Making Mathematical Notes
1
Notes On Making Mathematical Notes For Your Course
C.T.J. Dodson, School of Mathematics, Manchester University
This is a summary of guidance notes for students on mathematical language, symbols, logic and
proofs, and on how to make their own course notes useful. It suggests some essential skills that a student
should acquire during a ﬁrst semester at university.
Language, symbols, logic and proofs
1.
Language
(i) Make sense to a computer (
not
a telepath) using same axioms.
(ii) Punctuate into sentences and paragraphs. Brackets are useful.
(iii) Signpost arguments : before, during and after the development.
2.
Symbols
(i) Declare the sets in use; eg
A
=
{
x
∈
R
m

(statement about
x
)
}
.
(ii) Introduce an element by declaring its origin and make clear how it was chosen or if arbitrary,
from which set.
(iii) Use ‘=’ as an abbreviation of aequare, ‘to equal’ (Descartes introduced it as
α
in the 17
th
cen
tury). It can be used
only
between sets, or between elements of one set;
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 Spring '08
 Any
 Math, Logic, Mathematical Notes

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