Courses

Undergraduate Courses

Code	Course Description
MATH 1.1	PREPARATION FOR COLLEGE MATHEMATICS I 3 units This course aims to develop basic mathematics competencies so that students may be able to use mathematics in day-to-day decision-making and functioning. It covers the real number system and operations, ratio and proportion, and variables and equations. Multiple representations of mathematical operations and relationships between variables are discussed to provide the students with more than one way of solving mathematical problems. The use of technology, like calculators and computers, is also highlighted.
MATH 1.2	PREPARATION FOR COLLEGE MATHEMATICS II 3 units Prerequisite: MATH 1.1 This course aims to provide students with the basic foundational knowledge of statistics. It discusses the tools of descriptive statistics (measures of central tendency, dispersion and position) and basic probability concepts. It prepares the students for the level of statistics required of the course Mathematics in the Modern World, for the use of quantitative methods in future research work, and for making decisions involving chance.
MATH 2	PREPARATORY COURSE TO CALCULUS 0 units MATH 2 is a non-credit bridging course for students who need to strengthen their knowledge of pre-calculus or who have insufficient mathematics background necessary for succeeding calculus courses. Topics include solutions of equations and inequalities, graphs of conic sections, and functions such as linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.
MATH 21	UNIVERSITY PRECALCULUS 3 units MATH 21 is a 3-unit course that aims to prepare students for succeeding calculus courses. Topics include solutions of equations and inequalities, conic sections and functions such as linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.
MATH 30.13	APPLIED CALCULUS FOR BUSINESS AND ECONOMICS I 3 units Prerequisite: MATH 21 for AB EC, AB MEC and BS ITE MATH 30.13 and MATH 30.14 are two 3-unit courses on calculus taken by business and economics students. The two courses may be taken consecutively in one semester. Topics in MATH 30.13 include limits, continuity and derivatives of functions of one variable.
MATH 30.14	APPLIED CALCULUS FOR BUSINESS AND ECONOMICS II 3 units Prerequisite: MATH 30.13 MATH 30.13 and MATH 30.14 are two 3-unit courses on calculus taken by business and economics students. The two courses may be taken consecutively in one semester. Topics in MATH 30.14 include integrals of functions of one variable and calculus of functions of several variables.
MATH 30.23	APPLIED CALCULUS FOR SCIENCE AND ENGINEERING I 3 units Prerequisite: MATH 21 for programs required to take MATH 21 This course is the first of two courses on calculus taken by science and engineering students. Topics include limits and continuity of functions of one variable, derivative of function of one variable, rules of differentiation and applications in solving optimization and related rates problems, antiderivative and definite integral of function of one variable, improper integrals, sequences of real numbers, series of constant terms, and power series.
MATH 30.24	APPLIED CALCULUS FOR SCIENCE AND ENGINEERING II 3 units Prerequisite: MATH 30.23 This course is the second of two courses on calculus taken by science and engineering students. Topics include calculus of several variables and vector calculus.
MATH 31.1	MATHEMATICAL ANALYSIS 1A 3 units Prerequisite: MATH 21, if required in the program The course is the first of two on the calculus of functions of a single variable. The course starts with a discussion of functions and its graphs. Then it proceeds to a discussion of limits and continuity for functions of one variable, the derivative of a function of one variable, rules of differentiation, and its applications in solving optimization problems, in sketching the graph of a function, and in simple root-finding algorithms. The course also places emphasis on the formal mathematical statements, proofs, and the applications of the definitions and theorems tackled.
MATH 31.2	MATHEMATICAL ANALYSIS 1B 3 units Prerequisite: MATH 31.1 The course is the second of two on the calculus of functions of a single variable. Its main focus is the Riemann integral of functions, its connection with the derivative via the Fundamental Theorem of Calculus, and the applications of integrals to lengths, areas, volumes. Various applications to economics, physics, and biology and other areas of science are also discussed. The course also places emphasis on the formal mathematical statements, proofs, and the applications of the definitions and theorems tackled.
MATH 31.3	MATHEMATICAL ANALYSIS II 3 units Prerequisite: MATH 31.2 This course is the third of a series of calculus courses. The major topics covered in the course are indeterminate forms and L’Hospital’s Rule, improper integrals, sequences and series of numbers, power series, and calculus of functions of two or more variables.
MATH 31.4	MATHEMATICAL ANALYSIS III 3 units Prerequisite: MATH 31.3 This is the last of a series of courses in elementary calculus taken by math majors. The major topics covered in this course are vectors in the plane and in space, vector-valued functions, and the calculus of vector fields.
MATH 40.1	LINEAR ALGEBRA 3 units Prerequisite: MATH 31.3 The course is an introduction to linear algebra covering matrices, vector spaces, inner product spaces, linear transformations, determinants, and eigenvalues. Applications include least squares approximation and curving-fitting, polynomial interpolation, and computer graphics.
MATH 40.2	ADVANCED LINEAR ALGEBRA 3 units Prerequisite: MATH 80.1 The course covers advanced topics in Linear Algebra, focusing on Module Theory: introduction to modules and module homomorphisms, generation of modules, direct sums and free modules, tensor products of modules, exact sequences, matrix of a linear transformation, dual vector spaces, determinants, tensor algebras, symmetric and exterior algebras, modules over principal ideal domains.
MATH 40.3	MATRIX ANALYSIS 3 units Prerequisite: MATH 40.1 Matrix Analysis may be described as that part of mathematics which blends linear algebra techniques with those of mathematical analysis. The primary topics this course covers are roughly: Gaussian Elimination, Issues of Algorithmic Sensitivity, Orthogonal Matrices and Orthonormality, Eigenvalues and Eigenvectors, and the Singular Value Decomposition.
MATH 40.4	LINEAR ALGEBRA FOR GAMES PROGRAMMING 3 units This course is an introduction to linear algebra with emphasis on applications for computer graphics and games programming. The theory part covers the algebra of matrices, vector spaces, inner product spaces, and linear transformations. Applications include projection matrices, rotators, reflectors, homogeneous coordinates and perspective projections.
MATH 50.1	ELEMENTARY NUMBER THEORY 3 units This course is an introduction to the fundamental concepts of number theory that are essential in higher areas of Mathematics. Topics include integers and divisibility, primes and factorization, Diophantine equations, congruences, the Chinese remainder theorem, quadratic residues, and the quadratic reciprocity law. Several theorems and algorithms are applied to solve computational problems and to derive and prove generalizations.
MATH 50.2	SECOND COURSE ON NUMBER THEORY 3 units Prerequisites: MATH 40.1, MATH 50.1 This course lays the foundation for undergraduate Algebraic Number Theory. The course covers the following topics: Field of algebraic numbers, rings of integers of number fields, cubic and quadratic fields, ideals, unique factorization domains and principal ideal domains, splitting of primes, the class group.
MATH 51.1	DISCRETE MATHEMATICS I 3 units This course is a 3-unit course taken primarily by math majors. The aim is to introduce them to topics in number theory and combinatorics, namely, fundamental principles of counting, symbolic logic, number theory, the principle of inclusion and exclusion, generating functions, and recurrence relations.
MATH 51.2	DISCRETE MATHEMATICS II 3 units Prerequisite: MATH 51.1 MATH 51.2 is a 3-unit course taken primarily by BS Math students to introduce them to other topics in discrete mathematics such as relations and graph theory. A survey of problem solving algorithms is also explored.
MATH 51.3	MATH FOR COMPUTER SCIENCE I 3 units This is a 3-unit course taken primarily by Computer Science majors. It serves as an introduction to discrete mathematics with a focus on its application to computer science. Topics include (1) propositional logic, (2) proofs, (3) number theory and (4) combinatorics.
MATH 51.4	MATH FOR COMPUTER SCIENCE II 3 units Prerequisite: MATH 51.3 This is a 3-unit course that extends the content taken up in MATH 51.3. The first part of this course deepens the discrete structures taken up by the students in other courses; namely, recurrence relations, matrices, graphs and trees. The second part focuses on algorithmic strategies which include brute force and greedy algorithm, recursive backtracking, and dynamic programming.
MATH 52.1	COMBINATORIAL MATHEMATICS 3 units Combinatorics is concerned with the study of arrangements, patterns, designs and configurations. The techniques of combinatorics have far-reaching applications in computer-science, information processing, management science, electrical engineering, coding and communications, experimental design, genetics, chemistry, and even political science.
MATH 52.2	COMBINATORIAL DESIGNS 3 units This course introduces the student to Combinatorial Design Theory which is the study of arranging elements of a finite set into patterns (subsets, arrays) according to specified rules. The course aims to present some of the basic concepts of block designs, emphasizing in particular the methods of constructing new designs. Moreover, it also introduces other combinatorial structures such as Latin squares and difference sets. Topics in this course include symmetric designs, resolvable designs, Hadamard matrices, Latin squares, difference sets and codes.
MATH 52.3	GAME THEORY 3 units Prerequisites: MATH 30.13, MATH 30.14 or equivalent This course covers the following topics: theory of matrix game; the minimax theorem for finite and continuous games; games in extensive form; the connection between game theory and linear programming; introduction to games against nature. As an extension of its present scope, and based on recent developments of the topic, this course further covers evolutionary games. Evolutionary game theory merges the concepts of Darwin’s natural selection with classical game theory, and has been applied in explaining the emergence of cooperation in ecological contexts.
MATH 52.5	GROUPS AND DESIGNS 3 units This is a course on permutation groups, designs and other combinatorial structures. The student must have a reasonable knowledge of abstract algebra, linear algebra, and combinatorics. A background on classical geometry is an advantage. Topics in this course include permutation groups, transitive groups, primitive groups, finite geometries, designs, automorphisms of designs, Hadamard matrices and designs.
MATH 53.1	GRAPH THEORY I 3 units This course offers basic introduction to graphs (directed and undirected) and networks. Topics include paths and circuits (Eulerian and Hamiltionian), connectedness, graph isomorphism, trees and fundamental circuits, adjacency and incidence matrices, matchings and covers, vertex/edge coloring and connectivity, planar graphs and duality.
MATH 53.2	GRAPH THEORY II 3 units This is a course on applications of graphs and networks covering both standard network optimization problems involving distance, time and flow as well as heuristic solutions to network problems. Newer applications involving the notion of centrality and the concept of Voronoi diagrams are also tackled.
