Programs
Doctor of Philosophy in Applied Mathematics (PhD AMAT)
The global trend in applied research necessitates the use of mathematical approaches. The Ph.D. Applied Mathematics in UPLB, the first doctorate degree program in applied mathematics in the Philippines, is an interdisciplinary program that focuses on the study and creation of mathematical and computational methods to solve complex problems in various fields and industries. The goal is to produce graduates who are innovative problem solvers, combining advanced-level mathematical science and domain knowledge to help address local and global issues and challenges. This program seeks to contribute to the existing pool of experts in the field of Mathematics who are competent not only in theory but also in the use of these theories in obtaining predictions and quantitative prescriptions for complex problems.
Research Focus
The Ph.D. program seeks to address specific present and future needs of science, technology, and society, to wit:
- Biomathematics to formulate quantitative solutions to the problems in biology, agriculture, biotechnology, environmental science, and medicine with the aid of data science;
- Complex Systems Modeling to analyze interactions and trends in dynamic, physical, and social systems at different scales;
- Financial Mathematics to manage the risks in human societies, businesses, natural environment, and agricultural economy;
- Data Science and Numerical Mathematics to approximate solutions to the problems in the natural, social, and engineering sciences using modern technologies and algorithms in machine learning and artificial intelligence;
- Partial Differential Equations to model properties of composite materials, and the evolution of the dynamics in spatio-temporal systems; and
- Quantitative Management and Decision Science to optimize the use of natural resources and design efficient processes and operations in various industries.
Ph.D. Applied Mathematics graduates can work in academic and research institutions as educators or researchers in colleges and universities. They can also be employed as scientists in government laboratories, research institutions, knowledge management agencies, and consulting firms. With growing interests in data mining and analytics, graduates of this program can also be data scientists working in e-commerce, business intelligence, bioinformatics and genomics, or management engineering. Financial service and investment management firms can also hire Ph.D. Applied Mathematics graduates as financial analysts who will use sophisticated math models and computational methods to support investment decisions, manage risks, develop and price new securities, and optimize operations. Engineering (computer, electronics, chemical, electrical, industrial) research organizations will also be interested in the modeling and computational strengths of Ph.D. Applied Mathematics graduates to rationalize the design and analysis of existing and new materials in fields like electronics and nanotechnology. With the emergence of ecological and environmental problems affecting the whole population, those who have the modeling and numerical knowledge can be tapped to apply quantitative techniques in the management of ocean fisheries, insect population growth, and spread of infection under various immunization protocols. Computer information and software firms can also employ graduates of Ph.D. Applied Mathematics program as analysts or head of R&D operations. Transportation and communication service providers can also take in Ph.D. Applied Mathematics graduates as consultants for efficient and effective delivery of services. Social enterprises can also hire these graduates to study social networks affecting their success or failure, and to simulate the dynamics and behavior of communities.
Courses
- Mathematics Division
| Code | Title | Description |
|---|---|---|
| AMAT 215 | Mathematical Theory of Choice and Games (3) | Mathematical modeling and analysis of games and rational choice. 3 hrs (class). PR. AMAT 105 or MATH 120 or COI. (2) |
| AMAT 250 | Numerical Simulation (3) | Computational techniques for the simulation of a large variety of systems and processes. 3 hrs (class). PR. COI. (2) |
| AMAT 255 | Mathematical Data Science (3) | Algebraic, geometric, fuzzy and probabilistic algorithms for discovering patterns in data sets. 3 hrs (class). PR. COI. (2) |
| AMAT 266 | Deterministic Mathematical Decision Models (3) | Linear models; inventory models; integer programming and combinatorial models; elementary dynamic programming models; introduction to nonlinear programming. 3 hrs (class). PR. AMAT 160 or COI. (1) |
| AMAT 267 | Probabilistic Mathematical Decision Models (3) | Basic concepts and application of probabilistic mathematical decision models such as queuing, inventory, dynamic programming and simulation, inventory, dynamic programming and simulation models. 3 hrs (class). PR. AMAT 160 or COI. (2) |
| AMAT 277 | Mathematical Finance (3) | Mathematical concepts and techniques used in the pricing of financial derivatives. 3 hrs (class). PR. COI. (2) |
| AMAT 280 | Biomathematics (3) | Mathematical modeling of biological systems. 3 hrs (class). PR. None. (1) |
| AMAT 310 | Dynamic Systems Modeling (3) | Deterministic and stochastic modeling of temporal and spatial evolution of dynamic systems. PR. COI. (1,2) |
| AMAT 350 | Advanced Numerical Analysis (3) | Theory and applications of numerical analysis. PR. COI. (1,2) |
