Doctor of Philosophy in Applied Mathematics

Philosophy of the Programme

The philosophy of this programme is to enhance the students’ capacity to apply mathematical and computational competencies in solving industrial and other real-life problems.

Rationale of the Programme

a) Needs assessment/Situation analysis

The Doctor of Philosophy in Applied Mathematics curriculum development was informed by the outcome of a needs assessment conducted to establish whether there was a need to develop and mount the programme at the University of Embu.  From the needs assessment, majority of the respondents supported the establishment of a Doctor of Philosophy in Applied Mathematics at the University of Embu. The needs assessment showed that there was need to have personnel who are able to apply knowledge and higher order skills in the various areas of applied mathematics to provide mathematical solutions to local and global problems. That the graduates of the programme would be able to communicate results of original and multidisciplinary research that seek innovative and effective quantitative solutions to relevant complex problems. And that they would be able to lead in mentorship and development of future experts in the mathematical sciences as well as providing scholarly and technical quantitative expertise in addressing national and global challenges.

b) Stakeholders Involvement

This programme was developed in consultation with a team from academia, students, and industry experts. The views expressed by these stakeholders were that the curriculum should focus on intensive research aligned to the current issues in applied mathematics. The stakeholders indicated that topics in advanced modelling and computing skills should be provided. This programme has responded to these concerns and it has included them in various course units. Detailed minutes of the stakeholders’ consultative meeting is provided in Appendix IV.

c) Justification of the need of the Programme

The Doctor of Philosophy in Applied Mathematics programme responds to the need to prepare professionals with mathematical background to enable them take up leadership roles in industries, computational-based organizations, academia and research organizations. Additionally, the proposed programme seeks to equip learners with the competencies necessary to implement analytical solutions in organizations. Based on the findings of the needs assessment analysis and stakeholders’ forum, the Doctor of Philosophy in Applied Mathematics programme was developed to provide an opportunity for graduates with a mathematical background to enhance their mathematical and computational skills. The needs assessment results showed that there is an increasing demand for mathematical-based solutions in organizations. With the growth of institutions of higher learning and successful implementation of devolution in Kenya, advanced competencies in Applied Mathematics are becoming increasingly necessary to foster economic development, attainment of Vision 2030, Sustainable Development Goals (SDGs), and the Africa 2063 Agenda. This course is also meant to serve national and regional development needs for staff development given the huge shortage of highly qualified experts in Applied Mathematics.

Goal of the Programme

The goal of this programme is to equip the students with mathematical and computational competencies that are required to solve industrial and other real-life problems and to enable them to become adept in independently conducting original research in the field of Applied Mathematics.

Expected Programme Learning Outcomes     

By the end of this programme, the student should be able to:

1. Apply higher orders skills in the various areas of Applied Mathematics to provide mathematical solutions to local and global problems.
2. Apply acquired knowledge and skills to develop and test new theories/solutions.

• Evaluate results of original and multidisciplinary research that address relevant complex problems in Applied Mathematics.

1. Develop future experts in Applied Mathematics to address national and global challenges.

Mode of Delivery of the Programme

The program will be delivered in a blended mode that utilizes both face-to-face interactions and online learning components. This shall include course work, workshops, seminar presentations, and thesis, which will primarily be based on student-led research.

Academic Regulations for the Programme

a) Admission Requirements

In addition to fulfilling the common university regulations for Doctor of Philosophy programmes, an applicant for the degree of Doctor of Philosophy in Applied Mathematics shall be a holder of a Masters Degree in Applied Mathematics or its equivalent from the University of Embu or any other University recognized by the Senate.

b) Regulations on credit transfers

A candidate may be exempted from some course units from approved institutions by relevant Government and/or University organ(s), subject to the following conditions.

1. Request for exemption should be made in writing, on admission, addressed to the Dean, School of Pure and Applied Sciences and must be accompanied by officially endorsed supporting documents including the institutions' syllabuses for the relevant courses.
2. No candidate shall be exempted from more than forty-nine percent of the total number of units required for a program.
3. A candidate may be required to sit and pass applicable University examinations in the relevant course units, provided they have paid the appropriate examination fees. 
4. The minimum grade for unit(s) sought exemption shall be “B” or its equivalent.

c) Course Requirements

1. A student is required to attend at least two-thirds of the class attendance to be allowed to sit for the end-of-semester examination in a given unit of the programme.
2. The lecturer shall ensure the programme course(s) are delivered in a manner that learning takes place.

d) Student Assessment Policy/Criteria

1. The course shall be evaluated in terms of units; a course unit being defined as a series of 45 one- hour lecture equivalents.  For this purpose, one 1-hour lecture is equivalent to one 2-hour tutorial or one 3-hour practical, or any combination of these that may be recommended by the School Board and approved by the Senate.
2. All courses taken shall be examined during the semester in which they are offered.  Such examination shall consist of continuous assessments and practicals, where applicable, and end of the semester Exam paper.
3. End of the semester Exam paper will comprise 40 percent of the total course marks whereas continuous assessment and practicals, where applicable, will account for 40 percent.
4. End of the semester Exam paper will be project based.
5. A candidate may, on the recommendation of the School Board of Examiners and approval by the Senate, be admitted to Special Examinations, in the course(s) for which the candidate failed to sit Ordinary Examinations at the prescribed time. Special Examinations shall be graded as Ordinary Examinations.

e) Grading System

Each course shall be graded out of a maximum of 100 marks and the pass mark for each course shall be 50 percent. Marks shall be translated into letter grades as follows: -

