Undergraduate Courses 2024-25

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; MATH 1012; MATH 1013; MATH 1014; 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Apply basic techniques in linear algebra and calculus that are commonly used for business school students
  • 2.
    Apply rigorous, analytic, highly numerate approach to analyzing and solving problems
  • 3.
    Communicate solutions effectively by using mathematical terminology and English
• 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; 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Express quantitative relationships using the language of functions
  • 2.
    Develop basic computational skills in calculus
  • 3.
    Apply the concepts and methods of calculus in modeling and problem solving
• 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)

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Apply the basic concepts and methods in one-variable differential calculus
  • 2.
    Apply the knowledge in functions and calculus to formulate and solve application problems
• 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)

  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)

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    To understand the basic concepts of one variable calculus and series students need as they pursue careers in business, engineering or science
  • 2.
    To apply the techniques of one-variable calculus and series in precise and logical way to solve various daily and professional problems
• MATH 1023

  Honors Calculus I

  3 Credit(s)
  Prerequisite(s)

  Level 5 or above in HKDSE Mathematics Extended Module M2

  Exclusion(s)

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Apply the basic concepts and methods in one-variable differential calculus with rigorous mathematical reasoning
  • 2.
    Apply the knowledge in functions and calculus to formulate and solve problems
• MATH 1024

  Honors Calculus II

  3 Credit(s)
  Prerequisite(s)

  MATH 1023

  Exclusion(s)

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explain and communicate basic concepts of mathematics such as set, functions, logic argument, number system (integers, rational numbers, real and complex numbers) counting principles, and equivalence relations
  • 2.
    Apply various methods of proofs including proof by contradictions, method of exhaustions, mathematical induction, etc.
  • 3.
    Demonstrate and acquire the skills of reading and writing mathematical proofs
• 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- or above in 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.
• 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 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 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Solve some basic and advanced problems in probability
  • 2.
    Understand more distributions of random variables
  • 3.
    Solve some complicated problems of finding a distribution of a random variable by a new technique --- moment generating function
  • 4.
    Understand how to prove some limit theorems in probability, like the central limit theorem
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the basic concepts related to time value of money, such as interest rates, discount rate, present value, future value, etc. and how to carry out related calculation
  • 2.
    Understand the concepts related to annuities with payments that are not contingent and how to carry out calculation related to the future or present value of an annuity
  • 3.
    Understand the concepts related to loans and sinking fund and how to carry out calculation related to a loan, such as outstanding balance and interest and principal repayment
  • 4.
    Understand the concepts related to bonds and how to carry out calculation related to a bond, such as bond value, bond yield, amortization of premium, etc.
  • 5.
    Understand the concepts related to general cash flows and portfolios and how to carry out calculation related to such portfolios, such as present value, yield rate, rate of return, duration, and convexity, etc.
  • 6.
    Understand the concepts related to immunization and how to construct an investment portfolio to immunize a set of liability cash flows
  • 7.
    Enhance the ability of using advanced mathematics, e.g., calculus, to solve real-world problems
  • 8.
    Enhance the ability of using computational software such as Excel
• 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 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand QR decomposition and its numerical algorithm
  • 2.
    Understand singular value decomposition and its algorithm
  • 3.
    Understand Schur decomposition and its algorithm
  • 4.
    Implement various matrix computation algorithms on a computing platform and apply them to solve data analysis problems
• 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).

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand continuous Fourier and wavelet transform and to do discrete Fourier and wavelet transform for a given data with a computing platform
  • 2.
    Understand various function expansions and use them to approximate given functions
  • 3.
    Understand basic functional analysis
  • 4.
    Understand basic convex analysis
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Elaborate the concept and philosophy of Bayesian statistics and its main difference form the frequentist statistical approach
  • 2.
    Explain the importance of prior distribution (e.g. flat and conjugate priors) in Bayesian inference and how we can conduct posterior inference by using Bayesian estimates and Bayesian hypothesis testing
  • 3.
    Formulate a Bayesian solution to some real-data problems and interpret the results
  • 4.
    Implement some Bayesian computational techniques like MCMC
  • 5.
    Apply the conceptual and practical skills in Bayesian statistics to problems in statistics, data science, and other areas
• MATH 3428

  Statistical Computing

  3 Credit(s)
  Prerequisite(s)

  Prerequisite(s): MATH 2411 AND (MATH 2421 OR MATH 2431)