MATH 54.1	INTRODUCTION TO CODING THEORY 3 units Prerequisite: MATH 40.1 This course is an introduction to Coding Theory discusses the basic definitions and concentrates on linear and cyclic codes. Properties of these codes are given and so are the more popular bounds such as the sphere-packing, Greismer, singleton and Gilbert-Varshamov bounds. Particular codes and families of codes like the Reed-Muller, Hamming, Golay, Bose-Chaudhuri-Mesner, and quadratic residue codes are likewise defined and characterized. The subject ends with a brief introduction to lattice-theory and its relationship to self-dual codes.
MATH 54.2	PRINCIPLES IN CRYPTOGRAPHY 3 units Prerequisites: MATH 40.1, MATH 50.1, MATH 80.1 In electronic data communication, two of the major concerns are data integrity and data security; coding addresses the first concern, while cryptography addresses the other. The coding portion of the course introduces the theory of error-correcting codes and discusses various families of error-correcting codes. The cryptography portion surveys the principles of network security and discusses classical, conventional, and public-key encryption algorithms.
MATH 55.1	FUNDAMENTAL CONCEPTS OF MATHEMATICS 3 units The course is on fundamental concepts of mathematics. Its main focus is mathematical logic, sets, methods of proof, equivalence relations, functions, sets with structures and operations, and concrete realizations of sets with structures. The course also places emphasis on the formal mathematical statements, proofs, and the applications of the definitions and theorems tackled. Moreover, it provides a few organizing principles to the many mathematical knowledge previously learned by the students.
MATH 55.4	HISTORY OF MATHEMATICS 3 units Prerequisites: MATH 80.1, MATH 90.1 This course is designed as an introduction and invitation to higher mathematics. The central topics are: abstract mathematical structures from algebra, geometry, and analysis; the axiomatic approach; and the foundations of set theory. These concepts are then applied to develop a system of hyperreal numbers which serves as an alternative foundation for the Calculus. Throughout the course, emphasis is placed on the context and intuitive development of the abstract ideas.
MATH 55.5	PROBLEM SOLVING TECHNIQUES 3 units Prerequisite: Recommendation by previous math teachers based on performance and motivation This course is about mathematical problem solving. It introduces the different levels of problem solving and the strategies for investigation. Fundamental tactics in solving, such as looking for a pattern, working backwards, solving a simpler problem, parity, pigeonhole principle, mathematical induction, symmetry, extreme principle, and invariants are covered. Special topics in Graph Theory, Combinatorics and Geometry are discussed, as well as Fermat’s Last Theorem and various types of problems in mathematics competitions such as Putnam, Asia-Pacific Mathematics Olympiad, and the International Mathematical Olympiad.
MATH 55.6	METHODS OF PROOF 3 units This is a course on construction of mathematical proofs. The course provides the tools and techniques used to prove mathematical theorems and to prepare students in writing correct mathematical proofs. Topics include an introduction to mathematical logic, common strategies used in proving theorems, and some mathematical concepts to illustrate mathematical proofs.
MATH 60.1	STATISTICS FOR LIFE SCIENCES 3 units This is an applied statistics course taken by majors in life and environmental sciences. The first half of the course introduces the students to the basics of descriptive statistics and probability theory. The latter part of the course deals with the necessary statistical methods needed in biological sciences such as confidence intervals, hypothesis testing, goodness-of-fit test, analysis of variance, and regression analysis. The software R is used for statistical computing.
MATH 60.2	INTRODUCTION TO STATISTICAL ANALYSIS 3 units Prerequisite: MATH 30.23 This is a course that includes descriptive statistics, elementary probability theory and applications, sampling theory and applications, estimation and hypothesis testing, regression and correlation analysis, and analysis of variance.
MATH 61.1	ELEMENTARY PROBABILITY THEORY FOR ENGINEERS 3 units Prerequisite: MATH 31.3 The course introduces to students basic probability theory, combinatorial methods, the concept of discrete and continuous random variables and their probability distributions, the concept of mathematical expectation, some probability distributions with special names, the moments and moment-generating functions of random variables, obtaining the probability distribution of functions of random variables, and their applications to engineering problems.
MATH 61.2	ELEMENTARY PROBABILITY THEORY 3 units Prerequisite: MATH 31.3 This is a three-unit course designed to introduce the concepts and techniques of probability modelling to areas such as operations research, financial mathematics, dynamical systems, and statistics. It focuses on techniques and methodologies towards a better understanding of inferential statistics through distribution theory. Topics such as conditional probability, random variables and distributions, and mathematical expectations are discussed.
MATH 61.3	ADVANCED PROBABILITY AND MARTINGALES 3 units Prerequisite: MATH 61.2 The course proves important results such as Kolmogorov’s Law of Large Numbers and the Three - Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. It assumes certain key results from measure theory.
MATH 62.1	INTRODUCTION TO STATISTICAL THEORY 3 units Prerequisite: MATH 61.2 This is a 3-unit course that aims to provide a rigorous introduction to the mathematics and practice of (parametric) statistical inference. It assumes that students have sufficient background in elementary calculus, elementary probability theory, and linear algebra. Topics in estimation, hypothesis testing, analysis of variance, simple linear regression, and goodness of fit tests are discussed.
MATH 62.2	TIME SERIES AND FORECASTING 3 units Prerequisites: MATH 40.1, MATH 62.1 This course provides a rigorous introduction to the basic concepts and techniques of time series and forecasting. Prerequisites to this course include mathematical statistics (MATH 62.1) and linear algebra (MATH 40.1). Topics include multivariate normal distribution, distribution of quadratic forms, multiple regression model, analysis-of-variance models, stationary process and autoregressive moving average models. Procedures in popular statistical software (SAS or R) shall be used for the analysis of real-life forecasting problems.
MATH 62.4	STATISTICAL METHODS 3 units Prerequisites: MATH 61.2, MATH 62.1 This course, delivered in three parts, tackles statistical methods that are used in a variety of financial situations. The first part discusses topics in multivariate statistical analysis, specifically principal component analysis, factor analysis, and cluster analysis. The second part involves the statistical techniques used in building credit scorecards and modelling credit risk. The third part covers the statistical methods used to model the distribution of operational risk exposures.
MATH 62.5	REGRESSION ANALYSIS 3 units Prerequisites: MATH 40.1, MATH 62.1 Topics such as projection theory in vector spaces, distribution of random vectors and quadratic forms, general linear model (full column rank), and remedial measures are discussed. All computations are done using R. It is important to note that regression analysis is one of the basic statistical modeling techniques. Many advanced models in practice such as logistic regression, spatial modeling, and time series analysis assume a strong background of regression analysis.
MATH 70.1	NUMERICAL METHODS FOR SCIENCE AND ENGINEERING 3 units Prerequisites: MATH 31.1, MATH 31.2 This is a course on numerical methods for science and engineering students. Topics include matrix operations, determinants of matrices, solutions of linear systems using matrices, and root-finding methods for nonlinear equations.
MATH 71.1	FUNDAMENTALS OF COMPUTING I 3 units This course provides an introduction to computer programming through the use of the Python programming language, MS Excel and VBA. The course covers introduction to computers, recursion, abstract data types, programming interfaces, In-class lectures and discussions are supplemented by computer hands-on sessions.
MATH 71.2	FUNDAMENTALS OF COMPUTING II 3 units Prerequisite: MATH 71.1 This course is a continuation of MATH 71.1; the course introduces other programming languages and software. The course also covers the fundamentals of object-oriented programming (OOP) and basic data structures.
MATH 71.3	SCIENTIFIC COMPUTING I 3 units Prerequisite: MATH 40.1 This is a survey course on the mathematics of scientific computing, emphasizing the numerical solution to linear systems, least-squares problem, least-norm problem, matrix factorizations, sensitivity and conditioning, root finding in of nonlinear functions in one and several variables, unconstrained optimization, and nonlinear least-norm problem.
MATH 71.4	SCIENTIFIC COMPUTING II 3 units Prerequisite: MATH 71.3 The first part of the course deals with the numerical solution to deterministic ordinary and partial differential equations. The main algorithm that is employed is the spectral collocation method. The second part, on the other hand, deals with stochastic simulations to approximate deterministic and stochastic integrals using Monte Carlo methods. Some properties of these methods are discussed. The above methods are illustrated using problems in Financial Mathematics.
MATH 72.1	ORDINARY DIFFERENTIAL EQUATIONS 3 units Prerequisites: MATH 31.4, MATH 40.1 This course is an introduction to the theory of ordinary differential equations and dynamical systems. The tools for both the quantitative and qualitative analyses of ordinary differential equations are presented. The first part focuses on some classical methods of solving ordinary differential equations, including Laplace Transforms. The second part presents some tools for qualitative analysis such as phase portrait of autonomous systems, linearization at a fixed point and stability analysis of equilibrium solutions. Mathematical models using ordinary differential equations in economics, physics, engineering and other areas are used to illustrate the applications of these concepts.
MATH 72.2	PARTIAL DIFFERENTIAL EQUATIONS 3 units Prerequisite: MATH 72.1 This course is an introduction to partial differential equations with applications in financial mathematics and other areas. The relevant topics included are Fourier series, separation of variables, Fourier transform, Black-Scholes partial differential equation, and the Black-Scholes formula.
MATH 72.5	NONLINEAR DYNAMICAL SYSTEMS 3 units Prerequisite: MATH 72.1 This course introduces and studies the basic concepts and ideas in the Theory of Dynamical Systems. A dynamical system is a pair consisting of a set of states and a mapping of this set to itself satisfying a condition that encodes the idea of determinacy, that is, a past state determining all future states. This definition includes a model of phenomena common to biological and physical systems, and the theory seeks to find and introduce unifying ideas or laws that should prove useful to science and mathematics.
MATH 80.1	FUNDAMENTAL CONCEPTS OF ALGEBRA 3 units Prerequisite: MATH 31.3 This is a 3-unit course on an introduction to abstract algebra. Topics include groups, subgroups, cyclic groups, permutation groups, isomorphisms, normal subgroups, factor groups, direct products, rings, integral domains and fields.
MATH 80.2	INTRODUCTION TO GALOIS THEORY 3 units Prerequisite: MATH 80.1 This is a 3-unit course for mathematics majors and the second undergraduate course in abstract algebra. Topics revolve around algebraic structures beyond groups, such as rings, fields and ideals in the undergraduate level. Solutions of polynomial equations in terms of algebraic structures are studied. The highlight of the course is the discussion on Galois groups and the Galois correspondence and the Fundamental Theorem of Galois Theory.
