How Much Math is REALLY in Engineering? 

Does medical engineering actually use math ? Like.... just a few math in there right ?

I think it's full of theory 😅

@@tienhung3112 We use actually a lot of math, because we are working with fluidic models, biomechanic forces, differential equations for dynamic systems, complex numbers for electrical engineering, fourier transform for MRT reconstruction & spectra. It's also quite important to get the models into programmed applications.

I’ve never heard of a medical engineer what is that?

@@realdotty5356 Medical engineering is an interdisciplinary study program with focus on mechanical, electrical engineering and informatics combined with medical contents. Typical fields for work are medical imaging for MRI/CT scans, active and passive implants and other hospital-/laboratory devices.

How much of this do you actually use? Any important advice you can give about the career? Curious and might go into Aerospace.

My advice is to study aerospace engineering only if you are passionate about the aviation/space world. Have a clear vision of what you want to achieve, be it working in your dream company, the job you will have or your future lifestyle. The undergraduate degree is sort of an introduction to all fields of aeronautics. It will be up to you to decide what you're going to specialize in, and how. Doing a master's degree, learning in a company as an intern or on your own. Some students will become aerodynamicists, some structural engineers, some materials engineers, control systems engineers, airport engineers, etc. Get my point? When you specialize, you will work with only a few of the things you will have learned in college, but all of them will be somehow connected in the company. It's not about how much math you will use in your working life, but that you need to have mathematical tools for all possible applications in the aeronautical world. In real life, as Tamer says, a computer will take care of calculations. I shall add that you learn math in order to train your mind and prove you can put in the work. Take care and be passionate!

@@aerospaceengenieeringknowl3204 Thank you so much, I really needed this.

@@aerospaceengenieeringknowl3204 - thank you!

@@aerospaceengenieeringknowl3204 thanks!

Agreed

So is this engineering copium?

@@YuTEM yes, this literally applies to anything, look at medicine, a substance can treat a symptom but if you don't treat the cause of the symptom are you really treating the person? Or music, when writing a song you don't just look at "the next 3 notes" a good song feels complete if it all works together, or mathematics, focusing on solving just a single specific problem isn't very useful, the usefulness comes form understanding the general solution to the general problem, and so on...

@@zirkereuler5242 'mkay

do you work as a mathematician? or some math heavy job like Data analyst?

The point of certain algorithms is to know which one to use and understand A statistician can know normal distribution best but what happens when the model cannot be approximated by normal distribution? You need to either design your own distribution or understand that the model fits something else instead. But notice you’re not expected to compute out everything (mean, median, std dev) the computer will do that for you but your numbers are meaningless if you compute with normal instead of the more accurate model

A problem solver! That’s what i will learn to be.

But how much of that is used in your actual job tho. Like %

@@jayevans6146 I have yet to get a real engineering job, so I can’t give you an accurate answer. I did an internship though and the engineers used math and calculus to verify that their code was working properly. As the video states, many types of software exists to help with engineering, but it is definitely useful to know the science and math behind the software to verify that it works properly.

@@infinitespace8313 It was mostly rhetorical. I already know. In reality, about 5%-10% of your actual job will involve actual higher level math/Cal DEs etc

@@jayevans6146 but even then if you didn't learn about those higher level math in school then you wouldn't know it in industry. Even if something constitutes only 1% of your job, you should still be learning of what it is and how it works rather than not knowing it. Of course there is the obvious time investment as these higher level classes take much longer to learn due to their difficulty, but even so if it is used in the field no matter how miniscule you should still learn it in school

@@jayevans6146 Not every engineering field is the same, aerospace is one of the strongest if not the strongest math related engineering, biotech, nano, biomedical, systems, industrial engineers may not need the same amount of math than aerospace

Yes. I also noticed that in the American system one can enter a PHD program with only a bachelors and sufficient research experience, whereas for England, and I presume also italy, one must have a masters before being admitted into the PHD. Is this true of Italy?

who asked?

@@randallmcgrath9345 This is true in America, but the PhD program is usually longer, and would be almost equal to getting your master's along the way. Having your master's and then getting a PhD is probably still the more popular route in the US and of similar length in the grand scheme of graduate studies.

@@maxwellwallace8553 I was about to say this! Well put.

@REPUBBLICA ITALIANA ma dici sul serio?

