# Undergraduate Courses 2021-22

MATH

Mathematics

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

- MATH 1003Calculus and Linear Algebra3 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 1024DescriptionThis 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 1012Calculus IA4 Credit(s)Co-list withMATH 1013Exclusion(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 1024DescriptionThis 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 1013Calculus IB3 Credit(s)Co-list withMATH 1012Prerequisite(s)Level 3 or above in HKDSE Mathematics Extended Module M1/M2Exclusion(s)AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1012, MATH 1014, MATH 1020, MATH 1023, MATH 1024DescriptionThis 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 1014Calculus II3 Credit(s)Prerequisite(s)MATH 1012 OR MATH 1013 OR MATH 1023 OR grade A- or above in MATH 1003Exclusion(s)AL Pure Mathematics; AL Applied Mathematics; MATH 1020, MATH 1024DescriptionThis 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 1020Accelerated Calculus4 Credit(s)Prerequisite(s)Level 5* or 5** in HKDSE Mathematics Extended Module M2Exclusion(s)A passing grade in AL Applied Mathematics / AL Pure Mathematics; MATH 1013, MATH 1014, MATH 1023, MATH 1024DescriptionA 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 1023Honors Calculus I3 Credit(s)Prerequisite(s)Level 5 or above in HKDSE Mathematics Extended Module M2Exclusion(s)AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1012, MATH 1013, MATH 1014, MATH 1020DescriptionThis 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 1024Honors Calculus II3 Credit(s)Prerequisite(s)MATH 1012 OR MATH 1013 OR MATH 1023Exclusion(s)AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1014, MATH 1020DescriptionThis 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 1701Introductory Topics in Mathematical Sciences1-4 Credit(s)DescriptionThis 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 2011Introduction to Multivariable Calculus3 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014; OR MATH 1020; OR MATH 1024Exclusion(s)MATH 2023DescriptionDifferentiation in several variables, with applications in approximation, maximum and minimum and geometry. Integration in several variables, vector analysis.
- MATH 2023Multivariable Calculus4 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024Exclusion(s)MATH 2011DescriptionSequences, series, gradients, chain rule. Extrema, Lagrange multipliers, line integrals, multiple integrals. Green's theorem, Stoke's theorem, divergence theorem, change of variables.
- MATH 2033Mathematical Analysis4 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024Exclusion(s)MATH 2043DescriptionSets and functions, real numbers, limits of sequences and series, limits of functions, continuous functions, differentiation, Riemann integration, additional topics.
- MATH 2043Honors Mathematical Analysis4 Credit(s)Prerequisite(s)Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1020/MATH 1024Exclusion(s)MATH 2033DescriptionThe 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 2111Matrix Algebra and Applications3 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024Exclusion(s)MATH 2121, MATH 2131, MATH 2350DescriptionSystems of linear equations; vector spaces; linear transformations; matrix representation of linear transformations; linear operators, eigenvalues and eigenvectors; similarity invariants and canonical forms.
- MATH 2121Linear Algebra4 Credit(s)Prerequisite(s)Exclusion(s)MATH 2111, MATH 2131, MATH 2350DescriptionVector space, matrices and system of linear equations, linear mappings and matrix forms, inner product, orthogonality, eigenvalues and eigenvectors, symmetric matrix.
- MATH 2131Honors in Linear and Abstract Algebra I4 Credit(s)Prerequisite(s)Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1020/MATH 1024Exclusion(s)MATH 2111, MATH 2121, MATH 2350DescriptionThe 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 2343Discrete Structures4 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics; or MATH 1014; or MATH 1020; or MATH 1024Exclusion(s)COMP 2711, COMP 2711HDescriptionLogic: 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 2350Applied Linear Algebra and Differential Equations3 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024Exclusion(s)MATH 2111, MATH 2121, MATH 2131, MATH 2351, MATH 2352, PHYS 2124DescriptionThis 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 2351Introduction to Differential Equations3 Credit(s)Prerequisite(s)Exclusion(s)MATH 2350, MATH 2352, PHYS 2124DescriptionFirst 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 2352Differential Equations4 Credit(s)Prerequisite(s)MATH 2111 OR MATH 2121 OR MATH 2131Exclusion(s)MATH 2350, MATH 2351, PHYS 2124DescriptionFirst and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory.
- MATH 2411Applied Statistics4 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024Exclusion(s)IEDA 2510, IEDA 2540, ISOM 2500, LIFS 3150DescriptionA systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing.
