Enquiry for Science Major/Minor/Programme Requirements
MATH4404 Functional analysis (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Prof D Li, Mathematics < mathdl@hku.hk >
Teachers Involved (Prof D Li,Mathematics)
Course Objectives This course introduces students to the basic knowledge of linear functional analysis, an important branch of modern analysis.
Course Contents & Topics - Normed spaces, Banach spaces: Finite dimensional normed spaces and subspaces. Compactness and finite dimension. Bounded linear operators. Normed spaces of operators, dual space.
- Inner product spaces, Hilbert spaces: Orthogonal complements, direct sums. Orthonormal sets and sequences, series related to orthonormal sets and sequences. Total orthonormal sets and sequences. Special polynomials. Riesz's representation theorem. Adjoint operator, self-adjoint, normal and unitary operators.
- Fundamental theorems for normed and Banach spaces: Hahn-Banach theorem. Reflexive spaces. Category theorem, uniform boundedness principle. Open mapping theorem. Closed graph theorem.
- Spectral theory of linear operators.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 compare and contrast (i) finite and infinite dimensional linear spaces, (ii) complete and incomplete linear space, and (iii) normed and inner product spaces; in particular, recognize the importance of completeness and discuss how vectors are represented in these spaces
CLO 2 understand the notions of Banach spaces and Hilbert Spaces. State and apply fundamental theorems in these spaces
CLO 3 discuss the dual spaces of some standard Banach spaces
CLO 4 discuss the boundedness of linear operators and the spectra of special linear operators
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in MATH2101, MATH2102, MATH2211, MATH2241 and MATH3401
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Disciplinary Elective )
2025 Major in Mathematics (Intensive) ( Core/Compulsory )
2025 Minor in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics (Intensive) ( Core/Compulsory )
2024 Minor in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics (Intensive) ( Core/Compulsory )
2023 Minor in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics (Intensive) ( Core/Compulsory )
2022 Minor in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics (Intensive) ( Core/Compulsory )
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        1st sem    Examination Dec     
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 20.0 1,2,3,4
Examination 50.0 1,2,3,4
Test 30.0 1,2,3,4
Required/recommended reading
and online materials		 Erwin Kreyszig: Introductory Functional Analysis with Applications (John-Wiley and Sons, 1978)
Course Website http://moodle.hku.hk/
Additional Course Information


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