Program Learning Outcomes of Doctoral Programme in Mathematics
Programme Learning Outcomes(PLO) of the Doctoral Programme in Mathematics have been formulated as follows:
PLO1  :  Attitude
Devote to God Almighty, uphold the human values, internalize academic values and ethics, responsible for working in the area of expertise independently. 
PLO2  :  Knowledge:
Mastering philosophy of mathematics and one of the fields in mathematics (algebra, analysis, applied mathematics, statistics, computational mathematics, computational statistics). 
PLO3  :  Knowledge:
Able to think logically, analytically, inductively, deductively, and structured; having the ability to manage, lead, and develop research programs independently, and able to communicate the thoughts as well as his work to the scientific community and the general public 
PLO4  :  General Skill:
Creating new concepts and/or new methods (original) in the field of mathematics that is recognized nationally and internationally

PLO5  :  Distinctive Skill:
Able to apply mathematics according to their field of expertise to solve problems including those that require a multidisciplinary, crossdisciplinary, or transdisciplinary approach

PLO6  :  Attitude:
Having lifelong learning skills and adaptive to the development of science and technology, especially in fields related to Mathematics and its applications.

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Study Materials and Learning Experiences (LE) to achieve the PLO Doctoral Programme in Mathematics
The Curriculum 2017 of the Doctorate Programme in Mathematics UGM follows the Structured Curriculum pattern which is guided by the Academic Documents for the Implementation of the 2005 Postgraduate Program and the S3 Academic Policy which was approved by the Academic Senate of the Faculty of Mathematics and Natural Sciences UGM 2008. Of the minimum 46 credits required, a minimum of 12 credits is realized in the form of 3 credits of mandatory courses (Literature Review) and a minimum of 9 credits of elective courses. Treatment (treatment) related to the obligation to take elective courses for students is done depending on each student based on the background and topic of his dissertation design and is determined by a Selection Team specifically formed for each student candidate. The course that must be taken is a course that also reflects the prerequisites for achieving the learning achievements (PLO) outlined above.
Students have a residency obligation for 4 (four) semesters, which is served 2 semesters since being accepted at PS S3 Mathematics and 2 semesters after the student Qualification Examination (Comprehensive Examination). To be able to submit for a comprehensive examination, students must have passed all courses that must be taken with a GPA of ≥ 3.25.
Also, during the learning and research process, there was a monitoring and evaluation process. After students complete the preparation of their dissertation, students submit a feasibility assessment of the dissertation to PS S3 Mathematics. In submitting a dissertation feasibility assessment, students must meet the publication requirements required by the PS S3 Mathematics. After the dissertation is declared feasible by the assessment team, a closed final dissertation exam is held. Concerning the formulation of graduate profiles and to achieve the Learning Outcomes (PLO Learning Program) that have been formulated and take into account the recommendations and benchmarks in several universities, the study areas of PS S3 Mathematics are determined as follows:
Formulation of Study Material / Learning Outcome
For the achievement of PLO PS S3 Mathematics
No.  Study Material  Description 
1.  Take Mandatory Courses
Literature Review

Emphasis on:
· Originality, · Critical Evaluation, · Conjecture, · Theoretical Frame Work, · etc 
2.  Take the Elective Course according to the direction and interest of the research to underlie the research to be conducted  Selecting several courses from one or several existing interests (list of courses for each field of interest is presented in Appendix 1)
· Algebra · Analysis · Applied Mathematics · Statistics · Computational Statistics · Computational Mathematics 
3.  Conduct preliminary research with the guidance of the supervisor team and write a dissertation research proposal

