MATH
Mathematics

Undergraduate courses marked with [BLD] or [SPO] may be offered in the mode of blended learning or self-paced online delivery respectively, subject to different offerings. Students should check the delivery mode of the class section before registration.

• MATH 1003
Calculus and Linear Algebra
3 Credit(s)
Exclusion(s)
Level 5* or above in HKDSE Mathematics Extended Module M1 or M2; grade B or above in HKCEE Additional Mathematics, a passing grade in AS Mathematics and Statistics, AL/AS Applied Mathematics, or in AL Pure Mathematics; MATH 1012; MATH 1013; MATH 1014; MATH 1018 (prior to 2013-14); MATH 1020; MATH 1023; MATH 1024
Description
This course teaches basic application techniques in single-variable calculus and linear algebra. Key topics include: systems of linear equations and matrices, functions and graphing, derivatives and optimization, integration and applications.
• MATH 1012
Calculus IA
4 Credit(s)
Co-list with
MATH 1013
Exclusion(s)
Level 3 or above in HKDSE Mathematics Extended Module M1 or M2; AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1013, MATH 1014, MATH 1020, MATH 1023, MATH 1024
Description
This is an introductory course in one-variable calculus, the first in the Calculus I and II sequence, designed for students that have not taken HKDSE Mathematics Extended Module M1 or M2. Topics include functions and their limits, continuity, derivatives and rules of differentiation, applications of derivatives, and basic integral calculus.
• MATH 1013
Calculus IB
3 Credit(s)
Co-list with
MATH 1012
Prerequisite(s)
Level 3 or above in HKDSE Mathematics Extended Module M1/M2
Exclusion(s)
AL Pure Mathematics; AL Applied Mathematics; MATH 1012, MATH 1014, MATH 1020, MATH 1023, MATH 1024
Description
This is an introductory course in one-variable calculus, the first in the Calculus I and II sequence, designed for students that have taken HKDSE Mathematics Extended Module M1/M2. Topics include functions and their limits, continuity, derivatives and rules of differentiation, applications of derivatives, and basic integral calculus.
• MATH 1014
Calculus II
3 Credit(s)
Prerequisite(s)
MATH 1012 OR MATH 1013 OR MATH 1023 OR grade A- or above in MATH 1003
Exclusion(s)
AL Pure Mathematics; AL Applied Mathematics; MATH 1020, MATH 1024
Description
This is an introductory course in one-variable calculus, the second in the MATH 1013 – MATH 1014 sequence. Topics include applications of definite integral, improper integrals, vectors, curves and parametric equations, modeling with differential equations, solving simple differential equations, infinite sequences and series, power series and Taylor series.
• MATH 1020
Accelerated Calculus
4 Credit(s)
Prerequisite(s)
Level 5* or 5** in HKDSE Mathematics Extended Module M2
Exclusion(s)
A passing grade in AL Applied Mathematics / AL Pure Mathematics; MATH 1013, MATH 1014, MATH 1023, MATH 1024
Description
A concise introduction to one-variable calculus. Topics include functions, limits, derivatives, definite and indefinite integrals and their applications, infinite sequences and series, Taylor series, first order differential equations.
• MATH 1023
Honors Calculus I
3 Credit(s)
Prerequisite(s)
Level 5 or above in HKDSE Mathematics Extended Module M2
Exclusion(s)
AL Pure Mathematics; AL Applied Mathematics; MATH 1012, MATH 1013, MATH 1014, MATH 1020
Description
This is the first in the sequence MATH 1023 – MATH 1024 of honors courses in one-variable calculus, with particular emphasis on rigorous mathematical reasoning. Topics include inequalities, functions and their graphs, vectors, limit and continuity, extreme value theorem, intermediate value theorem derivatives and differentiation rules, mean value theorem, l'Hôpital's rule, Taylor expansion, and applications of derivatives.
• MATH 1024
Honors Calculus II
3 Credit(s)
Prerequisite(s)
MATH 1012 OR MATH 1013 OR MATH 1023
Exclusion(s)
AL Pure Mathematics; AL Applied Mathematics; MATH 1014, MATH 1020
Description
This is the second in the sequence MATH 1023 - MATH 1024 of honors courses in one-variable calculus, with particular emphasis on rigorous mathematical reasoning. Topics include integral calculus, techniques of integration, improper integrals, applications of integrals, infinite series. Some rigorous theoretical results on integration and infinite series will be discussed.
• MATH 1701
Introductory Topics in Mathematical Sciences
1-4 Credit(s)
Description
This is a general science course that introduces students to selected disciplines or topics of high popular interest. The crucial roles that mathematics play are emphasized. Materials are chosen to enrich and enhance students' appreciation of science and mathematics.
