In learning German, I like to keep track of a few goals, one of such being to learn 2000 unique german words. The thing is, the official German courses repeat a lot of words, whether as basic phrases to put the words into context or teaching the same lists of words in the later courses (e.g. the days of the week taught in both German 1 and 3).
What I want is simple, I want to find how many unique words I have learnt at any given time. It’s almost impossible, I know, but is there any way to do this. Like is there possibly a rule that says something like 5% per each previous course is repeated in the newest course, thus working out to find how ‘unique’ each course is.
Currently, I have memorised 1900 German words from official courses according to memrise. In reality, would this be: 1500, 1700 or 1800? Similarly, at what point will I actually have learnt 2000 words, would it be 2100, 2300, 2500?
Hope you can help me out!
Okay, quick update, I have manually calculated that:
German 1: 365 Unique words of the 468 words (not including grammar) it is exactly 78% unique from itself
Currently, I estimate that 65% of the German Course words are unique, but still calculating.
German 2:
496 unique words out of 468. (This means that there are actually a lot of unique words amongst the phrases given)
The overall uniqueness between German 1 and 2 is: 762 Unique words/950 Listed words = 80.2% Unique words
New Estimate: The overall german course is 75% unique
German 3:
595/640 Unique words of itself
1127/1590 Unique words amongst German 1, 2 and 3
How many unique words are held within the course itself:
German 1: 365/468
German 2: 496/468
German 3: 595/640
How many brand new unique words are added with each course:
German 1: 365/468
German 2: 361/482 → 726/950
German 3: 401/640 → 1127/1590
How much of each course repeats words of previous courses:
German 1: ----
German 2: 107/482 → 22.9%
German 3: 239/640 → 37.3%
How many words do I actually know after learning german 1, 2 and 3:
1127/1590 = 70.9% of the words it actually says
Patterns: As you complete more courses, you actually learn less and less new content than it says.
Mathematically, this follows the pattern of 1/3(ln(x)).
If this pattern holds true than,
German 4: 46% is already done in previous courses
German 5: 54%
German 6: 60%
How many words do I actually know if I have done ‘n’ German courses:
Let Tn = The total number of words that a single course says it teaches
= (1-(ln1)/3)T1 + (1-(ln2)/3)T2 + (1-(ln3)/3)T3 +… (1-(ln(n))/3)Tn
The most simplified version of this is:
= (T1+T2+T3+T4+T5…Tn) - 1/3(T1ln1 + T2ln2 + T3ln3 +… Tnln(n))
E.g. Once I have done German 1, 2, 3, 4 and 5 how many words have I actually learnt.
Well, Memrise tells me that there are supposedly, ‘T’ words in each course,
T1: German 1 gives me 468 words to learn
T2: German 2 gives me 482 words to learn
T3: 640
T4: 179
T5: 405
Therefore although I have supposedly learnt 2,174 words by doing German 1, 2, 3, 4 and 5, I have actually learnt only…
= 2174 - 1/3(468ln1 + 482ln2+640ln3+179ln4+405ln5).
(put into online calculator)
= 1528 words