
College of Science 
University of the Philippines Diliman 
COURSE CATALOGUE 









As of July 28, 2017 





Course Number 
Course Title 
Course Description 
Units 
Course Prerequisite 
Math 1 
General Mathematics 
The development of mathematical literacy and appreciation through a synoptic view of the different branches of mathematics with historical notes and applications. 
3.0 
none 
Math 2 
Practical Mathematics 
Basic mathematical skills and applications in everyday life. 
3.0 
none 
Math 11 
College Algebra 
Linear equations; algebraic and graphical solutions of the quadratic equations; exponents and radicals; complex numbers; binomial expansion; determinants; progressions; solutions of equations, several equations in several variables. 
3.0 
One year high school of algebra 
Math 14 
Plane Trigonometry 
Logarithms; graphs of the trigonometric functions; the general triangle; solutions of trigonometric, inverse trigonometric, exponential and logarithmic equations; complex numbers. 
3.0 
One year each of high school algebra and plane geometry 
Math 17 
Algebra and Trigonometry 
Sets and numbers; the algebra of numbers as logical system; inequalities; absolute values and coordinates systems; functions and graphs; circular, linear, quadratic, and polynomial functions; exponential and logarithmic functions; applications of the circular functions to angles. 
5.0 
One year each of high school algebra 
Math 53 
Elementary Analysis I 
Functions and their graphs; limits and continuity; the derivative; derivatives of algebraic and trigonometric functions; exponential and logarithmic functions; inverse functions; antiderivatives and definite integrals; fundamental theorem of calculus; applications of the definite integral. 
5.0 
Math 17 or equivalent 
Math 54 
Elementary Analysis II 
Integration methods; applications of the definite integral; plane and solid analytic geometry; polar coordinates; vectors; parametric equations. Sequences and series; power series. 
5.0 
Math 53 
Math 55 
Elementary Analysis III 
Partial differentiation; multiple integrals; infinite series; differential equations. 
3.0 
Math 54 or equivalent 
Math 60 
Precalculus 
Algebraic operations, functions, analytic, geometry, trigonometry, matrices. 
5.0 
none 
Math 63 
Calculus I 
Functions of a single variable; limits; continuity; the derivative and the Riemann integral; derivatives of algebraic, trigonometric and inverse trigonometric functions; applications; polar coordinates; conic sections. 
5.0 
Math 60 or equivalent 
Math 64 
Calculus II 
The exponential, logarithmic and hyperbolic functions; techniques of integration; vectors and vectorvalued functions; improper integrals; infinite series; power series; applications. 
5.0 
Math 63 or equivalent 
Math 65 
Calculus III 
Calculus of several variables and Fourier series. 
3.0 
Math 64 
Math 100 
Introduction to Calculus 
Limits; derivatives; integrals; applications. 
4.0 
Math 17 or COI 
Math 102 
Intermediate Calculus 
Integration techniques; multivariate calculus; sequences and series; introduction to matrices; applications to economics, business, life and social sciences. 
3.0 
Math 100 or equivalent, or Math 53 or equivalent 
Math 109 
Fundamental Concepts of Mathematics 
Algebra of sets and logic; methods of proof; functions and relations; logical nature and structure of mathematics; introduction to numbertheory; algebra arid geometry of complex numbers. 
3.0 
2nd year standing 
Math 110.1 
Abstract Algebra I 
Algebraic relations, lattices, Boolean algebra; groups; rings; integral domain. 
3.0 
Math 109 
Math 110.2 
Abstract Algebra II 
Fields; vector spaces; linear transformations; matrices; characteristic values; diagonalization; inner product; quadratic forms. 
3.0 
Math 110.1 
Math 110.3 
Abstract Algebra III 
Fields of quotients of integral domains; polynomial rings; field extensions; Galois theory; other systems. 
3.0 
Math 110.1 
Math 114 
Linear Algebra 
Vector spaces; linear transformations; matrices; eigenvalues; canonical forms; orthogonality; applications. 
3.0 
Math 54 or equivalent 
Math 117 
Elementary Theory of Numbers 
Properties of integers; divisibility; unique factorization theorem; solutions of congruences; residue systems; primitive roots and the quadratic reciprocity law; solutions of Diophantine equations. 
3.0 