70 – 100%                   A

60 and below 70%      B

50 and below 60%      C

Below 50%                 F

f) Examination Regulations

i) Written Examinations

The University Policy on University examinations shall apply. In addition;

1. All at least six units taken in the first year shall be examined during the semester in which they are offered. Such examination shall consist of continuous assessments and end of the semester Exam paper.
2. End of the semester Exam paper will comprise 40% of the total course marks whereas continuous assessment account for 60%. End-of-semester examinations will be project based for each 1 unit course.
3. To proceed to the second year, a candidate must pass all the six units.
4. Any student who fails to attain the pass mark in:
5. Less than 40% of the units taken in an academic year shall be required to do supplementary examinations for the failed units when next offered.
6. Between 40% and 75% of the units taken in an academic year shall be required to repeat the year.
7. More than 75% of the units taken in an academic year shall be discontinued.

ii) Thesis Examination

The Second year of study shall be by thesis (equivalent to twelve units) based on a research proposal submitted and approved after the first year of study. Each candidate will submit, with the approval of supervisors, a duly completed thesis for examination. All the Doctoral degree supervisors, Internal and External Examiners MUST at least be Senior Lecturers in Applied Mathematics. In addition, supervisors, Internal and External Examiners MUST have a Master and Ph.D. in Applied Mathematics. In special instances of Interdisciplinary research supervisor can be sourced from Applied Mathematics related disciplines. The thesis shall be examined in accordance with the common regulations governing Doctoral degree theses in the School of Pure and Applied Science or as determined by the Board of Postgraduate Studies.

g) Moderation of Examinations

University examinations will be set by internal examiners and moderated at the departmental level.  The moderated projects shall be forwarded to the external examiner for moderation and returned to the department.  Any suggestions by the external examiner shall be addressed by the department.

The roles of the internal examiners are:

1. To ensure unit content is delivered adequately and resources availed to the learners.
2. To set examinations as per the course requirements.
3. To review and moderate departmental drafts examinations in relevant areas of specialization
4. To administer and process examinations as per the university examinations regulations
5. To address the concerns raised by the external examiners as per departmental approval.
6. To participate in Departmental and School Examinations Board meetings.

The roles of external examiners are:

1. To review and moderate draft examinations and any other form of assessment.
2. To evaluate the structure, content, and academic standards of the programme.

h) Graduation Requirements

To qualify for the award of a degree, a candidate for the Doctor of Philosophy in Applied Mathematics shall be required to satisfy the department board of examiners in the first year of study. In the second year, the candidate shall undertake a mandatory research and thesis equivalent to eight-course units.

 i) Classification of Degrees

To qualify for the award of a degree, a candidate for the Doctor of Philosophy in
Applied Mathematics shall take 6 units (270 lecture hours) during the first year of
study. The candidate shall further be required to carry out supervised Thesis Research
in his/her chosen area of study, for a minimum period of two years, culminating in a
Doctoral Thesis.

 j) Description of Thesis

The research shall be examined by written thesis and oral presentation. Each student
shall present in at least four (4) seminars on the research proposal and thesis or as
otherwise advised by the Board of Postgraduate Studies. Each candidate shall submit
for examination a thesis, with the approval of the academic supervisors, at the end of
the final semester. The thesis shall be examined in accordance with the common
regulations of the Board of Postgraduate Studies of the University of Embu.

Course Evaluation

To facilitate high-quality teaching and learning, the University requires all courses to be evaluated every semester. To evaluate the delivery of courses, the University conducts a student-lecturer evaluation, at the end of every semester. The Student-Lecturer Evaluation exercise gives the students a chance to provide feedback on course content, instructional process, infrastructure and equipment for the delivery, instructional and reference materials and assessments. Furthermore, the department periodically conduct internal teaching reviews to critically evaluate their teaching and learning and subject their findings to a constructive dialogue with other members of the department, school or even management.

The procedure for student-lecturer evaluation is as outlined below:

1. The Director of Academic Quality Assurance informs students about student-lecturer evaluation at least three weeks before the start of examinations.
2. The Director then avails the student-lecturer evaluation form for filling, two weeks to examinations.

• Upon receipt of duly filled forms, the Director analyses the forms, compiles a report and within two months, submits the report to the Deputy Vice-Chancellor (Academics, Research and Extension) for necessary action. Furthermore, lecturers receive individual reports while Deans and Chairmen of Departments receive a summary of School or Departmental reports where applicable.

Management and Administration of the Programme

The programme will be housed in the Department of Mathematics and Statistics. The chairman of the department shall oversee the management and administration of the programme in collaboration with the dean of the school. An academic leader shall be responsible of students’ guidance in the programme. The academic leader will be at least in the rank of senior lecturer with an earned Doctorate degree in Applied Mathematics in the respective area of specialization. Additionally, the program will be supported by a minimum of two full- time staff having doctorate degrees in Applied Mathematics.  The program shall be subjected to internal quality assurance as determined by the University organs.

Course/Units Offered for the Programme

 A distribution table of units per semester

The distribution of the courses per semester and academic year for the two academic year periods shall be as shown in Table 1.

Table 1: Distribution of the courses per semester and academic year

S/No	Unit Code	Unit Name	Contact Hours
YEAR 1 SEMESTER 1
	SMA 801	Computational Techniques	45
	SMA 802	Applications of Numerical Analysis	45
	SMA 803	Scientific Writing and Communication	45
YEAR 1 SEMESTER 2
	SMA 804	Mathematical Programming	45
	SMA 805	Applications of Fluid Mechanics	45
	SMA 806	Mathematical Modelling	45
YEAR 2 AND YEAR 3
1.	SMA 900	Thesis	540