• MATH 2001
Foundation of Mathematics
2 Credit(s)
Prerequisite(s)
Level 5 or above in HKDSE Mathematics Extended Module M2 OR MATH 1012 OR MATH 1013 OR MATH 1020 OR MATH 1023
Description
This course covers a number of foundational concepts and rigorous reasoning in mathematics which are essential for intermediate- and upper levels mathematics courses especially in the field of pure mathematics. The main purpose of the course is to enhance students’ conceptual and logical understanding of mathematics, and strengthen students’ ability on writing mathematical proofs. Topics include mathematical induction, set notations and logic, complex numbers, inequalities, construction of real numbers, elementary number theory, etc.
• MATH 2011
Introduction to Multivariable Calculus
3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014; OR MATH 1020; OR MATH 1024
Exclusion(s)
MATH 2023
Description
Differentiation in several variables, with applications in approximation, maximum and minimum and geometry. Integration in several variables, vector analysis.
• MATH 2023
Multivariable Calculus
4 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2011
Description
Sequences, series, gradients, chain rule. Extrema, Lagrange multipliers, line integrals, multiple integrals. Green's theorem, Stoke's theorem, divergence theorem, change of variables.
• MATH 2033
Mathematical Analysis
4 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2043
Description
Sets and functions, real numbers, limits of sequences and series, limits of functions, continuous functions, differentiation, Riemann integration, additional topics.
• MATH 2043
Honors Mathematical Analysis
4 Credit(s)
Prerequisite(s)
Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1020/MATH 1024
Exclusion(s)
MATH 2033
Description
The MATH 2043 and 3043 is a rigorous sequence in analysis on the line and higher dimensional Euclidean spaces. Limit, continuity, least upper bound axiom, open and closed sets, compactness, connectedness, differentiation, uniform convergence, and generalization to higher dimensions. Enrollment in the course requires approval of the course instructor.
• MATH 2111
Matrix Algebra and Applications
3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2121, MATH 2131, MATH 2350
Description
Systems of linear equations; vector spaces; linear transformations; matrix representation of linear transformations; linear operators, eigenvalues and eigenvectors; similarity invariants and canonical forms.
• MATH 2121
Linear Algebra
4 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2111, MATH 2131, MATH 2350
Description
Vector space, matrices and system of linear equations, linear mappings and matrix forms, inner product, orthogonality, eigenvalues and eigenvectors, symmetric matrix.
• MATH 2131
Honors in Linear and Abstract Algebra I
4 Credit(s)
Prerequisite(s)
Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1020/MATH 1024
Exclusion(s)
MATH 2111, MATH 2121, MATH 2350
Description
The MATH 2131 and 3131 is a sequence of rigorous introduction to linear algebra and abstract algebra. Vector spaces over the fields of real numbers and complex numbers, linear transformations, geometry, groups, bases, abstract fields, rings, change of bases, spectral theorems.
• MATH 2343
Discrete Structures
4 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; or MATH 1014; or MATH 1020; or MATH 1024
Exclusion(s)
COMP 2711, COMP 2711H
Description
Logic: propositions, axiomatization of propositional calculus, deduction theorem, completeness and soundness. Combinatorics: permutations and combinations, generating functions. Set theory: basic operations on sets, relations, countable and uncountable sets. Third year and fourth year students require instructor's approval to take the course.
• MATH 2350
Applied Linear Algebra and Differential Equations
3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2111, MATH 2121, MATH 2131, MATH 2351, MATH 2352, PHYS 2124
Description
This course provides a concise introduction to linear algebra and differential equations, with exposure to the use of numerical computing software like MATLAB. Topics include systems of linear equations, matrix algebra and determinants, language of vector spaces and inner product spaces, eigenvalue and eigenvector, first order ODEs, linear second order ODEs and oscillations, and homogeneous system of first order ODEs with constant coefficients.
• MATH 2351
Introduction to Differential Equations
3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
MATH 2350, MATH 2352, PHYS 2124
Description
First order equations and applications, second order equations, Laplace transform method, series solutions, system of linear equations, nonlinear equations and linear stability analysis, introduction to partial differentiation and partial differential equations, separation of variables, and Fourier series.
• MATH 2352
Differential Equations
4 Credit(s)
Prerequisite(s)
MATH 2111 OR MATH 2121 OR MATH 2131
Exclusion(s)
MATH 2350, MATH 2351, PHYS 2124
Description
First and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory.
• MATH 2411
Applied Statistics
4 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024
Exclusion(s)
IEDA 2510 (prior to 2018-19), IEDA 2540, ISOM 2500, LIFS 3150
Description
A systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing.
