How to use the "w" in www

[fresh_42]

These are some - in my mind - useful insights I gathered over the years on PF. We have members from around the world, studying at universities around the world, in dozens of languages. The language of science nowadays is English, or as a guest professor at my alma mater once said in a terrible accent: "The language of science is broken English." That wasn't always the case. It had been Latin, German, or French to name others. However, whatever your native language is, we live in times where this becomes less and less important. University servers around the world provide lecture notes in English even in non-English speaking countries like Germany. And in case you stumble upon a language you cannot read, don't turn away, our modern world has a technical solution everybody can use. Here are some tricks how.

1. Translation by Wikipedia
   
   If you do not know a technical term in English, you can look it up on Wikipedia in your own language and switch to English.
   
   
   
   
   This is often better than a dictionary, especially for technical terms. It also works in the other direction.
   
   
   
2. Translation by Google
   
   If you use Google - Chrome, then there is an automatic translation feature. Select the website you want to translate, right-click on that page and then left-click "Translate to English".
   
   
   
   
   
   
   The result is probably not perfect and you shouldn't use it for your English classes, however, it is usually understandable. I guess it is safe to assume that it is the same application as Google - Translate: https://translate.google.com/
   
   
   
3. Wikipedia
   
   The language versions on Wikipedia are not translations of each other. They are usually separately written by native speakers who normally do not refer to each other. This means, that switching between languages can give you more information than one language alone. The more languages you can read, not necessarily speak, the greater your advantage. Of course, you can also switch to unknown languages and use Google's or Chrome's translation service. E.g. I observed that English pages are more general and technical than their German version which on the other hand often include little proofs.
   Furthermore, the language switch can be used to look up the proper spelling of names, e.g. Guillaume François Antoine, marquis de L'Hôpital. Chances are good that the appropriate language version to a page associated with a certain scientist is more detailed than any other language version. We have seen that translations are no problem anymore. E.g.
   
   
   
   
   The term "black body" has been introduced by Gustav Robert Kirchhoff who spoke German. And the German page has other content than the English page. Which is more detailed is a different question. Use both.
   
   
   
4. How to find good and reliable Sources on the Internet
   
   Many universities and professors publish their lecture notes on their servers. So if you search for a certain subject "<subject> + pdf", e.g. "Calculus II + pdf", then you will automatically have access to what is taught e.g. at MIT or UCLA, but also at K-town (the GIs' name for Kaiserslautern in Germany). The "+ pdf" part makes sure you get to an actual lecture note and not on someone's private homepage.
   
   Another example is where I look up integrals:
   https://de.wikibooks.org/wiki/Formelsammlung_Mathematik:_Integralrechnung
   https://de.wikibooks.org/wiki/Formelsammlung_Mathematik:_Integrale
   https://de.wikibooks.org/wiki/Formelsammlung_Mathematik:_Bestimmte_Integrale
   https://de.wikibooks.org/wiki/Formelsammlung_Mathematik:_Integraltransformationen
   Yes, it looks very German, and there are no English version pages, yet, so go ahead and write them! Technical terms of Latin origin such as rational, trigonometric, algebraic, etc. are so similar in many languages that they don't need a translation. The true reason I added those links here is, however, that those pages are so filled with formulas about integrals that you will not even need any translation tricks. Mathematics (and music) are already universal languages.
   
   
   
5. How to Write Formulas for Use on the Internet
   
   Use a TeX editor, e.g. https://texstudio.org/, to write posts independent from interruptions by lost connections or other inconveniences. The websites usually require minor format adjustments to the individual MathJaX version they use, but once you have written a TeX version, you can adjust your post to the various formats on different websites. Furthermore, I find that https://www.autohotkey.com/ is a good choice to implement keyboard shortcuts for frequently used TeX commands.
   
   
   
6. Link for Insight Articles about Self-Study
   
   This post contains many links to worth-to-read articles about self-studying, mathematics, and physics and an interesting interview with a professor about time management.
   https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947
   
   
   
7. Exams and Tests
   
   10 tips to avoid mistakes and save time:
   https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/
   
   
   
8. Online Calculators for any Occasion
   
   https://www.physicsforums.com/threa...h-physics-earth-and-other-curiosities.970262/
   
   
   
9. Mathematics Exercises and Solutions (pdf for download)
   
   https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/
   
   
   
10. Amazon
    
    Here's the Amazon link, PF gets a kickback if you use this link from your purchase on Amazon, see Greg's linked post for details.