Math 109 or COI 
Math 121 
Elementary Differential Equations 
Ordinary differential equations of order one; linear differential equations; differential operators; Laplace Transform; nonlinear equations; series solutions about an ordinary point. 
3.0 
Math 54 or equivalent 
Math 122 
Differential Equations and Applications 
Modelling systems; solutions of ordinary differential equations (ODE’s) of order one and system of ODE’s; Laplace transform; solutions of the classical partial differential equations; numerical methods. 
3.0 
Math 65 or equivalent 
Math 123.1 
Advanced Calculus I 
The real number system; point set topology; sequences of real numbers; limits and continuity; the derivative; the Riemann integral; series of real numbers; sequences and series of functions; uniform convergence; power series. 
3.0 
Math 65 or equivalent 
Math 123.2 
Advanced Calculus II 
Topology of R^{n}; continuity, chain rule; Taylor’s formula; implicit and inverse function theorems; multiple integration; improper integrals; transformations; metric and normed spaces. 
3.0 
Math 123.1 
Math 126 
Real Analysis 
Properties of real numbers; integral of step functions; Lebesgue integral; convergence theorems; measureable functions; measurable sets; selected topics. 
3.0 
Math 123.1 
Math 128 
Complex Analysis 
Analytic functions; elementary functions; complex integration; power series; residues; conformal mapping. 
3.0 
Math 109 or equivalent, and Math 123.1 
Math 131 
Elementary Set Theory 
Axioms of Set Theory; relations and functions; natural numbers, cardinal numbers and the Axiom of Choice; orderings and ordinals. 
3.0 
Math 110.1 
Math 140 
Introduction to Modern Geometries 
Development of modern geometries; finite geometries; geometric transformations; projective geometry; nonEuclidean geometries. 
3.0 
Math 109 or equivalent 
Math 142 
Elementary Topology 
Topologies and topological spaces; functions and homeomorphisms; continuity; metric spaces, compactness and connectedness. 
3.0 
Math 123.1 or COI 
Math 146 
Introduction to Differential Geometry 
Elementary topology; calculus of several variables; curves and surfaces; theorems of … 
3.0 
Math 65 or equivalent 
Math 147 
Introduction to Algebraic Geometry 
Projective varieties; algebraic and elliptic curves. 
3.0 
Math 110.1 and Math 140 
Math 148 
Introduction to Projective Geometry 
Projective planes and spaces. 
3.0 
Math 110.1 and Math 140 
Math 150.1 
Mathematical Statistics I 
Combinatorial probability; probability distributions; joint and conditional distributions; random variables; distributions of functions of random variables; mathematical expectation; momentgenerating functions; sampling distributions. 
3.0 
Math 65 or equivalent, and Stat 101 
Math 150.2 
Mathematical Statistics II 
Limiting distributions; estimation of parameters; tests of hypotheses; regression and correlation; analysis of variance; applications. 
3.0 
Math 150.1 
Math 157 
Discrete Mathematical Structures 
Fundamentals of set theory; algebraic relations; combinatorial algorithms; algebraic structures and their applications in computer science. 
3.0 
Math 54 
Math 162 
Theory of Interest 
Simple interest; compound interest; continuous interest; annuities; amortization schedules and sinking funds; bonds and other securities; special topics. 
3.0 
COI 
Math 164 
Mathematics of Life Contingencies 
Mathematical theory of life contingencies involving singlelife functions; mortality; life annuities and insurances; reserves; expense factor; population theory. 
3.0 
Math 150.1 and Math 162 
Math 171 
Introduction to Numerical Analysis 
Error analysis; solution of a single nonlinear equation; solution of systems of equations; solution of ordinary differential equations; series. 
3.0 
Math 110.2 or equivalent, and Math 122 or equivalent (2lec, 3lab) 
Math 180.1 
Operations Research I 
Review of classical optimization theory; introduction to linear programming, quadratic programming; nonlinear programming and dynamic programming; networks (Path, PERT/CPM) and inventory problems. 
3.0 
Math 114 or equivalent 
Math 180.2 
Operations Research II 
Review of probability theory; Stochastic models; Markov chains; introduction to queueing theory; introduction to simulation; games, replacement and reliability theory. 
3.0 
Math 180.1 and Math 150.1 
Math 196 
Undergraduate Seminar 

