Policies and Standards for the Doctor of Philosophy in Mathematics (Ph.D. Mathematics) Program

May 12, 2011

CHED MEMORANDUM ORDER NO. 011-11

 

In accordance with the pertinent provisions of Republic Act (RA) No. 7722, otherwise known as the "Higher Education Act of 1994", by virtue of Commission en banc Resolution No. 060-2011 dated 05 April 2011, and for the purpose of rationalizing the graduate mathematics education in the country with the end view of keeping apace with the demands of global competitiveness, the following Policies and Standards are hereby adopted and promulgated by the Commission.

ARTICLE I

Introduction

Graduate level study is the advanced preparation and mastery of a specialized field or discipline. It occurs within an atmosphere of intellectual and creative rigor that encourages scholarly inquiry, research and study of the evolving formulation of knowledge. Graduate education results in the candidate's ability to shape the direction of one's discipline, to become a leader in one's respective profession, and to contribute to the rapidly changing global community.

ARTICLE II

Authority to Operate

All private higher education institutions (HEIs) intending to offer degrees stated above must secure proper authority from the Commission in accordance with existing rules and regulations. State Universities and Colleges (SUCs), and Local Universities and Colleges (LUCs) should likewise strictly adhere to the provisions stated in these policies and standards. EATcHD

ARTICLE III

Program Specifications

SECTION 1. Degree Name. —

The degree program herein shall be called Doctor of Philosophy in Mathematics.

SECTION 2. Program Description. —

The Ph.D. Mathematics program is a research-oriented program that prepares students for careers in academe, industry and government that depend on advanced mathematics. Through a combination of advanced course work and research, the program aims to produce graduates with the knowledge, skills, perspective and understanding to be capable of self-directed and independent scientific work.

The program is planned to develop in the student a fundamental understanding of certain basic fields of mathematics, a deep understanding of a major field of interest, and the ability to undertake advanced mathematical research, as evidenced by the completion and defense of a doctoral dissertation, the major requirement of the Ph.D.

2.1. Objectives of the Program

The main objective of the Ph.D. Mathematics program is to develop mathematics in the Philippines by producing highly trained mathematicians whose research work contribute towards pushing the frontiers of mathematical knowledge. Corollary to this main objective is the upgrading of tertiary and graduate mathematics instruction and scientific research and development in academe, industry and government.

ARTICLE IV

Competency Standards

SECTION 3. Competency Standards. —

A graduate of the Ph.D. Mathematics program is expected to:

1. acquire the requisite knowledge and skills in mathematics and move beyond the relatively passive role of receiving knowledge to become active and self-motivated scholar; AETcSa

2. develop a commitment to the professional standards and practices of mathematics;

3. attain a level of training and knowledge suitable for advanced and independent research;

4. possess the competence to sit as member of a panel in a thesis/dissertation defense;

5. have the ability to referee or review a research article in his or her field of specialization for possible publication in a journal;

6. demonstrate a commitment to the continued improvement of teaching that utilizes research-based practices;

7. participate in course and curriculum development and provide public or professional service; and

8. have the maturity and desire to conduct research and direct or advise graduate students.

ARTICLE V

Curriculum

SECTION 4. Curriculum Description. —

Two aspects of mathematics and its modern development are reflected in the design of the Ph.D. programs herein: its internal structure marked by a foundation in the core areas of algebra, analysis and geometry as well as deep interconnections between mathematics' various branches; and its interdisciplinary nature, traditionally with physics and engineering, but now extending to other fields. The required courses provide substantial background in the traditional foundational areas of mathematics. Mastery of a mathematical specialty is enhanced by a good choice of specialization and elective courses.

The major external influence on mathematics is the computer and everything related to this domain will be of central importance to mathematics in the coming century. A good graduate program must reflect these developments in scientific computing and information technology by providing opportunities for students to venture into cutting-edge areas requiring advanced mathematics such as Mathematical Finance, Mathematical Biology, and Mathematical Modeling for the Life and Physical Sciences. HEIs are therefore encouraged to develop competent faculty and researchers in these niche areas. AcSIDE

Two (2) Ph.D. programs are described in this document: the regular Ph.D. program and the straight Ph.D. program.