• MATH 2421
Probability
4 Credit(s)
Prerequisite(s)
MATH 1014 OR MATH 1020 OR MATH 1024
Corequisite(s)
MATH 2011 OR MATH 2023
Exclusion(s)
IEDA 2510 (prior to 2018-19), IEDA 2520, MATH 2431, ELEC 2600, ELEC 2600H, ISOM 3540
Description
Sample spaces, conditional probability, random variables, independence, discrete and continuous distributions, expectation, correlation, moment generating function, distributions of function of random variables, law of large numbers and limit theorems.
• MATH 2431
Honors Probability
4 Credit(s)
Prerequisite(s)
(Grade A- or above in MATH 1014) OR MATH 1020 OR MATH 1024
Corequisite(s)
MATH 2011 OR MATH 2023
Exclusion(s)
ELEC 2600, ELEC 2600H, ISOM 3540, MATH 2421
Description
This is an honors undergraduate course in probability theory. Topics include probability spaces and random variables, distributions (absolutely continuous and singular distributions) and probability densities, moment inequalities, moment generating functions, conditional expectations, independence, conditional distributions, convergence concepts (weak, strong and in distribution), law of large numbers (weak and strong) and central limit theorem. Some rigorous theoretical results in probability will be discussed.
• MATH 2511
Fundamentals of Actuarial Mathematics
3 Credit(s)
Prerequisite(s)
MATH 1003 OR MATH 1014 OR MATH 1020 OR MATH 1024
Description
This course covers the fundamental concepts of actuarial financial mathematics and how these concepts are applied in calculating present and accumulated values for various streams of cash flows. The topics covered include interest rates, present value, annuities valuation, loan repayment, bond and portfolio yield, bond valuation, rate of return, yield curve, term structure of interest rates, duration and convexity of general cash flows and portfolios, immunization, stock valuation, capital budgeting, dynamic cash flow processes, and asset and liability management.
• MATH 2731
Mathematical Problem Solving
3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics/AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024
Description
Discussions on problem solving techniques. Basics materials in combinatorics, number theory, geometry and mathematical games.
• MATH 2741
Geometric Constructions
3 Credit(s)
Prerequisite(s)
MATH 1014 OR MATH 1020 OR MATH 1024 OR AL Applied Mathematics / AL Pure Mathematics
Mode of Delivery
[BLD] Blended learning
Description
This course is intended for students with some mathematical maturity. This course teaches geometric constructions using tools like straightedge and compass. Moreover, geometric constructions will be associated with algebraic fields of numbers and hence related to various famous constructability problems. Topics covered by the course include Euclidean constructions, compass-only constructions, straightedge-only constructions, constructability, three classical problems and regular polygons.
• MATH 3033
Real Analysis
4 Credit(s)
Prerequisite(s)
(MATH 2011 / MATH 2023) AND (MATH 2033 / MATH 2043) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350)
Exclusion(s)
MATH 3043
Description
Functions of several variables, implicit and inverse function theorem, uniform convergence measure and integral on the real line.
• MATH 3043
Honors Real Analysis
4 Credit(s)
Prerequisite(s)
Grade A- or above in MATH 2043
Exclusion(s)
MATH 3033
Description
The MATH 2043 and 3043 is a rigorous sequence in analysis on the line and higher dimensional Euclidean spaces. Differentiation and integration in higher dimensions, implicit function and inverse function theorem, Stokes theorem, and Lebesgue measure.
• MATH 3121
Abstract Algebra
3 Credit(s)
Prerequisite(s)
MATH 2111/MATH 2121/MATH 2131/MATH 2350
Exclusion(s)
MATH 3131
Description
Polynomials; Jordan canonical form, minimal polynomials, rational canonical form; equivalence relation; group, coset, group action; introduction to rings and fields.
• MATH 3131
Honors in Linear and Abstract Algebra II
4 Credit(s)
Prerequisite(s)
Grade B- or above in MATH 2131
Description
The MATH 2131 and 3131 is a sequence of highly rigorous introduction to linear algebra and abstract algebra. Groups, rings, homomorphisms, quotients, group actions, polynomial rings, Chinese remainder theorem, field extensions.
• MATH 3312
Numerical Analysis
3 Credit(s)
Prerequisite(s)
(COMP 1021 / COMP 1022P / COMP 1022Q (prior to 2020-21)) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (MATH 2031 / MATH 2033 / MATH 2043)
Exclusion(s)
MECH 4740, PHYS 3142
Description
Basic numerical analysis, including stability of computation, linear systems, eigenvalues and eigenvectors, nonlinear equations, interpolation and approximation, numerical integration and solution of ordinary differential equations, optimization.
