420. ALGEBRA I (3). Introduction to group theory. Properties of the integers, functions, and equivalence relations. A concrete approach to cyclic groups and permutation groups; isomorphisms and the theorems of Lagrance and Cayley. PRQ: MATH 240 or consent of department. Additional information
421. ALGEBRA II (3). Continuation of MATH 420. Homomorphisms and factor groups; introduction to commutative rings, with emphasis on polynomial rings; fields and algebraic extensions. Applications to classical geometric problems. PRQ: MATH 420 or consent of department. Additional information
423. LINEAR AND MULTILINEAR ALGEBRA (3). General theory of vector spaces, linear transformations, and matrices. Topics selected from determinants, tensor products, canonical forms, and bilinear and quadratic forms. PRQ: MATH 240 and MATH 420, or consent of department.
521. ALGEBRAIC STRUCTURES II (3). Ring theory including the Artin-Wedderburn theorem, the Jacobson radical. Commutative algebra, Noetherian rings, and Dedekind domains. PRQ: MATH 520 or consent of department.
Recent history of the Math 520 - 521 sequence: Year taught by required text recommended text 2006-2007 Blair None Lang 2005-2006 Ellers Isaacs 2004-2005 Beachy Lecture notes (520) Hungerford Beachy (521) 2003-2004 Stephen Hungerford 2002-2003 Blau Rotman 2001-2002 Ellers Dummit and Foote 2000-2001 Blair None Hungerford 1999-2000 Wolfskill (520) Dummit and Foote McAlister (521) Dummit and Foote 1998-1999 Beachy Dummit and Foote (520) Beachy (521) 1997-1998 Seelinger Hungerford (520) Beachy (521) 1996-1997 McAlister Isaacs 1995-1996 Thunder None Hungerford 1994-1995 Ellers Isaacs 1993-1994 Blair Lecture notes Lang 1992-1993 Beachy Lecture notes Hungerford 1991-1992 Blau, Rusin Rotman, Garling 1990-1991 Leonard Grove
522. HOMOLOGICAL ALGEBRA (3). Categories and functors, projective and injective modules, complexes and homology, Ext, Tor, and dimensions. Applications to cohomology of groups and ring theory. PRQ: MATH 521 or consent of department.
Recently the course has been taught as a section of Math 620 Semester taught by text 1999, Fall Beachy Rotman 1996, Fall Beachy Rotman 1993, Fall Beachy Rotman 1991, Fall Beachy Rotman
523. MODERN APPLIED ALGEBRA (3). Concepts and techniques of modern algebra which are useful in applied mathematics. Topics covered include applications of group theory to coding, applications of lattice theory to switching theory, and aplications of ring theory to linear automata. PRQ: MATH 420 or consent of department.
620. TOPICS IN ALGEBRA (3). Content varies; may include courses in semigroup theory, finite group theory, ring theory, and homological algebra. May be repeated to a maximum total of 15 semester hours. PRQ: Consent of department.
Semester taught by topic 2006, Spring Blair Commutative Algebra 2005, Fall Beachy Homological Algebra (Osborne) 2003, Fall Beachy Homological Algebra (Rotman) 2001, Spring Beachy Module Categories 2001, Spring Blau Algebraic Combinatorics II 2000, Fall Blau Algebraic Combinatorics I 2000, Spring Ellers Representation Theory II 1999, Fall Ellers Representation Theory I 1998, Fall Seelinger Commutative Algebra 1998, Spring McAlister Semigroups II 1997, Fall McAlister Semigroups 1997, Spring Ellers Representation Theory II 1996, Fall Ellers Representation Theory 1996, Spring Blau Algebraic Combinatorics II 1995, Fall Blau Algebraic Combinatorics I 1995, Spring Rusin Elliptic Curves 1994, Spring Beachy Module Categories 1992, Spring Beachy Module Categories 1990, Spring Sigurdsson Noetherian Rings 1989, Fall Beachy Rings and Modules 1989, Spring Lorenz K-theory 1989, Spring Leonard Representation Theory II 1988, Fall Leonard Representation Theory I 1988, Fall Lorenz Homological Algebra 1988, Spring Blair Noncommutative Rings 1988, Spring Blau Group Characters II 1987, Fall Blau Group Characters I 1987, Spring Blair Homological Algebra 1987, Spring Kambayashi Algebraic Geometry 1986, Spring Blau Lie Algebras II 1985, Fall Blau Lie Algebras IMath 620 has also been offered as a reading course, and recent topics include:
Rings: Rings, ideals, homomorphisms, field of fractions of an integral domain.
Fields and Galois theory: characteristic, prime fields, algebraic and transcendental extensions, separability, perfect fields, normality, splitting fields, Galois group, fundamental theorem of Galois theory, solvability by radicals, structure of finite fields.
Linear algebra: Linear independence, basis, dimension, direct sums, linear transformations and their matrix representations, linear functionals, dual spaces, determinants, rank, eigenvalues and eigenvectors, minimal and characteristic polynomials, canonical forms.
Unique factorization, Euclidean domains, principal ideal domains, polynomial rings, maximal, prime, and primary ideals, Noetherian rings, Hilbert basis theorem, Lasker-Noether decomposition, integral elements, integral closure, fractional ideals, Dedekind domains.
for Part I only:
Herstein, Topics in Algebra
Beachy and Blair, Abstract Algebra
Clark, Elements of Abstract Algebra
Rotman, The Theory of Groups
Garling, A Course in Galois Theory
Curtis, Linear Algebra
Friedberg, Insel, and Spence, Linear Algebra
Hoffman and Kunze, Linear Algebra
NIU Graduate Catalog
NIU Graduate Program