  Description

  This course covers the models, methods and algorithms in computational statistics. Topics include: basics of R programming; basic statistical data analysis and visualisation tools; R implementation of non-standard estimators; simulate random variables and random experiments; estimate variance and prediction performance by data partitioning and randomization (Jackknife, Bootstrap and Cross-Validation); expectation-maximization algorithm and applications; Markov Chain Monte Carlo sampling and applications. The students will learn computation-oriented statistical methods with hands-on experience on real data examples.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Use R for standard data analysis and visualization
  • 2.
    Implement R-code for non-standard estimators (more advanced R programming)
  • 3.
    Explore Re-sampling technique for variance estimate and cross validation
  • 4.
    Understand EM algorithm and its applications
  • 5.
    Understand MCMC and its applications
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Create educational material, communicate mathematical knowledge to unfamiliar audiences
  • 2.
    Show judgment in the selection and presentation of material to communicate
  • 3.
    Demonstrate essential communication skills such as verbal, visual, video, or online/social media communication
  • 4.
    Examine the value of and assume ownership of their mathematics education
• 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

  3 Credit(s)
  Prerequisite(s)

  (MATH 3043 OR MATH 4061) AND (MATH 2131 OR grade A- or above in MATH 2121)

  Description

  Banach space. Hahn-Banach theorem, open mapping theorem, closed graph theorem, uniform boundedness theorem, separation theorem, Krein-Milman theorem. Weak topologies and weak topologies, reflexive spaces, separable spaces, Arzela-Ascoli theorem, uniform convexity. Hilbert space, Riesz representation theorem and Lax-Milgram theorem. Adjoints and duality. Compact, Fredholm, self-adjoint operators and their spectrum. Sobolev spaces, Sobolev inequalities, elliptic boundary value problems, and other applications.
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Be equipped with of fundamental knowledge of optimization
  • 2.
    Develop an understanding of basic algorithms of optimization and their implementations
  • 3.
    Set up optimization models for applications problems
  • 4.
    Solve optimization problems independently
  • 5.
    Implement some algorithms by software such as MATLAB
  • 6.
    Communicate using correct mathematical terminology
• 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 3130

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Be equipped with theoretical knowledge, principles and techniques to image processing problems
  • 2.
    Acquire a good appreciation of roles of mathematics in image processing
  • 3.
    Implement image processing algorithms on computers
  • 4.
    Apply computer algorithms to real-life problems
  • 5.
    Present numerical output from a computer code in a systematical way
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Formulate related problems in graph language and graph models
  • 2.
    Master standard useful matrix methods such as incidence matrix, Laplace matrix, matrix‐tree formula, and graph Fourier transforms, etc.
  • 3.
    Master basic concepts, ideas, techniques and core theorems of graph theory that may be applicable to network analysis and other practical problems
  • 4.
    Demonstrate abilities in applying algorithms, graph analytic skills, and theoretical thinking for software development
  • 5.
    Demonstrate ability in working with unsolved problems and explore new problems for future advanced studies
• 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 4360

