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Math15A - Discrete Mathematics
Suggestions on How to Write Proofs
Sam Buss - April 1999

One way to define mathematics is that is the study of structures which can be precisely and unambiguously defined. These structures include things like the integers, real numbers, geometrical objects, functions, relations, etc. Since these objects can be unambiguously defined, it is possible to establish truths about these objects which are known to be true beyond any reasonable doubt. Mathematical proofs are used to establish these kinds of mathematical truths: the purpose of proof is convince both its author and its readers that certain theorems are true.

In Math 15A, we will teach (mainly by example) various approaches to writing proofs: these approaches tend to be oriented towards how to use common proof strategies, and how to obey the generally accepted conventions of writing proofs.

Reading proofs: Before one can write proofs, one needs to be able to read proofs. Here the general guidelines are:

Some general guidelines for writing proofs are:

Finding proofs can be a tremendously hard process and require a lot of both creativity and luck. Even after the creative insight, it may take a lot of work to structure the proof clearly and actually write out the proof.

In Math 15A, you will be asked to prove only relatively straightforward theorems. The following guidelines should be helpful for finding proofs:

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Sam Buss
Mon Apr 26 22:00:37 PDT 1999