### Bachelor of Science in Mathematics (BSMTH) with specialization in

Business Applications (BSMTH-BAP)

Computer Applications (BSMTH-CAP)

In answer to the growing needs of business, industry, government and academe, the Department instituted the B.S. Applied Mathematics program with specialization in Operations Research in 1978. Since then, other fields of specialization have been included as options for students in this program, namely, Computer Applications and Actuarial Science /Statistics. The quality of the program was further enhanced when it was revised in 1990 into a B.S. in Mathematics program in accordance with the policies and standards for the basic sciences and mathematics education given out by the DECS and the DOST in 1986.

The new program not only incorporates all the core courses for a B.S. in Mathematics program prescribed by the DECS – DOST but also includes enough specialized courses to build up capability in Computer Applications and Actuarial Science/Statistics. Hence, in addition to the strong theoretical background, the program also provides training in these two streams. Starting with school year 1998-1999, a new stream of specialization in Business Applications was implemented.

Today, the department offers the Bachelor of Science in Mathematics with specialization in Business Applications or Computer Applications.

In the Business Application stream, students are equipped with a solid foundation in the theory and business applications of statistics and operations research to be better qualified for top level management positions.

In the Computer Application stream, computers are extensively used in the courses offered. This ensures that the students learn both the theoretical and practical aspects of computers.

OBJECTIVES AND GOALS OF THE BS MATHEMATICS PROGRAM

- To prepare the student for a mathematics – oriented career in industry, business and public administration.
- To provide the student with the mathematical training that will enable him to teach basic service courses in mathematics.
- To prepare the student for more advanced studies in mathematics.
- To develop the creative potential of the student through research.

LENGTH OF THE PROGRAM – 10 terms and a Summer Practicum

ALGEBRA AND TRIGONOMETRY

College Algebra (MATH111)

3 units

A course covering the number systems, algebraic functions, relations and graphs, equations, systems of equations, inequalities, and inverse functions.

Trigonometry (MATH112)

3 units

A course including polynomial functions, exponential and logarithmic functions, circular functions, trigonometric identities and equations, complex numbers, law of sines, law of cosines and solution of triangles.

Mathematical Analysis 1 (MATH113)

4 units

A first course in Analysis covering plane analytic geometry, limits and continuity, derivatives of algebraic functions, and their applications.

Prerequisite: College Algebra

Mathematical Analysis 2 (MATH114)

4 units

A continuation of Analysis 1. It covers differentials, indefinite and definite integrals and their applications, derivatives and integrals of logarithmic and exponential functions, trigonometric and inverse trigonometric functions, and techniques of integration.

Prerequisite: Mathematical Analysis 1

Mathematical Analysis 3 (MATH115)

4 units

A continuation of Analysis 2. It covers polar coordinates, indeterminate forms and improper integrals, infinite sequences and series, 3-dimensional space, quadratic surfaces, functions of several variables and evaluation of multiple integrals in Cartesian coordinates.

Prerequisite: Mathematical Analysis 2

Mathematical Analysis 4 (MATH116)

3 units

A continuation of Analysis 3. It covers vectors in the plane and 3 – dimensional space, directional derivatives to extrema of functions of several variables, evaluation of multiple integrals in spherical and cylindrical coordinates and their applications.

Prerequisite: Mathematical Analysis 3

Ordinary Differential Equations (DIFEQUA)

3 units

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

Prerequisite: Mathematical Analysis 3

Introduction to Statistics 1 (INTSTA1)

3 units

A course covering descriptive statistics, basic rules of probability, discrete probability distributions, normal distribution, sampling distributions, confidence intervals and tests of hypotheses for means, difference of means and variance, t and chi-square distribution and proportion.

Prerequisite: College Algebra

Linear Algebra (LINEALG)

3 units

A study of systems of linear equations, vector spaces, linear dependence, bases dimensions, linear transformations, matrices, determinants, eigenvalues and eigenvectors.

Prerequisite: Mathematical Analysis 2

Modern Algebra (MODEALG)

3 units

A course in partitions and equivalence relations; properties of integers, groups, subgroups, normal subgroup and factor group, fundamental homomorphism theorem for groups, isomorphism theorems; and Cayley’s theorem.

