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

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Discussion Overview

The discussion revolves around personal conventions and styles used in pen-and-paper calculations within physics and mathematics. Participants share their experiences and preferences regarding notation, formatting, and organization of calculations, aiming to improve clarity and consistency in their work.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants express a lack of consistent conventions in their calculations, leading to difficulties in following their work.
  • One participant adopts a style similar to their lecturer, incorporating explanatory sentences between mathematical lines for better comprehension.
  • Another participant emphasizes the importance of good notation and conventions for success in calculations.
  • A participant mentions using Roman numerals to order the question-solving process.
  • One approach involves performing substitutions literally to avoid mistakes, with separate notation for sub-expressions.
  • Judicious use of various types of brackets and parentheses is highlighted as a key tool for clarity.
  • Boxing intermediate results is a common practice among some participants to keep track of important calculations.
  • One participant shares a method of distinguishing between different uses of the same letter (e.g., index vs. imaginary number) through handwriting styles.
  • Several participants advocate for rewriting messy calculations on clean sheets to maintain clarity, especially for lengthy problems.
  • Some participants prefer to write calculations as if they were preparing a textbook chapter, mixing equations with explanatory text and numbering important equations.
  • There is mention of varying acceptance of notation styles among professors, leading to challenges in maintaining consistency.
  • A link to a guide on writing mathematics and proofs is shared, although it is noted as somewhat tangential to the main topic.

Areas of Agreement / Disagreement

Participants generally agree on the importance of clear conventions and notation in calculations, but there are multiple competing views on specific practices and styles. The discussion remains unresolved regarding the best approaches to adopt.

Contextual Notes

Some participants express challenges with different professors' preferences for notation, indicating a lack of consensus on acceptable styles. Additionally, there are references to personal habits and preferences that may not be universally applicable.

Who May Find This Useful

Students and professionals in physics and mathematics who seek to improve their calculation methods and notation practices may find this discussion beneficial.

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

Good conventions / notation is a large part of success.
 
I order the question-solving process using Roman numerals.
 
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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.
 
Another key tool to me is the judicious use of several types of brackets and parenthesis.
 
If I have a lot of intermediate results that I need later on, I usually box them.
 
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.
 
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.
 
  • #10
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 \LaTeX, and turn that in.

I try to use a consistent notation, e.g. vectors have underbars, \underline{x}, unit vectors are underbars with hats, \underline{\hat{x}}.
 
  • #11
Vanadium 50 said:
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.

+1

I wish I could bring myself to practice that more. Somehow I always am miserly about using paper.
 
  • #12
Vanadium 50 said:
For long problems (think Jackson) this is a life saver.

What's Jackson? :confused:
 
  • #13
rollingstein said:
What's Jackson? :confused:
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 :-p 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 \partial _{\mu } so I have to consciously refrain from doing that. I'm not sure how other people here or elsewhere cope with that.
 

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