Enquiry for Science Major/Minor/Programme Requirements
MATH4302 Algebra II (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Prof J H Lu, Mathematics < jhlu@maths.hku.hk >
Teachers Involved (Prof J H Lu,Mathematics)
Course Objectives This course is an extension of MATH3301 and continues with more advanced topics in algebra. The course may be followed by MATH7501 and MATH7502.
Course Contents & Topics - Principal ideal domains and unique factorization domains;
- Structure theorem for finitely generated modules of principal ideal domains with applications to finitely generated abelian groups and canonical forms of matrices;
- Field extensions; introduction to Galois theory.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 understand basic examples of principal ideal domains and why principal ideal domains are unique factorization domains
CLO 2 understand the classification of finitely generated modules of principal ideal domains and certain canonical forms of matrices
CLO 3 understand and compute splitting fields of irreducible polynomials
CLO 4 compute examples of Galois groups
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in MATH2102 and MATH3301
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Disciplinary Elective )
2025 Major in Mathematics (Intensive) ( Disciplinary Elective )
2025 Minor in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics (Intensive) ( Disciplinary Elective )
2024 Minor in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics (Intensive) ( Disciplinary Elective )
2023 Minor in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics (Intensive) ( Disciplinary Elective )
2022 Minor in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics (Intensive) ( Disciplinary Elective )
2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping 2025 Major in Mathematics < PLO 1,2,3 >
2025 Major in Mathematics (Intensive) < PLO 1,2,3 >
2024 Major in Mathematics < PLO 1,2,3 >
2024 Major in Mathematics (Intensive) < PLO 1,2,3 >
2023 Major in Mathematics < PLO 1,2,3 >
2023 Major in Mathematics (Intensive) < PLO 1,2,3 >
2022 Major in Mathematics < PLO 1,2,3 >
2022 Major in Mathematics (Intensive) < PLO 1,2,3 >
2021 Major in Mathematics < PLO 1,2,3 >
2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026 Y        2nd sem    Examination May     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems.
B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors.
C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors.
D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors.
Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course N
Course Type Lecture-based course
Course Teaching
& Learning Activities
Activities Details No. of Hours
Lectures 36.0
Tutorials 12.0
Reading / Self study 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments 10.0 1,2,3,4
Examination 50.0 1,2,3,4
Test 40.0 1,2,3,4
Required/recommended reading
and online materials		 F.M. Goodman: Algebra Abstract and Concrete (Online book) url: http://homepage.math.uiowa.edu/~goodman/algebrabook.dir/download.htm
T.W. Hungerford: Abstract Algebra: An Introduction (Brooks/Cole, 1997, 2nd ed.)
David S. Dummit, Richard M. Foote: Abstract Algebra (Wiley, 2003, 3rd ed.)
Course Website http://moodle.hku.hk/
Additional Course Information


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