1) Overview (1000-level math courses)

Math Department currently offers five single variable calculus courses at different levels and with different intensions. They are:
 Math1013*/1014 (Math013/014), Math1023*/1024 (Math023/024), Math1018 (Math021), Math1020* (New for 4Y with 5* or above in M2) Math1003* (Math006).

The first two are year long sequences, and the last three are semester long courses.
* common core courses under QR

2) Purpose of each course

Math1013/1014: Complete single variable calculus at normal level. Students are expected to know the basic concepts and carry out the computations.

Math1023/1024: Complete single variable calculus at more advanced level. Students are expected to understand the basic concepts and make simple theoretical arguments (such as providing reason for the specific computation, quite a bit of proofs). This is an honor course of Math1013/1014.

(Student with a level 5 or above in HKDSE Mathematics Extended Module M2 are encouraged to try out these honor classes)

Math1018: Basic material in single variable calculus. The course contains enough material so that students who passed Math1018 can continue studying the other math courses. For 3Y students with A-level Pure Math.

Math1020: Advance material in single variable calculus. Expected students have learnt well in calculus before (M2 with 5* or above). The course contains advance material so that students who passed Math1020 can continue studying the other higher level math courses. For 4Y students.

Math1003: Minimum material in single variable calculus. The course provides the basic knowledge of calculus but not enough for further study in more advanced math courses.

3) Relation between different courses

Math1023/1024 > Math1013/1014  = Math1020 > Math1018 > Math1003

If you pass Math1023 in fall, then you can take either Math1024 or Math1014 in spring.

If you pass Math1013 in fall, then you can take Math1014 in spring. If you perform exceptionally well in Math1013, then you can take Math1024 in spring.

If you pass Math1018, Math1020 or Math1003, then you cannot take other single variable calculus courses.

4) How does the choice affect further study

Math(1013/1014) / (1023/1024) / 1020 is the prerequisite for

Math2043 (honor analysis course) or

Math2031/2033 (the normal analysis course).

Although according to the official rule, getting A- or above in

Math1014 / 1020 / 1024 can allow you to register Math2043,

it is strongly advised that only those who took Math1023/1024

(or MATH1020) continue with Math2043

because otherwise you will be guaranteed to have a tough time and low grade in Math2043. The same applies to Math2131 (another honor course).

Students intend to do research in Math are strongly advised to Math1023/Math1024.

5) Other math courses that are offered at different levels

The following is the list of other equivalent math courses that are offered at different levels.

Math2021 (Math102) > Math2023 (Math101) > Math2011 (Math100)
Math2131 (Math217) > Math2121 (Math111)
Math2352 (Math151) > Math2351 (Math150)
Math2043 (Math203) > Math2031 (Math202) > Math2033 (Math201)

[Course codes in ( ) denote the old 3-digit codes)]

For further enquiry, contact Jimmy at majfung@ust.hk

 Mathematics

 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)] [Previous Course Code(s): MATH 006] 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. 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 1013; MATH 1014; MATH 1018; MATH 1020; MATH 1023; MATH 1024; any MATH course at or above 100-/2000- level

 MATH 1013 Calculus I [3 Credit(s)] [Previous Course Code(s): MATH 013] This is an introductory course in one-variable calculus, the first in the MATH 1013 – MATH 1014 sequence. Topics include complex numbers, functions and their limits, continuity, derivatives and rules of differentiation, applications of derivatives, and basic integral calculus. Exclusion(s): AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1018, MATH 1020, MATH 1023, MATH 1024; any MATH course at or above 100-/2000- level

 MATH 1014 Calculus II [3 Credit(s)] [Previous Course Code(s): MATH 014] 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. Exclusion(s): AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1018, MATH 1020, MATH 1024; any MATH course at or above 100-/2000- level Prerequisite(s): MATH 1013 or MATH 1023