The regular Ph.D. program is a three (3)-year program designed for an entering student who has already earned an accredited M.S. Mathematics degree (and has taken all the required courses as specified in the Policies and Standards for the M.S. Mathematics degree). The curriculum for the regular Ph.D. Mathematics program should contain a total of at least 39 units, broken down into 9 units of Required Courses, 18 units of Electives and 12 units of Dissertation.

The straight Ph.D. program is a four (4)-year program designed for talented and highly motivated graduates of accredited B.S. Mathematics programs. The curriculum for the straight Ph.D. Mathematics program should contain a total of at least 57 units, broken down into 24 units of Required Courses, 21 units of Electives and 12 units of Dissertation.

Since the mathematics departments of different schools will have their particular strengths and orientation, the elective courses will allow for flexibility and accommodate the special interests of the various departments.

HEIs may offer Ph.D. Mathematics courses beyond those specified in the recommended programs, according to their faculty and institutional resources, and thrusts.

SECTION 5. Curriculum Outline. —

The minimum requirements for Ph.D. Mathematics, regular and straight programs, are outlined in Table 1 and Table 2.

Table 1. Components of the Regular Ph.D. Mathematics Curriculum and their Corresponding Units.

Component	Units
Required Courses	9
Electives	18
Comprehensive Examination	-
Dissertation	12
	––––
Total	39
	====

Table 2. Components of the Straight Ph.D. Mathematics Curriculum and their Corresponding Units. IcTEaC

Component	Units
Required Courses	24
Electives	21
Qualifying Examination 1	-
Comprehensive Examination	-
Dissertation	12
	––––
Total	57
	====

1 Optional. May be instituted by the unit/department to determine if student should proceed with the straight Ph.D. program, usually taken after the 1st year of enrolment.

SECTION 6. Required Courses. —

The required courses for the regular and straight Ph.D. Mathematics programs are outlined in Table 3 and Table 4.

Table 3. List of Required Courses for the Regular Ph.D. Mathematics Program

Descriptive Title	Units
Abstract Algebra II	3
Real Analysis II	3
Topology or Geometry Course	3
(whichever course has not been
taken in the M.S. Mathematics
program of the student)
	––––
Total	9
	===

Table 4. List of Required Courses for the Straight Ph.D. Mathematics Program CScaDH

Descriptive Title	Units
Abstract Algebra I	3
Abstract Algebra II	3
Complex Analysis	3
Linear Algebra	3
Real Analysis I	3
Real Analysis II	3
Topology	3
Geometry	3
	––––
Total	24
	===

SECTION 7. Sample Electives. —

Table 5. Sample Electives for the Ph.D. Mathematics program

Descriptive Title	Units
Algebraic Geometry	3
Algebraic Number Theory	3
Algebraic Topology	3
Approximation Theory	3
Coding Theory	3
Combinatorial Mathematics	3
Design Theory	3
Differential Geometry	3
Functional Analysis	3
Geometric Crystallography	3
Graph Theory	3
Group Theory	3
Hyperbolic Geometry	3
Lie Algebra	3
Mathematics in Population Biology	3
Mathematics in Finance	3
Multivariate Analysis	3
Numerical Analysis I	3
Numerical Analysis II	3
Numerical Optimization	3
Probability Theory	3
Projective Geometry	3
Stochastic Calculus	3
Theory of Ordinary Differential Equations	3
Theory of Partial Differential Equations	3

SECTION 8. Graduate Seminar. — ICASEH

In addition to the prescribed curriculum, a department may include a graduate seminar requirement, with or without credit. Two types of graduate seminars are envisioned. One type aims to improve the research and communication skills of a student by (i) training the student to carry out extensive literature search, (ii) exposing the student to various areas of Mathematics by special lecturers from faculty members, and (iii) training them in the oral delivery of a technical paper. A second type of seminar may simply be a requirement for a student who is near the completion of the dissertation research to conduct a seminar talk or lecture on his/her results before the faculty and peers. The recommended credits, if any, are 1 to 3 units.

SECTION 9. Dissertation. —

The Dissertation is a written research output that:

1. embodies an original, independent and significant research in mathematics;

2. shows the student's capacity to make critical evaluation on previous work done in his/her chosen research topic; and

3. demonstrate his/her ability to present scientific research findings in a clear, systematic and scholarly manner.

