English is not my native-language. So if you could help me :). Here it
is (it is a statement of purpose for graduate admission to a bigUNIV):

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Statement of Purpose.

In what follows, I will describe what research I hope to do, how it is
related to research I have done, and why I would like to joint the PhD
research program in Mathematics at the University of CITY1.

I am interested, in a broad sense, in the following general areas of
research: Algebra and Foundations. Especially any meaningful mixture of
both. The Professors on the Faculty who may be interested includes the
ones cited below.

My M.Sc. focused mainly on algebra and number theory. There we proved,
by other means, a result concerning finitely generated torsion-free
nilpotent groups in the same localization genus by exhibiting some
arithmetical examples. Also, not so recently, I have been quite excited
about new possibilities of learning and research in those topics which
build upon mathematical logic.

Hence, I have looked over the work of Professor BIGPROF1 on set theory
and (set-theoretic) topology. I like the ideas and the methods inherent
in these topics. And since there seems to be a well established
``network" of topologists there at NEARBYCITY2-CITY1, I thought I
could ``also" benefit from the teachings of Professor BIGPROF1.

Likewise, I am also interested in the work of Professor BIGPROF2 on
that subject of computational complexity over general algebraic
structures. Here are additional miscellaneous facts which justifies
this interest: During my bachelor's degree program (in Physics), I once
did some research project in the theory of Lempel-Ziv ``complexity"
of pseudo-random binary sequences (from a dynamical systems point of
view); there was ultimately some links with mathematical logic. Then
during my M.Sc. program (in Mathematics), I encountered again those
ideas of randomness in the Cryptography & Codes course, through the BBS
generator. Also, the fact that I have had in the past, as an amateur,
some contact with the computer engineering world may explains my
interest in those topics of computability and computational complexity.

Finally, there is one more reason why I am considering the University
of CITY1; though this might seems a little superficial. The
availability of quiet on-campus graduate housing facilities that would
suit the needs of a PhD student is a main concern for me.

Continuing up to a PhD degree seems to me quite like a natural path,
rather than an exception. At least just for the joy to know a little
more, to gain a little more sophistication in the understanding of the
underlying concepts. And more importantly I guess, since this is a
research-oriented program, to obtain new results.

(Just to mention it explicitly: I have applied, with some hope, for an
BIGNATINSTITUTE scholarship.)