Why is math so hard? Can anyone truly understand it?

[beamthegreat]

I used to like math when I was in high school. Calculus (integration and derivatives) seem intuitive to me and made me understand math so much better.

Now I'm currently in university majoring in civil engineering taking Calc III and I feel overwhelmed by everything taught in class. No matter how hard I try, I cannot understand things intuitively and everything feels disconnected. I can solve problems given by my professor but I have no clue what I am doing or what the answers even mean.

Why is math so hard?

 

[Logical Dog]

I don't know, and that is probably part of the problem. :( I still find mathematical induction something I HAVENT been able to understand completely. Calculus 3 is very far away for me -_-

 

[PeroK]

I used to like math when I was in high school. Calculus (integration and derivatives) seem intuitive to me and made me understand math so much better.

Now I'm currently in university majoring in civil engineering taking Calc III and I feel overwhelmed by everything taught in class. No matter how hard I try, I cannot understand things intuitively and everything feels disconnected. I can solve problems given by my professor but I have no clue what I am doing or what the answers even mean.

Why is math so hard?

Can you give an example of the sort of thing you are talking about?

 

[Dr. Courtney]

Sometimes I didn't understand what was really happening in Calculus courses until much later.

There are harder Calc 1 and 2 sequences that better prepare students for Calc 3, and easier Calc 1 and 2 sequences where students get hit harder in Calc 3. Some students also have a harder time visualizing calculus in 3D.

Stick with it. Do not despair. Keep working hard. It will come to you.

 

[beamthegreat]

Can you give an example of the sort of thing you are talking about?

We're currently learning about the Cauchy Goursat theorem and complex integration.

 

[PeroK]

We're currently learning about the Cauchy Goursat theorem and complex integration.

Complex Analysis is not easy, if that is any consolation. It's difficult even to visualise a complex function because it's four-dimensional. If you have a grasp of vector calculus and differential equations then I wouldn't worry.

I think most people struggle with complex analysis and it will probably take more effort to master.

 

[Logical Dog]

I have a question...why do civil engineers need to learn complex analysis? O: its not part of my sylabus (afaik) and i am an EECS student

 

[vela]

We're currently learning about the Cauchy Goursat theorem and complex integration.

In Calc 3? That's weird.

If you want to develop intuition, it might help to see how the math is used in physics. For example, you're probably already familiar with using Ampere's Law to calculate the magnetic field around a straight wire. That's just an application of Stokes' theorem. Personally, reading the Feynman Lectures where he talked about curl and divergence helped me a lot.

I have a question. Why do civil engineers need to learn complex analysis? O: It's not part of my syllabus (afaik) and I am an EECS student.

You might be in for a rude awakening. Are you sure you don't have to learn complex analysis eventually? As far as I know, complex analysis is typically part of an EE major.

 

[Dr. Courtney]

I have a question...why do civil engineers need to learn complex analysis? O: its not part of my sylabus (afaik) and i am an EECS student

The math class is the weight room for the mind.

Those brain cells need a good workout to get strong for engineering.

 

[PeroK]

The math class is the weight room for the mind.

Those brain cells need a good workout to get strong for engineering.

Yes, but you need flexibility as well as strength, so don't forget the stretching exercises!

 

[Guy Madison]

Math is about learning how to think, that's the biggest hurdle for most people.

 

[Guy Madison]

Yeah.. I have no idea why a Civil Engineer would be learning Cauchy Goursat theorem and complex integrations, I didn't know Civil Engineers took a full calc series. My sister-in-law is a CE and she gets that deer-in-headlights look when I talk about math so I keep it simple.

 

[FactChecker]

Yeah.. I have no idea why a Civil Engineer would be learning Cauchy Goursat theorem and complex integrations, I didn't know Civil Engineers took a full calc series. My sister-in-law is a CE and she gets that deer-in-headlights look when I talk about math so I keep it simple.

The failure of the bridge "Gallopin' Gertie" (see ) is one reason why a Civil Engineer might need to understand complex analysis and its application to stability analysis. There are new materials and systems being developed that will make structures more durable and resistant to earthquake damage. Some of them require feedback systems that are studied using complex analysis. Also, analytic functions are used to get irrotational, incompressible approximations of flow.

 

[The Bill]

We're currently learning about the Cauchy Goursat theorem and complex integration.

If you want intuition on the way complex functions and analysis work, I recommend you find a copy of Visual Complex Analysis by Tristan Needham. You should be able to get a copy through your library, even if you may need to use interlibrary loan.