 MATH 1018 Concise Calculus [4 Credit(s)] [Previous Course Code(s): MATH 021] This course teaches fundamental concepts in calculus and provides mathematical preparation for students who are going to take further courses in mathematics. Key topics include: logic and sets, functions, limits and continuity, differentiation and graphing, integration; improper integrals, sequence and series, power and Taylor series. Exclusion(s): Grade D or above in either AL Pure Mathematics or AL Applied Mathematics; MATH 1003, MATH 1013, MATH 1014, MATH 1020, MATH 1023, MATH 1024; any MATH course at or above 100-/2000- level Prerequisite(s): A passing grade in HKCEE Additional Mathematics / AS Mathematics and Statistics / AS Applied Mathematics, OR grade E in AL Applied Mathematics / AL Pure Mathematics

 MATH 1020 Accelerated Calculus [4 Credit(s)] [Previous Course Code(s): MATH 022] 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. Exclusion(s): A passing grade in AL Applied Mathematics / AL Pure Mathematics; MATH 1013, MATH 1014, MATH 1018, MATH 1023, MATH 1024; any MATH course at or above 100-/2000- level Prerequisite(s): Level 5* or 5** in HKDSE Mathematics Extended Module M2

 MATH 1023 Honors Calculus I [3 Credit(s)] [Previous Course Code(s): MATH 023] 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. Exclusion(s): AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1013, MATH 1014, MATH 1018, MATH 1020; any MATH course at or above 100-/2000- level Prerequisite(s): Level 5 or above in HKDSE Mathematics Extended Module M2

 MATH 1024 Honors Calculus II [3 Credit(s)] [Previous Course Code(s): MATH 024] 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. Exclusion(s): AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1014, MATH 1018, MATH 1020; any MATH course at or above 100-/2000- level Prerequisite(s): MATH 1013 OR MATH 1023

 MATH 1701 Introductory Topics in Mathematical Sciences [1-4 Credit(s)] [Previous Course Code(s): MATH 092] 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 1702 Information Technology Practical Training [0 Credit(s)] [Previous Course Code(s): MATH 099] For students in the Science School only. A practical training course for a total duration of two weeks covering basic PC hardware architecture, an introduction to Windows 2000/XP operating systems and web based learning application software. Graded P or F.

 MATH 1712 Mathematics in Daily Life [3 Credit(s)] [Previous Course Code(s): MATH 162] This course aims to help students develop the mathematical literacy to see the connections and applications of mathematics to daily life activities. The course consists of two components: (i) introducing different topics of mathematics in daily life such as mathematics in voting, finance, scheduling, etc, and (ii) guiding projects on the students' chosen topics of mathematics related to real life problems or other branches of study. Year 3 and 4 students are required to seek approval from instructor prior to enrollment.

 MATH 1713 Flattening the Earth: Maps and Map Projections [3 Credit(s)] Maps are graphical representations of our surroundings. Mathematically, a map of the earth is a function from the two-dimensional sphere into the plane. To understand whether it can be done or how it can be done involves concepts from topology and differential geometry. There are also many fascinating stories about the development of various map drawing methods and their impacts ton the development of human civilization Prerequisite(s): Level 3 or above in HKDSE Mathematics Extended Module M1/M2

 MATH 2010 Multivariable Calculus and Basic Probability [3 Credit(s)] [Previous Course Code(s): MATH 106] This course teaches basic application techniques in multivariable calculus and concepts in probability. Key topics include: vectors and vector valued functions, functions of several variables, partial derivatives, constrained optimization, multiple integrals, and basic probability. Exclusion(s): MATH 2011, MATH 2021, MATH 2023 Prerequisite(s): MATH 1003 OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024 OR a passing grade in AS Mathematics and Statistics / AL Applied Mathematics / AS Applied Mathematics / AL Pure Mathematics

