IMSC1038 - Algebra I - 2025/26

Course Name: 
Algebra I
Teacher: 
Prof. Ziquan YANG
Course Year: 
2025/26
Term: 
1

Announcement

  • Assignments will be due each Monday at midnight. Please submit a Latexed PDF via blackboard. You have free access to Latex at overleaf.com.

General Information

Lecturer

  • Yang, Ziquan
    • Office: IMS 410
    • Tel: 33717
    • Email:

Teaching Assistant

  • Ng, Ming Ho
    • Office: LSB 223
    • Tel: 37971
    • Email:
    • Office Hours: Tu 14:00 - 16:00

Time and Venue

  • Lecture: Mon 9:30 - 11:15, Thu 14:30 - 15:15. Both at BMS 2.

Course Description

Groups and subgroups. Cyclic groups, permutation groups and dihedral groups. Lagrange’s Theorem. Group homomorphisms and group isomorphisms. Normal subgroups and quotient groups. Product groups. Correspondence Theorem. Isomorphism Theorems for groups. Group action. Cayley’s Theorem. Centralizer and normalizer. Class equation for finite groups. p-groups, Sylow Theorems. (Refer to Artin, Chapters 2, 7, supplemented by Chapter 6.)

Rings, integral domains and fields. Polynomial rings. Fields of fractions. Ring homomorphisms. Subrings, ideals and quotient rings. Prime and maximal ideals. Factorization in integral domains. Principal ideal domains. Unique factorization domains. Quadratic number fields Algebraic and transcendental elements. Field extension, and degree of a field extension. Irreducible polynomials. Adjoining roots. Finite fields. Primitive elements. Function fields. (Refer to Artin, Chapters 11, 12, 15 supplemented by Chapter 13.)


Textbooks

  • Algebra (2nd Edition) by Michael Artin.

References

  • Abstract Algebra by Dummit, David S., Foote, Richard M.

Lecture Notes


Assignments

  • Assignment 1 (due 22/09): Textbook Ch 2 Exercise 5.6, 6.6, 8.10, 11.9, 12.2
  • Assignment 2 (due 29/09): Textbook Ch 7 Exercises 2.17, 3.3, 4.2, 5.12, 7.10
  • Assignment 3 (due Oct. 6th) Textbook Ch 7 Exercises 7.8, 8.2, 8.4, 8.6, 10.6
  • Assignment 4 (due Oct. 13th) Textbook Ch 11 Exercise: 1.1, 2.2, 3.3, 3.9, 5.6
  • Assignment 5 (due Oct. 27th) Textbook Ch 12 Exercise 3.2, 3.5(b), 3.6, 5.3, 5.6
  • Assignment 6 (due Nov. 3rd) Textbook Ch 15 Exercises 2.1, 2.3, 3.1, 3.2, 3.9
  • Assignment 7 (due Nov. 10th) Textbook Ch 15 Exercises 4.1, 5.3, 6.1, 7.4, 7.8
  • Assignment 8 (due Nov. 17th) Textbook Ch 15 Exercises 3.5, 6.3, 7.9, 7.10, 7.12

Quizzes and Exams

  • Final Exam Time and Venue: 09 Dec 2025 Tuesday 09:30 - 11:30 Sir Run Run Shaw Hall (Stage)

Assessment Policy

Last updated: November 10, 2025 20:56:03