INSTITUTE OF MATHEMATICS
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 vector-valued 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 number-theory; 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 Rn; 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; non-Euclidean 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; moment-generating 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 single-life 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 non-linear 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; non-linear 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 n-dimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, complex-valued 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 non-euclidean 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 Hamilton-Cayley; 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, semi-simple 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, Whittaker-Shannon 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 risk-sharing. 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 non-linear equations, numerical integration, numerical linear algebra. 3.0 Math 171 or COI
Math 271.2 Numerical Analysis II Numerical methods for ordinary differential equations, finte-difference methods for partial difference equations, numerical methods for conservation laws, multi-grid 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 real-time 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 upper-bounded variables. 3.0 Math 114 and Math 180.2
Math 281 Nonlinear Programming Properties of convex sets and functions; unconstrained optimization; Kuhn-Tucker Thoerem. Lagrange multipliers; Saddle-point Theorems; algorithms. 3.0 COI
Math 282 Integer Programming and Combinatorial Optimization Applications of integer programming. Converging dual and primal cutting plane algorithms. Branch-bound 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