Prerequisite: Introduction to Set Theory

Advanced Calculus 1 (ADVACA1)

3 units

A course covering the real number system as a complete, ordered field; topological properties of R and R2 , limits and continuity; sequences and series of constants; sequences and series of functions.

Prerequisite: Mathematical Analysis 4

Advanced Calculus 2 (ADVACA2)

3 units

A course covering uniform convergence, fundamental theorems of differential and integral calculus involving functions of several variables.

Prerequisite: Advanced Calculus 1

Complex Analysis (COMANAL)

3 units

A course covering De Moivre’s theorem, analytic functions of complex variables, harmonic functions, multiple – valued functions, contour integration, the Jordan curve theorem, the Cauchy Integral theorem, Taylor series, Laurent series, residues and poles, and conformal mappings.

Prerequisite: Advanced Calculus 1

Introduction to Numerical Analysis (NUMENAL)

3 units

A course in linear and non-linear equations, system of linear equations, numerical differentiation and integration, and numerical solutions to differential equations.

Prerequisite: Mathematical Analysis 4,

Co-requisite: Differential Equation

Basic Computer Concepts (BASCONC)

3 units

This course is a general introduction to computers: number systems, data representations, logic systems, _oolean algebra, compilers, operating systems and network.

Prerequisite: Introduction to Computing and Information Technology for Science Students

Computer for Math1 (COMMAT1)

3 units

This course covers the fundamentals of logic formulation and their implementation using the Turbo Pascal programming language. Topics discussed in the course include simple data types, arithmetic operators, built-in functions, assignment operation, IO operation, _oolean expressions, conditional statements, looping structures, compound statements, procedures and functions, parameter passing, arrays and scoping.

Prerequisite: Introduction to Computing and Information Technology for Science Students.

Computer for Math2 (COMMAT2)

3 units

This course discusses topics which include strings and string manipulation, records, dynamic data structures particularly pointers, and abstract data types implemented using pointers like the singly linked lists, the doubly linked lists and the circular lists. Recursion as an approach in programming and topics in file handling are also discussed in this course. Turbo Pascal is used as the programming language tool.

Prerequisite: Computer for Math 1

Computer for Math3 (COMMAT3)

3 units

This is a course in computer programming using C and C++ programming languages. The first part of the course discusses non-object-oriented constructs that are features of the C language. The second part of the course introduces object-oriented programming concepts using C++. Concepts of object-oriented programming, their semantics and implementation as well as programming methodology and application development in C++ are discussed in the second part.

Prerequisite: Computer for Math 2

Computer Systems (COMPSYS)

3 units

This course discuss the hardware and software components that make up a complete computer system. The functional units of a computer system such as the processing unit, the arithmetic logic unit, the input and output units and the memory unit are also discussed. Memory organization and computer peripherals and workstations, as well as the basic theories of interpreters, compilers and language translators, are also covered.

Prerequisite: Basic Computer Concepts

Introduction to Computing and Information Technology for Science Students (COMSCI1)

2 units

This course is an introduction to the fundamental concepts of computer systems such as the computer’s software and hardware components, data and computer security and the DOS and Windows operating systems. Students are also taught how to use Windows application softwares for text processing, graphing and spreadsheets. Internet services such as the electronic mail and Netscape are also discussed.

Data Structures (DATSTRU)

3 units

This course discusses the different linear and nonlinear data structures such as arrays, stacks, queues, trees and graphs. Storage allocation, representation and implementation of these data structures are discussed as well as the algorithms used in creating, updating and accessing them. Topics in file organization are also discussed in this course.

Prerequisite: Computer Language 2

Database Language (DBLANGE)

3 units

In this subject, students are taught one relational database language and are expected to develop a relational database application system that is fully functional.

Prerequisite: Data Structures

Co-requisite: Theory of Databases

Theory of Databases (DATBASE)

3 units

This course covers the basic theories behind databases, data models and database design. The course concentrates mainly on relational databases.

Prerequisite: Data Structures

Co-requisite: Database Language

Management Information Systems Concepts (MIS-CON)

3 units

This course discusses information systems, their conceptual and technical foundations, their users, components, mission and capabilities and how they are developed and used in organizations. It also discusses both conventional and state-of-the-art information technologies and how they fit within a business organization, the kinds of processes they could support, the kinds of problems they could solve, their potential benefits and limitations, and the unique development, management and integration considerations associated with each.

