Division of Natural Sciences and Mathematics

Bachelor of Science in Applied Mathematics


BS Applied Mathematics students are required to finish these courses and number of units in four years or eight semesters:

Foundation Courses (17 units)

Foundation courses in the BS Applied Mathematics program consist of pre-calculus and calculus courses.





Math 18

Precalculus Mathematics

Polynomial functions and their zeros; rational and rational power functions; polynomial and rational inequalities; circular functions and their inverses; exponential and logarithmic functions; hyperbolic functions and their inverses; vector in two dimensions; matrices and determinants; systems of equations and inequalities; conics; parametric curves; polar and parametric equations.

5 units

Math 53

Calculus I

Limits and continuity; differentiation; derivatives of algebraic and trigonometry functions; extrema of functions; optimization; antidifferentiation; definite integrals; applications of integrals

4 units

Math 54

Calculus II

Integration techniques; further applications of definite integrals; separable differential equations; infinite sequences and series; calculus with polar and parametric curves; three-dimensional space; vectors; quadric surfaces

4 units

Math 55

Calculus III

Vector functions and their derivatives and integrals; multivariable functions and their limits and continuity; partial derivatives; directional derivatives; extrema of multivariable functions; cylindrical and spherical coordinates; multiple integrals; line integrals; surface integrals

4 units

Core Courses (53 units)

Core courses provide students with the fundamental knowledge and skills needed in using mathematics as a tool to solve problems in other fields. These include logic and set theory, abstract and linear algebra, analysis, optimization, statistics, numerical methods, and modeling.





Math 107

Logic and Set Theory

Mathematical logic and proof techniques; sets and functions; cardinal and ordinal numbers; axiomatic set theory

3 units

Math 110

Abstract Algebra

Binary operations; groups; rings, fields; integral domain

3 units

Math 114

 Linear Algebra

Vector spaces; linear transformations and matrices; eigenvalues; canonical forms; applications

3 units

Math 121

Differential Equations

Ordinary differential equations; Total differential equations; Partial differential equations of the first and second orders

3 units

Math 123

Advanced Calculus

Topology of real line; limits; continuity; derivatives; Reiman integrals

3 units

Math 128

Complex Analysis

Functions of a complex variable; Holomorphic functions; Taylor and Laurent expansions; Residue theory; Complex integration

3 units

Math 135

Combinatorial Mathematics

Basic and advanced counting techniques; analysis of discrete mathematical structures and patterns

3 units

Math 153

Computer Programming I

Fundamental concepts and methods of computer programming

3 units

Math 154

Computer Programming II

Statistical and other scientific applications of computer programming

3 units

Math 162

Theory of Interest

Measures of interest; annuities, yield rates, extinction of debts by amortization and sinking funds; bonds and other securities

3 units

Math 173

Numerical Methods I

Numerical methods for solving roots of single nonlinear equations and systems of linear equations; polynomial interpolation; numerical differentiation and integration

3 units

Math 174

Numerical Methods II

Numerical methods for solving ordinary and partial differential equations; spline and least-square approximation; optimization and selected advanced topics in numerical methods

3 units

Math 175

Mathematical Modeling

Formulation, analysis, and implementation of mathematical models for a wide range of application areas

3 units

Math 183

Linear and Integer Programming

Origin and nature of operations research; linear programming models and formulation, graphical method, simplex method, duality theory, sensitivity analysis; transportation problem, transshipment problem, assignment problem; integer-linear programming model and formulation, branch and bound method, cutting-plane algorithm, implicit enumeration

3 units

Math 198.1

Special Problem I

Exploration of research topics; research proposal development

1 unit

Math 198.2

Special Problem II

Conduct of research; writing and presentation of research results

2 units

Stat 110

Non-Bayesian Probability

Definitions and properties of events, probability and random variables; joints, conditional and marginal distributions; some important probability distributions

4 units

Stat 111

Statistical Methods and Inference

Population and sample; data collection and presentation methods; measures of location and dispersion; sampling estimators and estimation techniques; test of hypothesis

4 units

Elective Courses (9 units)

These are pure and applied mathematics courses that provide for an in-depth study of the selected mathematical theories and their applications in various fields. Students may choose any three mathematics elective courses, equivalent to 9 units, from the following list, subject to completion of the prerequisite courses.