 MATH 2011 Introduction to Multivariable Calculus [3 Credit(s)] [Previous Course Code(s): MATH 100] Differentiation in several variables, with applications in approximation, maximum and minimum and geometry. Integration in several variables, vector analysis. Exclusion(s): MATH 2010, MATH 2021, MATH 2023 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014; OR MATH 1018; OR MATH 1020; OR MATH 1024

 MATH 2021 Multivariable and Vector Calculus [4 Credit(s)] [Previous Course Code(s): MATH 102] This is a one-year course with focus on limits, one variable calculus, sequences, series, gradients, chain rule, extrema, Lagrange multipliers, line integrals, multiple integrals, Jacobians, Implicit function theorem, Green's theorem, Stoke's theorem, divergence theorem. Exclusion(s): MATH 2010, MATH 2011, MATH 2023 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2023 Multivariable Calculus [4 Credit(s)] [Previous Course Code(s): MATH 101] Sequences, series, gradients, chain rule. Extrema, Lagrange multipliers, line integrals, multiple integrals. Green's theorem, Stroke's theorem, divergence theorem, change of variables. Exclusion(s): MATH 2010, MATH 2011, MATH 2021 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2031 Introduction to Real Analysis [4 Credit(s)] [Previous Course Code(s): MATH 202] This is a one-year course with focus on sets and functions, real numbers, open and closed sets, limits of sequences and series, limits and continuity of functions, Taylor's series, differentiations, Riemann integrations, uniform convergence. Exclusion(s): MATH 2033, MATH 2043 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2033 Mathematical Analysis [4 Credit(s)] [Previous Course Code(s): MATH 201] Sets and functions, real numbers, limits of sequences and series, limits of functions, continuous functions, differentiation, Riemann integration, additional topics. Exclusion(s): MATH 2031, MATH 2043 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2043 Honors Mathematical Analysis [4 Credit(s)] [Previous Course Code(s): MATH 203] 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. Exclusion(s): MATH 2033, MATH 2031 Prerequisite(s): Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1018/MATH 1020/MATH 1024

 MATH 2111 Matrix Algebra and Applications [3 Credit(s)] [Previous Course Code(s): MATH 113] Systems of linear equations; vector spaces; linear transformations; matrix representation of linear transformations; linear operators, eigenvalues and eigenvectors; similarity invariants and canonical forms. Exclusion(s): MATH 2121, MATH 2131, MATH 2350 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2121 Linear Algebra [4 Credit(s)] [Previous Course Code(s): MATH 111] Vector space, matrices and system of linear equations, linear mappings and matrix forms, inner product, orthogonality, eigenvalues and eigenvectors, symmetric matrix. Exclusion(s): MATH 2111, MATH 2131, MATH 2350 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2131 Honors in Linear and Abstract Algebra I [4 Credit(s)] [Previous Course Code(s): MATH 217] 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. Exclusion(s): MATH 2121, MATH 2111, MATH 2350 Prerequisite(s): Grade A in AL Pure Mathematics; or grade A- or above in MATH 1014/MATH 1018/MATH 1020/MATH 1024

 MATH 2343 Discrete Structures [4 Credit(s)] [Previous Course Code(s): MATH 132] 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. Exclusion(s): COMP 2711 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; or MATH 1014; or MATH 1018; or MATH 1020; or MATH 1024

 MATH 2350 Applied Linear Algebra and Differential Equations [4 Credit(s)] [Previous Course Code(s): MATH 152] First order equation, linear second order equations, Laplace transform, Euler and Runge-Kutta methods, introduction to partial differential equations, matrix, systems of linear equations, eigenvalue and eigenvector, systems of differential equations, orthogonal projection. Exclusion(s): MATH 2111, MATH 2121, MATH 2131, MATH 2351, MATH 2352 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2351 Introduction to Differential Equations [3 Credit(s)] [Previous Course Code(s): MATH 150] First order equations, second order equations, Laplace transform method, numerical solution of initial value problems, boundary-value problems. Exclusion(s): MATH 2350, MATH 2352 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2352 Differential Equations [4 Credit(s)] [Previous Course Code(s): MATH 151] First and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory. Exclusion(s): MATH 2350, MATH 2351 Prerequisite(s): MATH 2111 OR MATH 2121 OR MATH 2131

