The following post is written by John Webb from The Department of Mathematics and Applied Mathematics at The University of Cape Town. With his permission I include it here as an advert for a book which is discussed at the bottom of the post. Mathemafrica receives no payment for including this text. I hope that in addition to being an advert for the book, this may be a chance for students to discuss some of the problems they see with the transition between school and University here in South Africa for maths students.

Why do so many first-year students fail varsity maths?
Thousands of students across South Africa have started their university careers, and many of them have enrolled for a course in Mathematics. Some will be aiming at a maths major, in particular those who hope to teach mathematics at school level. But far more will be doing maths as a requirement for their degrees in a whole range of areas.…

Mathematics can sometimes seem dream-like, at least on first encounter. Later on, one gets
used to a new mathematical object, and it seems everyday. I remember how strange the idea of
a group was to me, how mysteriously it grew from three almost trivial axioms to a forest
of subgroups and quotient groups and equivalence classes and so on. Of the few dreams I
now recall, there was one with a huge hall full of people, perhaps a giant cave, and I was descending a long,
rickety staircase — or was I sliding down a cable? — feeling myself among a heretofore
completely unsuspected part of humanity, who perhaps nobody from above ground had ever seen.
Groups were a bit like that, and saying that a square had a symmetery group did not
make them appear any less unexpected.

Furthermore, dreams and mathematics have a lot in common—I mean here the dreams that
people, when awake, remember having had when asleep.…