Personal writing/math conventions when doing physics/math calculations?

MissSilvy

I believe this post is allowed here, but if it belongs elsewhere I apologize.

I am now almost at the end of my undergraduate degree and looking back over my old work and old calculations from semesters prior made me realize that I have absolutely no consistent conventions when doing physics calculations. Usually this is fine but sometimes it impedes progress on the work and almost always it makes the work very hard to follow later, even if the rough work is rewritten to a final form.

Half the calculations would be scribbled on another page entirely and in random places (top left then lower right then margin) and even those that are all on the same page and in order are a little hard to follow. New equations look exactly the same as the parts of the calculation I am working on, mathematical definitions and calculations are written randomly, and rearranged equations look to be just as unique as the original equations above them because I have no consistent symbol or formatting to denote it was just a different form of the above.

[Someone recently pointed me to a page that gives tips for mathematical handwriting to make distinguishing letters and Greek symbols easier, which helped enormously. I am looking for similar tips for equations.]

My question is what are some of the conventions that the rest of PF uses when doing pen-and-paper calculations? Specifically:

• Do you just start at the top of the page and start a new line for every operation?
• Is there any way you denote when an equation need to be broken up into two lines because it cannot fit in the width of the paper?
• Are certain steps of a calculation 'indented' to denote a relationship between the header equation and the ones inside it? Which ones?
• How are equations that are not derived denoted to distinguish them from the ones you are calculating (such as when calculating the speed of sound and the ideal gas law is called in the context of the calculation) ?
• Do you distinguish between new step in a calculation and a merely rearranged form of a previous step?
• How do you denote when two equations are combined ( for example, one substituted into the other to yield a third equation)?

This may be a little neurotic to lay out conventions for everything but my current method is nonexistent and I am genuinely curious how physicists with more experience keep track of what I assume are increasingly complex calculations. I've asked some of my fellow students and professors and gotten some very broad tips but everyone was very interested in learning what I had heard so far, so I am hoping this would prove of some use to people other than myself.

NascentOxygen

I believe I basically migrated my "style" to that of the best of my lecturers. He was never afraid to insert explanatory sentences or phrases between lines of mathematics to lead the reader's comprehension smoothly from one line of maths to the next. The result was that his handiwork could be read aloud like a well-constructed English essay.

Professional journals (peer reviewed) are often good examples of style, and illustrate the usefulness of labelling each equation that will later be referenced.

rollingstein

I don't think you are being neurotic at all.

Good conventions / notation is a large part of success.

TheAbsoluTurk

I order the question-solving process using Roman numerals.

I like Serena

When doing substitutions I have learned to do *only* the substitution.
I write the equation replacing symbols literally without doing anything else.
The reason is that this is where mistakes typically come in.
And if mistakes do come in, it's handy to still be able to understand what I did, and to check the steps separately.

When deriving a sub expression, it becomes a challenge to keep that derivation separate from the main derivation.
To do so, I usually put a large circle around a sub derivation, with an arrow like a text balloon where it is used.
Or alternatively I indent it, or box it.

When I'm finished with something I often put a white square behind it (the qed symbol), to mark where that is.

rollingstein

Another key tool to me is the judicious use of several types of brackets and parenthesis.

I like Serena

If I have a lot of intermediate results that I need later on, I usually box them.

ModusPwnd

Cool thread! I liked the link too. Many of those tips I have adopted for the very reasons they say. My graduate quantum professor had the neatest and most meticulous handwriting of all my professors and I copied some from him. One is to distinguish between i as an index and i as an imaginary number by writing the index in script and the number in print. I do the same for j and k. He was fond of using the same letter for two things distinguished in this way...

I recall in early undergrad I got a remark on an assignment about mixing up capital and lower case for the variable. What a noob thing to do! Then in graduate school I learned to distinguish between script and print. lol

I also had a lot of British professors, particularly in undergrad. They liked to underline their vectors. I adopted the habit from them and like it. But I know its not convention so when I interact with others I try to remember to draw arrows rather than underlines.

I've always been fairly neat and correct even with scratch work. Maybe sloppy legibility, but ordered on the page.

Vanadium 50

My rule is "paper is cheap". If after a page things are a mess, rewrite it on a clean sheet. For long problems (think Jackson) this is a life saver.

jhae2.718

I try and write as if I were doing a derivation in a textbook chapter or paper. Mixed equations with interspersed explanatory text. Important equations get numbers, and results are boxed.

Depending on available time I will solve homeworks/assignments on paper, write it up in [itex]\LaTeX[/itex], and turn that in.

I try to use a consistent notation, e.g. vectors have underbars, [itex]\underline{x}[/itex], unit vectors are underbars with hats, [itex]\underline{\hat{x}}[/itex].

rollingstein

+1

I wish I could bring myself to practice that more. Somehow I always am miserly about using paper.

rollingstein

What's Jackson?

WannabeNewton

It is a graduate electrodynamics text. I never seem to have a paper problem when doing math problems but when it comes to physics problems the paper just runs out before I can even finish the problem. I have OCD when it comes to writing down solutions and even if it's a draft and I make a small mistake I have a need to throw it all out and start over. What's up with that One problem I have with notation is different professors seem to be ok / not ok with different things e.g. some professors for some reason seem hate when I use the very common and very pretty notation [itex]\partial _{\mu }[/itex] so I have to consciously refrain from doing that. I'm not sure how other people here or elsewhere cope with that.

Sankaku

A little tangential to the original question, but this is an excellent guide to writing mathematics and, in particular, proofs:

http://www.math.washington.edu/~lee/...ing-proofs.pdf


(John Lee is the author of several excellent books on Manifolds.)
http://www.math.washington.edu/~lee/