• MATH 3322
Matrix Computation
3 Credit(s)
Prerequisite(s)
MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350
Description
This course will introduce some basic matrix analysis theory and some popular matrix computation algorithms, and illustrate how they are actually used in data science. Specific topics include advanced linear algebra such as orthogonal projections and vector and matrix norms; the theories and computations of matrix factorizations such as QR decomposition, Singular Value Decomposition (SVD), and Schur decomposition; and applications to data analysis problems such as principle component analysis via SVD and collaborative filtering via matrix completion.
• MATH 3332
Data Analytic Tools
3 Credit(s)
Prerequisite(s)
(MATH 2011 OR MATH 2023) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)
Description
This course will introduce to the students some mathematical analysis tools that are useful for data analysis. The topics include Fourier analysis, wavelet analysis, function expansions, and basic functional analysis (Banach space, Hilbert spaces, linear operators, contract mapping, etc), and basic convex analysis (subgradient, convex conjugate).
• MATH 3343
Combinatorial Analysis
3 Credit(s)
Prerequisite(s)
MATH 2121/MATH 2111/MATH 2350/MATH 2131; or MATH 2343/COMP 2711
Description
An introduction to combinatorics: What is combinatorics? Permutations and combinations, binomial theorem, generating permutations and combinations, pigeonhole principle, Ramsey theory, inclusion-exclusion principle, rook polynomials, linear recurrence relations, nonhomogeneous linear recurrence relations of the first and second order, generating functions, Catalan numbers, Stirling numbers, partition numbers, matchings and stable matchings, systems of distinctive representatives, block designs, Steiner triple systems, Latin squares, Burnside's lemma, Polya counting formula.
• MATH 3423
Statistical Inference
3 Credit(s)
Prerequisite(s)
MATH 2421 OR MATH 2431
Description
Sampling theory, order statistics, limiting distributions, point estimation, confidence intervals, hypothesis testing, non-parametric methods.
• MATH 3424
Regression Analysis
3 Credit(s)
Prerequisite(s)
MATH 3423
Exclusion(s)
ISOM 5520
Description
Estimation and hypothesis testing in linear regression, residual analysis, multicollinearity, indicator variables, variable selection, nonlinear regression.
• MATH 3425
Stochastic Modeling
3 Credit(s)
Prerequisite(s)
MATH 2421 OR MATH 2431
Description
Discrete time Markov chains and the Poisson processes. Additional topics include birth and death process, elementary renewal process and continuous-time Markov chains.
• MATH 3426
Sampling
3 Credit(s)
Prerequisite(s)
MATH 2411
Description
Basic and standard sampling design and estimation methods. Particular attention given to variance estimation in sampling procedures. Topics include: simple random sampling, unequal probability sampling, stratified sampling, ratio and subpopulation and multistage designs.
• MATH 3427
Bayesian Statistics
3 Credit(s)
Prerequisite(s)
MATH 2421 OR MATH 2431 OR ELEC 2600 OR ELEC 2600H OR ISOM 3540
Description
This course provides a basic training of Bayesian statistics. Some ideas and principles of Bayesian including prior and posterior distributions, conjugate priors, Bayesian estimates, empirical Bayes, Bayesian hypothesis testing, Bayesian model selection and Bayesian networking are covered. Other Bayesian tools such as Bayesian decision theory, Bayesian data analysis, and Bayesian computational skills will also be discussed. An open-source, freely available software R will be used to implement these computational and data analytics skills. Hands-on experience and case studies such as pattern recognition and spam filtering will also be provided to students. Completion of this course will give students access to a wide range of Bayesian analytical tools, customizable to real data.
• MATH 3900
Communicating Mathematics to the Public
1 Credit(s)
Description
This project-based course allows students to develop expertise in mathematics outreach and knowledge transfer, as well as understand industrially and academically relevant skills. The course exposes students to promoting mathematics to the public. Activities may include lectures, seminars, workshops, and sharing sessions. Outputs will be diverse and may consist of exhibits, workshops, or presentations to be delivered in schools, online activities, and digital apps to be posted on websites or social media platforms. For MATH students only.
• MATH 4023
Complex Analysis
3 Credit(s)
Prerequisite(s)
(MATH 2011 OR MATH 2023 OR MATH 3043) AND (MATH 2033 OR MATH 2043)
Description
Complex differentiability; Cauchy-Riemann equations; contour integrals, Cauchy theory and consequences; power series representation; isolated singularities and Laurent series; residue theorem; conformal mappings.
