
What Math Do You Need for Physics? - seycombi
https://www.math.columbia.edu/~woit/wordpress/?p=8940
======
ivan_ah
Check out this short tutorial on mechanics with calculus that I've written. It
would make a good first introduction to physics[1]. There is another one for
linear algebra[2].

In general I think programmers shouldn't fear the math and physics: yes it's
hard to understand at first, but you can pick up things pretty fast. The ratio
of "knowledge buzz" to effort is very good when you're learning physics. A
symbolic computer algebra system like SymPy can be very helpful for "playing"
with math expressions—here is a third tutorial on that[3].

_____

[1]
[https://minireference.com/static/tutorials/mech_in_7_pages.p...](https://minireference.com/static/tutorials/mech_in_7_pages.pdf)

[2]
[https://minireference.com/static/tutorials/linear_algebra_in...](https://minireference.com/static/tutorials/linear_algebra_in_4_pages.pdf)

[3]
[https://minireference.com/static/tutorials/sympy_tutorial.pd...](https://minireference.com/static/tutorials/sympy_tutorial.pdf)

~~~
sillysaurus3
From the fist paper: _If you want to learn more university-level math and
physics, I invite you to check out my book, the No bullshit guide to math and
physics_

I just wanted to pop in and say this book has been excellent. These papers are
brief and therefore a bit cryptic, but the book is eminently readable.
[https://www.amazon.com/No-bullshit-guide-math-
physics/dp/099...](https://www.amazon.com/No-bullshit-guide-math-
physics/dp/0992001005)

~~~
Normal_gaussian
Is there any way to get it in electronic form?

~~~
ivan_ah
Yep, [https://gum.co/noBSmath](https://gum.co/noBSmath) More info and preview
of book on the website
[https://minireference.com/](https://minireference.com/)

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musgravepeter
I did math in the wrong order. I first was "exposed to it" as an engineer
undergrad - didn't care at all (just wanted to code) and barely passed eng.
math.

After working for two years, went back and did undergrad physics courses
(including math for phys) and started to "get it".

Then went on to a PhD in general relativity - which is a LOT of math. I went
back to software and most of it leaked away.

I am now trying to get it back (20 years later) - as I resurrect a Maple
package for GR, grtensor, which I co-wrote as part of my PhD. Curved space is
a beautiful thing.

Penrose's recent book reminded me of his wonderful "The Road to Reality: -
which is a great tour of math leading into physics.

~~~
bosie
What's your path to getting back into math after 20 years?

~~~
agumonkey
And if I may add, how often did you think about math ? daily ? monthly ?

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ssivark
In my experience, it's a moving goal post. Physicists usually start off with
the goal of explaining certain natural phenomena. Over the decades the
specific parts of math this entails has evolved rapidly, as new phenomena
become novel.

One might naively think that only "some" parts of math are useful for physics,
but over the last 2-3 decades, many connections between physics and math have
been discovered, that has brought the communities closer together, reversing
the trend in the middle of the 20th century. For a very interesting take on
the interplay between physics and math, by one of the masters of math/physics,
see [1].

[1]: [http://pauli.uni-muenster.de/~munsteg/arnold.html](http://pauli.uni-
muenster.de/~munsteg/arnold.html)

To quote an excerpt from Arnold's talk: " Mathematics is a part of physics.
Physics is an experimental science, a part of natural science. Mathematics is
the part of physics where experiments are cheap. "

~~~
Koshkin
> _Mathematics is a part of physics_

Somehow I have a strong feeling it's the other way around. When trying to
_really_ understand the ways of Nature, you end up having to do a lot of
calculations. Then you get quickly drawn into the depths of very complicated
mathematics. Finally, you realize that there is nothing in (theoretical)
physics that is not mathematics. Historically, much of mathematics evolved in
connection with physics, but this fact does not change anything.

~~~
TeMPOraL
The way I look at it is this: mathematics is just formalized perfect
reasoning. Its job is to get you from a thing you assume to be true, through
steps of formal inference, to a new thing that you can be sure is true if the
original assumption holds. You then keep on chaining this, so from a small set
assumptions you enumerate all the facts that follow from them.

Physics is a field of study that does experiments to identify what things are
fact in our universe, and then tries to pick such a subset of math that best
fits the observed data. If further experimental results deviate from what the
chosen mathematical model predicts, physicists will pick a different model, up
until the maths align perfectly with what they see. The reason physicists use
math is thus simply because alternative to math is hand-waving and guessing,
and physics is a _serious_ field.

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IgorPartola
I studied physics in undergrad, and took a few grad courses. I also minored in
math. The reason I dropped the math major to a minor was because of the amount
of time mathematicians spent proving obvious things. Physics uses math, the
way that a car mechanic uses a wrench without worrying about its atomic
structure.

At the beginning of one particular interesting class on quantum mechanics, the
professor wrote down a few shortcuts on the board: how a sum of a certain
series collapses, which parameters can be ignored at low or high velocity,
etc. It was glorious.

Also my big takeaway from this was that physicists really don't like non-
linearity. If something cannot be described as linear, it will be described as
a harmonic oscillator 99% of the time. The exception to this is statistical
and simulation physics where you can do whatever you want and just look for
emergent behavior.

