#### THE DEVELOPMENT OF NOTATION AND CONCEPTS IN ALGEBRA

#### Examples of the kind of questions that could be used for Assessments

N.B. IF YOU WISH TO DO ONE OF THESE QUESTIONS RATHER THAN MAKE UP YOUR OWN, YOU MUST STILL AGREE THIS WITH THE LECTURER BEFORE BEGINNING YOUR ANSWER. FAILURE TO DO THIS WILL RESULT IN A LOWER MARK.

- Discuss the liberation of algebra from arithmetical meaning in the 19th century, with particular reference to the algebraic systems developed by W. R. Hamilton and G. Boole (N.B. There is an O.U. video on this topic - MA 290/08 - "The Liberation of Algebra" - available in the library on Main Site for students to borrow and view on site. It is about 20 mins long).

- Summarise the contributions of N. Abel and E. Galois to the theory of the quintic equation. You may refer briefly to their life histories, but should concentrate on their relevant mathematical achievements.

- How would the cubic equation x - 6x + 11x - 6 = 0 have been written down at various stages in the development of algebraic notation? How can it be reduced to one of the three forms given in the Algebra in the Renaissance page?

- Describe, with an example, Cardano's method for solving quartic equations. Briefly suggest why no such method is taught in standard mathematics courses today.

- Describe the coordinate geometry of Descartes and/or Fermat, and comment on its role in the liberation of algebra from geometry.

- Write a critical analysis of the history of the notation used for powers and logarithms.

### REMEMBER:

What Criteria are you being judged on?

SECOND ASSESSMENT

The Development of Algebra

History of Mathematics Module

Links to other History of Mathematics sites

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