# Why is math so hard?

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1. Dec 6, 2016

### 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?

2. Dec 6, 2016

### Logical Dog

I dont 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 -_-

3. Dec 6, 2016

### PeroK

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

4. Dec 6, 2016

### 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.

5. Dec 6, 2016

### beamthegreat

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

6. Dec 6, 2016

### PeroK

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.

7. Dec 6, 2016

### 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

Last edited: Dec 6, 2016
8. Dec 6, 2016

### vela

Staff Emeritus
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.

9. Dec 6, 2016

### Dr. Courtney

The math class is the weight room for the mind.

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

10. Dec 6, 2016

### PeroK

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

11. Dec 6, 2016

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

12. Dec 6, 2016

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.

13. Dec 6, 2016

### FactChecker

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.

14. Dec 6, 2016

### The Bill

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.

15. Dec 6, 2016

### Logical Dog

Yes we have already learnt 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.

I guess my brain cells arent up to the mark.

16. Dec 6, 2016

### Staff: Mentor

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.

17. Dec 6, 2016

### FactChecker

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.

18. Dec 6, 2016

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.

19. Dec 6, 2016

### 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).

Last edited: Dec 6, 2016
20. Dec 6, 2016

### Staff: Mentor

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.

21. Dec 6, 2016

### 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.

Last edited: Dec 6, 2016
22. Dec 7, 2016

### pasmith

- Timothy Gowers

23. Dec 7, 2016

### John d Marano

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

24. Dec 7, 2016

Staff Emeritus
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.

25. Dec 7, 2016

### John d Marano

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!