| AMAT 360 | Convex Optimization (3) | Mathematical programming and combinatorial optimization based on convexity. PR. COI. (1) |
| AMAT 361 | Optimal Control (3) | Mathematical models and methods in solving optimal control problems. PR. COI. (2) |
| AMAT 391 | Special Topics (1-3) | PR. COI. (1,2) |
| AMAT 398 | Research and Development Internship (3) | The student should have passed the 12 units of core and major courses. Minimum of 200 hours. (1,2,M) |
| AMAT 399 | Graduate Seminar (1) | PR. COI. (1,2,M) |
| AMAT 400 | PhD Dissertation (12) | PR. COI. (1,2,M) |
| Code | Title | Description |
|---|---|---|
| MATH 211 | Abstract Algebra (3) | Binary operations, algebraic systems such as semigroups, rings integral domains, field, extensions. 3 hrs (class). PR. MATH 111. (1) |
| MATH 213 | Theory of Matrices (3) | Operations on matrices; canonical forms, determinants; characteristic equations; eigenvalues. 3 hrs (class). PR. MATH 120. (1,2) |
| MATH 215 | Coding Theory and Cryptography (3) | Concepts and mathematical theory of error-correcting codes, encryption and decryption schemes. 3 hrs (class). PR. MATH 111. (1) |
| MATH 217 | Algebraic Combinatorics (3) | Discrete structures from an algebraic perspective. 3 hrs (class). PR. MATH 211. (2) |
| MATH 220 | Algebraic Geometry (3) | Concepts and theorems of algebraic geometry. 3 hrs (class). PR. MATH 211. (1) |
| MATH 222 | Finite Geometries (3) | The finite plane, projective plane, affine plane, hyperbolic plane; Galois geometries; combinatorial applications of finite geometries; finite inversive geometry and block design. 3 hrs (class). PR. MATH 211. (2) |
| MATH 225 | Topology (3) | Topological spaces; bases and subbases; continuity; metric spaces; separation axioms; compactness; product spaces; connectedness. 3 hrs (class). PR. MATH 101 or its equivalent. (1, 2) |
| MATH 230 | Real Analysis (3) | The real number system; Lebesque measures; Riemann and Lebesque integrals; differentiation and integration. 3 hrs (class). PR. MATH 155 (1, 2) |
| MATH 231 | Functions of a Complex Variable (3) | Complex differentiation and integration; analytic continuation; residue theorem; conformal mapping; and some special functions. 3 hrs (class). MATH 155. (2) |
| MATH 235 | Functional Analysis (3) | Concepts, principles, methods, and applications of functional analysis; normed and Banach spaces; Hilbert space theory. 3 hrs (class). PR. MATH 213. (2) |
| MATH 243 | Graph Theory and Applications (3) | Concepts and theorems involving graphs and networks and their applications. 3 hrs (class). PR. None. (2) |
| MATH 252 | Theory of Partial Differential Equations (3) | Concepts and techniques in solving partial differential equations arising from applications. 3 hrs (class). PR. MATH 151 or COI. (1) |
| MATH 281 | Probability and Stochastic Processes (3) | Theories and techniques in probability and stochastic processes. 3 hrs (class). PR. MATH 182 or COI. (1) |
| MATH 291 | Special Topics (1-3). | May be taken twice provided that total number of units to be credited to the student’s program will not exceed 4 units. May be taken twice. PR. COI. |
| MATH 299 | Graduate Seminar (1) | May be taken twice. PR. COI (1,2) |
| MATH 300 | Master’s Thesis (6) | (1, 2, S) |
| Code | Title | Description |
|---|---|---|
| MAED 201 | Mathematics Education (3) | Mathematical thoughts and ideas as bases of school mathematics. 3 hrs (class). PR. None. (1) |
| MAED 202 | Mathematical Didactics (3) | Pedagogical philosophies, principles and praxis in mathematics education. 3 hrs (class). PR. None. (1) |
| MAED 203 | Mathematics Curriculum (3) | Analysis, design, and evaluation of school mathematics curriculum. 3 hrs (class). PR. MAED 202. (2) |
- Physics Division
| Code | Title | Description |
|---|---|---|
| PHYS 221 | Classical Mechanics I (3) | Classical dynamics of particles and systems of particles in translational, rotational, and oscillatory motion in the Lagrangian and Hamiltonian formalisms. 3 hrs (class). PR. PHYS 121 or COI. (1,2) |
| PHYS 225 | General Relativity (3) | Einstein field equations and their vacuum solutions for isotropic homogeneous systems. 3 hrs (class). PR. PHYS 221. (2) |
| PHYS 231 | Classical Electrodynamics I (3) | Electrostatics and magnetostatics and their unification through Maxwell’s equations. 3 hrs (class). PR. PHYS 131 or COI. 3 hrs (class). PR. PHYS 131 or COI. (1,2) |
| PHYS 232 | Classical Electrodynamics II (3) | Nature and propagation of electromagnetic fields. 3 hrs (class). PR. PHYS 231. (1,2) |
| PHYS 241 | Quantum Mechanics I (3) | Analytical techniques in quantum mechanics. 3 hrs (class). PR. PHYS 141 or COI. (1,2) |
| PHYS 242 | Quantum Mechanics II (3) | Approximation techniques in quantum mechanics. 3 hrs (class). PR. PHYS 241. (1,2) |
| PHYS 251 | Statistical Mechanics I (3) | Thermodynamics ensembles and quantum statistics. 3 hrs (class). PR. PHYS 151 or COI. (1,2) |
| PHYS 252 | Statistical Mechanics II (3) | Statistical mechanics of ideal Bose and Fermi systems, phase transitions, and nonequilibrium thermodynamic systems. 3 hrs (class). PR. PHYS 251. (2) |
| PHYS 275 | Electrons and Phonons in Solids (3) | The properties of solids emerging from the band structure and the interactions of constituent electrons, phonons, and their collective excitations. 3 hrs (class). PR. COI. (1) |
| PHYS 299 | Graduate Seminar (1) | May be taken twice. PR. COI. (1,2,M) |
| PHYS 300 | Master’s Thesis (6) | (1,2,M) |