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 daytoday decisionmaking 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 noncredit bridging course for students who need to strengthen their knowledge of precalculus 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 3unit 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 3unit 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 3unit 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 30.33

APPLIED CALCULUS FOR LIFE SCIENCES I 3 units Prerequisite: MATH 21 for programs required to take MATH 21
MATH 30.33 is a 3unit course designed to introduce students to basic trigonometry and differential calculus and provide them with techniques for solving practical problems involving functions that model reallife situations within the realm of life and environmental sciences. Topics taken include trigonometry, limits, differentiation and its applications.

MATH 30.34

APPLIED CALCULUS FOR LIFE SCIENCES II
3 units Prerequisite: MATH 30.33
MATH 30.34 is the second in a series of two 3unit calculus courses taken primarily by majors of B.S. Environmental Science and related programs. The course introduces the student to integral calculus and multivariable calculus and their applications such as area, net change and optimization. There is strong emphasis on applications to life sciences. Topics include integration, area, functions of several variables, and applications to optimization.

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 rootfinding 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, vectorvalued 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 curvingfitting, 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 3unit 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 3unit 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 3unit 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 3unit 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 farreaching applications in computerscience, 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 spherepacking, Greismer, singleton and GilbertVarshamov bounds. Particular codes and families of codes like the ReedMuller, Hamming, Golay, BoseChaudhuriMesner, and quadratic residue codes are likewise defined and characterized. The subject ends with a brief introduction to latticetheory and its relationship to selfdual 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 errorcorrecting codes and discusses various families of errorcorrecting codes. The cryptography portion surveys the principles of network security and discusses classical, conventional, and publickey 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, AsiaPacific 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, goodnessoffit 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 momentgenerating 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 threeunit 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 3unit 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, analysisofvariance models, stationary process and autoregressive moving average models. Procedures in popular statistical software (SAS or R) shall be used for the analysis of reallife 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 rootfinding 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, Inclass lectures and discussions are supplemented by computer handson 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 objectoriented 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, leastsquares problem, leastnorm problem, matrix factorizations, sensitivity and conditioning, root finding in of nonlinear functions in one and several variables, unconstrained optimization, and nonlinear leastnorm 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, BlackScholes partial differential equation, and the BlackScholes 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 3unit 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 3unit 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 3unit 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 3unit 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 3unit 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 RiemannStieltjes 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 riskreturn 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. ValueatRisk (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, valueatrisk, 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 CoxRossRubinstein 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 noarbitrage valuation and the BlackScholes 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 singleperiod, as well as continuoustime 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 decisionmaking 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.