- MATH 2421Probability4 Credit(s)Prerequisite(s)MATH 1014 OR MATH 1020 OR MATH 1024Corequisite(s)MATH 2011 OR MATH 2023Exclusion(s)IEDA 2510, IEDA 2520, MATH 2431, ELEC 2600, ELEC 2600H, ISOM 3540DescriptionSample 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 2431Honors Probability4 Credit(s)Prerequisite(s)(Grade A- or above in MATH 1014) OR MATH 1020 OR MATH 1024Corequisite(s)MATH 2011 OR MATH 2023Exclusion(s)ELEC 2600, ELEC 2600H, ISOM 3540, MATH 2421DescriptionThis 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 2511Fundamentals of Actuarial Mathematics3 Credit(s)Prerequisite(s)MATH 1003 OR MATH 1014 OR MATH 1020 OR MATH 1024DescriptionThis 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 2731Mathematical Problem Solving3 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics/AL Applied Mathematics; OR MATH 1014 OR MATH 1020 OR MATH 1024DescriptionDiscussions on problem solving techniques. Basics materials in combinatorics, number theory, geometry and mathematical games.
- MATH 2741Geometric Constructions3 Credit(s)Prerequisite(s)MATH 1014 OR MATH 1020 OR MATH 1024 OR AL Applied Mathematics / AL Pure MathematicsMode of Delivery[BLD] Blended learningDescriptionThis 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 3033Real Analysis4 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 3043DescriptionFunctions of several variables, implicit and inverse function theorem, uniform convergence measure and integral on the real line.
- MATH 3043Honors Real Analysis4 Credit(s)Prerequisite(s)Grade A- or above in MATH 2043Exclusion(s)MATH 3033DescriptionThe 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 3121Abstract Algebra3 Credit(s)Prerequisite(s)MATH 2111/MATH 2121/MATH 2131/MATH 2350Exclusion(s)MATH 3131DescriptionPolynomials; Jordan canonical form, minimal polynomials, rational canonical form; equivalence relation; group, coset, group action; introduction to rings and fields.
- MATH 3131Honors in Linear and Abstract Algebra II4 Credit(s)Prerequisite(s)Grade B- or above in MATH 2131DescriptionThe 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 3312Numerical Analysis3 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 3142DescriptionBasic 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 3322Matrix Computation3 Credit(s)Prerequisite(s)MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350DescriptionThis 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 3332Data Analytic Tools3 Credit(s)Prerequisite(s)(MATH 2011 OR MATH 2023) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)DescriptionThis 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 3343Combinatorial Analysis3 Credit(s)Prerequisite(s)MATH 2121/MATH 2111/MATH 2350/MATH 2131; or MATH 2343/COMP 2711DescriptionAn 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 3423Statistical Inference3 Credit(s)Prerequisite(s)MATH 2421 OR MATH 2431DescriptionSampling theory, order statistics, limiting distributions, point estimation, confidence intervals, hypothesis testing, non-parametric methods.
- MATH 3424Regression Analysis3 Credit(s)Prerequisite(s)MATH 3423Exclusion(s)ISOM 5520DescriptionEstimation and hypothesis testing in linear regression, residual analysis, multicollinearity, indicator variables, variable selection, nonlinear regression.
- MATH 3425Stochastic Modeling3 Credit(s)Prerequisite(s)MATH 2421 OR MATH 2431DescriptionDiscrete time Markov chains and the Poisson processes. Additional topics include birth and death process, elementary renewal process and continuous-time Markov chains.
- MATH 3426Sampling3 Credit(s)Prerequisite(s)MATH 2411DescriptionBasic 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 3427Bayesian Statistics3 Credit(s)Prerequisite(s)MATH 2421 OR MATH 2431 OR ELEC 2600 OR ELEC 2600H OR ISOM 3540DescriptionThis 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 4023Complex Analysis3 Credit(s)Prerequisite(s)(MATH 2011 OR MATH 2023 OR MATH 3043) AND (MATH 2033 OR MATH 2043)DescriptionComplex differentiability; Cauchy-Riemann equations; contour integrals, Cauchy theory and consequences; power series representation; isolated singularities and Laurent series; residue theorem; conformal mappings.
- MATH 4033Calculus on Manifolds3 Credit(s)Prerequisite(s)Grade A- or above in MATH 2023 AND B- or above in MATH 2131DescriptionIntroduction to manifolds, metric spaces, multi-linear Algebra, differential forms, Stokes theorem on manifolds, cohomology.
