Revisiting Mathematical Concepts in Physics: Is It Worth the Frustration?

[paulo84]

I'm trying to revisit maths used in physics and I'm finding it so confusing. Every time I see f(x) I get so frustrated because my brain automatically thinks it's f multiplied by x.

I don't know whether I would ever be able to make any contribution to physics. Am I simply wasting my time trying to do this as an amateur?

 

[.Scott]

You will need algebra. How old are you? And what type of Algebra courses have you taken?

 

[lekh2003]

Before jumping into quantum physics and relativistic physics, I strongly suggest you revise:

• Kinematics,
• Newton's Laws,
• Mathematical Properties of Waves,
• Sound Waves,
• Doppler Effect,
• Wave-particle duality of light,
• Diffraction and Refraction of waves,
• Relativistic kinematics and effects,
• Quantum physics (double slit experiments),
• Electron transitions and photon emissions.

You may find resources online or in any textbooks you have. I studied most of these subjects from this textbook: http://fcis.aisdhaka.org/personal/chendricks/IB/Giancoli/Giancoli Chapters.html

I initially suggested that you follow this learning scheme, but you need even more help. Please visit Khan Academy or another courseware website. Start from the very beginning of Algebra 2, work your way up to pre-calculus. Then you can follow the above scheme for learning physics.

 

[paulo84]

I am 33, I haven't done maths since age 17. I did algebra in University of Cambridge, Local Examinations Syndicate, Advanced International Certificate of Education, Mathematics and Further Mathematics. Further Mathematics included Mechanics and it didn't come naturally to me at all. I only did Physics to IGCSE level.

 

[Mark44]

I'm trying to revisit maths used in physics and I'm finding it so confusing. Every time I see f(x) I get so frustrated because my brain automatically thinks it's f multiplied by x.

I don't know whether I would ever be able to make any contribution to physics. Am I simply wasting my time trying to do this as an amateur?

You will not be able to make any contribution as an amateur. Euclid's comment to Ptolemy was that "there is no royal road to geometry." Likewise, there is no "royal road" to physics. If you want to try to understand physics, you will need to spend a lot of time reviewing mathematics first, starting with basic algebra and trigonometry. Without a solid foundation in these areas, you have no hope of understanding physics.

 

[paulo84]

I think it's going to be beyond me to try and cover that much maths and physics from textbooks. I am going to try hanging around the Physics Forums, asking questions, try not to write nonsense, and try not to get banned.

 

[Mark44]

I think it's going to be beyond me to try and cover that much maths and physics from textbooks. I am going to try hanging around the Physics Forums, asking questions,

Why do you think it would be beyond you? Hanging around here is a shortcut that probably won't be effective as actually cracking open the textbooks. If you don't have at least a basic understanding of the math and/or physics, you won't be able to even formulate good questions.

try not to write nonsense, and try not to get banned.

A review of algebra and trig would likely have prevented these nonsense posts (among others).
From "Shape of Pi" thread (now deleted):

Does it follow that the shape of pi is a circle with a square hole in the centre, or would that be pi=a-r^2 (which is incorrect).

From "Radians Functions?" thread

0 = 2π/3
π/6 =3π/4

 

[paulo84]

Why do you think it would be beyond you? Hanging around here is a shortcut that probably won't be effective as actually cracking open the textbooks. If you don't have at least a basic understanding of the math and/or physics, you won't be able to even formulate good questions.

A review of algebra and trig would likely have prevented these nonsense posts (among others).
From "Shape of Pi" thread (now deleted):

From "Radians Functions?" thread

I'm not saying I won't read up. I just think it'll be easier on me if I read up in bits when it relates to a topic at hand. That also makes it far more likely that I'll actually understand what I'm reading.

 

[Mark44]

I just think it'll be easier on me if I read up in bits when it relates to a topic at hand.

IMO, a scattershot approach isn't the most effective way.

That also makes it far more likely that I'll actually understand what I'm reading.

Not necessarily. If you're reading some topic that assumes knowledge of a more basic concept, you won't really understand. The misconceptions of yours that I've seen suggest that you should take some time to review algebra and trig. Since you studied algebra before (but years ago), reviewing this material wouldn't be as hard as it was the first time.

If I can make a metaphor of your piecemeal strategy of review, it's a bit like someone who wants to learn how to read, but instead decides to learn only the letters b, j, r, and y.

