Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clear Thinking, vague thinking and paradoxes   Many undergraduate students of engineering and the exact sciences have
difficulty with their mathematics courses due to insufficient proficiency in
what we in this paper have termed clear thinking. We believe that this lack of
proficiency is one of the primary causes underlying the common difficulties
students face, leading to mistakes like the improper use of definitions and the
improper phrasing of definitions, claimes and proofs. We further argue that
clear thinking is not a skill that is acquired easily and naturally - it must
be consciously learned and developed. The paper describes, using concrete
examples, how the examination and analysis of classical paradoxes can be a fine
tool for developing students' clear thinking. It also looks closely at the
paradoxes themselves, and at the various solutions that have been proposed for
them. We believe that the extensive literature on paradoxes has not always
given clear thinking its due emphasis as an analytical tool. We therefore
suggest that other discipkunes could also benefit from drawing upon the
strategies employed by mathematicians to describe and examine the foundations
of the problems they encounter.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph