Department of Mathematics and Statistics

University of Jaffna

DEPARTMENT PROFILE & SUBJECT PROFILE

Orientation Program – 2022

The Department of Mathematics and Statistics: Beginnings and Mission

“Genius is 1 percent inspiration and 99 percent perspiration.”
― Thomas A. Edison

The University of Jaffna began functioning as the sixth campus of the University of Ceylon in 1974. The first intake to the Faculty of Science was in October 1974, which was then situated in the Undergraduate Section of Jaffna College. The first head of the Department of Mathematics and Statistics was Professor P. Kanagasabapathy who came from the Peradeniya Campus (now University of Peradeniya). Jaffna was the first to start a degree course in Statistics. The first Professor of Statistics was J. Balan Selliah who was previously attached to Jaffna College. Professor V.Tharmaratnam who specialised in Algebra, and had previously taught in the Colombo Campus (now University of Colombo), joined the Jaffna Campus in 1976. The Jaffna Campus became the University of Jaffna in 1978.

The Campus being new, the new staff worked hard to make it outstanding. Prof. Kanagasabapathy’s selfless dedication left a strong impression on those who studied under him. He strongly believed that the foundations were of utmost importance to the development of a mathematician and insisted that beginners should be taught by the more experienced hands. Some of the early staff members were Miss. Ponnuthurai and Dr.M.Z.M. Malhardeen, who made the students feel at ease, and Mr. Varatharajaperumal was a highly respected teacher of Statistics, who instilled the basics very firmly. Mr. Makinan later became the head of department and served through difficult times until his passing away in 2008. Prof. Tharmaratnam whose counsel was always important was with us until his retirement in 2001, and holds the honorable position of emeritus Professor in Mathematics.

At the start, a third of the students were Sinhalese. The Campus faced a crisis during the August 1977 communal violence. The staff and students saw to the protection of the Sinhalese students and ensured their safe conduct to the South. From that time until 2010, Sinhalese students were not admitted to the University. It was a blow to the University as a place where different views and political persuasions could be aired and discussed openly.

The onset of the civil war in the early 1980s resulted in rising insecurity and saw the departure of several senior academics. Few who went abroad for doctoral studies returned. Yet paradoxically, Jaffna continued to have one of the strongest departments of Mathematics in the country and, but for the war, would have kept this position.

In Lanka, we had the good fortune of inheriting a strong Mathematical tradition, which we need to preserve and strengthen. In developed countries, and especially North America, maintenance of this tradition has become a pressing issue for the future direction of education. In the past, strong grounding in the Mathematical tradition was founded on Euclidian Geometry, Calculus and Algebra and students were encouraged to work many problems on their own. Stakeholders think that, graduates should be readily employable and curriculum should incorporate the necessary soft skills. However, the value of analytical thinking and independent learning should be retained.

The crisis for Mathematics has been aggravated in this country by the inexplicable delay from the O Levels to the university. Ideally it should be not longer than two years, but here it takes nearly four years or more. Someone who gets a pure science degree at the age of 21 has many options for further study and careers. Unfortunately the pressure of advancing age is to take job-oriented courses where the intellectual development is limited, and consequently a reluctance to take Mathematics, especially Pure Mathematics.

We wish that those of you who have the patience and confidence in your ability would opt to specialize in Mathematics. Mathematics, it has been said by Carl Friedrich Gauss, is the Queen of Sciences. If we fail to protect the tradition of Mathematics, it would lead to decay in all other sciences. Path-breaking ideas often come from Pure Mathematics. You also need patience. We began with a quote from Edison. To cite him once more:  “I have not failed. I’ve just found 10 000 ways that won’t work.” That is the kind of patience you need for Mathematics, where the satisfaction in discovery or in getting to the bottom of something hard, is correspondingly great.

In upholding standards, the contribution of students is no less important than that of teachers. Teachers could at best guide, but the hard work is yours. You must go to the Library, master your subject matter and feel challenged to learn more. When there is no communication between the teacher and the student, the activity of learning becomes moribund. When you go to a teacher with a difficulty, it is challenging and encouraging to the teacher, who often sees something he has not noticed before. When students do not work tutorials or problems on their own, and rely exclusively on what has been worked on the board, there is pressure on the system, and on us, to lower standards. And what is in the syllabus may not be a reflection on the standard of the degree or what our graduates are capable of.

While we will endeavor to enrich your learning experience, do keep in mind that you play an important role in upholding a strong Mathematical tradition and the value of the degree with which you will soon go out into the world. We are a poor country with meager resources. You do not need costly laboratories for Mathematics. Most of the labour is performed by your intellect. Our Mathematical tradition helped many to go to other countries and shine. Many of our graduates shone in the applied sciences in foreign universities because their basic Mathematics was sound. It is your duty to ensure that the coming generations will have the benefit of this tradition.

Allowed Subject Combinations – Level 1G

Level 1G students are expected to register for three principal subjects along with Auxiliary/ Enhancement course units. The allowed subject combinations from the principal subjects are given in the following table.

Serial   No.	Principal Subject
	1	2	3
1	Pure Mathematics	Applied Mathematics	Statistics
2.	Pure Mathematics	Applied Mathematics	Computer Science
3.	Pure Mathematics	Applied Mathematics	Physics
4.	Pure Mathematics	Applied Mathematics	Chemistry
5.	Statistics	Pure Mathematics	Computer Science
6.	Computer Science	Pure Mathematics	Physics
7.	Computer Science	Applied Mathematics	Physics
8.	Computer Science	Applied Mathematics	Chemistry
9.	Computer Science	Applied Mathematics	Statistics
10.	Chemistry	Computer Science	Pure Mathematics

 

Principal Subject: Statistics

We are the pioneering Department in Sri Lanka to offer a special degree in Statistics since 1975.  At present, in Sri Lanka only four Departments are offering Statistics special degree.

1.What is Statistics?

Even though you may not have realized it, you probably have made some statistical statements in your everyday conversation or thinking. Statements like “I sleep for about eight hours per night on average” and “You are more likely to pass the exam if you start preparing earlier” are actually statistical in nature.

Statistics is the science of learning from data. As a discipline it is concerned with the collection, organization, analysis, interpretation and presentation of data.  It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.  When analyzing data, it is possible to use one or both of statistics methodologies: descriptive and inferential statistics in the analysis of data.

Descriptive statistics are used simply to describe or summarize a collection of data. This is particularly useful in communicating the results of experiments and research.  Inferential statistics involves methods of using information from a sample to draw conclusions about the population.

Applied statistics comprises descriptive statistics and the application of inferential statistics.  Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

 Therefore, the field of statistics provides the scientist with some of the most useful techniques for evaluating ideas, testing theory, and discovering the truth.

Nowadays, statistics has become an important tool in the work of many academic disciplines such as medicine, agriculture, psychology, education, sociology, engineering, astronomy, biology, economics, genetics, marketing, public health, sports, and physics. Statistics is also important in many aspects of society such as business, industry and government. Because of the increasing use of statistics in so many areas of our lives, it has become very desirable to understand and practice statistical thinking. This is important even if you do not use statistical methods directly.

2.Learning Objective of Statistics:

Have a sound knowledge of the theoretical foundation of statistics including probability, distribution theory and stochastic processes.

Develop the fundamental skills of Applied Statistics, including the design of experiments, sampling and data analysis, time series analysis, forecasting, inference and decision theory.

Be competent in analyzing statistical and mathematical problems arising in the scientific, industrial and financial sectors.

3.Pathway with Statistics as a principal subject:

Irrespective of subject combination, students have the opening to obtain B.Sc. general degree or B.Sc. in special degree.  However, special degree programmes have prerequisites. The following Table indicates; openings for special degree programmes to those who offer Statistics as a principal subject.

Subject Combination	Special Degrees
Statistics   Pure Mathematics Applied Mathematics	Bachelor of Science Honours in Statistics   Bachelor of Science Honours in Mathematics
Statistics   Computer Science Pure Mathematics	Bachelor of Science Honours in Statistics   Bachelor of Science Honours in  Computer Science
Statistics   Computer Science Applied Mathematics	Bachelor of Science Honours in Computer Science

 

4.Why do we need Statistics?

• Modern technology generates more and more data therefore the decision-making processes in the business, research, public and government sectors are increasingly relying on data.\
• People trained in Mathematical Statistical theory and methodology (analytics) and related computer skills are in great demand in the business, industrial, research and government sectors.
• They are employed as statisticians; data miners or managers; statistical, business, quantitative or risks analysts; researchers in the marketing, information and management departments of large businesses; in research sections in the agricultural, medical and biological sciences; in the pharmaceutical industry; in the broader economy and many more.
• In this capacity, they form part of the stimulating and challenging management and decision-making processes in large organizations.

5.Career Opportunities:

Statistics is a universal discipline, finding application in all areas of science, and commerce. The truth is that no applied science is complete without statistical reasoning and support. A knowledge of statistics is essential not only to analyse data, but more importantly at the designing stage of an experiment. It is essential that every institute that conducts research must have at least one qualified statistician.