 

[Logical Dog]

In Calc 3? That's weird.

If you want to develop intuition, it might help to see how the math is used in physics. For example, you're probably already familiar with using Ampere's Law to calculate the magnetic field around a straight wire. That's just an application of Stokes' theorem. Personally, reading the Feynman Lectures where he talked about curl and divergence helped me a lot.

You might be in for a rude awakening. Are you sure you don't have to learn complex analysis eventually? As far as I know, complex analysis is typically part of an EE major.

Yes we have already learned a lot about complex numbers and complex sequences and series, their convergence. etc. But not as a standalone module, these theorems were packed together with calculus and algebra. I guess I confused OPs course for pure complex analysis.

The math class is the weight room for the mind.

Those brain cells need a good workout to get strong for engineering.

I guess my brain cells arent up to the mark.

 

[jtbell]

We're currently learning about the Cauchy Goursat theorem and complex integration.

In Calc 3? That's weird.

That might depend on which country we're talking about. I agree, here in the US it would be weird. I've never heard of complex analysis being included in Calculus III, only as a separate course later on. However, we have so many universities here it's possible that someplace does it that way.

 

[FactChecker]

I have a question...why do civil engineers need to learn complex analysis? O: its not part of my sylabus (afaik) and i am an EECS student

EE is full of feedback, stability analysis, control systems, Laplace transforms, etc. that require complex analysis. I don't know any EE majors who do not take complex analysis.

 

[Guy Madison]

EE is full of feedback, stability analysis, control systems, Laplace transforms, etc. that require complex analysis. I don't know any EE majors who do not take complex analysis.

I think EECS is more like computer engineering, not like a full blown analog EE degree. I have worked with a few of them, they all glaze over when you start describing a switching power supply and waveguides. For more of a challenge go analog EE and a CS degree and toss some digital stuff in there to get a job, that's what I did.

 

[atyy]

In engineering, complex variables are mainly a mathematical convenience. It is possible to think of the physics using only multivariable calculus. One example of how complex variables enter is via the Fourier or Laplace transforms, which make linear equations easy to solve.

Assuming Calc 3 is multivariable - I too found it very hard - till this day I always think of it in terms of the physics of Maxwell's equations to get a feel for things. Different pictures work for different people. Many find fluid flow easier to visualize than electromagnetic fields, but it's the opposite for me.

It also really helps to know that the determinant has a geometrical meaning as an area (otherwise the Jacobian is incomprehensible).

 

[jtbell]

till this day I always think of [multivariable calculus] in terms of the physics of Maxwell's equations to get a feel for things.

I agree. My third-year E&M course (Griffiths level, although not using that book) was where I first really started to be comfortable with "div, grad, curl and all that." It also helped to teach that course a few times, many years later.

 

[Logical Dog]

I have read a lot about mathematics, from peanos strict definition for natural numbers to the history, formalism vs. intuitionalism vs. logicism, aristotelean camp and plato..and other kinds of philosophy on mathematics.
one thing I learned is that Mathematics is far from perfect, as you will see criticisms about set theory, real numbers, the concept of infinity, even seen a proffesser complain against the arithmetisation of modern mathematics because real numbers arent properly defined.
i have books on logic and proof which I study. But I am still terrible at mathematics, all that study did nothing to improve my computation or problem solving skills, but surely i can tell you the history :P, so cheer up op...it is just naturally hard.
It is much easier to take it for granted, rather than investigate it to the point of madness. Also it helps to think of it as a field that is not perfect, maybe you feel less intimidated to study it.

 

[pasmith]

1. Mathematics becomes hard. Every mathematician will be able to tell you rather precisely when it was that they found that mathematics had stopped being an easy subject that they could understand with very little effort and became a difficult subject that they had to struggle with if they wanted to get anywhere. It isn’t necessarily an advantage if this happens to you later rather than sooner.

2. When the going gets tough, it is not some failing of yours. It simply means that, just like everybody else, you have to work. Up to now I’ve said this to many undergraduates, but I have come to think that it is a rather unhelpful thing to say if it is not backed up with instructions about how to work.

- Timothy Gowers

 

[John d Marano]

Why is math so hard?

No offense to anyone but math is hard because most (not all) Math teachers are terrible

 

[Vanadium 50]

No offense to anyone

Baloney. What you wrote was offensive.

but math is hard because most (not all) Math teachers are terrible

Evidence, please? I have had plenty of math teachers, and on average they were no better and no worse than teachers of other subjects.