 MATH 2411 Applied Statistics [4 Credit(s)] [Previous Course Code(s): MATH 144] A systematic introduction to statistical inference, including the necessary probabilistic background, point and interval estimation, hypothesis testing. Exclusion(s): IELM 2510, ISOM 2500, LIFS 3150 Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2421 Probability [4 Credit(s)] [Previous Course Code(s): MATH 241] 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. Exclusion(s): ELEC 2600, ISOM 3540 Corequisite(s): MATH 2010/MATH 2011/MATH 2021/MATH 2023/MATH 3043

 MATH 2511 Fundamentals of Actuarial Mathematics [3 Credit(s)] 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. Prerequisite(s): MATH 1003 OR MATH 1013 OR MATH 1020 OR MATH 1023

 MATH 2721 Concepts in Mathematics [2 Credit(s)] [Previous Course Code(s): MATH 110] 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. Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 2731 Mathematical Problem Solving [3 Credit(s)] [Previous Course Code(s): MATH 190] Discussions on problem solving techniques. Basics materials in combinatorics, number theory, geometry and mathematical games. Prerequisite(s): A passing grade in AL Pure Mathematics/AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 3033 Real Analysis [4 Credit(s)] [Previous Course Code(s): MATH 301] Functions of several variables, implicit and inverse function theorem, uniform convergence measure and integral on the real line. Exclusion(s): MATH 3043 Prerequisite(s): (MATH 2010 / MATH 2011 / MATH 2021 / MATH 2023) AND (MATH 2031 / MATH 2033 / MATH 2043) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350)

 MATH 3043 Honors Real Analysis [4 Credit(s)] [Previous Course Code(s): MATH 204] 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. Exclusion(s): MATH 3033 Prerequisite(s): Grade A- or above in MATH 2043

 MATH 3121 Algebra I [3 Credit(s)] [Previous Course Code(s): MATH 311] Polynomials; Jordan canonical form, minimal polynomials, rational canonical form; equivalence relation; group, coset, group action; introduction to rings and fields. Exclusion(s): MATH 3131 Prerequisite(s): MATH 2111/MATH 2121/MATH 2131/MATH 2350

 MATH 3131 Honors in Linear and Abstract Algebra II [4 Credit(s)] [Previous Course Code(s): MATH 218] 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. Prerequisite(s): Grade B- or above in MATH 2131

 MATH 3311 Introduction to Numerical Methods [2 Credit(s)] [Previous Course Code(s): MATH 230] Computer arithmetric, matrix computation, interpolation and approximation, numerical integration, solution of nonlinear equations. Exclusion(s): MATH 3312 Corequisite(s): MATH 2010 OR MATH 2011 OR MATH 2021 OR MATH 2023 OR MATH 3043

 MATH 3312 Numerical Analysis [3 Credit(s)] [Previous Course Code(s): MATH 231] 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. Fortran may also be taught. Exclusion(s): MATH 3311 Prerequisite(s): (COMP 1002 / COMP 1004 / COMP 1022P) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (MATH 2031 / MATH 2033 / MATH 2043)

 MATH 3343 Combinatorial Analysis [3 Credit(s)] [Previous Course Code(s): MATH 232] 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, Striling numbers, partition numbers, matchings and stable matchings, systems of distinctive representatives, block designs, Steiner triple systems, Latin squares, Burnside's lemma, Polya counting formula. Prerequisite(s): MATH 2721; or MATH 2121/MATH 2111/MATH 2350/MATH 2131; or MATH 2343/COMP 2711

 MATH 3423 Statistical Inference [3 Credit(s)] [Previous Course Code(s): MATH 243] Sampling theory, order statistics, limiting distributions, point estimation, confidence intervals, hypothesis testing, non-parametric methods. Prerequisite(s): MATH 2421