~~~
gragas
> The reason I dropped the math major to a minor was because of the amount of
> time mathematicians spent proving obvious things.

I think this is a poor reason to drop a math major. The point of a majoring in
math isn't learning "obvious things." Rather, the point is learning how to
prove things—it shows you how to get from point A to point B when the path
isn't immediately obvious.

~~~
Bahamut
Also there are many things a lot of people may call obvious, but is not quite
so obvious.

I actually went the reverse direction, from theoretical physics to
mathematics, because I was disappointed with the lack of mathematical rigor,
and that the workd of mathematics is a lot more interesting once you get to
proofs.

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bkcooper
The bullet points this article (and the one by Chad Orzel it links to)
mentions are the common most used things day-to-day by basically anybody doing
physics. However, I think stopping at that level of mathematical background
would make reading a lot of the existing literature hard. Woit mentions
complex analysis, but at least that usually comes up in mathematical methods
classes, at least at the level needed to understand the arguments where it is
used. Some math that I often found myself wanting more of includes
differential geometry (I find physics introductions to tensor manipulation to
be very heavy on mechanics and terrible on intuition for what you're actually
doing) and functional analysis.

Both articles leave out numerical analysis or scientific computing, which I
think is a huge gap. I certainly felt like my education left the impression
that these things were way more straightforward than they actually are.

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wayn3
Those bullet points are the absolute baseline necessities that you need to
have a shot at ever getting anywhere in physics.

On top of those, you will have to study a lot of other subject specific stuff
or you will struggle. Physics education is way too light on math.

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DarkContinent
I would make a strong case for numerical methods as well (putting statistics
to work on the computer).

~~~
mmmBacon
Agreed. I am a huge believer that you can get to answers quickly with a Monte-
Carlo analysis. But I'd take it a step further and include how to solve
differential equations numerically as well. You'd be amazed at how far you can
get with Crank-Nichols, Lax-Friderichs, and even simple central differences
methods.

Additionally a lot of stuff people use in machine learning today had its start
in solving physics or communications problems numerically. Stuff like maximum
likelihood detection, gradient descent, etc...

I also believe that implementing code to solve physical problems really can
deepen ones understanding of physics. Once you have something you can really
play with it and see where things break etc...

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analog31
I did a double major in math and physics, many years ago. At the time, I
didn't know if I was more interested in one than the other. I loved proofs.
But I also loved the lab. So I just took all of the courses that were offered
in both departments.

A few other people have mentioned that computation is missing from the list,
and I agree. I was lucky that while studying my school subjects, I was also
actively pursuing electronics and programming as hobbies, which drastically
influenced my graduate studies in physics, and my subsequent career. But I
didn't get that from my coursework.

I think that computation should be incorporated wherever possible in all of
the coursework, all the way back to kindergarten. My rationale is simply that
it expands the range of ideas that can be explored, and it's fun.

------
Philipp__
I was two years studying EE before I quit and transfer to CS program. I do bot
regret it at all, but man am i grateful for hard math course and
electromagnetics on EE. It was pretty painful, in terms of working hours and
doing homeworks, but since then my brain just worked in terms of 2D/3D vision
of geometry and space coordination in my head. Differential calculus, linear
algebra, everything was piece of cake when I got to CS.

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joggery
You need the math required to understand the language in which the current
best physical theories are written. It's unknown as yet which mathematical
objects will be required for their successors.

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santaclaus
Interesting to see differential geometry omitted -- it is useful even in
classical contexts.

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dschiptsov
Feynman gave a whole lecture on this subject - the second or third lecture of
the Messenger Lectures ( _much_ better timepass than night time TV show,
second only to the Wizards Lectures and the five three seasons of The
X-Files).

It seems that this is an ideal case for the Less Is More principle.

~~~
swimfar
If anyone else is wondering what "The Wizards' Lectures" are, they are a set
of MIT video lectures from 1986 by Abelson and Sussman on "Structure and
Interpretation of Computer Programs"

Here's the link: [https://groups.csail.mit.edu/mac/classes/6.001/abelson-
sussm...](https://groups.csail.mit.edu/mac/classes/6.001/abelson-sussman-
lectures/)

~~~
dschiptsov
Thanks! I was too enthusiastic to emphasize that the Abelson and Sussman
lectures are out of the context of Physics. Nevertheless these are no less
classic than Feynman's.

