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Exercising Mathematical Competence: Practising Representation Theory and Representing Mathematical Practice


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Title: Exercising Mathematical Competence: Practising Representation Theory and Representing Mathematical Practice
Authors: Säfström, Anna Ida
E-mail: anna.ida.safstrom@bredband.net
safstrom@chalmers.se
Issue Date: 5-Apr-2013
University: Göteborgs universitet. Naturvetenskapliga fakulteten
Institution: Department of Mathematical Sciences ; Institutionen för matematiska vetenskaper
Parts of work: Säfström, A.I. (2013). Skew symmetric matrix equations A+B+C=0. Unpublished manuscript.

Säfström, A.I. (2013). Unitary highest weight representations of $\mathfrak{gl}_\mathbb{C}(n+1)$. Unpublished manuscript.

Säfström, A.I. (2013). Developing a framework for competencies exercised. Unpublished manuscript.

Säfström, A.I. & Pettersson, K. (2013). Competencies exercised in the process of proving. Unpublished manuscript.
Date of Defence: 2013-04-26
Disputation: Fredagen den 26 april 2013, kl. 13.15, Sal KA, Kemigården 4
Degree: Doctor of Philosophy
Publication type: Doctoral thesis
Keywords: Mathematical competence
exercising competencies
young children
whole number arithmetic
tertiary level
proving
highest weight representation
tensor product decomposition
skew-symmetric matrix
moment map
infinite dimensional unitary representation
Abstract: This thesis assembles two papers in mathematics and two papers in mathematics education. In the mathematics part, representation theory is practised. Two Clebsch-Gordan type problems are addressed. The original problem concerns the decomposition of the tensor product of two finite dimensional, irreducible highest way representations of $GL_{\mathbb{C}}(n)$. This problem is known to be equivalent with the characterisation of the eigenvalues of the sum of two Hermitian matrices. In this thesis, th... more
ISBN: 978-91-628-8662-2
URI: http://hdl.handle.net/2077/32484
Appears in Collections:Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper

 

 

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