 MATH 3424 Regression Analysis [3 Credit(s)] [Previous Course Code(s): MATH 342] Estimation and hypothesis testing in linear regression, residual analysis, multicollinearity, indicator variables, variable selection, nonlinear regression. Exclusion(s): ISOM 5520 Prerequisite(s): MATH 3423

 MATH 3425 Stochastic Modeling [3 Credit(s)] [Previous Course Code(s): MATH 341] Discrete time Markov chains and the Poisson processes. Additional topics include birth and death process, elementary renewal process and continuous-time Markov chains. Prerequisite(s): MATH 2411/MATH 2421

 MATH 3426 Sampling [3 Credit(s)] [Previous Course Code(s): MATH 346] 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. Prerequisite(s): MATH 2411/MATH 3423

 MATH 4023 Complex Analysis [3 Credit(s)] [Previous Course Code(s): MATH 304] Complex differentiability; Cauchy-Riemann equations; contour integrals, Cauchy theory and consequences; power series representation; isolated singularities and Laurent series; residue theorem; conformal mappings. Prerequisite(s): (MATH 2010 OR MATH 2011 OR MATH 2021 OR MATH 2023 OR MATH 3043) AND (MATH 2031 OR MATH 2033 OR MATH 2043)

 MATH 4033 Calculus on Manifolds [3 Credit(s)] [Previous Course Code(s): MATH 305] Introduction to manifolds, metric spaces, multi-linear Algebra, differential forms, Stokes theorem on manifolds, cohomology. Prerequisite(s): MATH 3043/MATH 3033

 MATH 4051 Theory of Ordinary Differential Equations [3 Credit(s)] [Previous Course Code(s): MATH 303] Existence and uniqueness theorems of ordinary differential equations, theory of linear systems, stability theory, study of singularities, boundary value problems. Prerequisite(s): (MATH 2350 OR MATH 2351 OR MATH 2352) AND (MATH 3033 OR MATH 3043)

 MATH 4052 Partial Differential Equations [3 Credit(s)] [Previous Course Code(s): MATH 306] 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. Prerequisite(s): MATH 2011/MATH 2023/MATH 2021/MATH 2010/MATH 3043 and MATH 2121/MATH 2111/MATH 2350/MATH 2131 and MATH 2351/MATH 2352/MATH 2350

 MATH 4061 Topics in Modern Analysis [2 Credit(s)] [Previous Course Code(s): MATH 370, MATH 391G] 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. Prerequisite(s): MATH 3043 or MATH 3033

 MATH 4063 Functional Analysis [2 Credit(s)] [Previous Course Code(s): MATH 371, MATH 300K] 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. Prerequisite(s): MATH 4061

 MATH 4121 Algebra II [3 Credit(s)] [Previous Course Code(s): MATH 312] Groups and symmetry. Group actions. Symmetries of pictures, graphs, Euclidean spaces, platonic solids. Polynomials, field extensions, impossibility of certain geometric constructions. Finite fields. Applications to cryptography. Exclusion(s): MATH 3131 Prerequisite(s): MATH 2131 or MATH 3121

 MATH 4141 Number Theory and Applications [3 Credit(s)] [Previous Course Code(s): MATH 315] Prime numbers, unique factorization, modular arithmetic, quadratic number fields, finite fields, p-adic numbers, coding theory, computational complexity. Prerequisite(s): MATH 2131 Corequisite(s): (for students without prerequisites) MATH 3121

 MATH 4151 Introduction to Lie Groups [3 Credit(s)] [Previous Course Code(s): MATH 316] General linear groups, orthogonal groups, unitary groups, symplectic groups, exponential maps, maximal tori, Clifford algebra, spin groups. Prerequisite(s): (MATH 2010 OR MATH 2011 OR MATH 2021 OR MATH 2023 OR MATH 3043) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)