Math 116

Number Theory

An introduction to the fundamental and classical results in number theory, its applications in other fields, and some recent development in the field

3 units

Math 122

Dynamical Systems

Existence and uniqueness theory of ordinary differential equations; Equilibrium points and their stability; Periodic solution; Poincare maps; Local bifurcations of equilibria; Perturbation methods

3 units

Math 125

Introduction to Mathematical Biology

An introduction to the use of continuous and discrete differential equations in investigating biological problems such as in population dynamics and the spread of diseases

3 units

Math 140

Graph Theory and Its Applications

Graph characterization, operations and algorithms; planarity and colorability; connectivity and traversability; matching and factorization;network applications

3 units

Math 143

Modern Geometries and Their Applications

Principles, methods and applications of non-Euclidean, projective and other geometries

3 units

Math 146

Introduction to Topology

Topological spaces; convergence; product and quotient spaces; connectedness and compactness; countability and separation axioms; applications

3 units

Math 165

Financial Derivatives Markets

An introduction to futures, options and related securities with emphasis on arbitrage pricing and risk management

3 units

Math 178

Mathematical Methods in Economics

Mathematical methods applied to elementary economic theory

3 units

Math 184

Network Analysis and Dynamic Programming

Shortest-route problem, minimal spanning tree problem, maximal-flow problem, network simplex method, project scheduling with PERT-CPM; deterministic and probabilistic dynamic programming applied to resource allocation, equipment replacement, and other related problems; inventory models; Markovian decision processes

3 units

Math 185

Planar Location and Facility Theory

Median-and-center problems in a plane, one and multi-facility problems, relation of location problems, linear and network optimization

3 units

Math 186

Nonlinear Optimization

Nonlinear programming models and formulation, graphical approach; classical unconstrained and constrained optimization, nonlinear programming algorithms; analysis of selected nonlinear programming problems such as quadratic programming, stochastic programming, convex programming, geometric programming, and fractional programming

3 units

Math 195


Supervised practical experience in some areas of applied mathematics in an industrial, business, or governmental setting. Students are required to document their work experience and write a report which will be evaluated by their faculty supervisor in consultation with the employers

3 units

Math 197

Special Topics in Mathematics

3 units

Qualified elective courses (6 units)

Students may choose any two qualified elective courses, equivalent to 6 units, from the following list.






Discrete Mathematics in Computer Science I

Principles of logic, set theory, relations, and functions; Boolean algebra; matrices

3 units


Discrete Mathematics in Computer Science II

Principles of combinatorics, probability, algebraic systems, and graph theory

3 units

CMSC 123

Data Structures

Abstract data types and their implementations; lists, stacks, queue, trees, mappings, sets and graphs; searching and sorting techniques, dynamic storage management

3 units

CMSC 140

Advanced Programming

Intermediate programming PL/1 procedures; block structures; ON conditions; recursion; introduction to data structures and program analysis

3 units

CMSC 141

Automata and Language Theory

Finite automata and regular languages; push-down automata and context-free languages; Turing machine and recursively enumerable sets; linear bounded automata and context-free

languages; computability and halting problems; undecidable problems; recursive functions; and computational complexity

3 units

CMSC 142

Design and Analysis of Algorithms

Algorithm design techniques: use of data structures, divide and conquer, local and global search. Complexity analysis algorithms: asymptotic analysis, worst-case analysis and average-case analysis, recurrences, lower bounds, NP-completeness

3 units

CMSC 143

Advanced Algorithms

Constraint programming, local search, heuristics, metaheuristics, linear programming, mixed integer programming, genetic algorithms, swarm optimization, approximation algorithms

3 units

CMSC 153

Accounting and Informations Systems

Fundamental principles of accounting; programming of accounting modules: general ledger, journal ledger, transaction ledger, accounts receivable, accounts payable, etc.

