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fdef
What does it mean for a function to be well-defined?
A common addendum to a formula defining a function in mathematical texts is, “it remains to be shown that the function is well defined.” (...)
March 3, 2015 – Jakub MarianMathematics
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Irregular English verbs: -ake to -ook (take, shake, forsake)
A few English verbs follow the pattern -ake → -ook → -aken in the past tense. They are all derived from the verb “take”, apart from (...)
March 2, 2015 – Jakub MarianEnglish
life-expectancy
Map of life expectancy in Europe
Life expectancy at birth is defined as the number of years a newly born individual in the given country is expected to live on average, (...)
February 25, 2015 – Jakub MarianMaps
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Irregular English verbs: -eave to -eft
There are only three English verbs that follow the pattern -eave /iːv/ → -eft /ɛft/, namely (listed as infinitive – past tense – (...)
February 23, 2015 – Jakub MarianEnglish
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‘Than I’ vs. ‘than me’ in English
There has been an ongoing debate whether the correct form after “than” is I, he, she, we, and they or me, him, her, us, and them. (...)
February 23, 2015 – Jakub MarianEnglish
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One-syllable adjectives with comparative ‘more’ instead of -er
One of the first rules an English learner learns is that the comparative degree of monosyllabic (one-syllable) adjectives is formed by (...)
February 19, 2015 – Jakub MarianEnglish
raven-cover
How to write and publish a non-fiction book
I have recently published my fourth book, and I thought it would be interesting to let my readers know what it takes to self-publish a (...)
February 18, 2015 – Jakub MarianBlog
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Are statistical data and scientific results subject to copyright?
I have recently created a map showing the number of books published per year per capita by country in Europe. The figures in the map are (...)
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“In literature” vs. “in the literature” in English
When we write an essay or a scientific paper, we often say that it is possible to “find something in the literature”… But shouldn’t it (...)
February 1, 2015 – Jakub MarianEnglish
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‘Got’ vs. ‘gotten’ in English
Let’s not beat around the bush with a large number of linguistic terms; the difference between “got” and “gotten” is relatively simple. (...)
January 30, 2015 – Jakub MarianEnglish
books-published-per-capita
Number of books published per year per capita by country in Europe
Being an author myself, I was very much interested in the number of books published in different European countries. I wasn’t able to find (...)
January 27, 2015 – Jakub MarianMaps
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‘Help do’ vs. ‘help to do’ vs. ‘help doing’ in English
Both “help someone do something” and “help someone to do something” are acceptable. The form without “to” seems to be more common in (...)
January 25, 2015 – Jakub MarianEnglish
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Lie, lied, lay, laid (and layed) in English
The verbs “lie” and “lay” are perhaps the two most confusing irregular English verbs. “Lie” has two meanings: it can mean “not to tell the (...)
January 23, 2015 – Jakub MarianEnglish
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‘Clothes is’ vs. ‘clothes are’ in English
The word for “clothes” is singular in many languages, e.g. la ropa in Spanish or die Kleidung in German, and its plural in most contexts (...)
January 20, 2015 – Jakub MarianEnglish
german-199_640
German ä, ö, ü – what’s the difference?
German alphabet contains three additional symbols for vowels which are often misunderstood or mispronounced by learners whose mother (...)
January 18, 2015 – Jakub MarianGerman
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Pronunciation of French ‘e’ in open and closed syllables
Pronunciation of the letter “e” in French changes when it belongs to a larger group of letters or when it is supposed to be silent—you (...)
January 18, 2015 – Jakub MarianFrench
parliament-total
Number of seats in the national parliament by country in Europe (total & per capita, map)
The following map shows the total number of seats in the national parliament of each country as of 2015 (national parliament here refers (...)
January 14, 2015 – Jakub MarianMaps
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‘And’, ‘but’, ‘or’, and ‘so’ at the beginning of a sentence
Most people were told at some point in their lives that starting a sentence with a conjunction is ungrammatical. Long story short, no such (...)
January 12, 2015 – Jakub MarianEnglish
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‘In office’ vs. ‘in the office’ vs. ‘at the office’ in English
After I published my article about being in/at school, one of my readers asked me about the difference between “in office” and “at (...)
January 9, 2015 – Jakub MarianEnglish
german-199_640
Difference between -ung in German and -ing in English
One of the most common mistakes among German learners who just started off is overuse of the German ending -ung, which looks like the (...)
January 8, 2015 – Jakub MarianGerman
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