Statistics offers a wide range of career opportunities in many fields. In general, applied statisticians can easily fit into careers in, pharmaceutical, information and communication technology,  agriculture,  insurance companies, finance companies and banks, market research companies, manufacturing, as private consultants,  government departments (e.g. Treasury, Census and Statistics, etc.),  and as academics/researchers in universities.

Job Characteristics:

• Use data to solve problems in a wide variety of fields
• Apply mathematical and statistical knowledge to social, economic, medical, political, and ecological problems
• Work individually and/or as part of an interdisciplinary team
• Travel to consult with other professionals or attend conferences, seminars, and continuing education activities
• Advance the frontiers of statistics, mathematics, and probability through education and research

6.Course Units in Statistics:

Level 1G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
STA101G3	Probability Theory	03	45		150
STA102G2	Introduction to Statistics	02	30		100
Semester 2
STA103G3	Basic Statistical Inference	03	45		150
STA104G2	Applied Statistics I	02	30		100

 

Level 2G
Course Code	Course Title	Credit Value	Contact hours			Notional hours
			Theory	Practical
Semester 1
STA201G3	Statistical Theory	03	45			150
STA202G2	Sampling Techniques	02	30			100
Semester 2
STA203G3	Design and Analysis of Experiments	03	40		10	150
STA204G2	Statistical Inference	02	30			100

 

Level 3G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
STA301G3	Regression Analysis	03	40	10	150
STA302G3	Stochastic Processes	03	45		150
Semester 2
STA303G2	Quality Control	02	25	10	100
STA304G2	Applied Statistics II	02	25	10	100
STA305G2	Statistical Computing	02		60	100

 

Principal Subject: Pure Mathematics

1.What is Pure Mathematics?

Mathematics is the science that deals with the logic of shape, quantity   and arrangement. Mathematics is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since the beginning of recorded history, mathematic discovery has been at the forefront of every civilized society, and in use in even the most primitive of cultures. The needs of mathematics arose based on the wants of society.

Pure mathematics lies at the heart of Mathematics. Pure mathematics explores the boundary of mathematics and pure reason. It has been described as “that part of mathematical activity that is done without explicit or immediate consideration of direct application,” although what is “pure” in one era often becomes applied later. Finance and cryptography are current examples of areas to which pure mathematics is applied in significant ways.

2.Learning Objectives of Pure Mathematics:

In generic sense, students offering Mathematics attain proficiency in

Critical thinking

The ability to identify, reflect upon, evaluate, integrate, and apply different types of in- formation and knowledge to form independent judgments. Analytical and logical thinking and the habit of drawing conclusions based on quantitative information.

Problem solving

The ability to assess and interpret complex situations, choose among several potentially appropriate mathematical methods of solution, persist in the face of difficulty, and present full and cogent solutions that include appropriate justification for their reasoning.

Effective communication

The ability to communicate and interact effectively with different audiences, developing their ability to collaborate intellectually and creatively in diverse contexts, and to appreciate ambiguity and nuance, while emphasizing the importance of clarity and precision in communication and reasoning.

Specific Objectives

• Acquire fundamental knowledge and understanding of theory and techniques in selected areas of mathematics.
• Be able to understand, use and develop abstract concepts.
• Develop problem solving skills and the ability to think logically and analytically.
• Develop a sound understanding of and strong skills in the use of fundamental mathematics, including linear algebra and abstract algebra, set theory, real and complex analysis, geometry and topology.
• Have the ability to apply the basic concepts involved in these subjects to other areas of study, especially applied mathematics, statistics and computer science.
• Understand the basic rules of logic, including the role of axioms or assumptions
• Appreciate the role of mathematical proof in formal deductive reasoning
• Be able to distinguish a coherent argument from a fallacious one, both in mathematical reasoning and in everyday life
• Recognize real-world problems that are amenable to mathematical analysis and formulate mathematical models of such problems
• Apply mathematical methodologies to open-ended real-world problems
• Recognize connections between different branches of mathematics
• Appreciate the role of mathematical proof as a means of conveying mathematical knowledge
• Understand the differences between proofs and other less formal arguments
• Make vague ideas precise by formulating them in mathematical language
• Describe mathematical ideas from multiple perspectives

3.Career Opportunities:

One of the reasons that mathematically-trained people are needed in almost every field is that we are known for our excellent problem-solving and critical thinking skills.