MATH 80.3	TOPICS FROM ALGEBRA I 3 units Prerequisite: MATH 31.3 This is a 3-unit course on introductory group theory and some special topics. Isometries in R, R2, and R3, dihedral and symmetry groups, rotation groups, frieze groups, and crystallographic groups, symmetry and counting are discussed.
MATH 80.4	TOPICS FROM ALGEBRA II 3 units Prerequisite: MATH 80.1 This 3-unit course is an introduction to the representation theory and character theory of finite groups. Topics in representation theory include linear actions and modules over group rings, Wedderbum’s Theorem and some consequences, Maschke’s Theorem. Topics in character theory include Schur’s Lemma, inner products of characters, character tables and orthogonality relations, lifted characters, number of irreducible characters, inner products of characters, restriction to a subgroup, induced modules and characters.
MATH 80.7	FINITE PERMUTATION GROUPS 3 units Prerequisite: MATH 80.1 The objective of this course is to introduce the students to the development of permutation groups, explaining the motivation for various problems and their solutions. Both finite and infinite groups are considered. Permutation groups play an important role in modern group theory; both finite and infinite permutation groups continue to be interesting topics of research. Through this course, the department intends to include as many topics indicative of the current development of the subject hoping the students are motivated to explore possible areas of research.
MATH 81.1	MODERN GEOMETRY I 3 units Prerequisite: MATH 40.1 This is a 3-unit course taken by BS Mathematics majors. This course exposes students to other types of geometries beyond Euclidean geometry. This course recalls Euclidean geometry, explains the consequences of the parallel postulate, and then proceeds to the discussion of hyperbolic (Lobachevskian), and elliptic geometries, finite geometries, projective geometries, and transformation geometry. The geometric concepts are studied through the axiomatic method and using synthetic/coordinate geometry. Emphasis is given to studying and formulating geometric proofs. Attention is given to the modern alliance of geometry with linear and abstract algebra. The approaches to the study of modern geometries are supported with technology. Geometric constructions and explorations are carried out via dynamic geometry software, interactive websites and other technological tools. The applications of modern geometry are presented. Some examples are Escher tilings, Celtic knotwork, polyhedra sculptures, spherical and hyperbolic designs, physical and crystal structures, tilings and honeycombs. Current developments in the area and possible research topics in the undergraduate level for projects and collaborative work are also discussed.
MATH 81.2	MODERN GEOMETRY II 3 units Prerequisites: MATH 80.1, MATH 81.1 The course covers the following topics: notions of points, lines, the concept of parallelism, polygons and congruence in Hyperbolic space. It also discusses the notions of groups specifically hyperbolic symmetry groups and special problems leading to research in Hyperbolic geometry. It uses the Geometer’s sketchpad and Java applets to investigate the notions in Hyperbolic Space.
MATH 81.3	FINITE GEOMETRY 3 units Prerequisite: MATH 80.1 This course is designed for math majors who wish to learn about finite geometries and/or use it in other areas in combinatorics. It is also an introductory course for those who wish to do research in finite geometries. The aim of the course is to present the basic concepts of finite geometries and to expose the students to the different finite incidence structures. Topics in this course include Finite Incidence Structures, Affine Geometry, Projective Geometry, Generalized Quadrangles, Designs and Permutation Groups.
MATH 90.1	ADVANCED CALCULUS I 3 units Prerequisite: MATH 31.4 This is the first higher analysis course taken by a mathematics major. It is a preparation for courses such as real analysis, topology, measure theory, stochastic calculus, and advanced probability theory. The course covers basic properties of real numbers and functions on the set of real numbers, as well as integration theory.
MATH 90.2	ADVANCED CALCULUS II 3 units Prerequisite: MATH 90.1 MATH 90.2 is the second of two courses in advanced calculus taken by BS Math and BS/M AMF majors. Specifically, the course discusses metric spaces, differentiation in RN, integration in RN, and the Riemann-Stieltjes integral and functions of bounded variation.
MATH 91.1	REAL ANALYSIS I 3 units Prerequisite: MATH 90.1 The course discusses the basic concepts and theorems in real analysis, in particular Lebesgue integration theory. These include sigma algebras, measure, measurable sets, measurable functions, Lebesgue integral, and the Lp spaces.
MATH 91.7	INTEGRATION THEORY 3 units Prerequisite: MATH 91.1 This course is a survey of the different integrals studied in real analysis — Riemann, Lebesgue, and Henstock. Focus is on Henstock. Topics include definitions of the stated integrals and their properties, convergence theorem, and the Stieltjes integrals.
MATH 92.1	COMPLEX ANALYSIS I 3 units Prerequisite: MATH 90.1 The study of complex numbers and their properties is known as complex analysis. Extending the real number system to the complex number system, this course discusses the basic concepts, fundamental theorems, and some applications of complex numbers. At the end of the course, the students should be able to (1) apply the arithmetic and algebraic properties of complex numbers to problems in algebra and geometry of real numbers, and (2) to solve algebraic and calculus problems using tools in complex analysis.
MATH 93.1	INTRODUCTION TO TOPOLOGY 3 units Prerequisite: MATH 90.1 This course is concerned with the study of topological structures and their applications in other areas of mathematics. The major topics covered are topological spaces, metric spaces, continuous functions, connectedness and compactness.
MATH 100.1	TOPICS IN FINANCIAL MATH I 3 units This course introduces the students to the mathematics of financial markets. Topics include interest rates, bond pricing, portfolio risk-return analysis using efficient frontier and the capital asset pricing model (CAPM).
MATH 100.2	TOPICS IN FINANCIAL MATH II 3 units This course is an introduction to financial derivatives and risk management. Financial derivatives such as forward rate agreements (FRA), and forward contracts on stocks, currencies and bonds are discussed. Value-at-Risk (VaR) as a tool for measuring market risk in portfolios of traditional securities is also presented.
MATH 100.4	INTRODUCTION TO FINANCIAL RISK MANAGEMENT 3 units This course offers an overview of the basic principles of financial risk management. It clarifies the meaning of risk and risk aversion and explores the steps in the risk management process: identifying and assessing risks, selecting techniques for risk management, and implementing and revising risk management decisions. Topics include risk and economic decisions, risk assessment, selection of risk management techniques, value-at-risk, portfolio theory, standard deviation as a measure of risk, credit risk, and credit derivatives.
MATH 100.5	MATHEMATICS OF FINANCE AND ECONOMICS 3 units Using a mathematical treatment, this course introduces students to selected topics in finance and economics such as the theory of interest rates, valuation of annuities and debt repayment, bond pricing, and investment analysis.
MATH 100.6	FINANCIAL DERIVATIVES 3 units Prerequisite: MATH 101.6 This course introduces the concept of financial derivatives and models for the valuation of financial derivatives. Derivative instruments discussed in this course include futures, forward contracts, swaps, credit derivatives, and options.
MATH 100.7	STOCHASTIC CALCULUS FOR FINANCE 3 units Prerequisites: MATH 61.2, MATH 91.1 This course is an introduction to stochastic modelling, stochastic calculus, and techniques from stochastic analysis. Topics include the Cox-Ross-Rubinstein model, Brownian motion, Ito’s Lemma, solution of stochastic differential equations, martingale techniques, and advanced numerical methods. Results are applied to the general theory of no-arbitrage valuation and the Black-Scholes model.
MATH 101.3	TOPICS IN ACTUARIAL MATHEMATICS I 3 units Prerequisite: MATH 31.3 This course provides an introduction to the mathematics of life insurance. Students learn to use life tables for evaluating future lifetime at age x, analyzing mortality patterns, and calculating benefit premiums and reserves. Survival functions are used to illustrate actuarial concepts and formulas. Various life insurance products are explained and then used for illustration of the basic principles of life insurance (e.g. Life Annuities, Net Premiums, and Benefit Reserves).
MATH 101.4	TOPICS IN ACTUARIAL MATHEMATICS II 3 units Prerequisite: MATH 101.3 This course is a continuation of Actuarial Mathematics I. Discussion of Individual Life Insurance Model is extended to include operational and business constraints such as expenses, accounting requirements, and the impact of contract terminations. Actuarial concepts are also used to define actuarial present values, benefit and contract premiums, and benefit reserves for selected special insurance plans.
MATH 101.5	RISK THEORY FOR INSURANCE 3 units Prerequisites: MATH 31.3, MATH 61.2 The first part of the course discusses two main ideas: that random events can disrupt the plans of decision makers, and that insurance systems are developed and designed to reduce the impact and the adverse financial effects of these events. Individual and collective risk models are introduced. Models for both single policies, and a portfolio of policies are developed. These ideas are then extended to collective risk models, with respect to single-period, as well as continuous-time considerations. An overview of the applications of risk theory to insurance models is also discussed.
MATH 101.6	THEORY OF INTEREST 3 units This course is an introduction to the underlying formulas and theory regarding interest and interest rates and how they are used in financial calculations. Topics include the measurement of interest, equations of value, basic and general annuities, investments and yields, loan amortization and sinking funds, and bond pricing.
MATH 102.1	TOPICS IN OPERATIONS RESEARCH 3 units Prerequisites: MATH 40.1, MATH 61.2 Operations Research (OR) consists of the application of mathematical methods to the optimization of decision-making in organizations. This course covers several areas of OR and the algorithms and solution procedures for problems in these areas, together with their mathematical justification and appropriate software.
MATH 192	UNDERGRADUATE RESEARCH SEMINAR 1 unit Prerequisite: MATH 31.3 The course introduces the students to mathematical research and thesis writing. From choosing a topic to writing and presenting a proposal, from scratch work to typography, from related literature to research ethics, from thesis writing to thesis presentation, and from presentation of results in a conference to writing a paper for publication, all these are studied, discussed, and evaluated in this course.
MATH 199.1	UNDERGRADUATE RESEARCH IN MATHEMATICS I 2 units Prerequisite: MATH 192 This is the first of two research courses where the student (or group of students) is guided by an adviser towards the formulation of a thesis or project proposal and the collection of preliminary results and materials. In this course, students are expected to finalize their research topic, prepare and present a research proposal, and commence a review of literature related to their chosen topic.
MATH 199.2	UNDERGRADUATE RESEARCH IN MATHEMATICS II 2 units Prerequisite: MATH 199.1 This is the second of two research courses in which the student (or group of students) is guided towards the production and presentation of a final written output based on their progress in MA196.2. The required final output is a paper in thesis form that follows the format defined by the Department of Mathematics. Students are also required to present the results of their study to a panel of faculty members of the Department.