  Mathematical Modeling

  3 Credit(s)
  Prerequisite(s)

  MATH 2350 OR MATH 2351 OR MATH 2352

  Description

  This is an introductory course to mathematical modeling in science and engineering. The first part covers foundations of mathematical modelling. The second part discusses the applications, including mechanical vibrations, population dynamics, and traffic flow. Students will learn diverse modeling approaches to formulate, analyze and evaluate models mathematically. The course comprises both lectures and tutorials.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the foundations of mathematical modeling, including principles, methods, dimensional analysis, scale, approximation, and model validation
  • 2.
    Understand a range of mathematical models built in a range of disciplines, with a focus on mechanical vibrations, population dynamics, and traffic flow
  • 3.
    Analyze problems by building mathematical models, carrying out theoretical analysis, and performing numerical computation
  • 4.
    Apply analysis and computation skills for mathematical models
  • 5.
    Understand the technique used by mathematical modeling to develop mathematical maturity for undertaking higher level studies in applied mathematics and related fields
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Estimate failure time and loss distributions for empirical models
  • 2.
    Estimate of the variance of estimators and confidence intervals for failure time and loss distributions for empirical models
  • 3.
    Estimate of the parameters of failure time and loss distributions for parameter models
  • 4.
    Estimate the parameters of failure time and loss distributions with censored and/or truncated data for parameter models
  • 5.
    Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions for parameter models
  • 6.
    Estimate failure time and loss distributions
  • 7.
    Determine the acceptability of a fitted model and/or compare models
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand commonly used survival models, how to create new families of loss distributions, how to choose the appropriate loss distributions and apply them in concrete applications
  • 2.
    Understand commonly used frequency models, how to choose the appropriate frequency models, and how to apply them in concrete applications
  • 3.
    Understand how to compute relevant parameters and statistics for collective risk models, how to evaluate compound models for aggregate claims, and how to compute aggregate claim distributions
  • 4.
    Calculate risk measures of VaR and TVaR and understand their use and limitations
  • 5.
    Understand how to apply limited fluctuation credibility including criteria for both full and partial credibility and how to apply Buhlmann and Buhlmann-Straub models
  • 6.
    Understand how to apply conjugate priors in Bayesian analysis and how to apply empirical Baysian methods in the nonparametric and semiparametric cases
  • 7.
    Enhance the ability of using advanced mathematics (calculus, probability, statistics, etc.) to solve real-world problems
  • 8.
    Enhance the ability of building stochastic and statistical models for insurance
  • 9.
    Enhance the ability of using computational software such as Matlab and implementing mathematical models using computer programs
• MATH 4429

  Credibility Theory and its Applications

  3 Credit(s)
  Prerequisite(s)

  MATH 2421 OR MATH 2431

  Description

  Credibility theory is statistical inference used to make prediction based on both individual risk data and collective risk data. It is widely used in the insurance industry to predict the future claim payment, determine the insurance premium and determine the size of required reserve. This course will provide a mathematical treatment on credibility theory and explore the application of the theory in prediction of future claim payment, premium calculation. Topics include limited fluctuation credibility theory, greatest accuracy credibility theory, credibility premium, Buhlmann models, Buhlmann-Straub models and applications of credibility theory in solving insurance problems such as future loss prediction, premium calculation etc.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the basic idea of credibility theory. Be able to apply the limited fluctuation credibility theory and understand the criteria for both full and partial credibility
  • 2.
    Study the solution of credibility problem using the Buhlmann model and Buhlmann-Straub model
  • 3.
    Apply empirical Bayesian estimation in non-parametric model and semiparametric model; Understand the strengths and weaknesses of nonparametric model and semiparametric model
  • 4.
    Apply credibility theory in insurance problem
• MATH 4432

  Statistical Machine Learning

  3 Credit(s)
  Prerequisite(s)

  (COMP 1021 OR COMP 1022P OR COMP 1022Q (prior to 2020-21)) AND ((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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the fundamental principles and techniques of statistical learning
  • 2.
    Apply these techniques to the study of real-world datasets in class
  • 3.
    Learn advanced materials with the aid of internet and reference
  • 4.
    Work independently and collaborate effectively in a team
  • 5.
    Communicate mathematical concepts effectively both orally and in writing
• MATH 4433

  Spatial Data Analysis

  3 Credit(s)
  Prerequisite(s)

  MATH 2421 OR MATH 2431

  Description

  This course provides an overview of and a basic training of spatial statistics with data analysis and examples including meteorological measurements from weather stations, demographics from census, and the incidence of disease over a particular geographic area. Some ideas and principles of spatial statistics including exploratory spatial analysis (e.g. Moran’s I), spatial data visualization, spatial interpolation (e.g. kriging), spatial correlation, spatial clustering, spatial map comparison, and spatial regression models are covered. An open-source, freely available software R and other software will be used to implement the computational and data analytics skills. Hands-on experience and case studies such as disease surveillance will also be provided to students. Completion of this course will give students access to a wide range of spatial analytical tools, customizable to real data.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Elaborate and master the concepts of spatial statistics
  • 2.
    Explain the importance of spatial analysis (e.g. disease outbreak/surveillance) in real world such as epidemiology and the recent pandemic of COVID-19
  • 3.
    Formulate real-data problems in the context of spatial analysis and interpret the results by using appropriate spatial methods and implement some spatial analysis and models in R and other software
  • 4.
    Explore spatial patterning in variables (e.g. does the concentration of some pollutant vary spatially) and perform statistical inference (parameter estimation, prediction) for spatial models
  • 5.
    Apply the conceptual and practical skills in spatial statistics to problems in statistics, epidemiology, public health, data science, and other areas
• MATH 4434

