Croeso i Dudalen Fathemateg Gareth Evans / Welcome to Gareth Evans' Mathematics Page.
Adnewyddiad Diwethaf / Last Update: 25/07/2010
Thesis: Noncommutative Involutive Bases (2,684 KB)
Dyma gopi o'n nhraethawd hir a gyflwynais yn ystod mis Medi 2005 ac a dderbyniwyd yn ystod mis Ionawr 2006. Here is a copy of my thesis which I submitted during September 2005 and which was accepted during January 2006.
Pedwar: A collection of four programs for computing Gröbner or Involutive Bases for polynomial
ideals over commutative and noncommutative polynomial rings.
Download(for i386 based FreeBSD systems): ZIP (1,018 KB)
Download (for other FreeBSD systems): ZIP (1,025 KB)
Modiwlau / Modules
Cliciwch ar y linc uchod i weld casgliad o ddogfennau PDF yn crynhoi'r holl gyrsiau mathemateg rwyf wedi cymryd ers lefel TGAU. Click on the above link to access PDF versions of notes of all the Maths courses I have taken since GCSE level.
Seminarau PhD / PhD Seminars
Casgliad o ddogfennau PDF yn crynhoi'r seminarau rwyf wedi mynychu tra bod yn fyfyriwr ymchwil (o Fedi 2002 ymlaen). A collection of PDF files covering the PhD seminars I have attended as a research student (from September 2002 onwards).
Conference Paper: Noncommutative Involutive Bases (233 KB)
Dyma bapur ymchwil a dderbyniwyd gan gynhadledd ACA2004 yn Beaumont, Texas, UDA a gynhaliwyd yn ystod mis Gorffennaf 2004. Here is a research paper that appears in the proceedings of the ACA2004 conference which was held at Beaumont, Texas, USA during July 2004.
Note: This paper was written soon after I had encountered commutative Involutive Basis theory for the first time, and as such contains some inaccuracies which I have (hopefully!) corrected in my thesis. In particular, the algorithms for autoreduction in the paper are incorrect (the set with which we take multiplicative variables against is the wrong one); and notions of noncommutative continuity and constructivity are nonsensical (they do not reflect the utility of continuity and constructivity in the commutative case). Note also that there is no notion of a 'thin' divisor in this paper, and that the Involutive Basis algorithms are based on Zharkov & Blinkov's algorithm, and so (at least in the commutative case) do not allow the termination of the algorithm to be proved for continuous, constructive and Noetherian divisions.
Cymesuredd / Symmetry
A page exploring the notion of symmetry. Tudalen yn ymchwilio i mewn i'r syniad o gymesuredd.
Countdown Numbers Game
Cliciwch i chwarae gêm sy'n adlewyrchu'r gêm rifau o'r sioe deledu 'Countdown'. An implementation of the numbers game from the popular UK television show 'Countdown'.
Safle We Prosiect G3M97 / G3M97 Project Website
Dyma ganlyniad fy mhrosiect trydedd flwyddyn "Calculating Groups, Subgroups and Hasse Diagrams from the Orthogonal Group O(3) in Java". Mae'r deunydd yn cynnwys sut datblygwyd y rhaglen, adroddiad y prosiect (mewn ffurf PDF) a'r còd ar gyfer y rhaglen (yn Saesneg yn unig). The result of my 3rd Year Project "Calculating Groups, Subgroups and Hasse Diagrams from the Orthogonal Group O(3) in Java". The material includes how the final program was developed, the project report (in PDF format) and the source code for the final program.
Dogfen Ysgoloriaeth 1998 / Scholarship Document 1998
Er mwyn derbyn ysgoloriaeth i Brifysgol Bangor yn 1998, ysgrifennais draethawd am batrymau ym Mathemateg. Mae'r traethawd yn cynnwys adrannau am batrymau rhif, patrymau teilsen a sgwariau hud, a gallwch weld y traethawd drwy glicio ar y linc uchod (yn Saesneg yn unig). In order to receive an entrance scholarship to Bangor University in 1998, I wrote an essay on the subject of 'Patterns in Mathematics'. By clicking on the above link, you can view the essay, which includes sections on number patterns, tile patterns and magic squares.
Pos / Puzzle: A fedrwch fesur 4L o ddŵr isod? Can you measure 4L of water below?
Pos / Puzzle: A fedrwch wneud sgwâr hud? Can you make a magic square?