 

[paulo84]

IMO, a scattershot approach isn't the most effective way.

Not necessarily. If you're reading some topic that assumes knowledge of a more basic concept, you won't really understand. The misconceptions of yours that I've seen suggest that you should take some time to review algebra and trig. Since you studied algebra before (but years ago), reviewing this material wouldn't be as hard as it was the first time.

If I can make a metaphor of your piecemeal strategy of review, it's a bit like someone who wants to learn how to read, but instead decides to learn only the letters b, j, r, and y.

I just found when Dale provided a calculus example for me relative to questions I was asking, that was really effective.

 

[Mark44]

I just found when Dale provided a calculus example for me relative to questions I was asking, that was really effective.

Maybe you think so, but if you're asking questions about the "shape of pi" and whether 0 = 2π/3, I'm not convinced that you understand a calculus example.

 

[paulo84]

Maybe you think so, but if you're asking questions about the "shape of pi" and whether 0 = 2π/3, I'm not convinced that you understand a calculus example.

I’m not sure I fully understand it either. I have some understanding.

 

[paulo84]

Here is an example which may show I have some limited understanding of calculus:

https://www.physicsforums.com/threads/rates-of-decay.936380/

 

[.Scott]

I just found when Dale provided a calculus example for me relative to questions I was asking, that was really effective.

I have to agree with @Mark44. "Shape of pi" and 0=2π/3 reflect a very incomplete study of algebra. Just so you know, pi (symbol π) is a number, about 3.1416, and exactly the ratio of the circumference of a circle to its diameter. So, being a number, it has no shape. And being a constant, along with 2 and 3, a precise value can be computed for 2π/3 and it isn't zero.

If you aren't at the level where you can parse an algebraic equation, I can only imagine what you might be thinking when presented with a calculus expression.

Let me get an idea of where you are starting from. Describe what each of these means:
2³
log(1)
cos(π/2)
x-7 = 3
(x+10)(x-10)
y = 3x+2; slope at x=1

All of these would be encountered early in physics and are expected to be part of your established foundation before tackling Calculus.

 

[paulo84]

I have to agree with @Mark44. "Shape of pi" and 0=2π/3 reflect a very incomplete study of algebra. Just so you know, pi (symbol π) is a number, about 3.1416, and exactly the ratio of the circumference of a circle to its diameter. So, being a number, it has no shape. And being a constant, along with 2 and 3, a precise value can be computed for 2π/3 and it isn't zero.

If you aren't at the level where you can parse an algebraic equation, I can only imagine what you might be thinking when presented with a calculus expression.

Let me get an idea of where you are starting from. Describe what each of these means:
2³
log(1)
cos(π/2)
x-7 = 3
(x+10)(x-10)
y = 3x+2; slope at x=1

All of these would be encountered early in physics and are expected to be part of your established foundation before tackling Calculus.

2 cubed (8)
Logarithm 1
Cosine of half pi
x=10
x^2 - 100
Unsure

 

[paulo84]

Furthermore, irrational numbers are very different to rational numbers, I have a wild imagination, and I’m certified slightly nuts.

 

[paulo84]

I mean y=5, but what does slope at mean? just that we're talking a graph?? like i said, slightly nuts...

 

[paulo84]

relative to the stupid effing π question, i didn't notice in the stupid effing table that the degree values were different, and i was imagining the radian inconsistency could maybe be explained by some kind of wild function, or something.

 

[paulo84]

also relative to the shape of pi:

we know that a=pi r^2

we know that x^2 represents a definite square shape.

so a=x^2 can be a square shape

so then why can't pi=a/r^2 be a circle with a square cut out? if it still seems like nonsense i'll shut up right away.

 

[Mark44]

Here is an example which may show I have some limited understanding of calculus:

https://www.physicsforums.com/threads/rates-of-decay.936380/

How does this show an understanding of calculus? All you have done is write a differential equation. Can you explain in words what that equation represents?

 

[paulo84]

just to emphasize, $$a = x^2/1$$, and if the area can represent the shape in the case of the square, why not in the case of the circle?

 

[Mark44]

2 cubed (8)
Logarithm 1

equals what?

