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;
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Any
 Math, Logic

Click to edit the document details