• MATH 4033
Calculus on Manifolds
3 Credit(s)
Prerequisite(s)
Grade A- or above in MATH 2023 AND B- or above in MATH 2131
Description
Introduction to manifolds, metric spaces, multi-linear Algebra, differential forms, Stokes theorem on manifolds, cohomology.
• MATH 4051
Theory of Ordinary Differential Equations
3 Credit(s)
Prerequisite(s)
(MATH 2350 OR MATH 2351 OR MATH 2352) AND (MATH 3033 OR MATH 3043)
Description
Existence and uniqueness theorems of ordinary differential equations, theory of linear systems, stability theory, study of singularities, boundary value problems.
• MATH 4052
Partial Differential Equations
3 Credit(s)
Prerequisite(s)
MATH 2011/MATH 2023/MATH 3043 and MATH 2111/MATH 2121/MATH 2131/MATH 2350 and MATH 2350/MATH 2351/MATH 2352
Description
Derivations of the Laplace equations, the wave equations and diffusion equation; Methods to solve equations: separation of variables, Fourier series and integrals and characteristics; maximum principles, Green's functions.
• MATH 4061
Topics in Modern Analysis
2 Credit(s)
Prerequisite(s)
MATH 3043 or MATH 3033
Description
Examples and properties of metric spaces. Contractive mapping theorem, Baire category theorem, Stone-Weierstrass theorem, Arzela-Ascoli theorem. Properties of normed spaces and Hibert spaces. Riesz theorem. Completeness of Lp functions, continuous functions and functions of bounded variations. Best approximation theorem on Hilbert space.
• MATH 4063
Functional Analysis
2 Credit(s)
Prerequisite(s)
MATH 4061
Description
Topological vector spaces. Hahn-Banach theorem, open mapping theorem, closed graph theorem, uniform boundedness theorem, separation theorem, Krein-Milman theorem. Weak topologies and reflexivity. Adjoints and duality. Compact and Fredholm operators with index. Normal operators. Spectral theorem for compact normal operators.
• MATH 4141
Number Theory and Applications
3 Credit(s)
Prerequisite(s)
MATH 2131
Corequisite(s)
(for students without prerequisites) MATH 3121
Description
Prime numbers, unique factorization, modular arithmetic, quadratic number fields, finite fields, p-adic numbers, coding theory, computational complexity.
• MATH 4151
Introduction to Lie Groups
3 Credit(s)
Prerequisite(s)
(MATH 2011 OR MATH 2023 OR MATH 3043) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)
Description
General linear groups, orthogonal groups, unitary groups, symplectic groups, exponential maps, maximal tori, Clifford algebra, spin groups.
• MATH 4221
Euclidean and Non-Euclidean Geometries
3 Credit(s)
Prerequisite(s)
MATH 2033 OR MATH 2043 OR MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350
Description
Axioms and models, Euclidean geometry, Hilbert axioms, neutral (absolute) geometry, hyperbolic geometry, Poincare model, independence of parallel postulate.
• MATH 4223
Differential Geometry
3 Credit(s)
Prerequisite(s)
MATH 2011/MATH 2023/MATH 3043 and MATH 2121/MATH 2131
Description
Curve theory; curvature and torsion, Frenet-Serret frame; surface theory: Weingarten map, first and second fundamental forms, curvatures, Gaussian map, ruled surface, minimal surface; instrinsic geometry: Theorema Egregium, Coddazi-Mainardi equations, parallel transport, geodesics, exponential map, Gauss-Bonnet theorem.
• MATH 4225
Topology
3 Credit(s)
Prerequisite(s)
MATH 2033/MATH 2043
Description
Metric, topology, continuous map, Hausdorff, connected, compact, graph, Euler number, CW-complex, classification of surfaces.
• MATH 4321
Game Theory
3 Credit(s)
Prerequisite(s)
(MATH 2011 OR MATH 2023 OR MATH 3043) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)
Exclusion(s)
ECON 4124
Description
Zero-sum games; minimax theorem; games in extensive form; strategic equilibrium; bi-matrix games; repeated Prisonner's Dilemma; evolutionary stable strategies; games in coalition form; core; Shapley Value; Power Index; two-side matching games.
• MATH 4326
Introduction to Fluid Dynamics
3 Credit(s)
Alternate code(s)
OCES 4326
Prerequisite(s)
MATH 4052
Exclusion(s)
CIVL 2510, MECH 2210
Description
Lagrangian and Eulerian methods for the flow description; derivation of the Euler and Navier-Stokes equations; sound wave and Mach number; 2D irrotational flow; elements of aerofoil theory; water wave dispersion relation; shallow water waves; ship wave pattern; dynamics of real fluid, stokes flow and boundary layer theory.