3 units

CMSC 161

Interactive Computer Graphics

Graphic system software and hardware, 2D drawing algorithms, geometrical transformations, surface modeling, 3D viewing, visible surface determination algorithms, illumination and reflection models, shading models for polygons, color theory, ray tracing. Students write their 3D rendering engine

3 units

CMSC 162

3D Computer Graphics and Animation

3D graphics systems software and hardware; 3D modeling, texturing, and lighting; animation basics; principles, armatures, constraints, IPO driver, rigging, effects and physical simulation; rendering; compositing, video sequence editing

3 units

CMSC 170

Introduction to Artificial Intelligence

Introduction to the major fields of application of AI: natural language processing; image recognition; pattern recognition; learning. Introduction to AI programming languages: PROLOG, LISP. Search and control strategies; probabilistic reasoning; matching techniques; knowledge and state space representation

3 units

CMSC 173

Data Mining

Fundamental concepts in data mining. Big data and basic statistics; databases and data warehouses; preprocess: data preparation for data mining; patterns, association correlations; classification and prediction; clustering, applications in data mining

3 units

CMSC 180

Computer Simulation and Modeling

Algorithms and packages for standard graphics; advanced 2-D and 3-D rendering techniques; realism; visualization of scientific data. Use of statistical tools and techniques, knowledge in expert systems and artificial intelligence for data representation and analysis. Problems in other disciplines of science will be chosen as examples to be used for modeling and simulation

3 units

CMSC 181

Introduction to Parallel Computing

Parallel computer architecture; principles of parallel algorithm design, programming shared- and distributed- memory systems, understanding parallel performance; numerical and non-numerical parallel algorithms; programming models; shared memory, message passing, and global address space languages

3 units

CMSC 182

Scientific Computing

Different methods in numerical computing; introduction to dynamical systems and chaos; computation of fluid dynamics and implementation in programming

3 units

CMSC 197

Special Topics

Lecture course in topics of current interest, such as data communications, parallel computation, artificial intelligence, neural networks

3 units

Physics 72

Elementary Physics II

Electricity and magnetism, wave phenomena, and optics

4 units

Physics 72.1

Elementary Physics Laboratory II

This is the laboratory component for Physics 72

1 unit

Stat 104

Descriptive Statistics

Statistics; statistical measurement; statistical notations; collection, organization, and presentation of data; measures of central tendency, location, dispersion, skewness, kurtosis; letter values, box plots and stem and leaf display; measure of association and relationship; rates, ratios, and proportions; construction of index numbers and indicators

3 units

Stat 129

Regression and Correlation Analysis

Linear regression model; model selection; regression diagnostics; use of dummy variables; remedial measures

3 units

Stat 130

Introduction of Experimental Designs

Principles of experimental design; completely randomized design; randomized complete block design; Latin-square design; factorial experiments; analysis of variance; transformations

3 units

Stat 133

Introduction to Exploratory Data Analysis

Exploratory data analysis techniques; robust estimators for location and scale parameters

3 units

Stat 138

Use of Statistical Software Packages

Use of database software. spreadsheet and statistical software packages for data management

3 units

Stat 140

Introduction to Sample Surveys

Designs of surveys; sample designs; estimation of population characteristics; biases and non-sampling errors

3 units

Stat 145

Introduction to Time Series Analysis and Forecasting

Classical methods; ARIMA models; Box-Jenkins methods; intervention analysis

3 units

Stat 149

Introduction to Categorical Data Analysis

Categorical data; cross-classification tables; analysis using log linear, logistic and logit models

3 units

Stat 150

Survey Operations

Research process; techniques of data measurement; issues of reliability and validity; scale construction; principles of questionnaire design; preparation of questionnaires and interview schedules; data collection; data coding and encoding; data quality control; presentation of research findings

3 units

Stat 171

Elementary Economics Statistics

The system of national accounts; input-output analysis

3 units

Stat 172

Statistical Methods in Fisheries and Agriculture

Planning for and determining appropriate statistical methods for fisheries and agricultural researches

3 units

Stat 175

Introduction to Biostatistics

Descriptive and inferential statistics in the biological and medical sciences; epidemiologic studies; clinical trials; survival analysis

3 units

Stat 176

Statistical Procedures in Market Research

Market research process; design of market research; data collection techniques; data analysis using descriptive and inferential statistics in market research

3 units

Stat 180

Introduction to Stochastic Processes

Probability spaces; random variables; definition of stochastic process; classification of stochastic process; Markov chains; continuous time Markov chains, renewal processes

3 units

Stat 197

Special Topics in Statistics

3 units

Other required courses

Applied Mathematics students must also complete 12 General Education courses, the legislated PI 100 course (The Life and Works of Jose Rizal), four Physical Education courses, and two National Service Training Program courses.