?

No, having someone design anything without a understanding of how and why it works is a bad idea. 

 

15 minutes ago, MyName13 said:

What separates engineers from mathematicians then?

Engineers have jobs. 

[MyName13]

1 minute ago, JoeyDM said:

This is insane. What do you think engineers do? What field of engineering are you even talking about? Mechanical? Chemical? Electrical? Do you think they just play around with CNCs and motors, or chemicals all day? You do all of the work on paper, including the diagrams and (if applicable) mathematically proving your process... Then put it to somebody else for fabrication. 

  

And FYI - the shit you're learning is nowhere near the level of a mathematician, stop spouting that. You're learning engineer-level math, nothing more.

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?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).

[MyName13]

5 minutes ago, Real_PhillBert said:

For all intents and purposes, mathematicians arent a thing. Engineers do their own math. 

 

No, having someone design anything without a understanding of how and why it works is a bad idea. 

 

 

1)What?

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.)?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?