\(\newcommand{\Aut}{\operatorname{Aut}}\)\(\newcommand{\from}{\colon}\)\(\newcommand{\cross}{\times}\)\(\newcommand{\cover}[1]{{\widetilde{#1}}}\)\(\newcommand{\CC}{\mathbb{C}}\)\(\newcommand{\FF}{\mathbb{F}}\)\(\newcommand{\QQ}{\mathbb{Q}}\)\(\newcommand{\RR}{\mathbb{R}}\)\(\newcommand{\ZZ}{\mathbb{Z}}\)Questions handed in by students before 2018-12-02.

Exercises -

1. In the last assignment sheet, a (non-marked) question asked us to
numerically approximate roots of a polynomial.  Are we expected to
know the formula for Newton-Rhapson method (and similar) for the exam?

Answer: No.  For the assignment I expected you to use a computer to
obtain the numerical approximations (but of course any method would
have been acceptable).  Exam problems will be phrased differently, to
minimise numerical computations.

General mathematics -

1. Is there an algebraic structure (that is a field) with a third
group which has the properties

i) a * b = b * a
ii) a * (b . c) = a . b * a . c
iii) for all a there is a b st ab = e_* where e_* is the neutral element for *

Answer: I assume that you mean "with a third operation" making (part
of?) the underlying set a group.  But I don't have a good answer to
this.  Googling around I found this:

https://mathoverflow.net/questions/120875/ring-with-three-binary-operations

The comments here tend in two directions.  The first is towards
examples: Hopf algebras, Lie algebras, Poisson algebras, Gerstenhaber
algebras, and more.  The second is towards non-existence results such
as the Eckmann-Hilton theorem.

Administration -

1. Would it be possible to have more lecture notes printed and
available at the undergraduate office.

Answer: More notes are now available.