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University Library, University of Illinois at Urbana-Champaign

Algebra at the University of Illinois at Urbana-Champaign: Home


"Algebra is one of the oldest branches of mathematics, and the study of algebra in the Department of Mathematics has traditionally been rich and strong. Such eminent mathematicians as C. A. Miller (Group Theory), R. D. Carmichael (Group Theory and Number Theory), A. B. Coble (Algebraic Geometry), and R. Baer (Group Theory Abelian Groups) began a tradition in algebra that is continued today by a strong and active group of approximately 20 mathematicians, supplemented by visitors who divide their time between teaching and research.

The research strengths of the faculty are in the theory of rings (commutative and noncommutative), the theory of groups, algebraic number theory, the representation theory of groups and algebras, and algebraic geometry.

The algebraic life of the Department is very active. In addition to the courses offered there is a comprehensive seminar program, usually 4-6 seminars each week, covering almost every aspect of algebra. These are almost equally divided between current topic seminars in which current research is presented in one or two lectures and in-depth seminars in which a subject is studied through a longer series of lectures. These seminar lectures are presented by faculty members, graduate students, and visitors. Graduate students are encouraged to participate in these seminars because participation in a combination of seminars and advanced courses leads a student more quickly to the frontiers of research. Often the weekly departmental colloquium lecture is presented by a noted algebraist. The Department has a number of visiting scholars and there are frequent algebraists among them."

Books on algebra can be found in the Mathemathics Library Stacks on the main level shelved under call number range 512 to 512.55.

What Is Algebra?

"Algebra, branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. The notion that there exists such a distinct subdiscipline of mathematics, as well as the term algebra to denote it, resulted from a slow historical development.."   from "algebra." Encyclopaedia Britannica. Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2015. Web. 29 May 2015.

"Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics, together with number theorygeometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols;[2] it is a unifying thread of almost all of mathematics.[3] As such, it includes everything from elementary equation solving to the study of abstractions such as groupsrings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Most early work in algebra, as the Arabic origin of its name suggests, was done in the Near East, by such mathematicians as Omar Khayyam (1048–1131).[4][5]From Wikipedia contributors. "Algebra.Wikipedia, The Free Encyclopedia. Wed. 29 May 2015.



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