- MATH 4051Theory of Ordinary Differential Equations3 Credit(s)Prerequisite(s)(MATH 2350 OR MATH 2351 OR MATH 2352) AND (MATH 3033 OR MATH 3043)DescriptionExistence and uniqueness theorems of ordinary differential equations, theory of linear systems, stability theory, study of singularities, boundary value problems.
- MATH 4052Partial Differential Equations3 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 2352DescriptionDerivations 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 4061Topics in Modern Analysis2 Credit(s)Prerequisite(s)MATH 3043 or MATH 3033DescriptionExamples 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 4063Functional Analysis2 Credit(s)Prerequisite(s)MATH 4061DescriptionTopological 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 4141Number Theory and Applications3 Credit(s)Prerequisite(s)MATH 2131Corequisite(s)(for students without prerequisites) MATH 3121DescriptionPrime numbers, unique factorization, modular arithmetic, quadratic number fields, finite fields, p-adic numbers, coding theory, computational complexity.
- MATH 4151Introduction to Lie Groups3 Credit(s)Prerequisite(s)(MATH 2011 OR MATH 2023 OR MATH 3043) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)DescriptionGeneral linear groups, orthogonal groups, unitary groups, symplectic groups, exponential maps, maximal tori, Clifford algebra, spin groups.
- MATH 4221Euclidean and Non-Euclidean Geometries3 Credit(s)Prerequisite(s)MATH 2033 OR MATH 2043 OR MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350DescriptionAxioms and models, Euclidean geometry, Hilbert axioms, neutral (absolute) geometry, hyperbolic geometry, Poincare model, independence of parallel postulate.
- MATH 4223Differential Geometry3 Credit(s)Prerequisite(s)MATH 2011/MATH 2023/MATH 3043 and MATH 2121/MATH 2131DescriptionCurve 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 4225Topology3 Credit(s)Prerequisite(s)MATH 2033/MATH 2043DescriptionMetric, topology, continuous map, Hausdorff, connected, compact, graph, Euler number, CW-complex, classification of surfaces.
- MATH 4321Game Theory3 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 4124DescriptionZero-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 4326Introduction to Fluid Dynamics3 Credit(s)Alternate code(s)OCES 4326Prerequisite(s)MATH 4052Exclusion(s)CIVL 2510, MECH 2210DescriptionLagrangian 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 4333Mathematical Biology3 Credit(s)Prerequisite(s)MATH 2121/MATH 2111/MATH 2131 and MATH 2351/MATH 2352; or MATH 2350DescriptionPopulation, ecology, infectious disease, genetic, and biochemistry models. Additional topics chosen by instructor.
- MATH 4335Introduction to Optimization3 Credit(s)Prerequisite(s)(MATH 2011 OR MATH 2023) AND (MATH 2111 OR MATH 2121 OR MATH 2131)DescriptionThis 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 4336Introduction to Mathematics of Image Processing3 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 4130DescriptionThis 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 4343Introduction to Graph Theory4 Credit(s)Previous Course Code(s)MATH 4821BPrerequisite(s)MATH 2343DescriptionThis 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 4351Numerical Solutions of Partial Differential Equations3 Credit(s)Prerequisite(s)(MATH 2350 OR MATH 2351 OR MATH 2352) AND MATH 3312 AND MATH 4052DescriptionIntroduction 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 4423Nonparametric Statistics3 Credit(s)Prerequisite(s)MATH 2411DescriptionThe 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 4424Multivariate Analysis3 Credit(s)Prerequisite(s)MATH 3423 and MATH 3424Exclusion(s)ISOM 5530DescriptionInferences of means and covariance matrices, canonical correlation, discriminant analysis, multivariate ANOVA, principal components analysis, factor analysis.
- MATH 4425Introductory Time Series3 Credit(s)Prerequisite(s)MATH 3423 and MATH 3424DescriptionStationarity, (partial) auto-correlation function, ARIMA modeling, order selection, diagnostic, forecasting, spectral analysis.
