BS Applied Mathematics students are required to finish these courses and number of units in four years or eight semesters:
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COURSE CATEGORIES
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UNITS
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Foundation courses in the BS Applied Mathematics program consist of pre-calculus and calculus courses.
CODE | TITLE | DESCRIPTION | UNITS |
|---|---|---|---|
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 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.
CODE | TITLE | DESCRIPTION | UNITS |
|---|---|---|---|
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 |
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.
CODE | TITLE | DESCRIPTION | UNITS |
|---|---|---|---|
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 | Practicum | 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 |
Students may choose any two qualified elective courses, equivalent to 6 units, from the following list.
CODE | TITLE | DESCRIPTION | UNITS |
|---|---|---|---|
CMSC 56 | Discrete Mathematics in Computer Science I | Principles of logic, set theory, relations, and functions; Boolean algebra; matrices
| 3 units |
CMSC 57 | 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 |
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.