• MATH 4333
Mathematical Biology
3 Credit(s)
Prerequisite(s)
MATH 2121/MATH 2111/MATH 2131 and MATH 2351/MATH 2352; or MATH 2350
Description
Population, ecology, infectious disease, genetic, and biochemistry models. Additional topics chosen by instructor.
• MATH 4335
Introduction to Optimization
3 Credit(s)
Prerequisite(s)
(MATH 2011 OR MATH 2023) AND (MATH 2111 OR MATH 2121 OR MATH 2131)
Description
This course introduces fundamental theory and techniques of optimization. Topics include linear programming, unconstrained optimization, and constrained optimization. Numerical implementations of optimization methods are also discussed.
• MATH 4336
Introduction to Mathematics of Image Processing
3 Credit(s)
Prerequisite(s)
MATH 2011/MATH 2023 and [MATH 2350 or (MATH 2111/MATH 2121/MATH 2131 and MATH 2351/MATH 2352)]
Exclusion(s)
COMP 4421, ELEC 4130
Description
This course introduces digital image processing principles and concepts, tools, and techniques with emphasis on their mathematical foundations. Key topics include image representation, image geometry, image transforms, image enhancement, restoration and segmentation, descriptors, and morphology. The course also discusses the implementation of these algorithms using image processing software.
• MATH 4343
Introduction to Graph Theory
4 Credit(s)
Previous Course Code(s)
MATH 4821B
Prerequisite(s)
MATH 2343
Description
This course is to equip students with basic knowledge of graph theory that will be needed in mathematics, computer science, and engineering (in particular network analysis). Topics include but not restricted to: Euler tours and Chinese postman problem, Hamilton cycles and traveling salesman problem; minimum spanning trees and searching algorithms; block decomposition, ear decomposition, connectivity and edge connectivity; network flows, Ford‐Fulkerson (Max‐Flow Min‐Cut) theorem, augmenting‐path algorithm; planar graphs, Euler formula, duality, classification of Platonic solids, Kuratowski (planarity) theorem; maximum matchings and perfect matchings, matchings in bipartite graphs, matchings in general graphs, Tutte‐Berge theorem, Petersen theorem; probabilistic method, page rank problem, random walks; cycle spaces and bond spaces, graph Laplace operator, matrix‐tree theorem; Four‐Color problem, colorings and flows, chromatic number and flow number, chromatic polynomials, flow polynomials, Tutte polynomials; matroids.
• MATH 4351
Numerical Solutions of Partial Differential Equations
3 Credit(s)
Prerequisite(s)
(MATH 2350 OR MATH 2351 OR MATH 2352) AND MATH 3312 AND MATH 4052
Description
Introduction to finite difference and finite element methods for the solution of elliptic, parabolic and hyperbolic partial differential equations; including the use of computer software for the solution of differential equations.
• MATH 4423
Nonparametric Statistics
3 Credit(s)
Prerequisite(s)
MATH 2411
Description
The sign test; Wilcoxon signed rank test; Wilcoxon rank-sum test; Kruskal-Wallis test; rank correlation; order statistics; robust estimates; Kolmogorov-Smirnov test; nonparametric curve estimation.
• MATH 4424
Multivariate Analysis
3 Credit(s)
Prerequisite(s)
MATH 3423 and MATH 3424
Exclusion(s)
ISOM 5530
Description
Inferences of means and covariance matrices, canonical correlation, discriminant analysis, multivariate ANOVA, principal components analysis, factor analysis.
• MATH 4425
Introductory Time Series
3 Credit(s)
Prerequisite(s)
MATH 3423 and MATH 3424
Description
Stationarity, (partial) auto-correlation function, ARIMA modeling, order selection, diagnostic, forecasting, spectral analysis.
• MATH 4426
Survival Analysis
3 Credit(s)
Prerequisite(s)
MATH 3423
Description
The topics discussed in this course include basic quantities like hazard rate function, survival function, censoring and/or truncation; parametric estimation of the survival distribution by maximum likelihood estimation method; nonparametric estimation of the survival functions from possibly censored samples; parametric regression models; Cox's semi-parametric proportional hazards regression model; and multivariate survival analysis.
• MATH 4427
Loss Models and their Applications
3 Credit(s)
Prerequisite(s)
(ELEC 2600 OR ISOM 3540 OR MATH 2421 OR MATH 2431) AND (MATH 2011 OR MATH 2023) AND MATH 2511
Description
This course covers the construction of casualty loss models and their applications to insurance. Topics include severity models, frequency models, aggregate loss models, coverage modifications, effect of inflation on losses, risk measures, parameter and variance estimation in loss models, and construction of empirical models.
