C121310, Algebra I, Fall 2009
Department of Mathematics
Date
Plan to cover
Homework problems
Tues
Sep. 15
點名及課程介紹.
Thur
Sep. 17
0. Sets and Relations.
P8# 15, 19, 20, 21, 36.
Tues
Sep. 22
I.1. Introductions and Examples.
I.2. Binary Operations.
I.3. Isomorphic Binary Structures.
P19# 35, 37.
P27# 23, 24, 31, 36, 37.
P36# 19, 24, 25, 27, 33.
Thur
Sep. 24
I.4. Groups.
P35# 9, 10, 15, 19, 29, 32, 41.
Tues
Sep. 29
I.5. Subgroups.
P55# 13, 25, 26, 40, 41, 45, 49, 52, 53.
Thur
Oct. 1st
I.6. Cyclic Groups (continued...).
Tues
Oct. 6
I.6. Cyclic Groups.
I.7. Generating Sets.
P66# 3, 18, 20, 27, 40, 47, 48, 52, 53.
P72# 3, 5.
Thur
Oct. 8
II.8. Groups of permutations.
P83# 3, 8, 11, 21, 36, 40, 41, 44, 47.
Tues
Oct. 13
II. 9. Orbits, Cosets, and the alternating group.
P94 #5, 13, 17, 20, 21, 23, 27, 29, 34.
Thur
Oct. 15
II.10. Cosets and The etheorem of Lagrange. (continued...)
Tues
Oct. 20
First midetrm in class. (10%)
Cover Section 0. through Section 7.
Thur
Oct. 22
II.10. Cosets and The etheorem of Lagrange.
P101 #6, 15, 19, 28, 32, 36, 43, 45, 46.
Tues
Oct. 27
II.11. Direct products and finitely generated abelian groups.
Thur
Oct. 29
II.11. Direct products and finitely generated abelian groups.
P111 # 8, 14, 15, 16, 26, 36, 38, 39, 40, 47.
Tues
Nov 3.
III.13. Homomorphisms.
Thur
Nov. 5
Review.
Tues
Nov 10.
2nd Midterm in Class (20%).
Plan to cover chapter I and II. (Sec 12 is not included.)
Thur
Nov. 12
III.13. Homomorphisms.
P133 # 5, 13, 23, 29, 32, 35, 44, 47, 49, 50.
Tues
Nov 17.
III.14. Factor groups (to be continued).
Thur
Nov. 19
III.14. Factor groups.
P142 # 7, 15, 23, 33, 34, 35, 37, 39.
Tues
Nov 24.
III.15. Factor group computation and simple groups.
P152 # 3, 9, 15, 19, 29, 39, 40, 41, 42.
Thur
Nov 26.
III.16. Group action on a set.
P159 # 1, 2, 3, 10, 13, 15.
Tues
Dec 1
III.17. Applications of G-sets to counting.
IV.18. Rings and Fields.
P164 # 1, 3, 7.
Thur
Dec 3.
Review or continue IV.18. Rings and Fields.
Tues
Dec 8
Plan to have 3 midterm on chapter III, section 13~17.
Thur
Dec 10.
IV.18. Rings and Fields.
P175 # 22, 23, 25, 40, 46, 53, 55.
Tues
Dec 15
IV.19. Integral Domains.
P182 # 1, 11, 17, 25, 27, 29.
Thur
Dec 17.
IV. 20 Fermat's and Euler's Theorems
P189 # 5, 9, 15, 17, 23, 27, 28, 29, 30.
Tues
Dec 22
IV.21. Quotient Fieds of Integral Domains.
IV.22. Rings of Polynomials.
P196 # 1, 4, 5, 12.
P207 # 5, 11, 17, 23, 24, 25, 27, 28.
Thur
Dec 24.
IV.23 Factorization of Polynomials over a Field.
Tues
Dec 29.
IV.23 Factorization of Polynomials over a Field.
P219 # 11, 15, 25, 31, 34, 35, 36, 37.
Thur
Dec 30.
IV.26. Homomorphism and Factor Rings.
P243 # 3, 15, 22, 26, 27, 29, 30, 34.
Tues
Jan 5.
Plan to have Final.