Thanks for sharing and that makes sense. Computer science majors at my school were under the faculty of mathematics…so it makes sense that there’s so much math involved in CS.

was this in the US, if so, did you touch deep into integration methods and applications in one semester?

I attest to that. I'm CS major also in Africa ghana. Ours is 80%. Less programming, more math and physics

That's an interesting setup. Where is the school?

In complex analysis the square root can be defined as a two-valued relation so i = \sqrt{-1} is correct ( i is the image of 1 in the principal branch)

@@santiago_moralesduarte The complex number system is a field and for that, at the introductory level, the definition i=\sqrt{-1} is really a very poor definition. Nice for high school level, not for serious college level. I vehemently agree with Abdusselam and that's how we learned it too. In fact, our notation was (0,1)x(0,1)=(-1,0)

i like your funny words magic man

I found out about the last part later on. I've warmed up to team and project management but it was difficult at first because I'm not a people person.

So is this the easiest one ?

Nothings ez my guy

What subject teaches the foundations?

@@12degreesnowman11 If you master calculus 1/2, physics, and differential equations you will have the best intuition when you get to the applied classes.

@@12degreesnowman11 Start with Real Analysis.

@@stevemenegaz9824 do you have any books to recommend?

@@12degreesnowman11 DId my reply show up?

It's not only that. You also need people to build the software to begin with. I worked in civil engineering in a firm where we did A LOT of in-house model building. So yeah, the math was used frequently when building the tools. Less when using them.

haha appreciate that :)

Yes the course overview he gave is typical of here in the US system. It will vary a great deal even in the US depending on the university and how the department is structured. If your courses are being offered by a university with a strong math research department you will be taught rigor using proofs and such, but a more engineering focused school will hammer on the applied problems and getting solutions for complex and/or unusual situations. At my school I took calculus 1 and 2 from instructors with math degrees, they were heavy on proofs and identities. Calculus 3 I took from a retired aerospace engineer, proofs meant next to nothing to him and the exams were 100% applied problem solving.

Here in Brazil I'm seeing boolean algebra in digital eletronics as well.

Frankly it's just about the same.

Math really rules the world of Engineering for a bright present and the future.

It is not that hard unless you are the one who is doing the proofing

Everything available online.. You don't need to get into a uni to learn maths..

@@i2keepitrealInreseach I agree, but the quality of education matters to me. Direct access to faculty, collaboration with peers, rigid schedule and lecture/exams etc.

@@stevenlopez1717 MIT, NPTEL, and many educators who even surpass some of the professors from MIT are on RU-vid.. Many paid courses.. AI which can help and you can debate with... You can make these as rigorous as you want.. Enroll in some paid courses and take tests... Once you put in the money you are now more serious... Tbh learning takes place when you have no rigid schedule and exams... The philosophical aspect can be then understood... And you can publish things if you want. No one stops you... I am in medicine and have studied physics before this for four years... Higher physics is easy for me but it's not because I attended uni... Uni taught me nothing... I bunked classes a lot and studied at home and from online courses.. Just appeared for exams... I used some other means for my attendance... I remember learning about partial derivatives from a book and a video and then understanding thermodynamics.. The uni skipped this chapter as the instructor was busy somewhere else... Everything will be online in the coming years... Collaborations can be done online... I think you are still the old-school type of guy... Even CS degrees from top-rated uni have been started online... You just need to take exams in nearby centers... In my country, online education has increased and quality is not an issue... Many institutions have started online academic programs ( they charge just like offline ) but you can see no difference in quality.. You will be provided with same material and same professors and the same interactive sessions... Now I'm in radiology... I did my postdoc via online mode.. Lol I am learning signal processing... And more abstract subjects... For quality check, I read standard books and solve questions... I can solve them.. Means I know those things.. I even debate with people in the maths and physics community... I am currently working on fluid dynamics of the pathology of CVS..

I enjoyed reading this comment and its insight.

I would say what an engineer sees as “math” is completely different to what a mathematician sees as math. They two completely different worlds. If u think about it, you learn “math” to apply it to the real world, whereas we mathematicians work on a new world with its own rules and develop that new world by creating new theorems and definitions. That is why for us mathematicians, engineering majors teach incredibly limited math and in my opinion I even question that it should be called math. Not trying to sound discouraging but want to be clear and point out the difference. Generally engineers just want to learn “math” that is useful to apply in the real world, so you dont need to understand math fully nor its essence.

