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COURSE SYLLABI DESCRIPTION

MTH101A FOUNDATION COURSE IN MATHEMATICS (5 units)

This is a course on pre-calculus covering the following topics: Basics of algebra, equations and inequalities in one variable, functions and their graphs, exponential and logarithmic functions, trigonometric functions, trigonometric identities, inverse trigonometric functions, trigonometric equations, polar coordinate system, coordinates and lines, curve sketching, conic sections, systems of equations, sequences, mathematical induction, and the binomial theorem. 

STT101A FOUNDATION COURSE IN STATISTICS (3 units)

This is a course covering basic rules of probability, discrete and continuous probability distributions, and introduction to inferential statistics.

GEMATMW MATHEMATICS IN THE MODERN WORLD (3 units)

This course aims to discuss the nature of mathematics leading to appreciation of its practical, intellectual, social, and aesthetic dimensions.  It includes the study of the nature of mathematics and how the perception of this leads to different tools for understanding and dealing with various aspects of present day living such as managing personal finances, making social choices, appreciating geometric designs, understanding codes used in data transmissions and security, and dividing limited resources fairly.

STT201A EXPLORATORY DATA ANALYSIS (3 units)

This is a course covering statistical concepts, statistical measurements, statistical notations, collection, organization and presentation of data, measures of central tendency, location, dispersion, skewness, kurtosis; boxplots and stem-and-leaf display; measures of association and relationships; rates, ratios and proportions; construction of index numbers and indicators/official statistics.

MTH201A MATHEMATICAL ANALYSIS 1 (5 units)

This is the first course in the calculus series for majors.  It covers limits, continuity, derivatives of algebraic and transcendental functions, applications of derivatives, differentials, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, and some applications of the definite integral.

MTH210A INTRODUCTION TO SET THEORY (3 units)

This is a course covering the principles of symbolic logic, valid arguments and methods of proof; axioms on sets, algebra of sets; relations and functions, the natural numbers, finite and infinite sets, and cardinal numbers.

MTPROG1 COMPUTATIONAL THINKING IN PYTHON (3 units)

This course covers the fundamentals of logic formulation, computational thinking and problem solving together with their implementation in the Python programming language. This course serves as a foundation for future courses that the students will encounter throughout their program. This course will cover topics on data representation, I/O, control structures, loops and functions as well as discussions on how to use them appropriately in constructing program code.

MTH202A MATHEMATICAL ANALYSIS 2 (5 units)

This is the second course in the calculus series for majors.  It covers techniques of integration, indeterminate forms, improper integrals, sequences and series, parametric equations, polar coordinates, functions of several variables and a quick look at evaluating multiple integrals.

STT203A STATISTICAL PACKAGES (3 units)

This is a course designed for Statistics/Mathematics majors, to familiarize students on the use of different statistical software (Microsoft Excel/PHStat2/MegaStat, SAS, and R) for creating and managing databases, as well as conducting simple statistical data analyses. 

MTH220A NUMBER THEORY (3 units)

This is an introductory course in Number Theory taken up as a major course by students in the mathematics programs.  Topics discussed include divisibility, the greatest common divisor and least common multiple, prime numbers and their properties, the unique factorization theorem, basic properties of congruences, linear congruences and linear Diophantine equations, the Chinese Remainder Theorem, applications of congruences, the theorems of Fermat, Euler and Wilson, arithmetic functions and their properties, quadratic congruences, quadratic residues and the Quadratic reciprocity law, and primitive roots.

MTH221A LINEAR ALGEBRA (3 units)

This is an introductory course in linear algebra taken up as a major course by students in the mathematics programs.  Topics discussed include matrices, vector spaces, linear transformation and its matrix representations, eigenvalues and eigenvectors, and diagonalization.

MTH203A MATHEMATICAL ANALYSIS 3 (5 units)

This is the third course in the calculus series for majors.  It covers multiple integration, vector spaces, and planes and lines in in , calculus of functions of several variables, and line and surface integrals.

MTH223A ABSTRACT ALGEBRA 1 (3 units)

This course is an introduction to group theory. It covers abelian and cyclic groups, subgroups, dihedral and permutation groups, normal subgroups and factor groups, Lagrange’s Theorem, fundamental homomorphism theorems and Cayley’s theorem.

MTH257A STATISTICAL THEORY 1 (3units)

A course in probability theory. Topics include the concept of sample space and events, conditional probability, probability density function, cumulative distribution functions, mathematical expectations, joint and marginal distribution functions of several random variables. Special distributions such as uniform, binomial, poisson, geometric, gamma, beta, exponential, normal, etc. are covered.