MATH 199.11	UNDERGRADUATE RESEARCH IN APPLIED MATHEMATICS I 2 units Prerequisite: MATH 192 This is the first of two research courses where the student (or group of students) is guided by an adviser towards the formulation of a thesis or project proposal and the collection of preliminary results and materials. In this course, students are expected to finalize their research topic, prepare and present a research proposal, and commence a review of literature related to their chosen topic.
MATH 199.12	UNDERGRADUATE RESEARCH IN APPLIED MATHEMATICS II 2 units Prerequisite: MATH 199.11 This is the second of two research courses in which the student (or group of students) is guided towards the production and presentation of a final written output based on their progress in MATH 199.11. The required final output is a paper in thesis form that follows the format defined by the Mathematics Department. Students are also required to present the results of their study to a panel of faculty members of the Department.

Graduate Courses

Code	Course Description
MATH 211.1	Elementary School Mathematics from a Modern Viewpoint I 3 units The course is the first of two courses on elementary school mathematics. It covers concepts on numeration systems and number systems, operations on numbers, order properties of the set of real numbers. Then these concepts are applied to solve problems involving number operations, ratio and proportion. Finally, basic numbers theory is introduced to study properties of integers.
MATH 211.2	Elementary School Mathematics from a Modern Viewpoint II 3 units This is the second of two courses on elementary school mathematics. It covers concepts on Euclidean geometry. Topics include basic definitions, plane and space figures, measurement, similarity and congruence, rigid geometric transformations and symmetry.
MATH 212.1	FUNDAMENTALS OF ALGEBRA FROM A MODERN VIEWPOINT 3 units This course introduces to the student the basic concepts of algebra – the theories, operations, representations, and applications. It introduces to the student the formal, symbolic approach to numbers leading to the development of algebraic concepts. Using the student’s solid knowledge of numbers as a foundational base, the course takes the student to a broad understanding of the real number system, numbers and variables, numbers and algebraic symbols, operations and processes, number representations and graphs, equations and inequalities, and applications. Teaching strategies that will make these concepts more concrete and comprehensible will be explored and utilized.
MATH 212.2	INTERMEDIATE ALGEBRA FROM A MODERN VIEWPOINT 3 units
MATH 212.3	ALGEBRA AND GEOMETRY FOR TEACHERS 3 units
MATH 212.4	Modern Algebra and Trigonometry 3 units This is a pre-calculus course offered to students needing the foundational concepts of calculus. It presupposes a firm understanding of basic algebraic concepts and processes. The course offers students the opportunity for a deeper understanding of equations and inequalities, analytic geometry; functions – linear, quadratic, polynomial, circular, exponential and logarithmic. Furthermore, it introduces to the students the beginning concepts of mathematical induction, the binomial theorem, polar coordinates, and limits.
MATH 213.1	GEOMETRY FOR TEACHERS I 3 units This course is designed to meet the current trends in the teaching and learning of geometry, particularly euclidean geometry. It begins with a general review of basic geometric concepts and moves on to a deeper treatment of more advanced topics. The course provides the students with an opportunity to scrutinize and analyze well-established theorems and constructions. Depending on the capability of the students, this course may cover non-euclidean and modern geometries, in the tradition of Hilbert and Pappus. Beyond the usual topics of angles, similarity, circles, areas and volume, the following can be included: projective planes, duality, homogeneous coordinates, geometric transformations, and isometries.
MATH 213.2	GEOMETRY FOR TEACHERS II 3 units Investigations in geometry will be the focal point of this course. An often-disliked area of mathematics, this geometry course will highlight geometric explorations that can be done using the technological tools. This course aims to broaden high school and grade school teachers’ knowledge of Euclidean geometry through the use of technology.
MATH 214.1	ELEMENTARY CALCULUS FOR TEACHERS I This course focuses on differential and integral calculus of functions of one variable, including applications of differentiation (related rates, rectilinear motion, rates of change, extrema of functions) and integration (areas and volumes). Analysis and reasoning in mathematics are stressed and hence, emphasis is placed on the formal statement of definitions and proofs of the different theorems presented in the course. Especially for teachers, this course also emphasizes the historical significance of the calculus in the development of modern mathematics. Teachers are encouraged to develop calculus concepts as they appear relevant in the secondary school mathematics curricula. Teachers are taught about extending problems in algebra using the differential calculus, and extending problems in geometry using the integral calculus. Teachers are also taught how calculus utilizes both algebraic and geometric representations.
MATH 214.2	ELEMENTARY CALCULUS FOR TEACHERS II 3 units This is a second course in elementary calculus. Topics include techniques of integration, sequences, series and calculus of several variables.
MATH 214.3	ELEMENTARY CALCULUS FOR TEACHERS III 3 units The course will cover the following topic: vectors in the plane and in space, vector-valued functions, and calculus of vector-valued functions.
MATH 215.1	AN INTRODUCTION TO PROBABILITY 3 units This course introduces students to basic probability theory, the concept of random variable and its probability distribution function, the concept of Mathematical Expectation, some special types of probability distributions, the Moment-Generating Function of random variables, how to obtain the probability distribution functions of functions of random variables, and their applications to real world problems.
MATH 215.2	BASIC STATISTICAL ANALYSIS 3 units The course introduces the students to descriptive statistics, basic probability, some probability distributions, the normal distribution and distributions derived from the normal, sampling, inferences about means, standard deviations, and proportions, simple linear regression and correlation.
MATH 216.1	INTRODUCTION TO THE FOUNDATIONS AND STRUCTURE OF MATHEMATICS 3 units
MATH 216.2	MATHEMATICS EDUCATION SEMINAR: METHODS OF PROOF 3 units The basic purpose of this course is to describe in detail some rules by which pure Mathematics is based. The course presents the fundamentals of mathematical proof in a systematic way. It aims to develop the student’s understanding of proof and their theorem-proving skills. It exposes the students to different proving techniques by using examples taken from various areas of mathematics such as abstract algebra, number theory, graph theory, combinatorics, geometry, and analysis. Moreover, it also explores the principles that underpin the various methods of proof and describes how proofs may be discovered and communicated. The topics in this course include Logic, Axiomatic Method, Set Theory, Methods of Proof, Induction and Pigeonhole Principle. The course is designed for those students who are beginning to embark on a serious study of pure mathematics. In articular, graduate students whose undergraduate course is not a B.S. Mathematics degree.
MATH 216.3	MATHEMATICS EDUCATION SEMINAR: HISTORY OF MATHEMATICS 3 units
MATH 216.4	PROBLEM SOLVING SEMINAR FOR TEACHERS 3 units The course is an introduction to mathematical problem solving. The definition of a problem is discussed followed by Polya’s steps in problem solving. Different heuristics or strategies for solving mathematical problems are also explored. The course ends with a discussion of the skills and attitudes required of a good problem solver and how these can be fostered and developed in the mathematics classroom.
MATH 217.1	MATHEMATICS EDUCATION SEMINAR: NUMBER THEORY I 3 units This course is designed to introduce the student to the fundamental concepts in number theory. It also intends to familiarize the student with the different methods of proof. The topics covered include: the integers and divisibility; the fundamental theorem of arithmetic; congruences; linear diophantine equations; residues; number theoretic functions; primitive roots; quadratic residues; quadratic reciprocity law; the Jacobi symbol.
MATH 217.2	MATHEMATICS EDUCATION SEMINAR: NUMBER THEORY II 3 units
MATH 218.1	MATHEMATICS EDUCATION SEMINAR: DISCRETE MATHEMATICS 3 units This is an introductory course in discrete mathematics. The course includes logic, numbers, combination, permutation, recurrence relations, generating functions, graphs, trees and network flows.
MATH 218.2	MATHEMATICS EDUCATION SEMINAR: COMBINATORICS 3 units Combinatorics is an area of modern mathematics which is concerned with the study of arrangements, patterns, designs and configurations. A chemist considers arrangements of atoms into molecules. A computer scientist considers patterns of digits to encode data. A space satellite uses such patterns to transmit information from space. A statistician considers alternative designs for an experiment. An electrical engineer considers alternative configurations for a circuit. A major reason for the rapid growth of combinatorics is its wealth of applications to many diverse fields.
MATH 218.3	MATHEMATICS EDUCATION SEMINAR: FINITE MATHEMATICS 3 units This course involves basic concepts and principles, as well as applications to social science, business problems, etc. of at least 5 topics in finite mathematics: matrices, counting techniques, elementary probability, statistics, basic linear programming, logic and graph theory.
MATH 218.4	MATHEMATICS EDUCATION SEMINAR: CONTEMPORARY MATHEMATICS 3 units This course is intended for users of mathematics. It is aimed at developing quantitative thinking through exposure to various contemporary and applied concepts in mathematics. The course discusses useful concepts in Graph Theory, Linear Programming, Statistics, & Measurements. Problems in these areas are illustrated, modeled, and solved through a variety of quantitative methods.
MATH 219.1	MATHEMATICS EDUCATION SEMINAR: LINEAR ALGEBRA AND MATRIX THEORY 3 units This is an introduction course in matrix theory and linear algebra. Matrices are used to motivate the more abstract notions of vector spaces, inner product spaces, linear transformation and eigenvalues. Determinants, other properties of matrices and how these can be used to solve systems of linear equations are also taken up. Especially for teachers, they are taught how other forms of mathematical representations enable a good grasp of basic, fundamental concepts in significant ways. Also, teachers are asked to see the significance of an abstract, deductive structure. Linear algebra and matrix theory also provide some of the unifying concepts in basic algebra and geometry.
MATH 219.2	MATHEMATICS EDUCATION SEMINAR: LINEAR AND ABSTRACT ALGEBRA 3 units This course covers the following topics: (1) Eigenvalues and eigenvectors (2) Inner product spaces (3) The spectral theorem and quadratic forms (4) Jordan canonical form (5) Determinants from a computational point of view and (6) normal matrices, unitary matrices.
MATH 219.3	MATHEMATICS EDUCATION SEMINAR: ABSTRACT ALGEBRA I 3 units The theory of matrix game; the minimax theorem for finite and continuous games; games in extensive form; the connection between game theory and linear programming; introduction to games against nature.
