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Rings and Fields - Period 1+2
OVERVIEW
CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Instruction in: English
Course Code: X_400630
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 3
Contact Hours: 84
DESCRIPTION
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, matrix rings, 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, for example, QR-codes or electronic train tickets).
Contact 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.
Contact 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.
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