MTH258A STATISTICAL THEORY 2 (3 units)

A course in estimation of parameters and tests of hypotheses.  Topics include order statistics, limiting distributions, methods of estimation, properties of estimators and hypothesis testing.

MTH224A ABSTRACT ALGEBRA 2 (3 units)

This is a major course for BS Mathematics students.  It is a second course in Abstract Algebra which introduces students to other algebraic structures such as rings, integral domains and fields.  It is designed to enhance the students’ skills in logical reasoning and analysis.

MTH300A THEORY OF INTEREST (3 units)

A three-unit course on the theory of measurement of interest, annuities, extinction of debts by amortization and sinking funds, bonds and other securities.

STT141A LINEAR MODELS (3 units)

A study of the various linear statistical models that arise in practice. Topics include multivariate normal distribution, distribution of quadratic forms, general linear models, estimation and tests of hypotheses about linear hypotheses and design matrices giving rise to analysis of variance models.

MTH241A DIFFERENTIAL EQUATIONS (3 units)

A course in the solution of first order differential equations and higher order differential equations, Laplace Transformations, power series method and boundary value problems.

MTH253A OPERATIONS RESEARCH 1 (3 units)

As an introductory course in Operations Research, this course focuses on the basic models, the analysis and the solution of linear optimization models.  The thrust is in the analysis of problems and their solution approaches.  This course provides a firsthand exposure to vast and highly relevant area of operations research.

MTH242A NUMERICAL ANALYSIS (3 units)

This is a course for mathematics and statistics majors. It introduces the students to numerical methods of approximating solutions to different classes of mathematics problems. It is designed to provide the students with real-life approaches to solving problems for which closed form solutions are not feasible.

STT161A APPLIED MULTIVARIATE ANALYSIS (3 units)

A course dealing with applications of the following multivariate techniques in real-life data: discriminant analysis, multivariate analysis of variance, canonical correlation, factor analysis and cluster analysis.

MTH254A OPERATIONS RESEARCH 2 (3 units)

This course is designed for BS Mathematics students who are majoring in Business Applications covering topics on game theory and dynamic programming.

MTH245A ADVANCED CALCULUS (3 units)

This course presents the real number system as a complete, ordered field. It discusses topological properties of Euclidean n-space, limits and continuity, sequences of constants, and sequences of functions. It also covers differentiation and pertinent results such as the Mean Value Theorem.

MTH243A COMPLEX ANALYSIS (3 units)

This course covers the definition of the complex number system.  It discusses functions of a complex variable and their derivatives and integrals. Topics include the Cauchy-Riemann conditions, contour integrals, the Cauchy – Goursat Theorem, the Cauchy Integral theorem, Taylor and Laurent series, and the applications of residues.

STT163A TIME SERIES ANALYSIS AND FORECASTING (3 units)

A course dealing with the different methods of forecasting time series data – classical smoothing procedures, time series decomposition  and deseasonalization, ARIMA models, and Box-Jenkins method.

MTH230A MODERN GEOMETRY (3 units)

A course dealing with the geometries of the Euclidean plane, the sphere and the projective plane.  The topics include congruence, isometrics, affine transformations, Desargues Theorem and Pappus Theorem.

MTH301A SELECTED TOPICS (3 units)

An introductory course in Stochastic Processes. It covers Markov chains, Poisson process, renewal, Markov chains, continuous time Markov chains and Brownian motion

MTH255A OPERATIONS RESEARCH 3 (3 units)

This course is designed for BS Mathematics students who are majoring in Business Applications covering topics on minimum cost network flow, transportation and assignment problems, integer programming, and nonlinear programming problems.

MTH421A MATHEMATICS SEMINAR (1 unit)

A course requiring eight hours of attendance in lectures or seminars conducted by visiting professors or faculty members on various topics and the remaining hours for lectures/presentations by the students.

MTH422A THESIS WRITING 1 (2 units)

This course introduces research techniques and research topics in Mathematics to enhance students’ capacity in developing a thesis proposal. The students are required to submit a thesis proposal and present it in the form of a proposal defense.

MTH411A PRACTICUM (3 units)

This is a course taken by students to allow them to apply what they have learned in class. This will also expose them to the work environment, and to the different companies employing mathematicians/statisticians.

MTH423A THESIS WRITING 2 (3 units)

The course requirement is a bachelor’s thesis done by student under the guidance of an adviser.