Cosine of half pi

equals what?

x=10
x^2 - 100
Unsure

 

[.Scott]

also relative to the shape of pi:

we know that a=pi r^2

we know that x^2 represents a definite square shape.

so a=x^2 can be a square shape

so then why can't pi=a/r^2 be a circle with a square cut out? if it still seems like nonsense i'll shut up right away.

x^2 does not represent a "definite square shape". It is simply the product of x with itself. It happens to be the formula for the area of a square with a side on length x.
The equation for the area of a circle of radius r with a square with side x cut out is:
πr² - x²

I have edited this statement because Mark44 has asked you for that info: As far as the question go, you are correct. I would add that the logarithm of 1 is <deleted> and the cosine of pi over 2 is <deleted>.

For: y = 3x+2; slope at x=1
the slope is 3 at all x.
The notion of slope is important for calculus. If you plot x and y, you will notice that y increase by 3 for each increase of 1 in x.

So you aren't at square 1. You have some understanding of algebra.

 

[paulo84]

π r^2 - x^2

let's say r = x

πr^2 - r^2

= r^2(π-1)

a=r^2(π-1)

a/r^2=π-1

π=a/r^2 + 1

??

 

[.Scott]

I don't know whether I would ever be able to make any contribution to physics. Am I simply wasting my time trying to do this as an amateur?

Getting back to this question: at this point, don't worry about making a contribution to physics. If you are interested, pursue the Math and pursue the Physics for your personal development.

 

[.Scott]

π r^2 - x^2

let's say r = x

πr^2 - r^2

= r^2(π-1)

a=r^2(π-1)

a/r^2=π-1

π=a/r^2 + 1

??

OK. So if you knew "a", the area of a circle minus the area of a square, and both the sides to that square and the radius of that circle were "r", then you could calculate pi with the equation you deduced.

 

[Mark44]

Furthermore, irrational numbers are very different to rational numbers, I have a wild imagination, and I’m certified slightly nuts.

But do you know how rational numbers and irrational numbers are different?

I mean y=5, but what does slope at mean? just that we're talking a graph?? like i said, slightly nuts...

Slope is something you would learn about in studying algebra at the precalculus level. By the way, in the equation y = 3x + 2, y = 5 only when x = 1. For other values of x, the y value is different.

also relative to the shape of pi:

we know that a=pi r^2

we know that x^2 represents a definite square shape.

No, we don't know that. If $x = i, x^2 = -1$. Here $i = \sqrt{-1}$. In any case x² represents the multiplication of a number by itself.

so a=x^2 can be a square shape

No.
a is a number, not a geometric shape. BTW, the usual letter for area is A.

so then why can't pi=a/r^2 be a circle with a square cut out?

Because $\pi$ is a number, not any sort of geometric figure.

if it still seems like nonsense i'll shut up right away.

Yes, this is complete nonsense. What would be more useful would be to come up with the area of a circle with a square cut out of its middle.

 

[PetSounds]

π r^2 - x^2

let's say r = x

πr^2 - r^2

= r^2(π-1)

a=r^2(π-1)

a/r^2=π-1

π=a/r^2 + 1

??

What did you expect? You defined $a = r^2(\pi - 1)$, so naturally dividing it by $r^2$ and adding 1 will equal $\pi$.

 

[paulo84]

ok, i appreciate the point about imaginary numbers relative to square roots. a rational number can be expressed on a numberline, an irrational number cannot. i can't remember if a rational number can always be expressed as a fraction? e.g. i can't remember if square root of 2 is irrational or not.

 

[paulo84]

What did you expect? You defined $a = r^2(\pi - 1)$, so naturally dividing it by $r^2$ and adding 1 will equal $\pi$.

yes i know. it's just not so 'natural' after over 15 years out of maths.

 

[paulo84]

can i just say, this is exactly what i was looking for when i meant learning by posting in the forums and getting replies!

 

[Mark44]

ok, i appreciate the point about imaginary numbers relative to square roots. a rational number can be expressed on a numberline, an irrational number cannot.

Both rational and irrational numbers are on the real number line.

i can't remember if a rational number can always be expressed as a fraction?

Bingo. That's how rational numbers are defined, as the quotient of two integers.

i can't remember if square root of 2 is irrational or not.

It's irrational.

 

[PetSounds]

ok, i appreciate the point about imaginary numbers relative to square roots. a rational number can be expressed on a numberline, an irrational number cannot. i can't remember if a rational number can always be expressed as a fraction? e.g. i can't remember if square root of 2 is irrational or not.

