### THE DEVELOPMENT OF THE FOUNDATIONS OF MATHEMATICS

ASSESSMENT

This assessment is allocated one sixth of the overall module marks. It should be the equivalent of 500 words long.

You must choose a suitable essay question on any of the Foundations of Mathematics topics, and submit it to your tutor for approval. The essay must not be commenced until this approval is obtained.

The criteria on which your assessment wil be marked are the same as for the "History of Algebra" assessment.

### Some sample questions:

(N.B. It must not be assumed that you can do one of these questions without previously agreeing the title with your tutor, and if you choose one of these, it would be preferred if you would rephrase the title in your own words).

- Discuss the development of the theory of irrational numbers in the nineteenth century, with particular reference to Dedekind's theory of sections.

- Describe how Cantor demonstrated the existence of transcendental numbers, and comment on the criticism made of his methods by contemporary mathematicians.

- Describe the theory of ordinal numbers as developed by Cantor, and discuss the Burali-Forti paradox which arose in connection with this theory.

- Describe the beliefs of the three schools of mathematical thought : Formalism, Platonism and Constructivism (=Intuitionism) . Argue in favour of one of them from your own point of view.

- Briefly outline the work of Godel and comment on it's significance in the development of the foundations of mathematics.

Foundations of Mathematics

History of Mathematics Module

Links to other History of Mathematics sites

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