Search for dissertations about: "foundations of mathematics"

Showing result 1 - 5 of 18 swedish dissertations containing the words foundations of mathematics.

  2. 1. On Axioms and Images in the History of Mathematics

    Author : Johanna Pejlare; Gunnar Berg; Anders Öberg; Leo Corry; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; SAMHÄLLSVETENSKAP; SOCIAL SCIENCES; HUMANIORA; HUMANITIES; NATURVETENSKAP; NATURAL SCIENCES; Mathematics; History of mathematics; axiomatization; intuition; visualization; images; Euclidean geometry; MATHEMATICS; MATEMATIK; History of mathematics; axiomatization; intuition; visualization; images; Euclidean geometry;

    Abstract : This dissertation deals with aspects of axiomatization, intuition and visualization in the history of mathematics. Particular focus is put on the end of the 19th century, before David Hilbert's (1862–1943) work on the axiomatization of Euclidean geometry. The thesis consists of three papers. READ MORE

  4. 2. Minimal models in algebra, combinatorics and topology

    Author : Alexander Berglund; Torsten Ekedahl; Alexandru Suciu; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Abstract : The thesis consists of seven papers.In Paper I, II, III, IV and V, we study homological invariants of monomial rings — rings of the form R = k[x1, . . . READ MORE

  5. 3. Mathematical Foundations of Equivariant Neural Networks

    Author : Jimmy Aronsson; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; symmetry; geometric deep learning; gauge theory; induced representations; fiber bundles; convolutional neural networks; equivariance;

    Abstract : Deep learning has revolutionized industry and academic research. Over the past decade, neural networks have been used to solve a multitude of previously unsolved problems and to significantly improve the state of the art on other tasks. However, training a neural network typically requires large amounts of data and computational resources. READ MORE

  6. 4. Partiality and Choice : Foundational Contributions

    Author : Jesper Carlström; Per Martin-Löf; Gilles Dowek; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; MATHEMATICS; MATEMATIK;

    Abstract : The subject of the thesis is foundational aspects of partial functions (Papers 1, 2 & 4) and some choice principles (Papers 3 & 4) in the context of constructive mathematics.Paper 1 studies the inversion functions of commutative rings. The foundational problem of having them only partially defined is overcome by extending them to total functions. READ MORE

  7. 5. Homogenization of some problems in hydrodynamic lubrication involving rough boundaries

    Author : John Fabricius; Guy Bayada; Luleå tekniska universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; partial differential equations; calculus of variations; homogenization theory; tribology; hydrodynamic lubrication; thin film flows; Reynolds equation; surface roughness; Weyl decomposition; Matematik; Mathematics; Matematik;

    Abstract : This thesis is devoted to the study of some homogenization problems with applications in lubrication theory. It consists of an introduction, five research papers (I–V) and a complementary appendix.Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficients. READ MORE