 

[John d Marano]

Baloney. What you wrote was offensive.
Evidence, please? I have had plenty of math teachers, and on average they were no better and no worse than teachers of other subjects.

Most math professors have absolutely no training in teaching. Additionally a mind that excels in mathematics usually lacks in soft skills like communicating. We all know it. The self absorbed math genius makes a poor teacher!

 

[symbolipoint]

No offense to anyone but math is hard because most (not all) Math teachers are terrible

Baloney. What you wrote was offensive.
Evidence, please? I have had plenty of math teachers, and on average they were no better and no worse than teachers of other subjects.

Math is hard because as the advancement level increases, the topics become unnatural for our minds. Study, practice, and good teaching help in learning the topics, but only for the more motivated learners.

 

[symbolipoint]

Most math professors have absolutely no training in teaching. Additionally a mind that excels in mathematics usually lacks in soft skills like communicating. We all know it. The self absorbed math genius makes a poor teacher!

That is misguided and the statement is unreliable.
Math professors having no training in how to teach, is unimportant and ignores THEIR own experience of their own efforts to study and learn their subject and their own organized efforts to help students, BEFORE these professors became teachers/instructors.

 

[MathematicalPhysicist]

I used to like math when I was in high school. Calculus (integration and derivatives) seem intuitive to me and made me understand math so much better.

Now I'm currently in university majoring in civil engineering taking Calc III and I feel overwhelmed by everything taught in class. No matter how hard I try, I cannot understand things intuitively and everything feels disconnected. I can solve problems given by my professor but I have no clue what I am doing or what the answers even mean.

Why is math so hard?

It's quite easy, easier than understanding human affairs.

 

[symbolipoint]

It's quite easy, easier than understanding human affairs.

You confused difficulty with complexity. These are very different things.

 

[Dr. Courtney]

No offense to anyone but math is hard because most (not all) Math teachers are terrible

Math will always be harder for students who give into the temptations to blame the teacher rather than taking ownership of responsibility for learning.

Half the math teachers are below average. When a student finds oneself in this situation, the student has a choice between blaming the teacher and being satisfied with not learning very much, or making use of alternate resources and finding a productive path to ensure learning.

Like all subjects, learning is more about the drive and efforts of the students than the abilities of the teacher.

Math was hard for me. Not because my teachers were bad, but because I was lazy. I never did homework outside of class in high school. I took my senior year off from math. My teachers explained all the concepts and problem solving skills well enough. If they have one fault, it was letting me get by with such mediocre efforts. This, more than anything else, put my success in college math courses in great peril.

 

[John d Marano]

I was a mostly terrible college student (for a lot of reasons) but I managed to get one of my degrees in Math. Upon learning a concept (while studying) I often found myself wondering why did the teacher make this seem so hard in class.

Although I had one really great math teacher who inspired me and I took four classes with him. Once I had a really great math teacher I realized what I had been missing . . .

 

[Vanadium 50]

Most math professors have absolutely no training in teaching

True for most professors. Why single out math?

Additionally a mind that excels in mathematics usually lacks in soft skills like communicating

Evidence, please?

We all know it.!

That is not evidence.

The self absorbed math genius makes a poor teacher!

What evidence do you have that most math professors are "self absorbed math geniuses"? And for that matter, what evidence do you have that they make poor teachers?

You said some offensive things. Are you going to back them up or not?

 

[John d Marano]

A lack of soft skills in STEMs ---> "Employers are increasingly concerned about STEM students’ lack of preparedness in soft skills" https://www.eab.com/research-and-insights/continuing-and-online-education-forum/expert-insights/2016/soft-skills-gap

There's this https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0

My opinion about math teachers is mostly an opinion. I feel a good teacher has a command of the subject, command of the classroom, humor and makes themselves accessible to students. "The self absorbed math genius makes a poor teacher!" aka Sheldon Cooper was a joke

 

[FactChecker]

It occurs to me that math may be the only field where there is abstraction for its own sake. Abstraction certainly has great benefits in math. Are there other fields like that?

PS. It will not hurt my feelings if you tell me that is a dumb statement. I may be saying more about my limited perspective than anything.

 

[John d Marano]

It occurs to me that math may be the only field where there is abstraction for its own sake. Abstraction certainly has great benefits in math. Are there other fields like that?

Philosophy . . .