#### Suggested Problems

Here is a list of suggested problems from textbook of the lecture.

(Elements of Modern Algebra by Jimmy Gilbert, Linda Gilbert )

Section |
Suggested Problems |

1.4 |
1,2,3,4,5,6 |

1.6 |
1,2,3,4 |

3.1 |
15, 16, 17, 18, 19, 20, 30, 31, 32. |

3.2 |
4, 9, 10, 13, 14, 15. |

3.3 (Subgroups) |
2, 3, 4, 6, 8, 14, 15, 17, 19, 20 |

3.4 (Cyclic Groups) |
6, 7, 8, 9, 14, 15, 16, 18, 21, 22, 25, 26, 28, 31, 32, 36. |

3.5 (Isomorphisms) |
1, 2, 6, 7, 15, 18, 20, 34 |

3.6 (Homomorphisms) |
1, 4, 5, 6, 8, 9, 19, 20 |

4.1 (Finite Permutation Groups) |
1(all), 2(all), 3, 4, 5, 6, 7, 8, 9, 10, 11 |

4.4(Cosets of a Subgroup) |
1, 2, 3, 4, 16, 18, 21 |

4.5(Normal Subgroups) |
1, 2, 4, 6, 8, 9, 10, 16, 17, 18, 19, 20, 22 |

4.6(Quotient Groups) |
1, 2, 3, 5, 6, 7, 8, 10, 11, 21, 22 |

5.1(Definition of a Ring) |
1, 2, 3, 4, 7, 19, 21, 27, 28, 29, 36, 37, 38 |

5.2(Intergral Domains and Fields) |
1, 2, 3, 4, 5, 8(replace the word “assume” with “prove” !) 9, 10, 11, 12, 20. |

6.1(Ideals and Quotient Rings) |
4, 6, 9, 10, 11, 16, 21, 24 |

6.2(Ring Homomorphisms) |
6, 8, 9, 13, 14, 15 |

7.2 (Complex Numbers and Quaternions) |
1 – 12, 19, 20, 21 |

8.1(Polynomials over a Ring) |
3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 17, 18 |

8.2(Divisibility and Greatest Common Divisor) |
1 – 6, 7 – 10, 11 – 14, 15, 16, 17, 1, 23, 25, 29, 34 |

8.3(Factorization in F[x]) |
1(all), 2(all), 3, 4(all), 9, 12(a, b), 13 |

8.4(Zeros of a Polynomial) |
1(all), 2(all), 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21 |