## History and applications

The history of algebra was touched on in the modules listed in the Motivation section. It is worth remembering that our modern algebraic notation is relatively recent. Here are some examples of the different notations used from the Middle Ages onwards.

Chuquet (1484) $$R)^2.18\bar{m}.R)^2150\\ \text{i.e.}, \ \sqrt{18-\sqrt{150}}$$ Trouame.1.n$$^0.\text{che gi}\bar{o}\text{to al suo} \ \bar{q}\text{drat}^0 \ \text{facia}.12$$i.e., $$x+x^2=12$$ 4 Se. -51 Pri. -30 N. dit is ghelijc $$45\frac{3}{5}$$i.e., $$4x^4-51x-30 =45\frac{3}{5}$$ cub$$^9$$ p: 6 reb$$^9 \ ae\bar{q}lis \ 20$$i.e., $$x^3+6x=20$$ 1 Q C -15 Q Q + 85 C -225 Q +274 N aequator 120i.e., $$x^6 -15x^4+85x^3 -225x^2+274x=120$$ $$aaa-3.bba ======= +2.ccc$$i.e., $$a^3-3b^2a=2c^3$$

It is obvious how much of an improvement our modern notation is, and how difficult it would be to perform the many algebraic operations discussed above without the relative ease of our modern system.

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