Mathematics Education
DOCTOR OF PHILOSOPHY IN MATHEMATICS EDUCATION
Approved: BOR No. 200719
Course Code 
Descriptive Title 
Prerequisites/ Corequisites 
Lec 
Lab 
Units 
CORE/FOUNDATION SUBJECTS (15 units)  
Philo 301  Advanced SocioAnthropological Foundation of Education 
None 
3 
3 

Philo 302  Advanced Ethics & Philosophy of Education 
None 
3 
3 

Philo 307  Psychological & Pedagogical Theories of Learning & Teaching 
None 
3 
3 

SSR 391  Research Methods 
None 
3 
3 

SSR 393  Advanced Statistics 
None 
3 
3 

MAJOR SUBJECTS (30 units)  
PDME 311  Number Theory 
None 
3 
3 

PDME 312  Advanced Calculus I 
None 
3 
3 

PDME 313  Advanced Calculus II 
PDME 312 
3 
3 

PDME 314  Set Theory & Math Logic 
None 
3 
3 

PDME 315  Modern Geometry 
None 
3 
3 

PDME 316  Advanced Linear Algebra 
None 
3 
3 

PDME 317  Linear Programming 
None 
3 
3 

PDME 318  Abstract Algebra 
None 
3 
3 

PDME 319  Real Analysis 
None 
3 
3 

PDME 320  Complex Analysis 
PDME 313 
3 
3 

ELECTIVE /COGNATE SUBJECTS (15 units)  
PDME 321  Combinatorics and Graph Theory 
None 
3 
3 

PDME 322  Differential Equations 
PDME 313 
3 
3 

PDME 323  Numerical Analysis 
None 
3 
3 

PDME 324  Vector Analysis 
None 
3 
3 

PDME 325  Theory of Probability 
None 
3 
3 

PDME 326  Mathematical Statistics 
None 
3 
3 

PDME 327  Special Problems in Mathematics 
None 
3 
3 

Institutional Requirements (4 units)  
Ted Mgt 327*  Advanced Information Technology & Management System 
None 
3 
3 

GS 399*  Dissertation Graduate Seminar 
All Academic Subjects 
1 
1 

Minor Subjects (Optional) (9 units) 
For those who do not want to follow the straight curriculum and opt to minor in allied/careerrelated program, they should enroll 15 units from the major subjects of the PhD ScieEd or PhD EdAd program subject to the approval of the college (Graduate Program Committee).
DW 300Dissertation Writing
GS 399
12
12
Total Number of Units
72
Summary 
PROGRAM
(CHED MEMO No. 53, s. 2007)