MATH 219.4	MATHEMATICS EDUCATION SEMINAR: ABSTRACT ALGEBRA II 3 units This course introduces students to recent advances in different areas of group theory and allied fields, through a discussion of recent results from published articles and other recent references. The topics and articles are chosen from several fields such as (but not limited to) mathematical crystallography, discrete geometry, substitution dynamical systems, and group representations. Content lectures in these areas serve as an introduction to each topic/article
MATH 220.1	FOUNDATIONS AND STRUCTURE OF MATHEMATICS 3 units The course aims to provide students with a comprehensive knowledge of the developments in mathematics, particularly the high and low points in its history. It is designed to help students consolidate their understanding of the structures and processes of mathematics. The course also introduces the students to contemporary issues in the foundations and structures of mathematics, from the structuralism of various foundationalist perspectives to the poststructuralism of postmodern philosophy of mathematics. It emphasizes the historical, sociological, and philosophical aspects of mathematics.
MATH 220.2	HISTORY OF MATHEMATICS 3 units This is a course on the history of mathematics. It follows the development of mathematics by identifying the political, sociological, economic and scientific forces that have shaped mathematical thinking over the ages, recognizing the individuals whose work and accomplishments have driven this development. It also discusses selected mathematical techniques and procedures which have led to mathematical advances.
MATH 221.1	PROBLEM SOLVING TECHNIQUES I 3 units The course is about mathematical problem solving. It introduces the students to the different levels of problem solving and the strategies for investigation. It discusses some fundamental tactics in solving such as symmetry, extreme principle. It also delves into special topics in Graph Theory, Generating Functions and Algebra.
MATH 221.2	PROBLEM SOLVING TECHNIQUES II 3 units The course aims to expose students to different types of problem solving in some special topics such as Algebra, Combinatorics, Number Theory, Complex Numbers and Calculus. It also presents problems and solutions from past International Mathematical Olympiads.
MATH 221.3	METHODS OF PROOF 3 units This course aims to provide the students with the skills needed to understand and construct mathematical proofs. The course presents students with the different tools and techniques used to prove mathematical theorems. It begins with an introduction to mathematical logic and proceeds to common strategies used in proving theorems. It also discusses some mathematical concepts and results which are helpful in proving other mathematical statements.
MATH 221.4	PROBLEM SOLVING AND METHODS OF PROOF 3 units
MATH 222.1	MATHEMATICAL LOGIC 3 units
MATH 222.2	LOGIC FOR MATHEMATICS AND COMPUTER SCIENCE 3 units The course introduces students to the syntax and semantics of propositional calculus and first- order logic. It begins with an introduction to Turing machines and computability. It handles semantics for propositional calculus through truth tables. It proves the Goedel’s Completeness Theorem, compact theorem and completeness theorem for propositional calculus. It also discusses the syntax and semantics of first-order logic using the number system as a basic example, the Halting Problem and its unsolvability . Finally, it deals with an introduction to complexity classes.
MATH 223.1	SET THEORY 3 units
MATH 225.1	BASIC COMBINATORICS 3 units
MATH 225.2	TOPICS IN COMBINATORIAL MATHEMATICS 3 units This course studies the area of combinatorics, an area of modern mathematics that is concerned with the study of arrangements, patterns, designs and configurations. It also tackles wide applications in diverse fields such as chemistry, computer science, coding and communications, experimental design, genetics, and electrical engineering.
MATH 225.3	COMBINATORIAL DESIGNS I 3 units This course is an introduction to Design Theory. It is designed primarily for undergraduate and graduate students who wish to learn about the subject and/or use designs in other fields. The course aims to present some of the basic concepts of block designs, emphasizing in particular, methods of constructing new designs. Moreover, it also introduces other combinatorial structures such as Latin squares and difference sets. Topics in this course include symmetric designs, resolvable designs, Hadamard matrices, Latin squares and difference sets.
MATH 225.4	COMBINATORIAL DESIGNS II 3 units This is a second course in Design Theory. It is designed primarily for graduate students who wish to enter the active field of designs. The course aims to present advanced results in Design Theory. It develops in-depth interaction between designs and groups, codes and finite geometries. Topics in this course include groups and designs, affine and projective geometry, Mathieu designs, codes.
MATH 225.5	ALGEBRAIC COMBINATORICS 3 units
MATH 225.6	ADVANCED STUDIES IN COMBINATORICS 3 units This is a course in Combinatorics, covering two main areas of the field, which are counting and graph theory. The course begins with the fundamental principles of counting, combinations and permutations, and their applications to enumeration problems. This is followed by proving exercises using mathematical induction and the Pigeonhole Principle. The second part of the course covers basic concepts and tools of graph theory: graphs and some classes of graphs, Hamiltonian and Eulerian problems, shortest path problems, coloring problems and scheduling.
MATH 226.1	ELEMENTARY GRAPH THEORY 3 units This seminar is an introduction to graph theory showing that it is applicable to a wide-variety of problems. Topics include introductory concepts of graph theory, graphs as mathematical models, problems in transportations, connections, party and games and puzzles and the relation of graph theory to social sciences.
MATH 226.2	TOPICS IN GRAPH THEORY 3 units The course includes the applications of graph theory as as models of computation and optimization. It discusses the following topics: trees, connectivity, planarity and coloring, network optimization models for operations analysis, graph models for electrical and communication networks and computer architectures and other topics that showcase the interplay between algebra and graph theory.
MATH 226.3	TOPICS IN GRAPH THEORY AND DISCRETE MATHEMATICS 3 units This course introduces students to the basic concepts of graph theory and their applications. It starts with the definition of a graph and the different situation and events it can model. It then discusses important topics such as connectivity, matching, coloring and network flows which have uses in communication reliability, scheduling and traffic flows.
MATH 226.4	ALGEBRAIC GRAPH THEORY 3 units
MATH 226.5	PROBLEM SEMINAR IN COMBINATORICS AND GRAPH THEORY 3 units This course introduces the application of computational techniques to graph theory and combinatorics problems. It discusses basic topics of coding theory, associated designs, number theory, cryptography and computational complexity will be discussed. It also presents methods of linear algebra in combinatorics and graph theory.
MATH 227.1	CODING THEORY 3 units This course discusses the basic definitions and concepts in linear and cyclic codes. Properties of these codes are given and so are the more popular bounds such as the sphere-packing, Greismer, singleton and Gilbert-Varshamov bounds. Particular codes and families of codes like the Reed-Muller, Hamming, Golay, Bose-Chaudhuri-Mesner, and quadratic residue codes are likewise defined and characterized. The subject ends with a brief introduction to lattice-theory and its relationship to self-dual codes.
MATH 228.1	GAME THEORY 3 units The course covers the following topics: theory of matrix game; the minimax theorem for finite and continuous games; games in extensive form; the connection between game theory and linear programming; introduction to games against nature.
MATH 230.1	INTRODUCTION TO MATHEMATICS OF FINANCE AND ECONOMICS 3 units This course provides an elementary introduction to the mathematics of economics and finance. Topics include time value of money, rate of return of an investment, cash-flow sequence, utility functions and expected utility maximization, optimal portfolio selection, contingent claims and arbitrage, and the capital asset pricing model.
MATH 231.1	INTRODUCTION TO FINANCIAL MATHEMATICS 3 units This course is an introduction to the mathematics of financial markets, particularly in the areas of portfolio optimization, valuation of financial products and financial risk management.
MATH 231.2	ADVANCED TOPICS IN FINANCIAL MATHEMATICS I 3 units This course deals with financial products and how to manage the risks arising from these products. The course also discusses how the products are used by financial institutions and institutional investors.
MATH 231.3	ADVANCED TOPICS IN FINANCIAL MATHEMATICS II 3 units
MATH 231.4	PRACTITIONERS' SEMINAR I 3 units This is a course handled by practitioners in the industry. In this course, students are presented the actual practice of financial mathematics in the banking industry, power industry, insurance industry and government institutions.
MATH 232.1	FINANCIAL DERIVATIVES I 3 units This course is an introduction to financial derivatives. In this course, students will be exposed to financial derivative products, from modelling to analysis and valuation. In this course, we will discuss futures, forwards, swaps, and credit derivatives.
MATH 232.2	FINANCIAL DERIVATIVES II 3 units This is a second course on financial derivatives. The course presents a detailed discussion and a rigorous treatment of commonly-used mathematical models for the valuation and analysis of European options, American options, and other financial derivatives, such as exotic options and interest rate derivatives.
MATH 232.3	FINANCIAL DERIVATIVES III 3 units This is a third course on financial derivatives. The course presents a detailed discussion and a rigorous treatment of commonly-used mathematical models for the valuation and analysis of financial derivatives, both standard and non-standard derivatives.
MATH 233.1	INTRODUCTION TO RISK MANAGEMENT 3 units This course offers an overview of the basic principles of risk management. It first clarifies the meaning of risk and risk aversion and then explores the steps in the risk-management process: identifying and assessing risks, selecting techniques to management risk, and implementing and revising risk-management decisions. Topics include risk and economic decisions, risk assessment, selection of risk-management techniques, value at risk, portfolio theory, standard deviation as a measure of risk, credit risk and credit derivatives.
MATH 233.2	FINANCIAL RISK MANAGEMENT I 3 units This course focuses on quantitative tools used in measurement, control and management of financial risks such as market risk, credit risk, liquidity risk and operational risk. The last part presents the regulatory framework for risk management in financial institution.
MATH 233.3	OPERATIONAL RISKS 3 units This course discusses the mathematical models and methods used in the management of operational risk in the banking and insurance sectors. It specifically includes major topics such as the following: (1) Modeling losses using frequency and severity, (2) Modeling potential losses using statistical tools and (3) Calculating economic capital required to support operational risk.
MATH 233.4	FINANCIAL RISK MANAGEMENT II 3 units This is the second of two courses on financial risk management. Financial risk management includes models for the quantification of market risk, liquidity risk, credit risk and operational risk. This second course focuses on mathematical models for measuring (i) Value-at-Risk and Tail Value-at-Risk for financial derivatives, (ii) counterparty credit risk, (iii) credit Value-at-Risk, and (iv) operational risk.
MATH 234.1	QUANTITATIVE METHODS FOR MANAGEMENT I 3 units This course is the first part of a two-part course which aims to equip the student with the mathematics needed in a management course. The topics include an introduction to the origins, nature and impact of Management Science, Linear Programming Formulation and Solution, Duality and Sensitivity Analysis, Integer Programming and Goal Programming.
MATH 234.2	QUANTITATIVE METHODS FOR MANAGEMENT II 3 units This course is the second part of a two-part course which aims to equip the student with the mathematics needed in a management course. The topics include Networks, Dynamic Programming, Inventory Theory, Queuing Theory, Inventory Theory, Simulation and Modeling.
