## MTH 316 Calendar and Syllabus  Spring 2007

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 22 Classes start Mon 1.1 Sets1.2 Mappings 1.5 Permutations and inverses1.7 Relations 1-3, 4ace, 5acegi, 9a, 13, 331ab, 2, 3bc, 4abcde, 6, 11, 13, 15ab(1-2)abcdef, 3, 6-101, 2abcd, 3, 4, 10, 23 Jan 29 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 5 2.5 Congruences   2.6 Congruence classes 1-15 odd1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 8ac, 16, 22-23 Feb 12 1.6 Matrices 1.4 Binary operations3.1 Groups 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 19 Monday no class 3.2 Subgroups3.3 Cyclic groups 2, 3, 5-9, 12, 17, 18ac, 355, 7ab, 8ab, 9ac, 10ac, 14-15, 19-21, 23-24 Feb 26 3.4 Isomorphisms3.5 Homomorphisms 4.1 Permutation groups 1-4, 7, 10, 13, 231, 2, 3, 7, 11, 12-14, 17(1-11)abc Mar 5 4.4 Normal subgroups4.5 Quotient groups 4.6 Direct sums 3-6, 32, 41, 42, 463, 4, 19, 309-12 Mar 12 5.1 Rings 5.2 Integral domains and fields 1, 2, 7, 8, 10, 14ac, 15, 20, 21, 24, 31, 38 1, 2, 6, 9-10, 16, 18 Mar 19 Spring Break Spring Break Spring Break Mar 26 5.3 Field of quotients6.1 Ideals and quotient rings 1, 7, 8, 163, 5-10, 13-15, 23 Apr 2 6.2 Ring homomorphisms6.3 Characteristic 1, 2, 4, 6, 15, 171-3, 8, 9, 13 Apr 9 6.4 Maximal ideals8.1 Polynomials over a ring 1-3, 5, 9-10, 17, 21-233, 5, 6, 13, 14 Apr 16 8.2 Polynomial Divisibility 8.3 Factorization in F[x} 1-4, 211, 2, 4, 6 Apr 23 8.6 Algebraic extensions 2ab, 3, 5, 10, 11ab Apr 30 Last day of class Mon