## MTH 316 Calendar and Syllabus  Spring 2008

Text: Elements of Modern Algebra, 6th edition by Gilbert & Gilbert.

The following calendar gives a timetable for the course. You should work out all of the problems given below.

Attendance at each class is expected.

 Week Events Sections Problems Jan 21 Classes start Wed Jan 23 1.5 Permutations and inverses 1.7 Relations (1-2)abcdefgk, 3, 6-10 1, 2abcd, 3, 4, 10, 23 Jan 28 2.2 Induction  2.3 Divisibility  2.4 Primes, GCDs 1-10 odd, 27-29 3-9 odd, 17, 31 2abc, 3cd, 7, 26 Feb 4 2.5 Congruences  2.6 Congruence classes 1-15 odd 1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 8ac, 16, 22-23 Feb 11 1.6 Matrices 1.4 Binary operations 3.1 Group 1ad, 3, 8, 9-12, 14, 16, 25,  26 1abcd, 2abcde, 3-6, 9, 10 1-7, 11-13, 21, 23, 25, 28, 29, 33, 42-44, 48, 49, 51 Feb 18 3.2 Subgroups 3.3 Cyclic groups 2, 3, 5-9, 12, 17, 18ac, 35 5, 7ab, 8ab, 9ac, 10ac, 14-15, 19-21, 23-24 Feb 25 3.4 Isomorphisms 3.5 Homomorphisms 1-4, 7, 10, 13, 23 1, 2, 3, 7, 11, 12-14, 17 Mar 3 4.1 Permutation groups   4.4 Normal subgroups 1-10 abc 3-6,32,41,42,46 Mar 10 4.5 Quotient groups 4.6 Direct sums 3, 4, 19, 30 9-12 Mar 17 Spring Break Spring Break Spring Break Mar 24 Last day to drop: Mar 24 5.1 Rings 5.2 Integral domains and fields   6.1 Ideals and quotient rings 1, 2, 7, 8, 10, 14ac, 15, 20, 21, 24, 31, 38 1, 2, 6, 9-10, 16, 18 3, 5-10, 13-15, 23 Mar 31 6.2 Ring homomorphisms 6.3 Characteristic 1, 2, 4, 6, 15, 17 1-3, 8, 9, 13 Apr 7 6.4 Maximal ideals 8.1 Polynomials over a ring 1-3, 5, 9-10, 17, 21-23 3, 5, 6, 13, 14 Apr 14 8.2 Polynomial Divisibility   8.3 Factorization in F[x] 1-4, 21 1, 2, 4, 6 Apr 21 8.6 Algebraic extensions 2ab, 3, 5, 10, 11ab Apr 28 Last day :Apr 29