MATH 234.3	LINEAR PROGRAMMING 3 units
MATH 234.4	TOPICS IN OPERATIONS RESEARCH I 3 units This course covers several areas of Operations Research, the algorithms and solution procedures for problems in the various areas, their mathematical justification, and applications. The topics include: The Simplex Method of Linear Programming up to the Duality Theorem; Dynamic Programming, both discrete and continuous models which are either deterministic or probabilistic; Queueing Theory, including single channel, multiple channel, finite queue and finite population models; Simulation Modeling; Network Optimization, including Minimal Spanning Tree, Shortest Route and Maximal Flow models.
MATH 234.5	TOPICS IN OPERATIONS RESEARCH II 3 units This course covers variations and extensions of Linear Programming: the transportation problem, the assignment problem, integer programming algorithms – branch and bound method and cutting plane method; project planning and scheduling; Markov chains and Markov decision process; Heuristic techniques for the traveling salesman problem and the vehicle routing problem. A group activity involving the reading, understanding and oral class presentation of an article from the Operations Research journal Interfaces is required.
MATH 234.6	ADVANCED TOPICS IN OPERATIONS RESEARCH 3 units This course covers several areas of Operations Research, the algorithms and solution procedures for problems in the various areas, together with their mathematical justification and appropriate software. The topics include Dynamic Programming, Linear Programming, Queueing Theory and Markov Models.
MATH 235.1	TOPICS FROM ACTUARIAL MATHEMATICS I 3 units This course is an introduction to the basic concepts in Actuarial Science. It includes detailed discussion of different insurance models that are fundamental to the practice of actuarial science. Topics includes the following: Survival Distributions and Life Tables, Life Insurance, Life Annuities and Net Premiums.
MATH 235.2	TOPICS FROM ACTUARIAL MATHEMATICS II 3 units This course is a continuation of Actuarial Mathematics I. It discusses the following topics on insurance: Net Premium Reserves, Multiple Life Functions, Multiple Decrement Models, Insurance Models including expenses and Nonforfeiture Benefits and Dividends.
MATH 235.3	ACTUARIAL MATHEMATICS: SEMINAR IN RISK THEORY 3 units This is a course on Risk theory or the study of deviations of financial results from those expected and methods of avoiding inconvenient consequences from such deviation. Topics include the collective risk model, more detailed models for use with insurance systems, and applications of risk theory to the insurance model.
MATH 235.4	ACTUARIAL MATHEMATICS: SEMINAR IN THEORY OF INTEREST 3 units This course is an introduction to the underlying formulas and theory regarding interest and interest rates and how they are used in financial calculations. It will cover the material for the Interest Theory component of the second Actuarial Exam. The primary focus will be on the financial models developed in the book Theory of Interest by S.G. Kellison.
MATH 235.5	MATHEMATICS OF LIFE INSURANCE 3 units
MATH 235.6	ACTUARIAL MATHEMATICS: SEMINAR ON LIFE CONTINGENCIES 3 units
MATH 235.7	ACTUARIAL MATHEMATICS: SEMINAR ON SURVIVAL MODELS AND THEIR ESTIMATION 3 units
MATH 235.8	ACTUARIAL MATHEMATICS: SEMINAR ON GRADUATION 3 units
MATH 235.9	ACTUARIAL MATHEMATICS: SEMINAR ON PENSION SCHEMES 3 units
MATH 236.1	STOCHASTIC CALCULUS I 3 units This course is an introductory graduate course in stochastic modeling and stochastic calculus. It aims to introduce some of the techniques from stochastic analysis that are employed in mathematical finance. It begins with an overview of the important concepts in probability and an elementary presentation of discrete models, including the Cox-Ross-Rubinstein. It then covers Brownian motion, Ito’s Lemma and the solution of stochastic differential equations, martingale techniques and advanced numerical methods.
MATH 236.2	STOCHASTIC CALCULUS II 3 units This course offers advanced topics in the study of stochastic calculus. It includes thorough discussion on the Feynman-Kac Formula, the Black-Scholes Partial Differential Equation, the Girsanov Theorem, and term-structure models.
MATH 236.3	TOPICS IN STOCHASTIC CALCULUS 3 units This course presents advanced topics in stochastic modeling, stochastic calculus, and techniques from stochastic analysis. Topics include the Cox-Ross-Rubinstein model; Brownian motion, Ito’s Lemma, and solution of stochastic differential equations, martingale techniques and advanced numerical methods. Results are applied to general theory of no-arbitrage valuation and Black-Scholes.
MATH 236.4	ADVANCED PROBABILITY AND MARTINGALES 3 units This course discusses important results such as Kolmogorov’s Law of Large Numbers and the Three-Series Theorem by martingales techniques, and the Central Limit Theorem via the use of characteristic functions. It assumes certain key results from measure theory.
MATH 240.1	COMPUTATIONAL MATHEMATICS WITH A COMPUTER ALGEBRA SYSTEM 3 units A Computer Algebra System (CAS) is a computer software that can manipulate mathematical expressions and perform symbolic computations. The first half of the course will introduce the students to the fundamentals of structured and functional programming in a CAS. Specifically, the course will focus on the use of two free and open-sourced software – SageMath and GAP. In the latter half, the programming concepts and skills learned will be applied to solve various problems in discrete mathematics and draw/render 2D and 3D figures/graphics in geometry.
MATH 240.2	COMPUTER MODELING AND SIMULATION 3 units The course provides students with an introduction to fundamental concepts of computer modeling and simulation. It exposes the students to different modeling and simulation techniques involving scientific computing and visualization. It also allows students to work with several mathematical and computational models in the natural and allied sciences such as biology, chemistry, physics, environmental science, health sciences, economics and finance. The course also includes special topics such as modeling dynamical systems using differential equations, high performance computing and grid computing.
MATH 240.3	ENVIRONMENT APPLICATIONS OF COMPUTER MODELING AND SIMULATION 3 units This course aims to provide students with an introduction to environmental applications of computer modeling and simulation. It exposes students to several mathematical models for the study of the environment. It also presents an overview of different environmental modeling software such as RAINS-ASIA, ER Mapper, ARC View/ARC Info, IDRISI, etc.
MATH 241.1	NUMERICAL ANALYSIS I 3 units This course covers graduate level study of numerical analysis. It includes the effects of machine arithmetic, error analysis, iteration methods, finding and evaluating a function on a set of given points, and approximation of problems by simpler problems. It uses the results and methods from many areas of mathematics, particularly those of calculus and linear algebra.
MATH 241.2	NUMERICAL ANALYSIS II 3 units This is a continuation of the Numerical Analysis I course. It aims to provide students with exposure to other numerical techniques/methods. It covers the following topics: Numerical Integration (Trapezoidal and Simpson's rules, Gaussian numerical integration), Numerical Differentiation, Solution of Systems of Linear Equations, Numerical Solution of Differential Equations, Monte Carlo Methods, and Special Topics (Adomian Method, Cellular Automata, Fast Fourier Transforms, etc.).
MATH 241.3	NUMERICAL ANALYSIS III 3 units The course presents advanced topics in numerical methods and culminates with the numerical solution of parabolic partial differential equation. Knowledge of matrix operations is assumed, but basic ideas regarding partial differential equations are incorporated into the course. Applications in finance are treated. The course covers the following topics: overview of numerical analysis, convergence and stability of numerical methods, computer arithmetic and errors, root finding methods, direct and iterative methods to solve systems of linear equations, numerical solutions to parabolic partial differential equations. Computer implementation of the methods discussed are required as projects.
MATH 241.4	SPECTRAL METHODS FOR DIFFERENTIAL EQUATIONS 3 units The course covers the following topics: Fourier differentiation matrices; semi-discrete Fourier transform; Chebyshev differentiation matrices; numerical solution to differential equations through spectral differentiation matrices; boundary value problems and eigenvalue problem; polar coordinates; and fourth-order equations.
MATH 242.1	THEORY OF DIFFERENTIAL EQUATIONS 3 units The course presents fundamental concepts in differential equations. It includes theories and methods of solving ordinary and partial differential equations.
MATH 242.2	ORDINARY DIFFERENTIAL EQUATIONS 3 units This course is an introduction to the theory of ordinary differential equations and dynamical systems. It deals with some classical methods of solving ordinary differential equations including Laplace transforms. It emphasizes the qualitative analysis of ordinary differential equations. It covers topics such as phase portrait of differential equations, linearization at a fixed point, stability analysis of equilibrium solutions, and Lyapunov functions. It presents models using ordinary differential equations of some physical phenomena.
MATH 242.3	NONLINEAR DYNAMICAL SYSTEMS 3 units This course presents a hands-on approach to dynamical systems, with concentration on non-linear differential equations. It reviews qualitative techniques for nonlinear equations in the plane, as well as the Hartman-Groban theorem, and the Poincare-Bendixson Theorem. It also discusses the basic concepts of topological dynamics and symbolic dynamics. This course applies this theory to obtain results in areas such as neurodynamics, systems biology, and time series analysis.
MATH 242.5	PARTIAL DIFFERENTIAL EQUATIONS 3 units This course is an introduction to partial differential equations with applications in financial mathematics and other areas. The relevant topics included are Fourier series, separation of variables, Fourier transform, Black-Scholes partial differential equation, and the Black-Scholes formula.
MATH 250.1	LINEAR ALGEBRA 3 units This course begins with the study of vector spaces which includes linear independence, bases and subspaces. It covers other major topics such as linear transformation and matrices, determinants, eigenvalues, canonical forms, bilinear forms and quadratic forms. Finally, it discusses inner product spaces.
MATH 250.2	ADVANCED STUDIES IN LINEAR ALGEBRA 3 units This course introduces the graduate student to the following fundamental concepts of linear algebra: systems of linear equations, matrices, determinants, vector spaces, and eigenvalues. The course will expose the student to the theory behind these concepts, as well as their applications to various areas such as geometry in the plane, graphs, demographics, Markov processes, recurrences, and differential equations.
MATH 250.3	MATRIX ANALYSIS 3 units This course deals with matrices and linear transformations. Topics include eigenvalues and eigenvectors, inner product spaces, the spectral theorem and quadratic forms, Jordan canonical form, determinants form a computational point of view, and normal and unitary matrices.
