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8/26 (Tue) Class 1. Introduction. Group axioms. (Sec.1.1) |
8/27 (Wed) Class 2. First examples of groups. (Sec.1.1) |
8/28 (Thu) Class 3. Subgroups, order. (Sec.1.1) |
8/29 (Fri) Class 4. Groups of orders 1, 2, 3, 4. (Sec.1.1) |
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9/01 (Mon) NO CLASSES. Labor Day. |
9/02 (Tue) Class 5. Dihedral groups. (Sec.1.2) |
9/03 (Wed) Class 6. Generators and relations.(Sec.1.2) |
9/04 (Thu) Class 7. Symmetric groups. (Sec.1.3) |
9/05 (Fri) Class 8. Matrix Groups and Q8. (Sec.1.4,1.5) |
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9/08 (Mon) Class 9. Homomorphisms. (Sec.1.6) |
9/09 (Tue) Class 10. Group Actions. (Sec.1.7) |
9/10 (Wed) Class 11. Centralizers. (Sec.2.2) |
9/11 (Thu) Class 12. Cyclic groups. (Sec.2.3,2.4) |
9/12 (Fri) Class 13. The lattice of subgroups of a group. (Sec.2.5). |
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9/15(Mon) Class 14. Cosets and index. (Sec.3.1) |
9/16 (Tue) Class 15. Normal subgroups. (Sec.3.1) |
9/17 (Wed) Class 16. Quotient groups. (Sec.3.1) |
9/18 (Thu) Class 17. Lagrange's theorem. (Sec.3.2) |
9/19 (Fri) Class 18. Isomorphism theorems. (Sec.3.3) |
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9/22 (Mon) Class 19. Composition Series. (Sec.3.4) |
9/23 (Tue) Class 20. Alternating Group. (Sec.3.5) |
9/24 (Wed) Class 21. Alternating Group. (Sec.3.5) |
9/25 (Thu) Class 22. Midterm #1 review. |
9/26 (Fri) Class 23. Midterm #1. |
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9/29 (Mon) Class 24. Orbits, stabilizers. (Sec.4.1) |
9/30 (Tue) Class 25. Cayley's theorem. (Sec.4.2) |
10/01 (Wed) Class 26. Burnside’s Theorem. |
10/02 (Thu) Class 27. Conjugation. (Sec.4.3) |
10/03 (Fri) Class 28. Automorphisms. (Sec.4.4) |
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10/06 (Mon) Class 29. Sylow's theorems. (Sec.4.5) |
10/07 (Tue) Class 30. Sylow's theorems. (Sec.4.5) |
10/08 (Wed) Class 31. Simplicity of An. (Sec.4.6) |
10/09 (Thu) Class 32. Simplicity of An. (Sec.4.6) |
10/10 (Fri) Class 33. Direct products. (Sec.5.1) |
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10/13 (Mon) Class 34. Finite abelian groups. (Sec.5.2) |
10/14 (Tue) Class 35. Finite abelian groups. (Sec.5.2) |
10/15 (We) Class 36. Groups of small order. (Sec.5.3) |
10/16 (Thu) NO CLASSES. Autumn Break. |
10/17 (Fri) NO CLASSES. Autumn Break. |
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10/20 (Mon) Class 37. Semidirect products. (Sec.5.4,5.5) |
10/21 (Tue) Class 38. Commutators subgroup. (Sec. 6.1) |
10/22 (Wed) Class 39. Solvable groups. (Sec. 6.1) |
10/23 (Thu) Class 40. Solvable groups. (Sec. 6.1) |
10/24 (Fri) Class 41. Free groups. (Sec.6.3) |
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10/27 (Mon) Class 42. Rings and fields. (Sec.7.1) |
10/21 (Tue) Class 43. Examples of rings. (Sec.7.2) |
10/29 (Wed) Class 44. Examples of rings. (Sec.7.2) |
10/23 (Thu) Class 45. Homomorphisms. (Sec.7.3) |
10/31 (Fri) Class 46. Ideals. (Sec. 7.4) |
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11/03 (Mon) Class 47. Principal ideals. (Sec. 7.4) |
11/04 (Tue) Class 48. Prime ideals. (Sec. 7.4) |
11/05 (Wed) Class 49. Maximal ideals. (Sec. 7.4) |
11/06 (Thu) Class 50. Midterm #2 review. |
11/07 (Fri) Class 51. Midterm #2. |
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11/10 (Mon) Class 52. Rings of fractions. (Sec.7.5) |
11/11 (Tue) NO CLASSES. Veterans Day. |
11/12 (Wed) Class 53. Chinese remainder theorem. (Sec.7.6) |
11/13 (Thu) Class 54. Euclidean domains. (Sec.8.1) |
11/14 (Fri) Class 55. Euclidean domains. (Sec.8.1) |
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11/17 (Mon) Class 56. Principal ideal domains. (Sec. 8.2) |
11/18 (Tue) Class 57. Principal ideal domains. (Sec. 8.2) |
11/19 (Wed) Class 58. Unique factorization domains. (Sec. 8.3) |
11/20 (Thu) Class 59. Quadratic integer rings. (Sec. 8.3) |
11/21 (Fri) Class 60. Prime elements in Z[i]. (Sec.8.3) |
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11/24 (Mon) Class 61. Polynomials. (Sec.9.1) |
11/25 (Tue) Class 62. Polynomials over fields. (Sec.9.2) |
11/26 (Wed) NO CLASSES. Thanksgiving. |
11/27 (Thu) NO CLASSES. Thanksgiving. |
11/28 (Fri) NO CLASSES. Columbus Day observed. |
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12/01 (Mon) Class 63. Gauss's lemma. (Sec.9.3) |
12/02 (Tue) Class 64. Irreducibility. (Sec.9.4) |
12/03 (Wed) Class 65. Irreducibility. (Sec.9.4) |
12/04 (Thu) Class 66. Roots of polynomials. (Sec.9.5) |
12/05 (Fri) Class 67. Roots of polynomials. (Sec.9.5) |
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12/08 (Mon) Class 68. Gröbner basis. (Sec.9.6) |
12/09 (Tue) Class 69. Gröbner basis. (Sec.9.6) |
12/10 (Wed) Class 70. Review for the final. |
| 12/18 (Thu) FINAL, 10:00--11:45am |