Prerequisite: Systems Analysis and Design

Operating Systems Concepts (OPERSIS)

3 units

This course discusses operating system concepts which include processor scheduling, disk scheduling, memory management, file management, deadlocks, multiprogramming environment and concurrent processes.

Prerequisite: Computer Systems

Mathematical Simulation (MATHSIM)

3 units

This is an applied subject wherein concepts learned from the major mathematics subjects are modeled and simulated using the C programming language.

Prerequisites: Numerical Analysis, Linear Algebra

Systems Analysis and Design (SYNALDE)

3 units

This course covers the different phases of information system development: initiation, development and implementation. Structured systems analysis and design tools, techniques and application are also included.

Prerequisite: Software Engineering

Modern Geometry (MODEGEO)

3 units

A course dealing with the geometries of the Euclidean plane, the sphere and the projective plane. Topics include congruence, isometries, affine transformations, Desargue’s Theorem and Pappus Theorem.

Prerequisites: Linear Algebra, Modern Algebra

Linear Programming (LINPROG)

3 units

As a first course in operations research, this course exposes the students to basic linear optimization analysis, the revised simplex method, duality, and the interior-point method.

Prerequisite: Linear Algebra

Operations Research Models (ORMODEL)

3 units

This is an introductory course on the basic operations research models. Topics to be covered are the transportation model, assignment model, _oolean_pment model, network models, PERT/CPM, basic inventory models, and integer linear programming.

Prerequisite: Linear Programming

Enumerative Approaches to Optimization (ENUMAPP)

3 units

This course introduces the student to the fundamental theory and the solution approaches to discrete/combinatorial optimization models. Essentially, the course covers dynamic programming, branch-and-bound, and the combinations of these two prominent optimization approaches.

Prerequisite: Operations Research Models

Decision Theory (DECITHE)

3 units

This course introduces the student to the complexity and the analysis of the decision making process. It covers game theory, decision making under uncertainty, strategies, decision making under risk, and multiple criteria decision making.

Prerequisite: Linear Programming, Introduction to Statistics

Seminar Course in Mathematics (MATSEMI)

1 unit

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

Prerequisite: Junior Standing

Thesis Writing 1 (THSMTH1)

2 units

Introduction to research techniques and research topics. The student is required to submit a thesis proposal.

Prerequisite: Senior Standing

Thesis Writing 2 THSMTH2)

3 units

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

Prerequisite: Thesis Writing 1

Introduction to Set Theory (INTOSET)

3 units

A course covering the review of principles of logic, valid arguments and methods of proof; axioms on sets; algebra of sets; relations and functions; the number systems, mathematical induction; countable and uncountable sets; axiom of choice and the continuum hypothesis; ordering and ordinals.

Applied Multivariate Analysis (APMULTI)

3 units

A course dealing with discriminant analysis, analysis of covariance, multidimensional scaling applied to business problems.

Prerequisite: Introduction to Linear Models

Introduction to Statistics 2 (INTSTA2)

3 units

A second course in statistics covering chi-square and F distributions, tests of hypotheses for difference of means, proportion, difference of proportions, variance, difference of variances, regressions, correlation, analysis of variance, and the use of non-parametric methods. It also includes the steps to be undertaken in conducting sample surveys, theoretical discussions on the different sampling designs, estimation procedures using the various designs, sample size estimation as well as variance reduction techniques.

Prerequisite: Introduction to Statistics

Linear Models for Business Applications (LIMOBAP)

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.

Prerequisite: Linear Algebra, Inferential Statistics

Mathematical Probability (MATPROB)

3 units

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 and functions of several random variables. Special distributions such as uniform, binomial, poisson, geometric, gamma, beta, exponential, normal distributions, etc., are covered.

Prerequisite: MATH115

Time Series Analysis and Forecasting (TIMEFOR)

3 units

A course dealing with the different methods of forecasting time series data – classical smoothing procedures and the use of statistical models. The theoretical and model building issues of techniques like exponential smoothing, moving average, seasonal decomposition, ARIMA models, and transfer function economic, agricultural, financial, meteorological among others.

Prerequisite: Introduction to Linear Models