MATH 251.1	ALGEBRAIC STRUCTURES I 3 units The course is an introduction to Groups and their elementary properties; subgroups, cyclic groups, normal subgroups and quotient groups; permutation groups, group homomorphisms and isomorphisms, group actions, direct product of groups, sylow theorems, finitely generated abelian groups, rings and their elementary properties, subrings, ideals, ring homomorphisms and isomorphisms.
MATH 251.2	ALGEBRAIC STRUCTURES II 3 units The course continues the discussion on Groups and their elementary properties. It deals with the following topics : Polynomial rings, Euclidean and unique factorization domains, field extensions, algebraic extensions, splitting fields, algebraically closed fields, finite fields, Galois Theory and applications, separability, cyclic and cyclotomic extensions.
MATH 251.3	GROUP THEORY 3 units The course covers the following topics: rings and homomorphisms, ideals, factorization in polynomial rings, field extensions, the fundamental theorem of Galois theory, splifting fields, Galois group of a polynomial, finite fields separability, cyclic and cyclotomic extensions, radical extensions.
MATH 252.1	ALGEBRAIC NUMBER THEORY 3 units This course lays the foundation for Algebraic Number Theory. The course covers the following topics: Field of algebraic numbers, rings of integers of number fields, cubic and quadratic fields, ideals, unique factorization domains and principal ideal domains, splitting of primes, the class group.
MATH 253	GROUPS AND DESIGNS 3 units This is a course on the theory of designs. It includes topics such as Bruck-Ryser-Chowla theorem, Singer groups and difference sets, projective and affine planes, Latin squares, nets, Hadamard matrices and Hadamard 2-designs, and biplanes.
MATH 254.1	FINITE PERMUTATION GROUPS I 3 units This is a course on the development of permutation groups, explaining the motivation for various problems and their solutions. Topics include basic ideas on permutation groups, action of a permutation group, and bounds on orders of permutation groups.
MATH 254.2	FINITE PERMUTATION GROUPS II 3 units This course presents the development of permutation groups, explaining the motivation for various problems and their solutions. It discusses following topics - Mathieu Groups and Steiner Systems, Multiply Transitive Groups and Structure of the Symmetric Groups.
MATH 255.1	REPRESENTATION THEORY 3 units The course is an introduction to the presentation theory of finite groups. It deals with the following topics: Linear actions and modules over group rings, Wedderbum’s Theorem and some consequences, and Maschke’s Theorem. It also discusses topics in character theory such as Schur’s Lemma, inner products of characters, character tables and orthogonality relations, lifted characters, number of irreducible characters, inner products of characters, restriction to a subgroup, and induced modules and characters.
MATH 256.1	MODERN GEOMETRY 3 units This is a 3-unit elective in modern geometry designed for graduate students and university/college teachers. This course exposes students to other types of geometries beyond Euclidean geometry. This course recalls Euclidean geometry, explains the consequences of the parallel postulate, and then proceeds to the discussion of hyperbolic (Lobachevskian), and elliptic geometries, finite geometries, projective geometries, and transformation geometry.
MATH 256.2	FINITE GEOMETRY 3 units This course is designed for graduate students who wish to learn about finite geometries and/or use it in other areas in combinatorics. It is also an introductory course for those who wish to do research in finite geometries. It presents the basic concepts of finite geometries and to expose the students to the different finite incidence structures. Topics in this course include Finite Incidence Structures, Affine Geometry, Projective Geometry, Generalized Quadrangles, Designs and Permutation Groups.
MATH 256.3	COLOR SYMMETRY 3 units This is a seminar course provided to graduate students which focuses on an applied area of Group Theory, Color Symmetry. It discusses the mathematical theories of color symmetry that have been developed in recent years and the various applications of color symmetry in group theory (subgroups, cosets, normality, conjugacy,etc) , representation theory, permutation groups, structural physics and chemistry and art and culture. It considers examples in the three geometries: Euclidean, elliptic and hyperbolic. It also presents research problems on Color Symmetry, focusing on open and new questions in the field.
MATH 256.4	TILINGS AND PATTERNS 3 units This course discusses the mathematical theory of tilings. Classification of Tilings relative to transitivity properties and symmetry groups will be studied. Detailed surveys of various aspects of tilings will be discussed. These include colored patterns and groups of color symmetry tilings by polygons, tilings in which the tiles are unused in a topological sense, as well as the topic on aperiodic tilings. It also presents open problems and questions for possible topics for research.
MATH 256.5	DIFFERENTIAL GEOMETRY 3 units
MATH 256.6	HYPERBOLIC GEOMETRY 3 units The course covers the following topics: notions of points, lines, the concept of parallelism, polygons and congruence in Hyperbolic space. It also discusses the notions of groups specifically hyperbolic symmetry groups and special problems leading to research in Hyperbolic geometry. It uses the Geometer’s sketchpad and java applets to investigate the notions in Hyperbolic Space.
MATH 256.7	GEOMETRIC CRYSTALLOGRAPHY 3 units This course deals with the geometric and group theoretic properties of crystalline structures. Situations will be considered on the two-dimensional Euclidean, Hyperbolic and Elliptic plane, as well as three dimensional Euclidean space. It discusses applications to chemistry and physics, as well as to the following areas in applied mathematics: mathematical modeling, tiling theory, color symmetry, etc. It exposes students to research possibilities through projects.
MATH 257.1	RESEARCH COURSE IN ALGEBRA AND GEOMETRY 3 units
MATH 257.2	RESEARCH COURSE IN MATRIX ANALYSIS 3 units This course supplements a basic linear algebra course. It illustrates how the methods of matrix theory can be used in both pure and applied mathematics. In particular, it covers topics related to electrical systems, mechanical systems, dynamical systems, the spectral representation of a symmetric matrix, column and null spaces and the methods of least squares.
MATH 260.1	FUNDAMENTAL CONCEPTS OF ANALYSIS I 3 units This is a course in advanced calculus in preparation for courses on real analysis and topology with emphasis on the basic properties of functions on R^1 and on the elementary theory of metric spaces.
MATH 260.2	FUNDAMENTAL CONCEPTS OF ANALYSIS II 3 units This course is the second of the two courses in advanced calculus taken by students pursuing a master’s degree. It continues to deal with metric spaces. The course also includes differentiation in RN and the Riemann-Stieltjes Integral and functions of bounded variation.
MATH 260.3	ADVANCED STUDIES IN MATHEMATICAL ANALYSIS 3 units This is an analysis course that bridges calculus and higher analysis courses such as real analysis, complex analysis, advanced probability theory, and topology. Concepts in calculus of functions of a single variable are discussed in a deeper level, with theorems proven. It begins with topological properties of real numbers then moves on to continuous functions, derivatives and integrals, finishing with sequences and series of functions. There is more focus on proving results rather than performing calculations.
MATH 261.1	MODERN REAL ANALYSIS I 3 units The course covers topics in Lebesgue integration theory such as Lebesgue measure, Lebesgue Integral and L^p spaces.
MATH 261.3	MODERN REAL ANALYSIS II 3 units This course covers advanced topics in real analysis including its applications.
MATH 262.1	MODERN COMPLEX ANALYSIS I 3 units The course discusses the following topics: elementary properties of analytic functions: Cauchy-Riemann equations, Cauchy Theorem and Integral Formula; Laurent series; calculus of residues; theorems of Liouville, Morera, Rouche; argument principle and maximum principle; harmonic functions; and elementary conformal mapping.
MATH 262.2	MODERN COMPLEX ANALYSIS II 3 units The course is a sequel to Modern Complex Analysis I. It begins with the development of the theory of complex functions using power series. It covers many deep and interesting results such as the global Cauchy integral theorem, Picard’s two theorems, and the Riemann mapping theorem.
MATH 263.1	TOPOLOGICAL STRUCTURES 3 units The course is an introduction to topology. It covers the following topics: topological spaces and continuous functions, connectedness and compactness, countability and separation axioms. It also discusses complete metric spaces.
MATH 263.2	ALGEBRAIC TOPOLOGY I 3 units The course covers the following topics: categories and functions, Homotopy, Convexity, contractibility and cones, Paths and path connectedness, Simplexes, the fundamental group, Singular homology, Long exact sequences, Excision and applications and Simplical complexes.
MATH 263.3	COMPUTATIONAL HOMOLOGY 3 units This course presents a computational approach to cubical homology, the type of homology best suited for use with digitalized data. Its main thrust is to encode algorithms to compute typical homology invariants for real-life applications. The course examines applications to areas such as 3-dimensional medical imaging, time series analysis, and dynamical systems analysis.
MATH 263.4	FUNCTIONAL ANALYSIS I 3 units The course delves on functional analysis which is primarily the study of infinite dimensional spaces of functions, or more generally, the study of topological vector spaces. It discusses major topics covered such as (1) Weak and Weak-Star Convergence in Banach Spaces, (2) Some Classes of Sobolev Spaces, (3) Some Variational Elliptic Problems. (4) The Heat Equation, and (5) The Wave Equation.
MATH 263.5	FUNCTIONAL ANALYSIS II 3 units This course aims to introduce to the students the theory of unitary operators on Hilbert space and one of its main results, the spectral theorem. The course also discusses topological groups and integration on groups. These two topics come together in the representation theory of groups. In this course, the basics of non commutative Harmonic Analysis is discussed, and the point of view offered by representations of groups is the most direct way of generalizing classical results. This course synthesizes previous knowledge of the students of topology, linear algebra, group theory and Fourier theory, thereby making the students aware of the essential unity of mathematics.
MATH 269.1	RESEARCH COURSE IN ANALYSIS 3 units This course introduces students to recent advances in different areas of analysis and allied fields, through a discussion of recent results from published articles and other recent references. The topics and articles are chosen from several fields such as (but not limited to) analysis, probability, and financial mathematics. Content lectures in these areas serve as an introduction to each topic/article.
MATH 269.2	THEORY OF SPECIAL FUNCTIONS 3 units The course covers the following topics: infinite series, improper integrals and infinite products, gamma functions and related functions, legendre polynomial and related functions, other orthogonal polynomials, Bessel functions and boundary-value problems.
MATH 269.3	INTEGRATION THEORY 3 units The main objective of this course is to introduce modern integration theory through the generalized Riemann integral. The course discusses the Riemann integral, the Henstock integral, Henstock’s Lemma, Cauchy and Harnack extensions, monotone convergence theorem, the McShane integral, dominated convergence theorem, measurable sets and measurable functions, fundamental theorem of calculus, and controlled convergence theorem.
