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Math 110ABC: Algebra |
Catalog Descriptions
110A-110B. Algebra. Lecture, three hours; discussion, one hour. Prerequisite: course 115A. 110A. Not open for credit to students with credit for course 117. Ring of integers, integral domains, fields, polynomial domains, unique factorization. 110B. Requisite: course 110A or 117. Groups, structure of finite groups.
110C. Algebra. Lecture, three hours; discussion, one hour. Prerequisite: courses 110A-110B. Field extensions, Galois theory, applications to geometric constructions, solvability by radicals. |
General Information
Math 110ABC is the basic undergraduate course sequence in abstract algebra.
Math 110A covers rings and fields, while Math 110B treats group theory.
An honors course sequence 110AH-110BH runs parallel to 110A-110B, however the
order of topics is juxtaposed. Math 110AH is devoted to the study of group theory. Groups are a mathematical expression of symmetry and are vitally important in many areas of Mathematics, e.g. Number Theory, Topology and Geometry. Group theory plays an important role in Physics, especially in Quantum Theory. The course will cover the definition and properties of groups as well as the structure of finite groups. The honors sequence in Algebra is essential for those interested in pursuing pure mathematics at any higher level as well as being one of the most interesting and challenging mathematics courses at UCLA. Students who take 110AH but not 110BH can take 110A or 117. Math 110C, offered in the Spring, is designed for students completing either the 110A-110B or the 110AH-110BH sequence. Math 110C covers Galois theory. This is the theory initiated by Evariste Galois (killed in a duel at age 21), which laid an abstract foundation for proving the theorem of N. Abel (died of consumption at age 27) that the general quintic equation is not solvable by radicals. |