• MATH 4428
Bayesian Analysis and Credibility Theory
3 Credit(s)
Prerequisite(s)
MATH 3423 OR MATH 4427
Description
This course provides a rigorous mathematical treatment of Bayesian analysis and its applications to credibility theory. The first part covers basic concepts and principles of Bayesian statistics such as prior and posterior distributions, conjugate priors, Bayesian estimates, credibility intervals, and Bayesian hypothesis testing. The second part introduces credibility theory and its development using a Bayesian analysis. Topics include limited fluctuation credibility theory, greatest accuracy credibility theory, credibility premium, Buhlmann models, Buhlmann-Straub models, empirical Bayesian methods in nonparametric and semiparametric cases, and the insurance problem. This course, combined with MATH 4427, prepares students to take the Exam C (Construction and Evaluation of Actuarial Models) of the Society of Actuaries.
• MATH 4432
Statistical Machine Learning
3 Credit(s)
Prerequisite(s)
(COMP 1021 OR COMP 1022P OR COMP 1022Q (prior to 2020-21)) AND (IEDA 2510 (prior to 2018-19) OR (IEDA 2520 AND IEDA 2540) OR ISOM 2500 OR LIFS 3150 OR MATH 2411 OR MATH 2421 OR MATH 2431)
Description
This course provides students with an extensive exposure to the elements of statistical machine learning in supervised and unsupervised learning with real world datasets. Topics include regression, classification, resampling methods, model assessment, model selection, regularization, nonparametric models, boosting, ensemble methods, random forests, kernel methods, support vector machines, neural networks, and some standard techniques in unsupervised learning such as clustering and dimensionally reduction. Lab sessions on using R or Python in data analysis with machine learning methods will be conducted in class. Scientific reports and/or poster presentations are required for project evaluations.
• MATH 4511
Quantitative Methods for Fixed Income Derivatives
3 Credit(s)
Prerequisite(s)
(MATH 2011 / MATH 2023) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (IEDA 2510 (prior to 2018-19) / IEDA 2520 AND IEDA 2540 / ISOM 2500 / LIFS 3150 / MATH 2411) AND (FINA 2203 / FINA 2303)
Description
Bond, bond markets and interest-rate derivatives markets. Yields, forward rate and swap rates. Yield-based risk management and regression-based hedging. Mortgage mathematics. Binomial models for equity and fixed-income derivatives. Arbitrage pricing and risk-neutral valuation principle. Eurodollar futures. Lognormal models and Black formula for caps and swaptions.
• MATH 4512
Fundamentals of Mathematical Finance
3 Credit(s)
Prerequisite(s)
(MATH 2011 / MATH 2023) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (IEDA 2540 / ISOM 2500 / LIFS 3150 / MATH 2411) AND (MATH 2511 / FINA 2203 / FINA 2303)
Description
Duration and horizon rate of return, bond portfolio management and immunization; mean-variance formulation of portfolio choices of risky assets; Two-fund theorem and One-fund theorem; asset pricing under the capital asset pricing models and factor models; investment performance analysis; utility optimization in investment decisions; stochastic dominance.
• MATH 4513
Life Contingencies Models and Insurance Risk
3 Credit(s)
Alternate code(s)
RMBI 4220
Prerequisite(s)
ELEC 2600 OR ISOM 3540 OR MATH 2421 OR MATH 2431
Description
The topics discussed in this course include survival models, life tables and selection, insurance benefits, annuities, premium calculation, and insurance policy values.
• MATH 4514
Financial Economics in Actuarial Science
3 Credit(s)
Prerequisite(s)
(MATH 2421 OR MATH 2431) AND MATH 2511
Exclusion(s)
FINA 3203
Description
The course aims to study some actuarial models and their applications in derivative pricing and financial risk management. Topics include introduction to various derivatives such as forward, futures, European/ American options, exotic options and interest rate derivatives, uses of various options strategies in portfolio management, pricing options using binomial tree model, Black Scholes formula for options pricing and its extension, Options Greeks and their applications in hedging, use of Monte Carlo simulation in options pricing, pricing of interest rate derivatives using the Black-Derman-Toy tree. The course also prepares students to take the Exam MFE (Models for Financial Economics) of the Society of Actuaries.
• MATH 4821
Special Topics
1-4 Credit(s)
Description
Focuses on a coherent collection of topics selected from a particular branch of mathematics. A student may repeat the course for credit if the topics studied are different each time.
• MATH 4822
Special Topics in Pure Mathematics
1-4 Credit(s)
Description
Supplementary study of specialized topics for students of pure mathematics.
• MATH 4823
Special Topics in Applied Mathematics
1-4 Credit(s)
Description
Supplementary study of specialized topics for students of applied mathematics.