• Many topics in “Pure Mathematics” have important applications in computer science.

• Mathematics is often done in conjunction with another field: biology, physics, economics, or a host of others.

• Mathematics assistswell with teaching and/or research.

4.Course Units in Pure Mathematics

Level 1G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
PMM101G3	Foundations of Mathematics	03	45		150
PMM102G2	Limit Process	02	30		100
Semester 2
PMM103G3	Algebra and Number Theory	03	45		150
PMM104G2	Calculus	02	30		100

 

Level 2G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
PMM201G3	Linear Algebra	03	45		150
PMM202G2	Advanced Calculus	02	30		100
Semester 2
PMM203G3	Analysis	03	45		150
PMM204G2	Linear Algebra and Analytic Geometry	02	30		100

 

Level 3G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
PMM301G3	Abstract Algebra	03	45		150
PMM302G3	Complex Analysis	03	45		150
Semester 2
PMM303G3	Discrete and Combinatorial Mathematics	03	45		150
PMM304G3	Geometry	03	45		150

 

5.Pathway with Pure Mathematics as a principal subject:

Irrespective of subject combination, all students have an opening to obtain B.Sc. General Degree. However, Special degree programmes have prerequisites. The following table indicates the openings to special degree programmes for those who offer Pure Mathematics as a principal subject.

Subject Combinations	Subject Specialization Degrees
Pure Mathematics   Applied Mathematics Statistics	Mathematics Special   Statistics Special
Pure Mathematics   Applied Mathematics Computer Science	Mathematics Special   Computer Science Special
Pure Mathematics   Applied Mathematics Physics	Mathematics Special   Physics Special
Pure Mathematics   Applied Mathematics Chemistry	Mathematics Special   Chemistry Special
Pure Mathematics   Statistics Computer Science	Statistics Special   Computer Science Special
Pure Mathematics   Computer Science Physics	Computer Science Special   Physics Special
Pure Mathematics   Computer Science Chemistry	Computer Science Special   Chemistry Special

 

Principal Subject: Applied Mathematics

1.What is Applied Mathematics?

These days mathematics is applied almost everywhere. Applied Mathematics involves using mathematics to solve real world problems, in particular, problems in scientific research and in the development of new technology. Applied Mathematics also involves the development of new mathematical and computational tools.

Applied Mathematics education is based on courses that provide a strong mathematical and computational background, while offering a selection of courses in areas of application. These application areas are quite diverse, and reflect the research interests of members of the department.

2.Why should you pursue an education in Applied Mathematics?

 In studying Applied Mathematics you will learn how to use a variety of mathematical and computational tools to solve problems in diverse fields, ranging from physics and engineering, to biology and medicine. You will develop the intellectual discipline and reasoning abilities needed to think through complex problems and develop sound practical solutions. A person with an education in Applied Mathematics is thus versatile and effective in meeting challenges in the workplace or in postgraduate education.

Education gives us not only knowledge, but also the ability to organize and use that knowledge profitably. Every Applied Mathematics course is geared toward providing the students with the ability to use a variety of mathematical and computational tools to solve problems in various fields.

3.Learning Objective of Applied Mathematics:

• Apply critical thinking and communication skills to solve applied problems.
• Use knowledge and skills necessary for immediate employment or acceptance into a graduate program.
• Maintain a core of mathematical and technical knowledge that is adaptable to changing technologies and provides a solid foundation for future learning.

4.Program Student Learning Outcomes:

• Apply mathematical concepts and principles to perform computations
• Apply mathematics to solve problems
• Create, use and analyze graphical representations of mathematical relationships
• Communicate mathematical knowledge and understanding
• Apply technology tools to solve problems
• Perform abstract mathematical reasoning
• Learn independently

5.Career Opportunities:

• Has a variety of career opportunities in industries, business and other places.
• Applied mathematics often done in conjunction with every discipline of science, engineering, technology, biology and economics, etc.
• Applied mathematics is an essential tools in the development of advances in science and technology.
• Goes well with teaching and/or research.