Date
Plan to cover
Homework problems
Tues
Sep. 15
點名及課程介紹.
Thur
Sep. 17
0. Sets and Relations.
P8# 15, 19, 20, 21, 36.
Tues
Sep. 22
I.1. Introductions and Examples.
I.2. Binary Operations.
I.3. Isomorphic Binary Structures.
P19# 35, 37.
P27# 23, 24, 31, 36, 37.
P36# 19, 24, 25, 27, 33.
Thur
Sep. 24
I.4. Groups.
P35# 9, 10, 15, 19, 29, 32, 41.
Tues
Sep. 29
I.5. Subgroups.
P55# 13, 25, 26, 40, 41, 45, 49, 52, 53.
Thur
Oct. 1st
I.6. Cyclic Groups (continued...).
Tues
Oct. 6
I.6. Cyclic Groups.
I.7. Generating Sets.
P66# 3, 18, 20, 27, 40, 47, 48, 52, 53.
P72# 3, 5.
Thur
Oct. 8
II.8. Groups of permutations.
P83# 3, 8, 11, 21, 36, 40, 41, 44, 47.
Tues
Oct. 13
II. 9. Orbits, Cosets, and the alternating group.
P94 #5, 13, 17, 20, 21, 23, 27, 29, 34.
Thur
Oct. 15
II.10. Cosets and The etheorem of Lagrange. (continued...)
Tues
Oct. 20
First midetrm in class. (10%)
Cover Section 0. through Section 7.
Thur
Oct. 22
II.10. Cosets and The etheorem of Lagrange.
P101 #6, 15, 19, 28, 32, 36, 43, 45, 46.
Tues
Oct. 27
II.11. Direct products and finitely generated abelian groups.
Thur
Oct. 29
II.11. Direct products and finitely generated abelian groups.
P111 # 8, 14, 15, 16, 26, 36, 38, 39, 40, 47.
Tues
Nov 3.
III.13. Homomorphisms.
Thur
Nov. 5
Review.
Tues
Nov 10.
2nd Midterm in Class (20%).
Plan to cover chapter I and II. (Sec 12 is not included.)
Thur
Nov. 12
III.13. Homomorphisms.
P133 # 5, 13, 23, 29, 32, 35, 44, 47, 49, 50.
Tues
Nov 17.
III.14. Factor groups (to be continued).
Thur
Nov. 19
III.14. Factor groups.
P142 # 7, 15, 23, 33, 34, 35, 37, 39.
Tues
Nov 24.
III.15. Factor group computation and simple groups.
P152 # 3, 9, 15, 19, 29, 39, 40, 41, 42.
Thur
Nov 26.
III.16. Group action on a set.
P159 # 1, 2, 3, 10, 13, 15.
Tues
Dec 1
III.17. Applications of G-sets to counting.
IV.18. Rings and Fields.
P164 # 1, 3, 7.
Thur
Dec 3.
Review or continue IV.18. Rings and Fields.
Tues
Dec 8
Plan to have 3 midterm on chapter III, section 13~17.
Thur
Dec 10.
IV.18. Rings and Fields.
P175 # 22, 23, 25, 40, 46, 53, 55.
Tues
Dec 15
IV.19. Integral Domains.
P182 # 1, 11, 17, 25, 27, 29.
Thur
Dec 17.
IV. 20 Fermat's and Euler's Theorems
P189 # 5, 9, 15, 17, 23, 27, 28, 29, 30.
Tues
Dec 22
IV.21. Quotient Fieds of Integral Domains.
IV.22. Rings of Polynomials.
P196 # 1, 4, 5, 12.
P207 # 5, 11, 17, 23, 24, 25, 27, 28.
Thur
Dec 24.
IV.23 Factorization of Polynomials over a Field.
Tues
Dec 29.
IV.23 Factorization of Polynomials over a Field.
P219 # 11, 15, 25, 31, 34, 35, 36, 37.
Thur
Dec 30.
IV.26. Homomorphism and Factor Rings.
P243 # 3, 15, 22, 26, 27, 29, 30, 34.
Tues
Jan 5.