The procedure to be followed in complying with this requirement shall be specified by the Graduate Committee (GC) consistent with relevant operating procedures of the HEI and in accordance with pertinent CHED memoranda. The oral defense of the dissertation may take place only after the student has passed the Comprehensive Exam.

SECTION 10. Comprehensive Examination. —

The Comprehensive Examination is a written examination that the student has to take after completing all the core or foundational courses, normally taken after or near the end of all course work. It is intended to determine whether the student has sufficient broad mathematical knowledge. It shall cover three (3) areas, two of which must be the areas of algebra and analysis. The third one may be chosen by the student in consultation with the adviser and Graduate Committee from other fields covered by the courses s/he has taken. AcEIHC

The GC shall administer the examination and shall set the requirements for passing and retakes.

A student who passes the Comprehensive Examination is advanced to candidacy for the Ph.D. in Mathematics degree.

A student in the straight Ph.D. program who has passed the Comprehensive Examination may be awarded the degree of Master of Science in Mathematics if the student applies for the M.S. Mathematics degree and has satisfied all other requirements set by the department and the HEI.

SECTION 11. Recommended Program of Study. —

Tables 6 and 7 below provide the recommended programs of study of the regular and straight Ph.D. Mathematics programs. HEIs may adhere to these, or when necessary, modify the sequencing of courses.

11.1  Regular Ph.D. Mathematics

A recommended program of study is outlined in Table 6 below.

Table 6. Recommended Sequence of Courses in the Regular Ph.D. Mathematics Program

1st Year/1st Semester	Units	1st Year/2nd Semester	Units
Abstract Algebra II	3	Elective I	3
Real Analysis II	3	Elective II	3
Topology or Geometry	3	Elective III	3
	––––		––––
Total	9	Total	9
	===		===
2nd Year/1st Semester		2nd Year/2nd Semester
Elective IV	3	Comprehensive Examination
Elective V	3	Dissertation	6
Elective VI	3
	––––		––––
Total	9	Total	6
	===		===
3rd Year/1st Semester		3rd Year/2nd Semester
Dissertation	3	Dissertation	3
		Defense
	––––		––––
Total	3	Total	3
	––––		––––
		Total	39
			===

11.2  Straight Ph.D. Program HIAESC

A recommended program of study is outlined in Table 7 below.

Table 7. Recommended sequence of courses in the Straight Ph.D. Mathematics Program

1st Year/1st Semester	Units	1st Year/2nd Semester	Units
Abstract Algebra I	3	Abstract Algebra II	3
Complex Analysis	3	Real Analysis I	3
Linear Algebra	3	Topology	3
		Geometry	3
	––––		––––
Total	9	Total	12
	===		===
2nd Year/1st Semester		2nd Year/2nd Semester
Real Analysis II	3	Elective III	3
Elective I	3	Elective IV	3
Elective II	3	Elective V	3
	––––		––––
Total	9	Total	9
	===		===

2nd Year/Summer

Comprehensive Examination

3rd Year/1st Semester		3rd Year/2nd Semester
Elective VI	3	Dissertation	3
Elective VII	3
Dissertation	3
	––––		––––
Total	9	Total	3
	===		===
4th Year/1st Semester		4th Year/2nd Semester
Dissertation	3	Dissertation	3
	––––		––––
Total	3	Total	3
	===		===
4th Year/Summer
Defense
			––––
		Total	57
			====

ARTICLE VI

Learning Resources and Support

Program Administration

SECTION 12. Qualifications of the Head of the Unit. —

The minimum qualifications of the head of the unit that implements the degree program are the following:

12.1  Dean of the Unit/College

The dean of a unit/college must be at least a master's degree holder in any of the disciplines for which the unit/college offers a program; and a holder of a valid certificate of registration and professional license, where applicable.

12.2  Head of the Mathematics Unit/Department

The head of the unit/department must be at least a master's degree holder in the discipline for which the unit/department offers a program or in an allied field (cf. Section 5 of CMO 19, s. 2007).

SECTION 13. Administration of the Doctorate Programs in Mathematics. —

The Department of Mathematics shall appoint a GC that will be responsible for administering the graduate programs in mathematics. The responsibilities of the GC include the following: cCHITA

1. set and implement policies on faculty, course offerings and research standards of the programs in accordance with pertinent CHED memoranda and policies of the HEI;

2. review and monitor the progress of students in the programs; and

3. attend to all development needs of the programs.