 MATH 4221 Euclidean and Non-Euclidean Geometries [3 Credit(s)] [Previous Course Code(s): MATH 320] Axioms and models, Euclidean geometry, Hilbert axioms, neutral (absolute) geometry, hyperbolic geometry, Poincare model, independence of parallel postulate. Prerequisite(s): MATH 2031 OR MATH 2033 OR MATH 2043 OR MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350 OR MATH 2721

 MATH 4223 Differential Geometry [3 Credit(s)] [Previous Course Code(s): MATH 321] 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. Prerequisite(s): MATH 2011/MATH 2021/MATH 2023/MATH 3043 and MATH 2121/MATH 2131

 MATH 4225 Topology [3 Credit(s)] [Previous Course Code(s): MATH 323] Metric, topology, continuous map, Hausdorff, connected, compact, graph, Euler number, CW-complex, classification of surfaces. Prerequisite(s): MATH 2031/MATH 2033/MATH 2043

 MATH 4321 Game Theory [3 Credit(s)] [Previous Course Code(s): MATH 310] 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. Exclusion(s): SOSC 1410 Prerequisite(s): (MATH 2010 OR MATH 2011 OR MATH 2021 OR MATH 2023 OR MATH 3043) AND (MATH 2111 OR MATH 2121 OR MATH 2131 OR MATH 2350)

 MATH 4326 Introduction to Fluid Dynamics [3 Credit(s)] [Previous Course Code(s): MATH 308] 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. Exclusion(s): CIVL 2510, CIVL 3520, MECH 3210 Prerequisite(s): MATH 4052

 MATH 4333 Mathematical Biology [3 Credit(s)] [Previous Course Code(s): MATH 365] Population, ecology, infectious disease, genetic, and biochemistry models. Additional topics chosen by instructor. Prerequisite(s): MATH 2121/MATH 2111/MATH 2131 and MATH 2351/MATH 2352; or MATH 2350

 MATH 4336 Introduction to Mathematics of Image Processing [3 Credit(s)] 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. Exclusion(s): COMP 4421, ELEC 4130 Prerequisite(s): MATH 2011/MATH 2021/MATH 2023 and [MATH 2350 or (MATH 2111/MATH 2121/MATH 2131 and MATH 2351/MATH 2352)]

 MATH 4351 Numerical Solutions of Partial Differential Equations [3 Credit(s)] [Previous Course Code(s): MATH 331] 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. Prerequisite(s): MATH 2350/MATH 2351/MATH 2352 and MATH 3311/MATH 3312 and MATH 4052

 MATH 4422 Data Analysis [3 Credit(s)] [Previous Course Code(s): MATH 343] 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. Prerequisite(s): MATH 2411/MATH 3423 and MATH 3424

 MATH 4423 Nonparametric Statistics [3 Credit(s)] [Previous Course Code(s): MATH 345] 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. Prerequisite(s): MATH 2411/MATH 3423

 MATH 4424 Multivariate Analysis [3 Credit(s)] [Previous Course Code(s): MATH 347] Inferences of means and covariance matrices, canonical correlation, discriminant analysis, multivariate ANOVA, principal components analysis, factor analysis. Exclusion(s): ISOM 5530 Prerequisite(s): MATH 3423 and MATH 3424

 MATH 4425 Introductory Time Series [3 Credit(s)] [Previous Course Code(s): MATH 348] Stationarity, (partial) auto-correlation function, ARIMA modeling, order selection, diagnostic, forecasting, spectral analysis. Prerequisite(s): MATH 3423 and MATH 3424

 MATH 4426 Survival Analysis [3 Credit(s)] 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. Prerequisite(s): MATH 3423

