Mathematics Education

Doctor of Philosophy in MAthematics Education
DOCTOR OF PHILOSOPHY IN MATHEMATICS EDUCATION

Approved: BOR No. 2007-19

Course Code

Descriptive Title

Pre-requisites/ Co-requisites

Lec

Lab

Units

CORE/FOUNDATION SUBJECTS (15 units)
Philo 301 Advanced Socio-Anthropological 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/career-related 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 301-Advanced Socio-Anthropological 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, data-gathering 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, Reimann-Stieltjes 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, well-ordered sets and ordinal numbers, axiom of choice, zorn’s lemma. well-ordering 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 Cauchy-Riemann 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, non-homogeneous 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 non-linear 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.

 

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