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Theoretical Computer Science

Mathematical aspects of computation, including algorithms, computational complexity, automata theory, formal methods, quantum computing theory, and the foundations of computer science

4 papers in this specialization

Paperzilla Papers in Theoretical Computer Science

Mathematics in the archives: deconstructive historiography and the shaping of modern geometry (1837–1852)

French geometer Michel Chasles intertwined historical research and mathematical practice, using "epistemic techniques" like archival research, deconstructive historiography, and periodization to shape his theories. His work demonstrates how analyzing past geometrical methods and notational technologies helped him develop novel approaches and modernize geometry.

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div-class-title-mathematics-in-the-archives-deconstructive-historiography-and-the-shaping-of-modern-geometry-1837-1852-div.pdf

Jul 14, 10:44 AM

Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice

This paper argues that Wittgenstein, not Lakatos, was the true forerunner of the philosophy of mathematical practice. It highlights Wittgenstein's concepts of "rule bending" and "mathematics as rules of description" as key contributions that challenge traditional views of mathematical foundations and emphasize the importance of studying actual mathematical practices.

History of mathematics in mathematics education: Recent developments in the field

The integration of history of mathematics into mathematics education is a growing field, focused on utilizing historical elements not just as motivational anecdotes but as tools to enhance understanding of mathematical concepts and the nature of mathematics itself. Key research areas include theoretical frameworks for integration, the impact of historical resources on student learning and teacher knowledge, and the role of history in interdisciplinary approaches like STEM.

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s11858-022-01442-7.pdf

Jul 14, 10:44 AM

Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

This paper explores leading singularities of traintrack integrals, a class of multi-loop Feynman integrals relevant to quantum field theory calculations. The authors identify "half traintracks" as the most general degenerations with conventional leading singularities and prove that full traintracks possess a rigidity of L-1, computing their leading singularities as integrals over (L-1)-dimensional Calabi-Yau manifolds.