SECTION 14. Institutional Responsibility. —

Through the GC, the institution shall see to it that the student completes the program of study on time and that the program maintains the expected academic standard.

SECTION 15. Dissertation Advising. —

The Dissertation Adviser should be a holder of Ph.D. degree in Mathematics or related fields with a proven track record in research and publication.

Dissertation advising is a crucial component of the Ph.D. program. Therefore, advising should be given a corresponding faculty load equivalent or a commensurate honorarium. The number of credit units or honorarium is left to each institution to determine.

SECTION 16. Faculty. —

16.1.  Qualification of faculty

HEIs that offer a Ph.D. program in mathematics must have competent full-time faculty whose qualifications include not only Ph.D. degree holder in mathematics and/or related fields but also a good track record in research.

To offer a Ph.D. Mathematics program, the unit/department must satisfy the following minimum qualifications.

1. The HEI must have at least five (5) faculty members with an earned Ph.D. Mathematics degree, or its equivalent; at least three (3) of these faculty members must have full-time status with the unit/department offering the program; HTCSDE

2. The faculty must be actively engaged in research and has published in reputable scientific journals;

3. The faculty is encouraged to be active members of recognized professional organizations in mathematics; and

4. The faculty is encouraged to be involved in extension activities related to the discipline.

The HEI must provide for the continued growth of the faculty through aid for continuous training, further studies, and travel grants to attend and/or present papers in congresses, symposia and conferences.

SECTION 17. Library. —

HEIs offering the Ph.D. Mathematics program must meet the minimum requirements for the BS Mathematics program. In addition, the library must maintain a collection of the latest editions of textbooks and references used for the core and elective courses in the curriculum, and constantly update and expand their collections. There must also be active subscriptions to mathematics journals either in print or online. Internet access is required for the doctoral programs in mathematics.

SECTION 18. Laboratory and Facilities. —

The minimum laboratory requirements for the BS Mathematics program must be met. Class size may vary depending on the allowable number of students as may be feasible to economically offer a graduate class.

The HEI should provide the necessary infrastructure for research in mathematics, such as computer facilities, relevant and up-to-date mathematical and computing software.

The institution should also provide facilities to allow preparation, presentation and viewing of audio-visual materials to support instruction.

Admission and Retention Requirements

SECTION 19. Admission and Retention. —

Admission in the Ph.D. programs in mathematics shall require the following:

1. A master's degree in mathematics (respectively, a bachelor's degree in mathematics) or its equivalent from a recognized institution of higher learning, for those applying for the regular (respectively, straight) Ph.D. program; CETDHA

2. A very high degree of intellectual capacity and aptitude for advanced study and research in mathematics;

3. Satisfaction of other special admission requirements that may be imposed by the GC based on an evaluation of the academic preparation of the applicant; and

4. Satisfaction of other usual admission requirements prescribed by the HEI.

SECTION 20. Grade Requirement. —

The HEI, through the GC, shall set the standards for the grade requirement for the student to stay in the Ph.D. Mathematics program.

SECTION 21. Rules on Residency. —

The Graduate Committee, in accordance with the general rules of the HEI regarding this matter, shall set residency rules.

ARTICLE VII

Transitory, Repealing and Effectivity Provisions

SECTION 22. Transitory Provision. —

HEIs that have been granted permit or recognition for Ph.D. Mathematics is required to fully comply with all the requirements in this CMO, within a non-extendable period of five (5) years after the date of its effectivity. State Universities and Colleges (SUCs) and Local Colleges and Universities (LCUs) shall also comply with the requirements herein set forth.

SECTION 23. Repealing Clause. —

All CHED issuances, rules and regulations or parts thereof, which are inconsistent with the provisions of this CMO are hereby repealed.

SECTION 24. Effectivity Clause. —

This CMO shall take effect fifteen (15) days after its publication in the Official Gazette, or in two (2) newspapers of national circulation. This CMO shall be implemented beginning Academic Year 2012-2013. TSDHCc

Quezon City, Philippines, May 12, 2011.

For the Commission,

(SGD.) PATRICIA B. LICUANAN, Ph.D.ChairpersonCommission on Higher Education

Attachments available upon request.