  Deep Learning

  3 Credit(s)
  Prerequisite(s)

  (MATH 2121 OR MATH 2131 OR MATH 2111) AND MATH 4432

  Description

  This course covers some basic concepts and underlying principles of deep learning with modern applications in artificial intelligence (AI). It delves into the fundamentals of machine learning methodologies with insights from case studies of relevant technologies. Allowing for the experimentation of applications of deep learning, this course is designed to encourage students to devise creative ways to put readily-available AI technologies to use to tackle problems in real life. Topics include: Perceptron/Adaline and linear models, gradient descent and boosting, stochastic approximation, convolutional neural networks, recurrent neural networks, long short term memory, resnet, transformers, generative adversarial networks, deep reinforcement learning, and self-supervised learning. The students will practice experiments with python programming.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explore the basic concepts and principles behind deep learning methodology
  • 2.
    Explore the principles of various designs of neural network architectures
  • 3.
    Explore the applications of deep learning in modern AI including image, time series, natural language processing
  • 4.
    Develop programming experience for modern machine learning and AI
• 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 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the models used to model decrements used in insurances, annuities, and investments and how to calculate probabilities based on those models
  • 2.
    Understand the models used to model cash flows of life insurances and annuities and how to calculate the present values of the cash flows based on those models
  • 3.
    Understand the methods for calculating benefit reserves for traditional life insurances and annuities and basic universal life insurances
  • 4.
    Understand the models used to model cash flows for basic universal life insurances and how to calculate present values and contract level values
  • 5.
    Understand the relationship between expenses and gross premium and how to calculate contract level values based on the gross premium for life insurances and annuities
  • 6.
    Enhance the ability of using advanced mathematics (calculus, probability, statistics, etc.) to solve real-world problems
  • 7.
    Enhance the ability of building stochastic and statistical models for life contingencies
  • 8.
    Enhance the ability of using computational software such as Excel
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Recognize various financial derivatives (forward, futures, options, exotic options and interest rate derivatives) and their applications in the financial market
  • 2.
    Recognize the general properties of options such as put-call parity, put-call duality for European currency options, relationship between option price and strike price and relationship between option price and time to maturity
  • 3.
    Understand various option strategies (option spreads, collar, straddle, strangle, butterfly spread etc.) and explain how these strategies be applied to control the risk induced by price movement of the asset price
  • 4.
    Construct suitable binomial tree models in pricing European options, American options and interest rate derivatives
  • 5.
    Understand various concepts and model assumptions in Black-Scholes option pricing model and apply suitable techniques (risk-neutral valuation and Monte-Carlo simulation) to deduce pricing formulas for some European options
  • 6.
    Understand various Option Greeks and their applications in risk management and identify arbitrage opportunities given a set of market data
• MATH 4515

  Statistical and Computational Methods in Financial Mathematics

  3 Credit(s)
  Prerequisite(s)

  (MATH 2121 OR MATH 2131 OR MATH 2111) AND (MATH 2421 OR MATH 2431)

  Description

  This course covers statistical and computational methods that are essential in financial data analysis, financial modeling, portfolio management and derivatives pricing. These tools are commonly used in quantitative financial models. Topics include: parametric models and parameter estimation, model fitting, multivariate analysis, linear regression, principal component analysis, bootstrapping method, Monto Carlo simulation methods and lattice tree algorithms. The students learn how to execute the tasks using computer software such as RStudio and Matlab.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explore the principles and theories behind various statistical methods
  • 2.
    Explore the principles of some computational methods (Monte Carlo simulation and lattice tree method) in derivative pricing
  • 3.
    Explore the application of statistical methods in financial data analysis, model selection and model fitting etc.
  • 4.
    Explore the application of computation methods in pricing financial derivatives and examine the strength and weakness of each method
  • 5.
    Develop programming experience for financial data analysis and derivative pricing
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Understand the multiple state model and how to calculate premiums under the model
  • 2.
    Understand how to value the benefits and contribution of a pension plan under multiple state model
  • 3.
    Understand how to carry out cash flow analysis for traditional life insurance contracts
  • 4.
    Understand how to estimate failure time and loss distributions using non-parametric methods
  • 5.
    Understand how to estimate failure time and loss distributions using parametric methods
  • 6.
    Understand how to determine the acceptability of a fitted model and how to compare models
  • 7.
    Understand how to apply the Vasicek, Cox-lngersoll-Ross, and Black-Derman-Toy model
  • 8.
    Understand how to use Black-sholes model for valuating and delta-hedging derivative securities
  • 9.
    Enhance the ability of using advanced mathematics (calculus, probability, statistics, etc.) to solve real-world problems
  • 10.
    Enhance the ability of building stochastic and statistical models for insurance
  • 11.
    Enhance the ability of using computational software such as Excel and Matlab and implementing mathematical models using computer programs
• MATH 4900