• MATH 4824
Special Topics in Statistics and Financial Mathematics
1-4 Credit(s)
Description
Supplementary study of specialized topics for students of statistics.
• MATH 4825
Special Topics in Actuarial Mathematics
3 Credit(s)
Description
The course discusses one or two of the following three advanced subjects in actuarial mathematics: (1) advanced life contingencies models, (2) advanced casualty loss models, and (3) advanced financial economics. Based on the specific subjects chosen by the instructor, the topics covered in the course may include: (1) multiple state models, pension mathematics, interest rate risk, and emerging costs for traditional life insurance; (2) estimation of failure time and loss distribution using nonparametric methods, estimation of parameters of failure time and loss distribution with censored and/or truncated data, the acceptability of a fitted model, model comparison, and bootstrap methods; (3) Vasicek and Cox-Ingersoll-Ross bond pricing models, Black-Derman-Toy binomial model, Ito's formula, Black-Scholes option pricing model, exotic options, variance reduction methods in simulation, and delta-hedging.
• MATH 4900
1 Credit(s)
Description
This course is for academic and professional development of students. The course arranges seminars and small group activities to expose students to mathematics in real life, explore their possible career choice, and enhance the interactions between students and faculties. Activities may include seminars, workshops, advising and sharing sessions, interaction with faculty and teaching staff, and discussion with student peers or alumni. Graded P or F. For MATH students only.
• MATH 4921
Student Seminars
1-3 Credit(s)
Prerequisite(s)
A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024
Description
Working in small teams, students are required to select a topic in pure mathematics, applied mathematics or statistics area. They will discuss and write up their learning and present it at the seminars. The level of the topics can range from simple calculus to advanced topology, geometry or statistics. Students may repeat the course for credit at most two times.
• MATH 4981-4985
Independent Study
1-3 Credit(s)
Description
Advanced undergraduate topics independently studied under the supervision of a faculty member. May be repeated for credit if different topics are studied. May be graded P/F or letter grade.
• MATH 4990
2-3 Credit(s)
Prerequisite(s)
MATH 4982
Description
Work in any area of mathematics under the guidance of a faculty member. The project either surveys a research topics or describes a small project completed by the student.
• MATH 4991
Capstone Project in Pure Mathematics
3 Credit(s)
Prerequisite(s)
MATH 3121 OR MATH 3131
Exclusion(s)
MATH 4992, MATH 4993, MATH 4994, MATH 4999
Description
This is a project-based course that provides students an opportunity to integrate and apply mathematical tools to analyze problems in pure mathematics. Specific topics will be chosen by the instructor. For MATH students in their fourth year of study only.
• MATH 4992
Capstone Project in Applied Mathematics
3 Credit(s)
Prerequisite(s)
MATH 3312
Exclusion(s)
MATH 4991, MATH 4993, MATH 4994, MATH 4999
Description
This is a project-based course that provides students an opportunity to integrate and apply mathematical tools to analyze problems in applied mathematics. Specific topics will be chosen by the instructor. For MATH students in their fourth year of study only.
• MATH 4993
Capstone Project in Statistics
3 Credit(s)
Prerequisite(s)
MATH 3424
Exclusion(s)
MATH 4991, MATH 4992, MATH 4994, MATH 4999
Description
This is a project-based course that provides students an opportunity to integrate and apply their statistical knowledge to analyzing data. Students may make use of the statistical package SAS to conduct their project. For MATH students in their fourth year of study only.
• MATH 4994
Capstone Project in Mathematics and Economics
3 Credit(s)
Exclusion(s)
MATH 4991, MATH 4992, MATH 4993, MATH 4999
Description
This is a project-based course that provides students an opportunity to integrate and apply mathematical tools to analyze problems in economics and social science. Specific topics will be chosen by the instructor. For MATH students in their fourth year of study only.
• MATH 4995
Capstone Project for Data Science
3 Credit(s)
Prerequisite(s)
MATH 3322 AND MATH 3332
Description
This is a project-based course that trains students on applying computational and analytical tools (matrix computation, Fourier and wavelet transform, convex optimization, etc.) to real-world data analysis problems (recommendation system, signal processing, computer vision, etc.). Familiarity with a programming language is preferred, such as R, Matlab, or Python. For BSc in Data Science and Technology students only.
• MATH 4999
Independent Capstone Project
3 Credit(s)
Exclusion(s)
MATH 4991, MATH 4992, MATH 4993, MATH 4994
Description
A capstone project conducted under the supervision of a faculty member. A written report is required. Students need to individually seek a faculty mentor's consent prior to enrollment in this course.