Plan to have Final.
|
Tues Sep. 15 |
點名及課程介紹. |
|
Thur Sep. 17 |
0. Sets and Relations. | P8# 15, 19, 20, 21, 36. |
|
Tues Sep. 22 |
I.1. Introductions and Examples. I.2. Binary Operations. I.3. Isomorphic Binary Structures. |
P19# 35, 37. P27# 23, 24, 31, 36, 37. P36# 19, 24, 25, 27, 33. |
Thur Sep. 24 |
I.4. Groups. | P35# 9, 10, 15, 19, 29, 32, 41. |
|
Tues Sep. 29 |
I.5. Subgroups. | P55# 13, 25, 26, 40, 41, 45, 49, 52, 53. |
Thur Oct. 1st |
I.6. Cyclic Groups (continued...). |
|
Tues Oct. 6 |
I.6. Cyclic Groups. I.7. Generating Sets. | P66# 3, 18, 20, 27, 40, 47, 48, 52, 53. P72# 3, 5. |
Thur Oct. 8 |
II.8. Groups of permutations. | P83# 3, 8, 11, 21, 36, 40, 41, 44, 47. |
|
Tues Oct. 13 |
II. 9. Orbits, Cosets, and the alternating group. | P94 #5, 13, 17, 20, 21, 23, 27, 29, 34. |
Thur Oct. 15 |
II.10. Cosets and The etheorem of Lagrange. (continued...) |
|
Tues Oct. 20 |
First midetrm in class. (10%) | Cover Section 0. through Section 7. |
|
Thur Oct. 22 |
II.10. Cosets and The etheorem of Lagrange. | P101 #6, 15, 19, 28, 32, 36, 43, 45, 46. |
|
Tues Oct. 27 |
II.11. Direct products and finitely generated abelian groups. | |
|
Thur Oct. 29 |
II.11. Direct products and finitely generated abelian groups. | P111 # 8, 14, 15, 16, 26, 36, 38, 39, 40, 47. |
|
Tues Nov 3. |
III.13. Homomorphisms. | |
|
Thur Nov. 5 |
Review. | |
|
Tues Nov 10. |
2nd Midterm in Class (20%). | Plan to cover chapter I and II. (Sec 12 is not included.) |
|
Thur Nov. 12 |
III.13. Homomorphisms. | P133 # 5, 13, 23, 29, 32, 35, 44, 47, 49, 50. |
|
Tues Nov 17. |
III.14. Factor groups (to be continued). | |
|
Thur Nov. 19 |
III.14. Factor groups. | P142 # 7, 15, 23, 33, 34, 35, 37, 39. |
|
Tues Nov 24. |
III.15. Factor group computation and simple groups. | P152 # 3, 9, 15, 19, 29, 39, 40, 41, 42. |
|
Thur Nov 26. |
III.16. Group action on a set. | P159 # 1, 2, 3, 10, 13, 15. |
|
Tues Dec 1 |
III.17. Applications of G-sets to counting. IV.18. Rings and Fields. | P164 # 1, 3, 7. |
|
Thur Dec 3. |
Review or continue IV.18. Rings and Fields. | |
|
Tues Dec 8 |
Plan to have 3 midterm on chapter III, section 13~17. | |
|
Thur Dec 10. |
IV.18. Rings and Fields. | P175 # 22, 23, 25, 40, 46, 53, 55. |
|
Tues Dec 15 |
IV.19. Integral Domains. | P182 # 1, 11, 17, 25, 27, 29. |
|
Thur Dec 17. |
IV. 20 Fermat's and Euler's Theorems | P189 # 5, 9, 15, 17, 23, 27, 28, 29, 30. |
|
Tues Dec 22 |
IV.21. Quotient Fieds of Integral Domains. IV.22. Rings of Polynomials. | P196 # 1, 4, 5, 12. P207 # 5, 11, 17, 23, 24, 25, 27, 28. |
|
Thur Dec 24. |
IV.23 Factorization of Polynomials over a Field. | |
|
Tues Dec 29. |
IV.23 Factorization of Polynomials over a Field. | P219 # 11, 15, 25, 31, 34, 35, 36, 37. |
|
Thur Dec 30. |
IV.26. Homomorphism and Factor Rings. | P243 # 3, 15, 22, 26, 27, 29, 30, 34. |
|
Tues Jan 5. |
Plan to have Final. |