@@rubengarciaquismondo Mathematicians tend to specialise in some area of pure maths. Applied mathematics is what engineers are interested in. Engineering is not really coming up with completely new ideas, it is knowing how to apply established technologies and methods to solve problems. All engineers are always mindful that the end result of their endeavours always has to be fully tracible to tested methods and technologies so coming up with your own brand new untested methods is really not useful.

@@schrodingerscat1863 That is correct but the term "deep understanding" is not really suited math for engineers. Not even in the small topics, not even in Calc 1.

@@schrodingerscat1863 I totally agree with you. Im well aware of that, we mathematicians have totally different goals and aren’t interested in real world applications. Its a matter of what you like.

Same for me, (Also from Germany)but partial differential equations is in the Master studies of EE. We’ve have a module there called higher maths.

Hatte bis jetzt analayis 1,2, lineare algebra und gewöhnliche DGL. Bin aber erst immer zweiten Semester

@@samuellandos785 which city are u in university? Munich, Duisburg , Essen or what? cause I heard Munich is the hardest

@@samuellandos785 Bei euch ist das heutzutage sowieso alles anders. Als ich studiert habe (Ende der Diplom-Ära) hieß das alles anders, war extrem konzentriert in wenige Vorlesungen und Prüfungen, und reichte *viel* weiter als bei euch heutzutage. Im Ingenieurwesen wurde in den letzten 15-20 Jahren so einiges an mathematischem und physikalischem Tiefgang gestrichen bzw. als Wahlpflicht ausgegliedert. Auf der anderen Seite werdet ihr aber auch extrem gegängelt. Bei mir gab es noch etwas, das hieß "Grundstudium" und ich mußte Scheine machen. Wortwörtlich Scheine. Zettel. Analoges Papier ;-) Die hat man ausgestellt bekommen, wie Akten fakturiert, und irgendwann als Stapel der ollen häßlichen Zicke im Prüfungsamt auf den Tisch gelegt, um zu den Klausuren der Diplom-Vorprüfung zugelassen zu werden. Wenn man das Grundstudium geschafft hatte, wiederholte sich dieses unverschulte, unbegleitete, frei vom Studenten zu gestaltende Verfahren bis zur Ablegung der Diplom-Hauptprüfung. Die Noten des Grundstudiums wurden nie wieder gesehen. Die Endnote berechnete sich nur aus den Prüfungsteilen des Hauptstudiums.

@@bobbwc7011 Das ist so typisches früher war alles besser Gelaber. Beweise doch dass es früher tiefer ging als heute mal abgesehen dass das vom Standort abhängt. Es ist eigentlich eher umgekehrt. Heute werden die Grundlagen aller fachähnlichen Diplomstudiengänge in ein Bachelorstudium gepfercht.

Probably because it involves a lot of differentiation an abstract thinking

That's cuz you don't know about category theory, homological algebra or maybe number theory.

@@Atistatic Hahah, I broke down laughing and crying when I read this comment! Recently *died* from my course in category theory and homological algebra! Super interesting though I must say, but I will need more time to internalize the concepts.

@@jacobskarby1389 surely that does take time. Even more than you need internalize abstract algebra for the first time.

Ok

Oh damn that’s crazy, so what more math do you do in the later semesters if you already did everything in the first two semesters?

@@TamerShaheen complex analysis, courses related to machine design, materials, processes of manufacturing, a whole course on thermal engineering, a course of refrigeration and air conditioning etc.

Tyre engineering, internal combustion engines.

@@bhupendrakumar2520 it explains why people from India are the best in IT

@@user-wg3kh4ox3t And get paid the least ngl

Me too ❤️

@@cedar4539 I don't know how similar it will be there but honestly I didn't think the math was the hardest part, it's the insane range of topics you have to master for me. Whatever specilization I chose the first year and a half are ton of courses from all science branches and not just some basic course they went advanced (hence the name engineering science). They are also often very very abstract and not very useable yet in you engineering career. I really had to power through these and I often found them uninteresting because they had nothing to do with what I wanted to specialize in. After that year and a half it changes alot though and at that point it starts to make sense. In the end I'm maybe kinda glad it is like that because after graduating my bachelor couple days ago you realise just how much you've learnt about the world around you.

