## Students

Contents

## Distinguished student achievements

### Mark Chimes

During his first year of study he unofficially attended Foundations of Abstract Mathematics II in 2011. He attended Categorical Algebra Honors course in 2012 as part of Foundations of Abstract Mathematics I, and obtained 100% in Foundations of Abstract Mathematics II in 2013.

### Deborah Grobler

While she was a third year biomathematics student, she took the course Foundations of Abstract Mathematics II in 2011, and obtained the highest mark 100% coming first in class. Among her achievements is an ingenious “visual method” for deciding transitivity of a relation, which is based on “matching columns” in its graph.

### Francois van Niekerk

During his first year of study he unofficially attended Foundations of Abstract Mathematics II in 2011. After this, in his second year of study, he switched his focus from Computer Science to Mathematics. He independently proved that in a group, if the number of elements x satisfying xx=1 is finite, then it is either equal to 1 or is even. He also independently discovered the well-known proof of the Cantor-Bernstein Theorem. In the second semester of 2012 he attended Categorical Algebra Honors course as part of Foundations of Abstract Mathematics I. He came first among Stellenbosch University students in the Mathematics Olympiad for university students held in October of 2012.

### VereesÃ© van Tonder

During her second year of studying engineering, she significantly improved her marks in Engineering Mathematics and eventually came first in her class. In the same year (2010) she participated in Seminar in Abstract Mathematics, and enrolled for Foundations of Abstract Mathematics II in 2011, completing the course with distinction.

### Thomas Weighill

Being in his third year of studying engineering, he enrolled for Foundations of Abstract Mathematics II in 2011, and completed it with distinction. During his studies for this course, he independently proved the well-known Cantor-Bernstein Theorem which states that if two sets can be injectively mapped into one another, then they are bijective. His proof first constructs a bijection on the partitions of the given sets (where each element of the partition is the “chain” obtained by repeatedly applying the composite of the given injections), and then lifts the bijection to the original sets. In his fourth year, he studied first few chapters from “Categories for the working mathematician”. He successfully graduated as an engineer in 2012, and continues studying Category Theory as an MSc student in Mathematics in 2013-2014.

## Foundations of Abstract Mathematics I and II

Lists of students for these courses as included in FAM seminars

## Seminar in Abstract Mathematics in 2010

Mr M Bailey,

Mr J Engelbrecht,

Ms C van Heerden,

Mr F I Michael,

Mr D A Popov,

Mr R M P Prenter,

Mr T J van Rooyen,

Ms V van Tonder,

Mr H L Uys

## Seminar in Abstract Mathematics in 2009

Mr E Alant,

Mr B Carswell,

Mr W Cloete,

Mr S Daniso,

Ms C van Heerden,

Mr M Lambrechts,

Mr Z Madikazi,

Mr R R M Mahomane,

Ms M McLeod,

Mr F I Michael,

Me E Nel,

Mr N Poets,

Mr R M P Prenter,

Mnr A Roos,

Mr T J van Rooyen,

Mr S Swarts,

Mr H L Uys,

Mr J Weideman