6.Course Units in Applied Mathematics (AMM)

Level 1G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
AMM101G3	Applied Methods I	03	40	10	150
AMM102G2	Mechanics I	02	30		100
Semester 2
AMM103G3	Applied Methods II	03	45		150
AMM104G2	Mechanics II	02	30		100

 

Level 2G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
AMM201G3	Mathematical methods	03	45		150
AMM202G2	Fluid Dynamics	02	30		100
Semester 2
AMM203G3	Linear Programming	03	40	10	150
AMM204G2	Numerical Analysis	02	30		100

 

Level 3G
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
Semester 1
AMM301G3	Mathematical Programming	03	45		150
AMM302G3	Classical Mechanics	03	45		150
Semester 2
AMM303G2	Numerical Methods	02	30		100
AMM304G2	Fluid Dynamics II	02	30		100
AMM305G2	Mathematical Modeling	02	30		100

 

7.Pathway with Applied Mathematics as a Principal Subject:

Upon successful completion of the necessary requirements the students are eligible for a B.Sc. General Degree irrespective of their subject choice. However, the Special Degree programmmes in science faculty have prerequisites. The following table indicates the possible choices of Special Degree programmes for a student who offers Applied Mathematics as a principal subject.

Subject Combinations	Subject Specialization Degrees
Applied Mathematics   Pure Mathematics Statistics	Mathematics Special   Statistics Special
Applied Mathematics   Pure Mathematics Computer Science	Mathematics Special   Computer Science Special
Applied Mathematics   Pure Mathematics Chemistry	Mathematics Special   Chemistry Special
Applied Mathematics   Pure Mathematics Physics	Mathematics Special   Physics Special
Applied Mathematics   Physics Computer Science	Computer Science Special   Physics Special
Applied Mathematics   Chemistry Computer Science	Computer Science Special   Chemistry Special
Applied Mathematics   Statistics Computer Science	Computer Science Special

The only way to learn mathematics is to do mathematics.

                                                                                              – Paul Halmos

B.Sc. Applied Science in Financial Mathematics and Industrial Statistics

Apart from the usual General and Special degree programs, the Department of Mathematics and Statistics of University of Jaffna runs a program in applied science leading to B.Sc. (Hons) in Applied Science in Financial Mathematics and Industrial Statistics.

Students, who offer Pure Mathematics and Statistics as principal subjects, at the end of their third year, can apply for the extended applied science degree program in Financial Mathematics and Industrial Statistics.

Students enroll for B.Sc. Applied Science in Financial Mathematics and Industrial Statistics should offer following subjects based course units amounting to 22 credits:

Course Units in Applied Science

Applied Science
Course Code	Course Title	Credit Value	Contact hours		Notional hours
			Theory	Practical
MMT401XS3	Financial Mathematics	03	45		150
MMT402XS3	Actuarial Mathematics	03	45		150
STA403XS3	Applied Multivariate Analysis for Real World Data	03	45		150
STA404XS2	Advanced Statistical Computing	02	30		100
MMT405XS3	Project Work	03
STA406XS8	Industrial Training	08

 

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Staff Profile – Department of Mathematics and Statistics

Academic Staff

• Prof.V.Tharmaratnam (Emeritus Professor in Mathematics)
• Prof.S.Srisatkunarajah (Professor in Mathematics and Vice Chancellor)
• Prof. R.Vigneswaran (Professor in Mathematics)
• Mr.S.Selvarajan (Senior Lecturer in Mathematics)
• Mrs.N.Satkunanathan (Senior Lecturer in Statistics)
• Dr.S.Arivalzahan (Senior Lecturer in Statistics and the Head of the Department)
• Mr.A.Laheetharan (Senior Lecturer in Statistics)
• Dr.K.Kannan (Senior Lecturer in Mathematics)
• Dr.N.Varathan (Senior Lecturer in Statistics)
• Dr. N.Ramaruban (Senior Lecturer in Mathematics)
• Dr. R. Prasanthan (Senior Lecturer in Mathematics)
• Dr.T.Mathanaranjan (Senior Lecturer in Mathematics)
• Mr.M.Khokulan (Senior Lecturer in Mathematics)
• Dr.S.Arumairajan (Senior Lecturer in Statistics)
• Dr.B.Kethesan (Senior Lecturer in Mathematics)
• Mr.B.Muraleetharan (Senior Lecturer in Mathematics)
• Mr.M.Annanthakrishna (Senior Lecturer in Mathematics)
• Mr.R.Tharshan (Lecturer in Statistics)
• Mrs.T.Anuthrika (Lecturer in Statistics, on study leave)
• Mrs.J.Duwarahan (Lecturer in Statistics)
• Mr.M.Arunmaran (Lecturer in Mathematics, on study leave)
• Dr.S.Mayuran (Lecturer in Mathematics)

Supporting Staff

• Mrs.K.Nijanthini (Management Assistant)
• Mr.R.Krtheepan (Technical Officer)
• Mr.T.Nanthakobe (Technical Officer)
• Mr. A. Aravinthan (Laboratory Attendant)