1. You can represent irrational numbers on a number line.
2. A rational number is defined as a number that can be expressed as a fraction (ratio) of two integers.

EDIT: Redundant information given the above post.

 

[Mark44]

yes i know. it's just not so 'natural' after over 15 years out of maths.

Which is why you should put in some time reviewing algebra and trig before starting in on calculus and physics.

can i just say, this is exactly what i was looking for when i meant learning by posting in the forums and getting replies!

All we have done is attempt to correct a few of your deep misconceptions. This is really a terrible way to learn.

 

[paulo84]

OK. So if you knew "a", the area of a circle minus the area of a square, and both the sides to that square and the radius of that circle were "r", then you could calculate pi with the equation you deduced.

i got the area of a circle mixed up with the area of a circle minus the area of a square in my head. i am very, very rusty.

 

[paulo84]

Which is why you should put in some time reviewing algebra and trig before starting in on calculus and physics.

All we have done is attempt to correct a few of your deep misconceptions. This is really a terrible way to learn.

i have found the most effective way for me to learn is by having a conversation with my teachers.

 

[Mark44]

i have found the most effective way for me to learn is by having a conversation with my teachers.

Speaking as someone who has taught college math for 20+ years, these "conversations" are far from effective in the use of the teachers' time, especially as you seem reluctant to do due diligence prior to the Q & A session.

 

[paulo84]

are there situations in physics which use $i$ to represent one side of a square?

 

[russ_watters]

Speaking as someone who has taught college math for 20+ years, these "conversations" are far from effective in the use of the teachers' time, especially as you seem reluctant to do due diligence prior to the Q & A session.

This is at least as big of an issue. @paulo84 you have to understand that we want our and our members' time to be productive too. You might be happy with the results (even though the rest of us agree these do not represent significant progress), but we're not paid personal tutors and even if we were, we'd set the curriculum and method, not you. So if you insist on this path, I'm afraid it's going to keep being problematic to us.

 

[paulo84]

I will try to adjust the frequency of my questions such that I'm asking less often, and do more reading.

 

[Jayalk97]

I will try to adjust the frequency of my questions such that I'm asking less often, and do more reading.

You really need to get textbooks, read through them, answer atleast a few questions related to every topic, and use forums only when you come across something you do not understand. It will take months and months but that's the only way you're going to learn anything of use. Don't be a pseudointellectual. Once you get through algebra and precalc you could just go off of some college's degree program and work your way through the class list.

 

[Mark44]

are there situations in physics which use $i$ to represent one side of a square?

I don't believe so. $i$ is the so-called "imaginary number," but it plays a significant role in electricity and electronics, particularly in AC circuits, and elsewhere in physics.

 

[paulo84]

As a final note, I have enjoyed doing some of the (admittedly very basic) algebra in this thread, which makes me somewhat optimistic I can stick to reading maths, given that I do take pleasure in it.

 

[lekh2003]

As a final note, I have enjoyed doing some of the (admittedly very basic) algebra in this thread, which makes me somewhat optimistic I can stick to reading maths, given that I do take pleasure in it.

If I can give you one last tip, stop trying to find an ulterior meaning in everything you are learning. Slow down and stop jumping to conclusions. It seems like you are on a wild goose chase. Just learn, don't ask. When you are done learning everything relevant, then you may ask.

 

[Jayalk97]

Honestly if you can't handle the criticism you've been given you wouldn't be able to handle the trials of learning anything. These people want to help you but you refuse it. You need to realize that becoming good at anything is hard, be it STEM, music, writing, or art. Anything worth pursuing is going to be difficult, and most if not all require some structured path of formal education.

 

[Jayalk97]

Honestly if you can't handle the criticism you've been given you wouldn't be able to handle the trials of learning anything. These people want to help you but you refuse it. You need to realize that becoming good at anything is hard, be it STEM, music, writing, or art. Anything worth pursuing is going to be difficult, and most if not all require some structured path of formal education.

And while I'm on my mini tirade I want to add that trying to find shortcuts around learning math is an insult to the rest of us who spent countless sleepless nights studying hours of material, hundreds of cups of coffee, literal tears to get through out education.

 

[DrClaude]

The OP is no longer with us. Time to close.