1.0 
Junior Standing 
Math 197 
Special Topics 
may be taken at most thrice provided topics are different; topics to be specified 
3.0 
COI 
Math 200 
Undergraduate Thesis 

3.0 
Senior Standing 
Math 201 
Concepts and Techniques in Abstract Algebra 
Groups, rings and homomorphism. 
3.0 
Math 109 or COI 
Math 202.1 
Analysis I 
Real numbers, sequences of real numbers and limits, continuity of functions, derivatives, Riemann integral. 
3.0 
COI 
Math 202.2 
Analysis II 
ndimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, complexvalued functions and their derivatives. 
3.0 
Math 202.1 
Math 203 
Matrices and Applications 
Linear systems of equations and matrices, matrix operations, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, applications. 
3.0 
COI 
Math 204 
Classical and Modern Geometry 
Finite geometries, euclidean and noneuclidean geometries, projective geometry, geometric transformations. 
3.0 
COI 
Math 205 
Concepts and Methods in Probability and Statistics 
Descriptive statistics, probability and probability distributions, sampling theory, estimation and test of hypothesis, linear correlation and regression analysis. 
3.0 
COI 
Math 208 
History and Development of the Fundamental Concepts of Mathematics 
The developent of mathematics: a historical overview; the nature of mathematics, issues and aspects of mathematics. 
3.0 
COI 
Math 209.1 
Selected Topics in Applied Mathematics 

3.0 
COI 
Math 209.2 
Selected Topics in Discrete Mathematics 

3.0 
Math 201 
Math 210.1 
Modern Algebra I 
Semigroups and groups; rings; fields; groups with operators. Selected topics. 
3.0 
COI 
Math 210.2 
Modern Algebra II 
A continuation of Mathematics 210.1. 
3.0 
Math 210.1 
Math 211 
Linear Algebra 
Vector spaces, linear mappings; theorem of HamiltonCayley; modules over principal ideal domains; Jordan canonical form, rational canonical form; bilinear forms, inner products; law of inertia, spectral theorem; multilinear forms; tensor products. 
3.0 
Math 110.2 or Math 114 or COI 
Math 212 
Theory of Groups 
Definitions and examples; normal subgroups and homomorphisms; Abelian groups; Sylow theorems; composition series and solvable groups. 
3.0 
COI 
Math 213 
Theory of Rings 
Representation and structure of rings; Ideal Theory. 
3.0 
COI 
Math 214 
Theory of Matrices 

