The Doctor of Philosophy in Mathematics Program (PhD Math) is a doctoral level graduate program that enables students to acquire advanced knowledge in pure and applied mathematics. It enhances the students’ research skills to help them produce quality research outputs and become prolific mathematicians, and future leaders in the academic, industry and professional organizations.


The Doctor of Philosophy in Mathematics Program is a doctoral level graduate program that enables students to: acquire advanced knowledge in pure and applied mathematics; enhance their research skills to help them produce quality research output; and become more prolific mathematicians, and future leaders in academe, industry, and professional organizations. The program will allow UP Baguio to contribute to the urgent need to train and develop more PhD Mathematics graduates who will go on to teach and engage in Mathematics and Math-related research. At the end of the program, graduates of PhD Mathematics are expected to become competent educators and professionals who can conduct advanced and high quality research, who are able to review researches in their areas of specialization, and who will help improve the quality of programs in their institutions. This will contribute to the upgrading of tertiary and graduate mathematics instruction and research in the Philippines.


A three-year program designed for students who have earned their Master of Science in Mathematics degree (or in an allied field).

Required Courses9 units
Elective Courses18 units
Graduate Seminar1 unit
Qualifying Examination-
Candidacy Examination-
Dissertation12 units
Total Units40 units


Math 223Abstract Algebra II3 units
Math 237Functional Analysis3 units
Math 240Topological Structures3 units


A four-year program designed for students who have earned their Bachelor of Science in Mathematics degree (or in allied field) who meet certain qualifications (consult the Graduate Program Office).

Required Courses21 units
Elective Courses24 units
Graduate Seminar1 unit
Qualifying Examination-
Candidacy Examination-
Dissertation12 units
Total Units58 units


CourseCourse TitlePrereq.
Math 221Abstract Algebra 3 units
Math 222Linear Algebra3 units
Math 223Abstract Algebra II3 units
Math 232Real Analysis3 units
Math 234Abstract Algebra II3 units
Math 237Functional Analysis3 units
Math 240Topological Structures3 units


CourseCourse TitlePrereq.Units
Math 213Theory of Differential EquationsCOI3.0
Math 214Dynamical SystemsCOI3.0
Math 215Introduction to Mathematical ModelingCOI3.0
Math 216Applied Partial Differential EquationsCOI3.0
Math 217Integral EquationsCOI3.0
Math 218Introduction to Applied MathematicsCOI3.0
Math 219Delay Differential EquationsDE Course3.0
Math 224Matrix AnalysisMath 222/Equivalent3.0
Math 225Number Theory with ApplicationsCOI3.0
Math 235Applied Complex Variable TheoryMath 2343.0
Math 236Numerical AnalysisCOI3.0
Math 238Semigroup Theory and ApplicationsMath 237/COI3.0
Math 239Numerical Partial Differential EquationsMath 237/COI3.0
Math 241Algebraic TopologyCOI3.0
Math 245Computational Topology with ApplicationsMath 241/COI3.0
Math 250Modern GeometryNone3.0
Math 251Differential GeometryMath 240/COI3.0
Math 255Applied CombinatronicsNone3.0
Math 256Graph TheoryCOI3.0
Math 260Probability and ApplicationsNone3.0
Math 280Linear and Nonlinear OptimizationCOI3.0
Math 296Selected Topics in Applied AnalysisNone3.0
Math 298Special Topics (May be taken twice)COI3.0

Qualifying Examination

A student is eligible to take the qualifying examination upon completion of the required courses and at least six units of electives, and with an average of 1.75 or better. The qualifying exam will be in three areas: (1) Algebra (Topics will come from Abstract Algebra I, II and Linear Algebra); (2) Analysis (Topics will come from Real Analysis, Complex Analysis and Functional Analysis), and (3) an area that the student may choose in consultation with the supervisor and/or the Graduate Committee. The third area may be chosen from any other fields covered by the electives taken by the student.

Candidacy Examination

A Candidacy Examination will be taken by the student after completing the required courses, the required number of units for elective courses, and passing the Qualifying Examination. The Candidacy Examination will consist of two parts: (1) presentation of any scholarly and novel research output preferably related to the thesis topic of the student and (2) thesis proposal.


The dissertation is a written research output that the student will write under the supervision of his/her adviser. The contents of the dissertation will be the outcome of the original and independent work done by the student, not previously submitted in any form for a degree in any other institution or university. The oral defense of the dissertation may take place only when the student has passed the Qualifying and Candidacy Examinations.




Regular Ph.D. Mathematics Program

Master’s degree in Mathematics (respectively a bachelor’s degree in Mathematics) is required, or any graduate degree in an allied field, e.g. Engineering, Physics, Statistics and Computer Science (respectively, a bachelor’s degree in the said allied fields) subject to evaluation.

Straight Ph.D. Mathematics Program

  1. Graduated with honors; or
  2. Belongs to the top 10% of the BS Math graduating class; or
  3. Earned a weighed average of at least 2.0 (or equivalent) in all higher math courses; or
  4. Published in a WOS/Scopus-indexed journal. The applicant must be the sole/lead author of the publication.
The applicant must obtain a favorable endorsement of the mathematics graduate faculty after undergoing interview.

Documents to be Submitted for Admission:

  • Application Form for admission to a graduate program (UPB-GP Form No. 1, available at
  • Transcript of Records undergraduate and graduate work, original and two (2) photocopies. (Validity of OTR will be determined from the remarks indicated thereof.)
  • Three Reference - Report Forms from the applicant’s immediate supervisor (1) and former professors (2)
  • A brief purpose for applying to the PhD Mathematics program
  • Recent 2” x 2” Photo (4 copies)
  • For working students: an official permit from his/her employer/supervisor indicating the maximum number of units the students is allowed to enroll.
  • For married women: 2 Photocopies of Marriage Certificate
  • For foreign students (non-English): passing the Test of English as a Foreign Language (TOEFL). A TOEFL score of 500 is required of an applicant whose medium of instruction in school/s attended is not English.
  • Birth Certificate (2 photocopies)



  1. A Ph.D. Math student must have an average of 2.00 or better in all graduate courses for one academic year (including Midyear term) in the program. A student who cannot meet this shall be disqualified from the program.
  2. If, after three/four academic years, the student fails to pass the required courses, the student will be automatically disqualified from the regular/straight Ph.D. Math program.
  3. A student will be given 2 chances to pass the Qualifying Examination. Failure on the 2nd try will disqualify the student from the program. The second take shall be made no later than 1 academic year.
  4. The university rules pertaining to Maximum Residency Rule for graduate programs shall be applied.


Subject to the recommendation of the Graduate Committee of the department, graduate courses taken by the student in another university may be credited for his/her doctoral program provided that:
  1. The courses should have been taken within five years prior to admission;.
  2. The Unit or Graduate Office validates the courses through appropriate means; the total number of credits transferred shall not exceed nine (9) graduate units.


To qualify for graduation, a student must satisfy the following requirements:
  1. Complete a minimum of 40/58 units of formal graduate courses for the regular and straight Ph.D. program, respectively. These courses should be taken while the student is enrolled in the Ph.D. program of UP Baguio.
  2. Pass the Qualifying and Candidacy Examinations.
  3. Must have a general weighted average of 1.75 or better.
  4. Successfully defend a dissertation.
  5. Submit at least three (3) bound and certified copies of the approved dissertation and an electronic copy of the dissertation.
  6. Must have a publication (or at least a proof of acceptance of publication) in a refereed journal.