What we do with our problems.
These are the most frequent collocates for the common nouns in mathematics.
In each cell the words are ordered approximately from the strongest collocate to the less used ones.
Those in parentheses are possible but not frequent.
Those with asterisks are NOT used.
The table is not an exhaustive list, it covers only the most frequent collocates in written mathematical texts.
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What do you do with them |
What do they do |
What are they like |
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assumptions |
make, contradict, satisfy, violate, write down, use, (meet) |
imply, hold, are satisfied, assumptions concerning sth., omit |
induction, additional, strong, mild, necessary, weak, reasonable, underlying, minimal |
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conditions |
satisfy, impose, follow, set, state, find, require, neglect, verify, meet |
hold, determine, imply, ensure, allow us to…, restrict (define) |
sufficient, necessary, restrictive, suitable, initial, n-th condition |
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theorem |
prove, generalize, state, apply, derive, formulate, introduce |
holds, requires, exists, states, has corollaries, is useful, build on sth., (simplify) |
converse, well-known, main, central, fundamental, provable, important, (long) |
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result |
prove, state, obtain, extend, present, recall, establish, simplify, make use of, verify, (underline) |
show, imply, follow from, indicate, allow us to do sth |
numerical, main, analogous, accurate, well-known, preliminary, similar, theoretical, better, desired, obtained, contradictory, proper, (shocking) (observed – in experimental context) |
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proof |
complete, conclude, omit, give, include, provide, adapt, present, simplify, sketch, postpone, write, leave to the reader, *prove |
shows, makes use of, is left as an [easy] exercise, (explains) |
rigorous, constructive, elementary, alternative, simple, detailed, original, complete, direct, indirect, by contradiction, by induction, long, short, complicated, hard |
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conclusions |
draw, obtain, reach, offer, give, present, implement *make |
follow from, remain the same |
similar, same, main, wrong, brief, desired, surprising, (false) |
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equation |
solve, satisfy, rewrite, multiply, deduce *evaluate, *calculate |
describe, define, hold, represent, appear |
differential, nonlinear, linear, polynomial, parametric, real, complex, (unsolvable) |