· Initial dissertation research
· Writing a dissertation proposal · Qualification / Comprehensive Examination – Basic research theory – Research plan – Preliminary results of research – Continuation of research 
4.  Take a comprehensive examination  Is a forum to see the ability of students in
· Formulate research directions for his dissertation. · Formulate hypotheses and conjecture problems that are formulated. · Formulate the initial results of the completion of his dissertation. 
5.  Conduct further research of the dissertation with the guidance of the supervisor team and pay attention to input
· A comprehensive team of examiners · Monitoring and evaluation team 
· Further research dissertation
· Monitoring and evaluation – Arrange portfolio – Arranging draft paper as dissemination of research results 
6.  Conduct further dissertation research and disseminate the results of research by writing it in paper form to be sent to international journals or accredited national journals.  · Further research dissertation
· Disseminate research results – Through seminars / conferences / koloqium – Through publication in international journals or accredited national journals 
7.  Compose a Dissertation  · By the rules of writing
· With comprehensive and selfcontent · Measure the ability to communicate in writing comprehensively 
8.  Dissertation Eligibility Assessment  · For checking the originality, novelty, comprehensive, selfcontent of the dissertation proposal. 
9.  Dissertation Final Examination  Dissertation Final Examination To measure · Mastery of the material · The ability to argue · Ability to communicate verbally 
Curriculum Structure
Referring to the credits regulation of Doctoral Program issued by the government and universities, as well as agreements at the faculty level, the draft structure of the curriculum of Mathematics Doctoral Programme as follows:
 Compulsory course: Literature Review, 3 credits.
 Elective course: Dipilih sesuai minat yang ada dalam daftar Lampiran 1 sebanyak 912 sks.
 Dissertation: 34 credits whose assessment is divided into the following components:

Comprehensive examination (Qualification Exam)

Scientific Publications

Dissertation Manuscript

Research

Closed Examination (Defense)
The completion of the study is designed for a period of 3 years, with the design of the complete process of study and the indicator that is expected to be fulfilled is presented in the following table:
Standard Operational Procedure Doctoral Programme in Mathematics of UGM
TABLE NOT AVAILABLE
Prerequisite Course
In preparing the learning process of each course that must be taken, students are advised to learn Semester Learning Plan and Program (RPKPS) or handbook module of related subjects first, to better understand the outline of the content of the course and better prepare themselves. Information on RPKPS and module handbooks can be obtained in the Doctoral Program’s office. Meanwhile, the syllabus as a short description of the Course can be seen appendix in the download section.
Graduation requirements
The graduation requirements of the Mathematics Doctoral Programme follow the provisions set by the faculty.
Method of Learning and Assessment
Learning Method: Lectures, Discussions, Programmed Instruction, Study Assignment, Seminar, and Brainstorming.
Assessment Method: In the evaluation of learning outcomes in the Mathematical Doctoral Programme the following provisions apply:
Appropriate Rector Decree No 11 the Year 2016 (Article 52): Total credits that must be pursued by students is 46 – 50 credits with the number of credits courses 12 – 16 credits and credits dissertation 30 – 36 credits which then by FMNS set 34 credits.
The courses taken are related to the dissertation research topic. The number and type of courses for each student may differ based on:
 Topics of Research Design Dissertation to be done,
 The academic background of the students in the sense based on the courses that have been taken at the time of the prospective students to take the master and bachelor programs are reflected from his/her master and bachelor transcript.
 Paper (research results) if any.
Students must pass all courses required by study program with GPA ≥ 3.25 and minimum score B. Students must complete the dissertation weighting 34 credits consisting of the component mentioned earlier.
Students have residency duty for 4 (four) semesters, which is 2 semesters since accepted in Prodi S3 Mathematics and 2 semesters after Qualification Exam (Comprehensive Examination). To be able to submit a comprehensive examination, the student must have passed all courses that must be taken with a GPA of 3.25 and a minimum score of B.
Implementation of a comprehensive examination, conducted no later than 4 semesters since the students received in the Mathematical Doctoral Program. Counseling is done regularly with guidance time arranged based on an agreement of the team supervisor and student. Every semester, every mentor reports to the Mathematical Doctoral Program. Also, during the process of learning and research held the process of monitoring and evaluation. Monitoring and evaluation of doctoral student progress twice per semester
In conducting his/her research, a student is guided by a team of supervisors, amounting to at least 2 people, consisting of 1 Promoter and 1 or 2 copromotor. After the student completes his dissertation, the student submits a dissertation eligibility assessment to the Mathematics Doctoral Programme and the Doctoral Program Manager then appoints a Dissertation Feasibility Assessment Team consisting of 3 persons determined based on the promoter team’s proposal. In submitting a feasibility assessment for the dissertation, the student must meet the publication requirements required by the Mathematics Doctoral Programme. After the dissertation is declared feasible by the assessment team, the final examination is held closed with the number of examiners 79 people.
The Curriculum Documents
Moreover, the curriculum documents Mathematics Study Program can be downloaded at the following link.