Would you say it's a good idea to double major in engineering and mathematics?

@@krustykrispy5781 i personally havent done a math degree but i could see the synergy. However, i think you might be better off pairing your double with something more practical. The engineering degree will equip you with applied science full of "good enough" math shortcuts and approximation methods, while i hear the mathematics side is a bit more full on. If i had the choice and you go in for the mathematics of it all. I would pair CS with mathematics or do an engineering major involving lots of CS such as CS, Mechatronics or Electrical . There are too many engineers out there scared to code and if you really want to unluck your inner mathematician or engineer you have to learn atleast python.

I can tell u the mathematical depth in engineering is incredibly low. If you really think you learn abstract thinking in engineering, please do the math major and u will open your eyes.

@@rubengarciaquismondo So here's the thing. I see what you were trying to say but only 4.9% of the entire work force in the united states hold an engineering job. we have to be considerate to the reality that generally speaking engineering mathematics is actually quite challenging for the general population, and it's not hard to see why. it requires an immense amount of investment and interest to tackle. What i'm trying to get it, is that you're absolutely correct that abstract maths is better for what i've mentioned. but, the entire purpose of your engineering specific classes is to tie all the skills together and apply them in a meaningful way, of course specific to whatever you chose to do. to some extent you can't really teach somebody to be proficient at abstraction anyways. it's actually personally what even attracted me to begin with, is that there really is a sort of creativity involved with designing and implementing things. it's the same reason you don't really see colleges for making your own music. anyways theres many takes on it, thats just my personal opinion

Someone needs to make the simulation software too you know?

Engineers have no idea about math, not even its essence (i am a mathematician)

@@rubengarciaquismondo hahahaha this is judging a book by its cover, cant say it in more accurate words. Then by your argument Nikola Tesla was invalid at math?? Hahaha definitely no. I agree with you in the fact that as engineers math is require to understand concept, but we dont work on a day to day basis with it. Anyone can become good at what you call real math if they put the work. I know the math spectrum is very wide, but i know even you as a math person cant cover all of it with the same level of depth.

@@rubengarciaquismondo You shouldn't generalize. Many mathematical transforms from signal processing and methods were actually developed by electrical engineers, see also optimal control.

@@anders5611Yes people like me (master physics), make this stuff.

I’m sorry but idk of any good MATLAB books 😅 I just learned it all through RU-vid videos

@@TamerShaheen could you recommend to me some courses or channels on RU-vid. Appreciate it bro!

Trust me.. u will need

Pretty sure every degree that have "engineering" in it will learn these maths

AHAHHAHAHAHAHAHAHA *laughs in fourier tranforms for EE, calc for Classical mechanics, Optics(phones, lightbulbs, etc), probability and stat(physics, statistical thermodynamics, machune learning, etc), Cryptology(Blockchain and Information security/Cybersecurity), Differential equations(growth and decay in physics as well as modeling the groeth of tumors and spread of disease), Real and Complex Analysis (engineering and computer science. Can validate models, helo construct new theorems and understand Calc and Analysis on a deeper level, Topology(has applicationsnin Physics and Matwrials science), Abstract Algebra(Organic chemistry and well as other applictations. Math degrees are highly flexible.

School is school. Work is work. Undergrad curriculum exposes you to concepts that help understand other abstract ideas. In the real world (“industry”), we just need to know enough to keep businesses running. Most of the time, theory/ideas are thrown out in favour of immediate, urgent, “common-sense” solutions and a bunch of existing rules/guidelines. Business is all about making money and jobs serve that function. Unless the business applies abstract Engineering like University/Research institutions do, don’t expect to use any Math.

I used to think the same as you, but trust me, Math its important, even if u dont see an aplication in real world, it will help you to increase your logical level and to think in ways you didnt before

Which semester are you in?

@@SH-mz6ec I am on third year which is the fifth semester.

@@HN-vu8pp great👌 I am the second semester civil engineering student. I am so worried about how to study. Because many lessons are difficult

@@SH-mz6ecWhich country are you studying in? Yes it gets difficult, but if you put in more hours of work things tends to get easier.

@@HN-vu8pp I am student in Afghanistan

Computer science