Undergraduate Courses 2018-19

For undergraduate courses, those coded from 1000 to 1600 are designed to standardize the varying range of mathematics background of students. Students should consult with their own school advisor which MATH course they should take.

• 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 1003, 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 1003, 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 1003, 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 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, Stroke'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, 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)

  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 2721

  Concepts in Mathematics

  2 Credit(s)
  Prerequisite(s)

  A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1020 OR MATH 1024

  Description

  Expository lectures and discussion on basic mathematical concepts and ideas, historical developments in various areas of mathematics, and selected trends and advances in mathematical sciences. Third year and fourth year students require instructor's approval to take the course.
• 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

  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 3311

  Introduction to Numerical Methods

  3 Credit(s)
  Corequisite(s)

  MATH 2011 OR MATH 2023 OR MATH 3043

  Exclusion(s)

  MATH 3312, MECH 4740, PHYS 3142

  Description

  Computer arithmetric, matrix computation, interpolation and approximation, numerical integration, solution of nonlinear equations.
• MATH 3312

  Numerical Analysis

  3 Credit(s)
  Prerequisite(s)

  (COMP 1021 / COMP 1022P / COMP 1022Q) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (MATH 2031 / MATH 2033 / MATH 2043)

  Exclusion(s)

  MATH 3311, 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 2121

  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 2023 AND MATH 2121

  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 2721; or 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 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)

  MATH 3033/MATH 3043

  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

  Derivatives 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 OR MATH 2721

  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, SOSC 1410 (prior to 2014-15)

  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)
  Prerequisite(s)

  MATH 4052

  Exclusion(s)

  CIVL 2510, CIVL 3520 (prior to 2014-15), 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 4351

  Numerical Solutions of Partial Differential Equations

  3 Credit(s)
  Prerequisite(s)

  MATH 2350/MATH 2351/MATH 2352 and MATH 3311/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 4422

  Data Analysis

  3 Credit(s)
  Prerequisite(s)

  MATH 2411/MATH 3423 and MATH 3424

  Description

  Computer-oriented statistical analysis including generalized linear models, classification, principal component analysis, survival analysis, binary data. Real data sets presented for analysis using statistical packages such as SAS, Minitab and S-plus.
• 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

  Exclusion(s)

  ISOM 4550

  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) AND (IEDA 2510 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 / 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 2510 / ISOM 2500 / LIFS 3150 / MATH 2411) AND (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)
  Previous Course Code(s)

  MATH 4825A

  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 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

  Undergraduate Project

  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)
  Corequisite(s)

  LANG 3010 OR LABU 2040

  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.