#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## study

**1**

[*see also*: consideration, discussion, examination, investigation, research] Our study grew out of some valuable conversations with Kirk Douglas.

Their study resulted in proving the conjecture for......

Much of the rest of the paper is devoted to a general study of......

In Section 2, we lay the foundations for a systematic study of......

In the study of infinite series ∑ a_{n} it is of
significance whether the a_{n} approach zero rapidly.

In Section 3 we proceed with the study of...... [= start or continue the
study]

**2**

[*see also*: consider, examine, investigate, explore] One can also study these
equations on manifolds, but we stick to R^{n} for simplicity.

If one studies the proof of...... it is apparent that (2) is never used.

The aim of this article is to study the relationship between the size of A,
as measured by its diameter, and the extent to which A fails to be convex.

This is part of a larger project to study the Galois groups of periodic
points of arbitrary polynomial maps.

This functor is much studied in [Ab] and [Ce].

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