MATH 269.4	FOURIER SERIES AND FOURIER TRANSFORMS, DISTRIBUTIONS 3 units This course aims to introduce to the students the theory of unitary operators on Hilbert space and one of its main results, the spectral theorem. The course also discusses topological groups and integration on groups. These two topics come together in the representation theory of groups. In this course, the basics of non commutative Harmonic Analysis is discussed, and the point of view offered by representations of groups is the most direct way of generalizing classical results. This course synthesizes previous knowledge of the students of topology, linear algebra, group theory and Fourier theory, thereby making the students aware of the essential unity of mathematics.
MATH 269.5	INTRODUCTION TO SINGULARITY THEORY 3 units This course studies determinacy, codimension, universal unfoldings, and transversality in a smooth category, leading to a complete classification of the elementary catastrophes of low dimension. The course also discusses the connection between singularities and reflection groups, Lie groups, braid groups, and ray groups. Included among course applications are light caustics, and biological morphogenesis.
MATH 270.1	PROBABILITY THEORY I 3 units
MATH 270.2	PROBABILITY THEORY II 3 units
MATH 270.3	PROBABILITY THEORY III 3 units
MATH 270.4	ADVANCED PROBABILITY AND MARTINGALES 3 units The course proves important results such as Kolmogorov’s Law of Large Numbers and the Three-Series Theorem by martingales techniques, and the Central Limit Theorem via the use of characteristic functions. It assumes certain key results from measure theory.
MATH 270.5	INTRODUCTION TO MALLIAVIN CALCULUS 3 units
MATH 271.1	STATISTICAL METHODS 3 units The course covers topics in applied Statistics including applied regression analysis and nonparametric statistics. The use of statistical software packages in carrying out computations will also be presented.
MATH 271.2	ADVANCED STATISTICAL METHODS 3 units The course is the continuation of Time Series Analysis for AMF majors. It discusses topics such as heteroscedastic models, unit roots, vector autoregressive models, and cointegration. It also analyzes some financial time series data to illustrate key concepts and methods.
MATH 271.3	REGRESSION AND TIME SERIES ANALYSIS 3 units This course is an introductory course in linear statistical modeling. It covers positive-definite matrices, multivariate normal distribution, distributions of quadratic forms, ordinary least-square estimation, hypothesis testing, simple and multiple linear regression, model validation and some transformations, and analysis of residuals.
MATH 271.4	REGRESSION ANALYSIS 3 units Topics such as projection theory, distribution of random vectors and quadratic forms, general linear model (full column rank), and remedial measures will be discussed. All computations will be done using R. It is important to note that regression analysis is one of the basic statistical modeling techniques. Many advance models in practice such as logistic regression, spatial modeling, and time series analysis assume a strong knowledge of regression analysis.
MATH 271.5	EXTREME VALUE THEORY 3 units The course gives an overview of modern extreme value theory and includes the following topics: Univariate extreme value theory; Threshold models; Point process characterization of extremes; Maximum-likelihood estimation: Peaks over thresholds: Hill-type estimation, Multivariate extremes and extremes of processes; Analyzing heavy-tailed data in insurance and finance; and Risk management (enhancing Value-at-Risk). At the end of the course the student is expected: (1) To have acquired understanding of Extreme Value Theory as it is used in Finance; and (2) To have acquired skills necessary to understand with ease papers on Extreme Value Theory and to pursue further studies on the subject.
MATH 290.1	GROUPS ALGORITHMS PROGRAMING 3 units
MATH 292	INTRODUCTION TO RESEARCH AND THESIS WRITING 3 units The course introduces the students into mathematical research and Ateneo thesis writing. It provides discussion and student evaluation on the following aspects of research: from choosing a topic to writing and presenting a proposal, from scratch work to typography, from related literature to research ethics, from thesis writing to thesis defense, and from presentation of results in a conference to writing a paper for publication.
MATH 296	COMPREHENSIVE EXAMINATIONS 3 units
MATH 299.1	THESIS DIRECTION 3 units
MATH 299.2	THESIS WRITING 3 units
MATH 299.3	[PRESENTATION REQUIREMENT] 3 units
MATH 299.4	ORAL DEFENSE (MASTERS) 3 units
MATH 299.5	RESIDENCY FOR MASTER'S LEVEL 3 units
MATH 299.6	FINAL PAPER SUBMISSION (MASTER'S) 3 units
MATH 299.7	FINAL PAPER SUBMISSION (MASTERS) 3 units
MATH 396	COMPREHENSIVE EXAMINATIONS 3 units
MATH 399.1	DISSERTATION DIRECTION 3 units
MATH 399.2	DISSERTATION WRITING 3 units
MATH 399.3	[SUBMISSION REQUIREMENT] 3 units
MATH 399.4	ORAL DEFENSE (DOCTORAL) 3 units
MATH 399.5	RESIDENCY FOR DOCTORAL LEVEL 3 units
MATH 399.6	FINAL PAPER SUBMISSION (DOCTORAL) 3 units
MATH 399.7	FINAL PAPER SUBMISSION (DOCTORAL) 3 units
MTHED 210	CURRICULUM AND INSTRUCTION IN MATHEMATICS 3 units The course provides an overview of current issues concerning school mathematics curricula as well as aspects of instruction. Topics to be covered include the following: general aspects of curriculum, the nature of mathematics and its place in the curriculum, issues of appropriate framework, use of technology and problem solving in school mathematics, and practical matters involving textbook, instruction, and program evaluation.
MTHED 221.1	SPECIAL TOPICS ON CLASSROOM TEACHING IN MATHEMATICS 3 units This course involves an exploration of theory on mathematics teaching and learning. The course entails an examination of what it means to be an effective mathematics teacher. Principles of learning and teaching are tackled. The course is practice-oriented. Different instructional approaches and issues involving the learning of mathematics will be discussed.
MTHED 221.2	SPECIAL TOPICS ON RESEARCH IN MATHEMATICS EDUCATION 3 units This course provides students with an overview of what research in the field of mathematics education is all about. Students will be exposed to a few key research studies to showcase the various methodologies utilized as well as to enable students to decide on possible research foci for their thesis or practicum. The final requirement of the course is a viable research proposal in the field of mathematics education.
MTHED 221.3	SPECIAL TOPICS ON TESTING AND EVALUATION IN MATHEMATICS 3 units This course is intended for teachers of mathematics in the grade school and high school level, mathematics supervisors, and designers of instructional and assessment materials in mathematics. Students in this course are introduced to the varied writings in classroom testing and evaluation in school mathematics. The course aims to enhance students’ knowledge about assessment, testing, and evaluation in mathematics by focusing on current theories and research that drive classroom assessment practices. In this course, students will be able to try out different methods of assessing and testing mathematics understanding at different levels with special focus on the proposed Mathematics Framework for Basic Education.
MTHED 221.4	SPECIAL TOPICS ON TECHNOLOGY IN MATHEMATICS EDUCATION 3 units This course introduces the student to the potential benefits of using technology in the mathematics classroom. The technological tools include graphing calculators, computer algebra systems, dynamic geometry software, the internet, spreadsheets, and curve-fitting software. This course will also focus on how technology may be used to develop student-centered lessons, inquiry-based activities, exploratory investigations, real-world projects. Through this course, the student will experience the use of technology as learners and as teachers.
MTHED 221.5	SPECIAL TOPICS ON PSYCHOLOGY OF MATHEMATICS INSTRUCTION 3 units This course introduces the student to the varied writings in the psychology of mathematics instruction. It exposes the student to the different trends in mathematics instruction. Some of the instructional methods that will be studied include behaviourist and constructivist-based instruction, as well as mathematics instruction from each of the following perspectives: discovery approach, problem solving, and cooperative learning.
MTHED 285	SPECIAL TOPICS IN MATHEMATICS EDUCATION 3 units This is a survey course that will look at various current and past influences on mathematics instruction in schools that every mathematics education student should be knowledgeable about and be able to discuss and analyze in light of policies and practices in Philippine schools. Examples of these are technology, international comparison studies like TIMSS, and the sociocultural aspects of mathematics education. The course engages students through assigned readings, classroom discussions, and synthesis papers.
MTHED 296	COMPREHENSIVE EXAMINATIONS 3 units
MTHED 298.1	PRACTICUM I 3 units
MTHED 298.2	PRACTICUM II 3 units
MTHED 299.1	THESIS WRITING I 3 units
MTHED 299.2	THESIS WRITING II 3 units
MTHED 299.4	ORAL DEFENSE (MASTER'S) 3 units
MTHED 299.5	RESIDENCY FOR MASTER'S LEVEL 3 units
MTHED 299.6	FINAL PAPER SUBMISSION (MASTER'S) 3 unit
MTHED 299.7	FINAL PAPER SUBMISSION (MASTER'S) 3 units
MTHED 340	ADVANCED SPECIAL TOPICS IN MATHEMATICS EDUCATION 3 units
MTHED 350	PROBLEM SOLVING, MODELING AND INVESTIGATIONS FOR TEACHING MATHEMATICS 3 units The course is an introduction to mathematical problem solving. The skills and attitudes required of a good problem solver are discussed and the different heuristics or strategies for solving and modelling mathematical problems are explored. The distinction between a mathematical problem and a mathematical investigation is illustrated and examples are provided as hands-on experience for the students. The definition of mathematical investigations and mathematical modelling is discussed and students are given an experience of doing a mathematical investigation.
MTHED 392.1	RESEARCH IN MATHEMATICS EDUCATION I 3 units
MTHED 392.2	RESEARCH IN MATHEMATICS EDUCATION II 3 units
MTHED 392.3	RESEARCH IN MATHEMATICS EDUCATION III 3 units
MTHED 399.1	DISSERTATION WRITING I 3 units
MTHED 399.3	DISSERTATION WRITING II 3 units
MTHED 399.4	ORAL DEFENSE (DOCTORAL) 3 units
MTHED 399.5	RESIDENCY FOR DOCTORAL LEVEL 3 units
MTHED 399.6	FINAL PAPER SUBMISSION (DOCTORAL) 3 units
MTHED 399.7	FINAL PAPER SUBMISSION (DOCTORAL) 3 units

Department of Mathematics

SEC-A-313, 3/F Building A, Science Education Complex

Ateneo de Manila University Loyola Heights campus

Katipunan Avenue, Loyola Heights

1108 Quezon City

Philippines

Telephone +63 2 8426 6001 local 5681 to 83

math.sose@ateneo.edu

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