DMMMSU 

Core/Foundation Subjects 
18 units 
15 units 

Major Subjects 
21 – 24 units 
30 units 

Electives/Cognates/ 
Minor Subjects
6 – 9 units
15 units
*Institutional Requirements
(4 units)
Thesis Writing
12 units
12 units
Total
60 units
72 units
*Institutional requirement for graduation (not included in the total no. of units
and in the GPA computation)
COURSE DESCRIPTION
Core/Foundation Subjects – 12 UNITS
Philo 301Advanced SocioAnthropological Foundation of Education. The course is a thorough study of sociological and anthropological factors underlying the educative process. Emphasis of the course is on the analysis and synthesis of these factors as they influence educational operations.
Philo 302 – Advanced Ethics & Philosophy of Education. This course involves understanding of the philosophical science and the morality of human acts. It involves the study of natural laws, human nature, duty and justice, and involves the quest for what truth, freedom, and love. It searches for the meaning of a human being as well as community and man’s relationship with his creator as evidenced by his moral acts.
Philo 307 – Psychological and Pedagogical Theories of Learning and Teaching. This course involves understanding of philosophical, psychological, and pedagogical theories as they operate in the educational context. It focuses on critical analysis, synthesis, and application of these theories in addressing pedagogical issues, problems, and concerns.
SSR 391 – Research Methods. This course covers different types of research methods, datagathering instruments, research designs, employing statistical and qualitative procedures to analyze data, as well as interpret and evaluate research reports.
SSR 393 – Advanced Statistics. This subject focuses on advanced statistical methods and the application of these techniques to practical research. It includes the use of statistical package in order to catch up with the advances in software technology and facilitate the conduct of research.
Major Subjects – 30 units
PDME 311 – Number Theory. This course deals with the fundamental concepts of number theory including prime numbers congruences, quadratic reciprocity, sums of squares, Diophantine equations, cryptography, and continued fractions.
PDME 312 – Advanced Calculus I. This course deals with the real number system, point set topology, limits and continuity, derivatives, multivariable differential calculus, implicit functions, and extremum problems.
PDME 313 – Advanced Calculus II. This course deals with series of real numbers, sequences and series of functions, uniform convergence, power series, functions of bounded variation and rectifiable curves, ReimannStieltjes integrals, multiple integration, improper integrals, and transformations.
PDME 314 – Set Theory & Math Logic. This course contains topics on sets and subsets & basic set operations, cardinal numbers, partially and totally ordered sets, wellordered sets and ordinal numbers, axiom of choice, zorn’s lemma. wellordering theorem, algebra of propositions, quantifiers and logical reasoning.
PDME 315 – Modern Geometry. This course deals with projective plane, projectivities, analytic projective geometry, cross ratio and harmonic sequences, geometric transformations and isometries.
PDME 316 – Advanced Linear Algebra. This course is an abstract treatment of Linear Algebra which deals with basic Algebraic tools such as vector spaces and Linear transformations, bases and coordinates, eigenvalues and eigenvectors and their applications.
PDME 317 – Linear Programming. Linear programming is the fundamental branch of optimization with application to several areas such as chemistry, computer science, defense, finance, telecommunications, transportation, etc. This course provides an integrated view of optimization theory, solution techniques, and application of linear optimization.
PDME 318 – Abstract Algebra. Abstract algebra is the study of operations, their properties, and the structures that support them. Hence, this course includes topics such as groups, group actions, vector spaces, and the theory of fields.
PDME 319 – Real Analysis. This course deals with the properties and real numbers, measurable functions, measurable sets, convergence theorems, integrals of simple and nonnegative functions, Lebesgue integral, and Lp spaces.
PDME 320 – Complex Analysis. This course deals with the study of complex numbers’ Analytic functions; elementary functions, its graphical representation, fundamental operations on complex numbers; complex differentiation and integration; residue poles; conformal mapping and CauchyRiemann Equations.
Cognate/Elective Subjects – 15 units
PDME 321 – Combinatorics and Graph Theory. This course deals with Algebraic methods, additive number theory, coloring problems for graphs and hypergraphs, combinatorics of symmetric functions, and problems in combinatorial geometry.
PDME 322 – Differential Equations. This course deals with the different techniques of solving different types of differential equations and the theory necessary to support these techniques and their applications in the physical sciences, geometry and other related field. Topics include first order ordinary differential equations including Bernoulli’s equations, substitution suggested by the equations, and Coefficients linear in two variables; linear differential equations, linear equations with constant coefficients, nonhomogeneous equations, undetermined coefficients and variation of parameters, linear systems of equations; the existence and uniqueness of solutions.
PDME 323 – Numerical Analysis. This course deals with error analysis, solutions of linear system and nonlinear equations, numerical interpolation, numerical integration and differentiation, numerical solution of ordinary differential equations.
PDME 324 – Vector Analysis. This course deals with the operations of vectors in three dimensional space (dot, cross and triple products), it also includes a concise and precise means of mathematical analysis of physical and geometric phenomena, vector differentiation and its applications, differential geometry, gradient, divergence and curl, integration of vectors and their applications, and integral theorems.
PDME 325 – Theory of Probability. This course deals with axiomatic probability space, conditional probability and independence, finite stochastic processes, Bayesian probability discrete and continuous random variables, special distributions, mathematical expectation, multivariate distributions, Law of Large numbers, the Central Limit Theorem, and Marcov Chains.
PDME 326 – Mathematical Statistics. This course deals with decision theory, estimation, confidence intervals, and hypothesis testing. Other topics include asymptotic efficiency of estimates, exponential families and sequential analysis.
PDME 327 – Special Problems in Mathematics. This course explores topics of current interest to students information, a point of view that stresses computation, investigation, making conjunctures, and visualization. The topics include standard topics such as calculus, linear algebra, and differential equations as they form part of the core of mathematics.
Ted Mgt. 327 – Advanced Information Technology and Management System. The course is an application of information technology in organizations specifically the roles and responsibilities of educational manpower and staff professionals in the planning and development of management information systems (MIS).
GS 399 – Graduate Seminar. This is a preparatory course in the conceptualization, development, and writing of dissertation following standards in research in terms of design, format, language, and style. It includes oral presentation and discussion of current researches in the discipline.