3.0 
COI 
Math 216 
Lie Groups and Lie Algebras 
Classical matrix Lie groups, Lie algebras of Lie groups, nilpotent and solvable algebras, semisimple algebras, representations. 
3.0 
Math 210.1 
Math 217 
Theory of Numbers 
Linear Congruences, Euler’s and Wilson Theorems, Quadratic residues, Quadratic Reciprocity Law, Jacobi’s and Kronocker’s symbols, Polian Equation, Positive Binary and Ternary quadratic forms. Theory of the sums of two and three squares. 
3.0 
COI 
Math 218 
Theory of Algebraic Numbers 
Algebraic number fields; algebraic integers; basic and discriminant; ideals; fundamental theorem on the decomposition of ideals; ideal classes; Minckowski’s theorem; the class formula; units; Fermat’s last theorem. 
3.0 
COI 
Math 220.1 
Theory of Functions of a Real Variable I 
Lebesgue and other integrals; differentiation; measure theory. 
3.0 
Math 123.1 or COI 
Math 220.2 
Theory of Functions of a Real Variable II 
Continuation of Math 220.1. Selected topics. 
3.0 
Math 220.1 
Math 221 
Partial Differential Equations 
Equations of the first and second order. Green’s function. Boundary value problems. 
3.0 
COI 
Math 222 
Approximation Theory 
Taylor’s theorem, Weierstrass approximation theorem, approximation in Hilbert spaces, Fourier Series and Fourier transform, direct and inverse theorems, algebraic and trigonometric interpolation, WhittakerShannon sampling theory, wavelet analysis. 
3.0 
Math 220.1 or COI 
Math 224 
Control Theory 
Elements of the calculus of variations. Naïve optimal control theory; Functional analysis; Generalized optimal control theory; the Pontrajgin maximum principle for chattering controls; Research problems. 
3.0 
Math 126, and Math 142 or equivalent 
Math 227 
Calculus of Variation 
Euler’s equations. Legendre conditions. Jacobi’s conditions. Isoperimetric problems. Lagrange’s methods. Dirichlet’s principle. 
3.0 
COI 
Math 228 
Theory of Functions of a Complex Variable 
Analytic functions; geometric function theory; analytic continuation; Riemann Mapping Theorem 
3.0 
COI 
Math 229 
Functional Analysis 
Linear operators, linear functions, topological linear spaces, normed spaces, Hilbert spaces, functional equations, Radon measures, distributive and linear partial differential equations, and spectral analysis. 
3.0 
Math 220.1 
Math 235 
Mathematics in Population Biology 
Continuous and discrete population models for single species, models for interacting populations, evolutionary models, dynamics of infectious diseases. 
3.0 
Math 121.1 or equivalent, or COI 
Math 236 
Mathematics in Biological Processes 
Biological oscillators and switches, perturbed and coupled oscillators, reaction diffusion, enzyme kinetics, chemotaxis, circadian systems models, coupled cell networks. 
3.0 
COI 
Math 240 
Geometric Crystallography 
Isometries, frieze groups, crystallographic groups, lattices and invariant sublattices, finite groups of isometries, geometric and arithmetic crystal classes. 
3.0 
Math 210.1 or equivalent 
Math 241 
Hyperbolic Geometry 
Moebius transformations, hyperbolic plane and hyperbolic metric, geometry of geodesics, hyperbolic geometry, groups of isometries on the hyperbolic plane. 
3.0 
Math 210.1 or equivalent 
Math 242 
General Topology 
Topological spaces; metric spaces; theory of convergence; bases; axioms of countability; subspaces; homeomorphisms. Selected topics. 
3.0 
COI 
Math 243 
Algebraic Topology 
Homotopy, fundamental group, singular homology, simplicial complexes, degree and fixed point theorems. 
3.0 
Math 242 
Math 246 
Differential Geometry 
Classical theory of curves and surfaces. Mappings of surfaces. Differential structures. Lie groups and frame bundles. 
3.0 
Math 123.1 or COI 
Math 247 
Algebraic Geometry 
The general projective space. Collineation and correlations in a projective space. Algebraic manifolds. Plane curves. Quadratic transformation of systems of plane curves. 
3.0 
COI 
Math 249 
Selected Topics in Geometry and Topology 
topic to be specified for record purposes 
3.0 
COI 
Math 250 
Probability Theory 
Random variables, law of large numbers, special probability distributions, central limit theorem, Markov chains, Poisson process, martingales. 
3.0 
Math 220.1 or COI 
Math 255 
Mathematics of Decision Making 
Some application of Bayesian statistics; use of experiments in decision problems; group decision making and risksharing. 
3.0 
