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Rings and Fields - Period 1+2
概述
CEA CAPA Partner 机构: Vrije Universiteit Amsterdam
地点: Amsterdam, 荷兰
Primary Subject Area: 数学
指令: 英语
课程代码: X_400630
记录来源: Partner 机构
课程详细信息: 300级
Recommended Semester Credits: 3
联系时间: 84
描述
This course studies an important algebraic structure (called a ring), which has an addition and a multiplication satisfying certain properties. Rings arise in many situations, and examples include the integers, the integers modulo n, 矩阵环, and polynomial rings, but also the set of complex numbers with integral real and imaginary parts. As is common in algebra, by formalising the common properties we can perform general constructions and prove general results that apply in many contexts, and we illustrate these by working out what they say in various concrete cases. We also study particular types of rings with properties similar to those of the integers (division with remainder, unique factorisation). We conclude by constructing finite fields and some of their properties. These finite fields are used frequently in combinatorics, and they are essential to the theory of error correcting codes (in, 例如, QR-codes or electronic train tickets).
联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.