# Topics and Assignments

 Week-of Topics Assignments Sep 6 Class starts: Thursday 9th. 2.3 Divisibility 2.4 Primes, GCDs 2.3: # 3--9 odd, 17, 20, 21, 24, 25, 26, 40 2.4: # 2abc, 3cd, 10, 21, 33, 34 Sep 13 2.5 Congruence of integers 2.6 Congruence classes 2.5: # 1--15 odd, 27, 28 2.6: # 1abcd, 2ab, 3abd, 4abc, 5abg, 6ac, 7ac, 8bde, 16, 18, 20--23 Sep 20 1.6 Matrices 1.4 Binary operations 1.6: # 3, 9--12, 14, 16, 30, 31 1.4: # 1abcd, 2abcd, 3--6, 7--8, 12--13 Sep 27 3.1 Definition of a group 3.2 Properties of group elements 3.1: # 1--7, 11--15, 17, 20, 21, 23, 25, 28, 29 3.2: # 1--6, 11--15, 17, 19--20 Oct 4 3.3 Subgroups 3.4 Cyclic groups Exam I: Thursday Oct 7th. 3.3: # 2, 3, 6a, 7a, 8, 13ac, 14ab, 17, 18a, 29, 30, 33, 40, 41 3.4: # 2, 5, 7, 8, 9ac, 10c, 11ac, 12a, 16, 18c, 23ab, 25, 27--28 Practice Problems Exam I Oct 11 Monday classes Oct 12 3.5 Isomorphisms 3.6 Homomorphisms 3.5: # 1--4, 7, 8, 10, 12, 15, 24, 26 3.6: # 1--5, 8, 9, 11, 15--18 Oct 18 4.1 Finite permutation groups 4.4 Cosets of a subgroup 4.1: # 1-10abc, 14 4.4: # 3, 7, 8, 12, 19, 20--22, 24 Oct 25 4.5 Normal subgroups 4.6 Quotient groups 4.5: # 1c, 32, 2, 4, 6, 22, 25, 29--30, 33 4.6: # 3, 7, 18--19, 21, 30, 34, 37 Nov 1 4.7 Direct Sums 5.1 Definition of a ring 4.7: # 1, 3, 7, 16--17, 19 5.1: # 1ab, 2abcdf, 7, 8, 10, 14ac, 16, 23--25, 27, 30, 39, 47--48 Nov 8 5.2 Integral domains and fields Exam II: Tuesday Nov 9th. No class Nov 11th. 5.2: # 1abeg, 2, 8, 11, 15--16, 18, 21, 23 Nov 15 6.1 Ideals and quotient rings 6.2 Ring homomorphisms 6.1: # 1, 3--4, 6--8, 11--15, 19acd, 20--21, 26--27, 31 6.2: # 1, 3, 6, 7, 10, 12, 14, 21--22, 24, 25a Nov 22 6.3 The characteristic of a ring No class Nov 25-26 6.3: # 1--4, 8, 9, 10, 14, 16, 18, 20 Nov 29 6.4 Maximal ideals 8.1 Polynomials over a ring 6.4: # 1--5, 9--11, 13--15, 19, 21--25, 27--28 8.1: # 3, 5--7, 10--12, 14, 16--18 Dec 6 8.2 Polynomial divisibility 8.3 Factorization in F[x] 8.2: # 1, 4, 21, 33--34 8.3: # 1, 2, 5, 6 Dec 14th. Final! 3:00--6:00 PM