 Programs
 Undergraduates
 Program Flowchart
 Regulations
 Course Flowchart
 Required Courses
 Current Courses
 Field Courses
 Connected Programs
 Cross Disciplinary
 Document Downloads
 Graduates
 Program Flowchart
 M.S. Regulations
 Ph.D. Regulations
 Courses
 Current Courses
 Joint Graduate Courses
 Document Downloads
Course Introduction
《Algebra》 

Abstract algebra is the subject area in mathematics that studies algebraic structures of mathematical objects, such as integers, complex numbers, matrices, roots of polynomials, symmetries of polyhedrons, and et al. Contemporary mathematices make extensive use of abstract algebra. For example, algebraic number theory and algebraic geometry apply algebraic methods to problems in number theory and geometry, respectively. In recent years, abstract algebra also figures prominently in coding theory and cryptography, which are essential in telecommunication nowadays. In this oneyear course, we will study three kinds of algebraic structures that appear most often in mathematics, namely, groups, rings, and fields, culminating in the proof of the theorem that a general quintic equation has no solutions in radicals.