  Academic and Professional Development

  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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Develop relationships with faculty members and staffs
  • 2.
    Become self-directed in planning and accomplishing academic goals
  • 3.
    Identify career and personal plans and work towards these by developing realistic plans
  • 4.
    Examine the value of and assume ownership of his/her education
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explain advanced mathematical theories, concepts and principles using precise mathematical language
  • 2.
    Apply independent judgment to investigative mathematical work
  • 3.
    Apply a rigorous logical and analytic approach to execute tasks and solve mathematical problems
  • 4.
    Work independently and collaborate effectively in a team
  • 5.
    Communicate mathematical concepts and methods effectively to a range of audiences, both orally and in writing
  • 6.
    Analyze the influence of mathematical sciences and their impact of human activity
  • 7.
    Draw on a global perspective and sound scientific evidence to evaluate the role of mathematical sciences in the international science community
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explain advanced mathematical theories, concepts and principles using precise mathematical language
  • 2.
    Apply independent judgment to investigative mathematical work
  • 3.
    Apply a rigorous logical and analytic approach to execute tasks and solve mathematical problems
  • 4.
    Work independently and collaborate effectively in a team
  • 5.
    Communicate mathematical concepts and methods effectively to a range of audiences, both orally and in writing
  • 6.
    Analyze the influence of mathematical sciences and their impact of human activity
  • 7.
    Draw on a global perspective and sound scientific evidence to evaluate the role of mathematical sciences in the international science community
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Examine the key theories, principles and techniques of data analysis
  • 2.
    Apply independent judgment to objective analysis and prediction of quantitative information
  • 3.
    Apply a rigorous analytic and highly numerate approach to analyze and solve both day-to-day and professional problems
  • 4.
    Work independently and collaborate effectively in a team
  • 5.
    Communicate statistical outcomes effectively to both lay and expert audiences by utilizing appropriate information and communication technology, through the report writing and project presentation
  • 6.
    Apply an appropriate method to analyze and solve both dayͲtoͲday and professional problems using statistical software
  • 7.
    Appraise the application of statistical modeling to a range of problems and persuade and influence others of its precision and value
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Appreciate how to use quantitative tools to analyze issues related to various mathematical models in economics and social science, including fair allocation, voting methods, proportional representation and traffic flows
  • 2.
    Recognize the importance of applying rigorous and numerate approach to analyze and solve problem in economics and social science
  • 3.
    Apply mathematical modeling and analytic proofs to describe and explain phenomena in economics and social science
  • 4.
    Communicate the solutions of mathematical models of economics and social science using mathematical terminology through oral presentation and written reports
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Formulate the problem to a mathematical problem
  • 2.
    Find proper analytical and computational tool to solve the problem
  • 3.
    Implement and test the algorithm in a programming language
  • 4.
    Present and interpret the results
• 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.

  Intended Learning Outcomes

  On successful completion of the course, students will be able to:

  • 1.
    Explain knowledge, principles and use of precise mathematical language in mathematical theories at college level
  • 2.
    Carry out investigative mathematical work with independent judgment
  • 3.
    Apply rigorous, logical, and analytic methods to execute tasks and solve mathematical problems
  • 4.
    Work independently and collaborate effectively in a team
  • 5.
    Communicate effectively, both in oral and written forms, about mathematical knowledge to audience
  • 6.
    Self-evaluate their own learning progress, and develop motivation and skills for lifelong learning
  • 7.
    Recognize the importance of complying with ethics of science and academic integrity
  • 8.
    Show appreciation of mathematical sciences and its interface with human activities
  • 9.
    View issues in mathematical sciences with reference to the practices of the international science community