 MATH 4427 Loss Models and Credibility Theory [3 Credit(s)] This course covers the construction of casualty loss models and credibility theory. The topics discussed in this course include severity models, frequency models, aggregate models, coverage modifications, loss elimination ratios, effect of inflation on losses, risk measures, limit fluctuation credibility, Bayesian credibility models for discrete and continuous models, Buhlman and Buhlman-Straub credibility models, conjugate priors in Bayesian analysis, and empirical Bayesian methods in non-parametric and semi-parametric models. Prerequisite(s): (IELM 2510 OR ISOM 2500 OR MATH 2411 OR MATH 3423) AND (ELEC 2600 OR ISOM 3540 OR MATH 2421)

 MATH 4511 Quantitative Methods for Fixed Income Derivatives [3 Credit(s)] [Previous Course Code(s): MATH 361] Random walk models for asset price and interest rate processes. Risk neutral valuation principle, binomial model. Lattice tree algorithms for pricing options. Monte Carlo simulation techniques. Yield curve fitting, no-arbitrage interest rate models. Pricing algorithms for embedded features in fixed income instruments. Prerequisite(s): (MATH 2010 / MATH 2011 / MATH 2021 / MATH 2023 / MATH 3043) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (ISOM 2500 / ISOM 3540 / MATH 2411 / MATH 2421)

 MATH 4512 Fundamentals of Mathematical Finance [3 Credit(s)] [Previous Course Code(s): MATH 362] Discrete securities models. Concept of arbitrage. Risk neutral probability measures, valuation of continge claims, complete and incomplete markets. Optimal consumption and investment problems. Actuarial stochastic investment models, insurance and pension applications. Risk theory, value at risk, ruin probability. Prerequisite(s): (MATH 2010 / MATH 2011 / MATH 2021 / MATH 2023 / MATH 3043) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (ISOM 2500 / ISOM 3540 / MATH 2411 / MATH 2421)

 MATH 4513 Life Contingencies Models and Insurance Risk [3 Credit(s)] This is an undergraduate-level one semester course on life contingencies models and insurance risk. The topics discussed in this course include survival models, life tables and selection, insurance benefits, annuities, premium calculation, and insurance policy values. Prerequisite(s): ELEC 2600 OR ISOM 3540 OR MATH 2421

 MATH 4821 Special Topics [1-4 Credit(s)] [Previous Course Code(s): MATH 300] 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)] [Previous Course Code(s): MATH 391] Supplementary study of specialized topics for students of pure mathematics.

 MATH 4823 Special Topics in Applied Mathematics [1-4 Credit(s)] [Previous Course Code(s): MATH 392] Supplementary study of specialized topics for students of applied mathematics.

 MATH 4824 Special Topics in Statistics and Financial Mathematics [1-4 Credit(s)] [Previous Course Code(s): MATH 393] Supplementary study of specialized topics for students of statistics.

 MATH 4825 Topics in Actuarial Mathematics [3 Credit(s)] 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. Prerequisite(s): (IELM 2510 OR ISOM 2500 OR MATH 2411 OR MATH 3423) AND (ELEC 2600 OR ISOM 3540 OR MATH 2421)

 MATH 4921 Student Seminars [1-3 Credit(s)] [Previous Course Code(s): MATH 309] 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. Prerequisite(s): A passing grade in AL Pure Mathematics / AL Applied Mathematics OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024

 MATH 4981-4982 Independent Study [1-3 Credit(s)] [Previous Course Code(s): MATH 397-398] Undergraduate research conducted under the supervision of a faculty member. A written report and presentation are required. Scope may include (i) identifying a non-reference problem and proposing methods of solutions, and (ii) acquiring a specific research skill. Students may take MATH 4981 or/and MATH 4982 for credits up to two times.

 MATH 4990 Undergraduate Project [2-3 Credit(s)] [Previous Course Code(s): MATH 399] 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. Prerequisite(s): MATH 4982

 MATH 4999 Capstone Project [3 Credit(s)] Independent work in an area of mathematics under the guidance of a faculty member. The project either surveys a research topic or describes a small project completed by the student. For MATH and MAEC Year 4 students only.