Math 155 
Math 258 
Combinatorial Mathematics 
Permutations and combinations. Generating functions. Principle of inclusion and exclusion. Recurrence relations. Occupancy. Matrices of zeros and ones. Partitions. Orthogonal Latin squares. Combinatorial designs. 
3.0 
COI 
Math 260 
Actuarial Theory and Practice 
Multiple life theory, multiple decrement theory, applications of multiple decrement theory, risk theory and introduction to credibility theory. 
3.0 
Math 164 or equivalent 
Math 261 
Survival and Loss Models 
Hazard rate function, analysis of various survival and loss models, credibility theory. 
3.0 
Math 164 or equivalent 
Math 262.1 
Actuarial Science I 
Gross premiums and asset shares, nonforfeiture options, expense analysis, distribution of surplus, valuation of liabilities, product development process, introduction to life insurance accounting. 
3.0 
Math 261 or COI 
Math 262.2 
Actuarial Science II 
Selection of risks, reinsurance, introduction to investment analysis and finance management, isurance code, actuarial principles in special lines of insurance. 
3.0 
Math 262.1 or COI 
Math 265 
Stochastic Calculus 
Conditional expectations, martingales, Brownian motion, Itô ingegral, Itô formula, stochastic differential equation, Girsanov Theorem, applications to mathematical finance. 
3.0 
Math 150.1 or COI 
Math 266 
Mathematical Finance 
Binomial asset pricing model, vanilla options, exotic options, American options, arbitrage probabilities, profit and loss, stochastic interest rates. 
3.0 
Math 265 or COI 
Math 271.1 
Numerical Analysis I 
Floating point representation, condition numbers, iterative methods for solving systems of linear and nonlinear equations, numerical integration, numerical linear algebra. 
3.0 
Math 171 or COI 
Math 271.2 
Numerical Analysis II 
Numerical methods for ordinary differential equations, fintedifference methods for partial difference equations, numerical methods for conservation laws, multigrid methods. 
3.0 
Math 271.1 or COI 
Math 272 
Automata Theory 
Finite state automata. Regular expressions, decomposition of finite automata and their realization. Turing machines. Introducton to formal languages. 
3.0 
COI 
Math 276 
Introduction to Computer Simulation 
Introduction to computer simulation of theoretical system and realtime processes. Examples of simulation for the solution of both theoretical and practical problems in various fields of application. 
3.0 
COI 
Math 280 
Linear Programming 
Simplex method, duality, geometry of linear programs, parametric programming, decomposition and upperbounded variables. 
3.0 
Math 114 and Math 180.2 
Math 281 
Nonlinear Programming 
Properties of convex sets and functions; unconstrained optimization; KuhnTucker Thoerem. Lagrange multipliers; Saddlepoint Theorems; algorithms. 
3.0 
COI 
Math 282 
Integer Programming and Combinatorial Optimization 
Applications of integer programming. Converging dual and primal cutting plane algorithms. Branchbound methods. Total unimodularity and the transportation problem. Applications of graph theory to mathematical programming. 
3.0 
Math 280 or equivalent 
Math 283 
Applied Dynamic Programming 
Deterministic decision problems; Analytical and computational methods; Applicatons to problems of equipment replacement, resource allocation, scheduling, search and routing. 
3.0 
Graduating status or COI 
Math 285 
Introduction to Stochastic Optimization 
Probability thoery and applications to discrete and continuous Markov chains; classification of states; algebraic methods, birth and death processes, renewal theory, limit theorems. 
3.0 
Math 114 and Math 150.1 
Math 286 
Finite Graphs and Networks 
Basic graph theory and applications to optimal path problems; flows in network; combinatorial problems. 
3.0 
Math 285 or COI 
Math 288 
Numerical Optimization 
Deterministic descent type methods, stochastic optimization methods, numerical implementation. 
3.0 
Math 271.1 or COI 
Math 290 
Research Paper on College Mathematics 

3.0 
COI 
Math 294 
Independent Study 
may be credited once in the M.S. Mathematics/Applied Mathematics programs and twice in the Ph.D. Mathematics program 
3.0 

Math 295 
Special Project 

3.0 
COI 
Math 296 
Graduate Seminar 

1.0 
COI 
Math 297 
Special Topics 
topic to be specified for record purposes 
3.0 
COI 
Math 300 
Master’s Thesis 

6.0 

Math 400 
PhD Dissertation 

12.0 