- MATH 4426Survival Analysis3 Credit(s)Prerequisite(s)MATH 3423DescriptionThe 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 4427Loss Models and their Applications3 Credit(s)Prerequisite(s)(ELEC 2600 OR ISOM 3540 OR MATH 2421 OR MATH 2431) AND (MATH 2011 OR MATH 2023) AND MATH 2511DescriptionThis 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 4428Bayesian Analysis and Credibility Theory3 Credit(s)Prerequisite(s)MATH 3423 OR MATH 4427DescriptionThis 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 4432Statistical Machine Learning3 Credit(s)Prerequisite(s)(COMP 1021 OR COMP 1022P OR COMP 1022Q (prior to 2020-21)) AND (IEDA 2510 OR (IEDA 2520 AND IEDA 2540) OR ISOM 2500 OR LIFS 3150 OR MATH 2411 OR MATH 2421 OR MATH 2431)DescriptionThis 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 4511Quantitative Methods for Fixed Income Derivatives3 Credit(s)Prerequisite(s)(MATH 2011 / MATH 2023) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (IEDA 2510 / IEDA 2520 AND IEDA 2540 / ISOM 2500 / LIFS 3150 / MATH 2411) AND (FINA 2203 / FINA 2303)DescriptionBond, 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 4512Fundamentals of Mathematical Finance3 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)DescriptionDuration 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 4513Life Contingencies Models and Insurance Risk3 Credit(s)Alternate code(s)RMBI 4220Prerequisite(s)ELEC 2600 OR ISOM 3540 OR MATH 2421 OR MATH 2431DescriptionThe topics discussed in this course include survival models, life tables and selection, insurance benefits, annuities, premium calculation, and insurance policy values.
- MATH 4514Financial Economics in Actuarial Science3 Credit(s)Prerequisite(s)(MATH 2421 OR MATH 2431) AND MATH 2511Exclusion(s)FINA 3203DescriptionThe 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 4632Machine Learning with Structured Data3 Credit(s)Previous Course Code(s)MATH 4824BAlternate code(s)COMP 4222Prerequisite(s)(COMP 2011/2012/2012H) AND (COMP 2711/2711H OR MATH 2343) AND (MATH 2111/2121/2131)Exclusion(s)COMP 4222DescriptionThis course provides an introduction to statistical machine learning algorithms for structured data such as text sequences, taxonomy trees, relational databases (such as knowledge bases), and graphs (including graph databases such as biomedical graphs and large heterogeneous information networks such as knowledge graphs), and using programming tools such as Python to implement them for real problems. It will use some of the following practical problems such as text and graph classification, statistical relational learning, information extraction, sequence modeling, graph modeling, protein 3D structure prediction, QA system, etc. as illustrations to demonstrate the power of the statistical learning algorithms.
- MATH 4821Special Topics1-4 Credit(s)DescriptionFocuses 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 4822Special Topics in Pure Mathematics1-4 Credit(s)DescriptionSupplementary study of specialized topics for students of pure mathematics.
- MATH 4823Special Topics in Applied Mathematics1-4 Credit(s)DescriptionSupplementary study of specialized topics for students of applied mathematics.
- MATH 4824Special Topics in Statistics and Financial Mathematics1-4 Credit(s)DescriptionSupplementary study of specialized topics for students of statistics.
- MATH 4825Special Topics in Actuarial Mathematics3 Credit(s)DescriptionThe 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 4900Academic and Professional Development1 Credit(s)DescriptionThis 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 4921Student Seminars1-3 Credit(s)Prerequisite(s)A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024DescriptionWorking 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 4981-4985Independent Study1-3 Credit(s)DescriptionAdvanced 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 4990Undergraduate Project2-3 Credit(s)Prerequisite(s)MATH 4982DescriptionWork 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 4991Capstone Project in Pure Mathematics3 Credit(s)Prerequisite(s)MATH 3121 OR MATH 3131Exclusion(s)MATH 4992, MATH 4993, MATH 4994, MATH 4999DescriptionThis 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 4992Capstone Project in Applied Mathematics3 Credit(s)Prerequisite(s)MATH 3312Exclusion(s)MATH 4991, MATH 4993, MATH 4994, MATH 4999DescriptionThis 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 4993Capstone Project in Statistics3 Credit(s)Prerequisite(s)MATH 3424Exclusion(s)MATH 4991, MATH 4992, MATH 4994, MATH 4999DescriptionThis 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 4994Capstone Project in Mathematics and Economics3 Credit(s)Exclusion(s)MATH 4991, MATH 4992, MATH 4993, MATH 4999DescriptionThis 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 4995Capstone Project for Data Science3 Credit(s)Prerequisite(s)MATH 3322 AND MATH 3332DescriptionThis 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 4999Independent Capstone Project3 Credit(s)Exclusion(s)MATH 4991, MATH 4992, MATH 4993, MATH 4994DescriptionA 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.