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GRK 1632: Experimental and Constructive Algebra

GRK 1632：实验和构造性代数

基本信息

批准号：
138846404
负责人：
金额：
--
依托单位：
Rheinisch-Westfälische Technische Hochschule Aachen
依托单位国家：
德国
项目类别：
Research Training Groups
财政年份：
2010
资助国家：
德国
起止时间：
2009-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/138846404?language=en
关键词：
GRK 1632 Experimental Constructive Algebra

项目摘要

The underlying idea of the Graduate School ¿Experimental and Constructive Algebra¿ is the experimental study of algebraic problems at an advanced theoretical level. Motivated by difficult and partly abstract questions stemming from both pure mathematics and applied sciences, an experimental approach including the use of computers yields insight leading to both relevant theoretical results and innovative algorithmic methods.The research group in algebra at RWTH Aachen University has been doing pioneering work in computer algebra since 1968, e.g. through the development of the computer algebra systems GAP, CHEVIE and CARAT, and the contributions to the modular ATLAS project. Group theory is the focus of our research; it is the mathematical abstraction of the ubiquitous concept of symmetry. The computer functions as a microscope the mathematician uses in studying abstract objects experimentally. The continuing further development of relevant methods allows increasingly deep insight into the world of mathematics. At the same time it enables people in other areas to use the algorithms and results without having to master with the often difficult theory that lies beneath. As the first period has shown this experimental approach provides a direct path for the young doctoral students to understanding abstract mathematical concepts.The second characteristic of this Graduate School is its cross cutting nature. The participating researchers work in different areas of mathematics which nonetheless are joined by numerous connections. These connections are expanded and strengthened in this Graduate School. The resulting synergistic effects yield innovative approaches and alternative points of view, leading to substantial improvements beyond the algorithmic methods. Both the constructive approach and the concept of symmetry are unifying common principles. Every dissertation lies at the intersection of at least two different research areas of the participating professors and is actively supervised by at least two professors. The insight into methodologically and thematically different fields ensures a broad education of the doctoral students and also enriches the scientific perspective of the supervisors.

研究生院“实验和构造代数”的基本理念是在高级理论水平上对代数问题进行实验研究。受纯数学和应用科学中困难且部分抽象的问题的推动，包括使用计算机在内的实验方法产生了洞察力，从而产生了相关的理论结果和创新的算法方法。亚琛工业大学的代数研究小组自 1968 年以来一直在计算机代数方面进行开创性工作，例如通过计算机代数系统 GAP、CHEVIE 和 CARAT 的开发，以及对模块化 ATLAS 项目的贡献。群论是我们研究的重点；它是普遍存在的对称概念的数学抽象。计算机的功能就像数学家用来实验研究抽象对象的显微镜。相关方法的不断进一步发展使得人们对数学世界的了解越来越深入。同时，它使其他领域的人们能够使用算法和结果，而无需掌握背后通常很困难的理论。正如第一阶段所表明的那样，这种实验方法为年轻的博士生理解抽象的数学概念提供了直接的途径。该研究生院的第二个特点是它的交叉性质。参与研究的研究人员在不同的数学领域工作，但这些领域之间存在着许多联系。这些联系在该研究生院得到了扩大和加强。由此产生的协同效应产生了创新方法和替代观点，从而带来了算法方法之外的实质性改进。建设性方法和对称概念都是统一的共同原则。每篇论文都位于参与教授的至少两个不同研究领域的交叉点，并受到至少两名教授的积极监督。对方法论和主题不同领域的洞察确保了博士生的广泛教育，也丰富了导师的科学视角。