Bachelor’s Degree Study Programme
Affirmed in the Council
of Faculty of Physics and Mathematics
on November 2, 1998
Bachelor’s Degree Programme in Mathematics
Table of Contents
Goal of Programme 3
Tasks of Programme 3
Annotation of Programme 3
Description of Programmes 3
Length of Studies and Score of Subject Matters 4
Immatriculation Terms 4
Requirements in Assessment of Studies and Assessment Order 4
Syllabus of Studies 5
Subject of Curriculum Studies Programme 6
Studies module in Technomathematics 8
Means of Fulfilment the Programme 10
Costs of Studies per Bachelor’s Degree Programme Student per Annum (Ls.) 12
Terms of Awarding academic degree’s 13
Possibilities of Acquiring Natural Sciences, Social Sciences and Humanities as well as Other Studying Possibilities 13
Goal of Programme
The goal of the studies programme for baccalaureate in mathematics is to provide for academic education in the science Mathematics, maintaining a historically established inheritance of the traditions of the science of Mathematics in Latvia and facilitating further development of a possibly greater number of directions in Mathematics.
Tasks of Programme
The tasks of the studies programme for a baccalaureate is:
to offer the students of this programme extended knowledge in one or several separate directions of Mathematics and their application;
to provide the required basis of academic knowledge to prepare highly qualified professionals for the application of mathematics in national economy (mathematical modelling and mathematical statistics) and to provide for the education of mathematics in all levels;
to prepare the specialists with an independent and creative approach in acquiring the latest achievements of Mathematics and putting them effectively into practice.
Annotation of Programme
Within the baccalaureate’s studies programme, the students obtain basic knowledge in the fundamental studies subjects of Mathematics and in the subjects which are topical for the practical applications of Mathematics as well as separate selected sub-programmes of Mathematics in the relevant subjects. Equally great attention has been paid to the theoretical aspects of these subjects and to ability of applying the acquired knowledge for the mathematical modelling of nature, technology and social processes. For the emphasis of the unity of theory and practice serve the course and the bachelor’s degree papers.
A significant role in the studies programme is played by the students acquiring proficient application of computing technologies, especially for the usage of solving different mathematical problems as well as by the courses in the Sciences. Within the programme, it is feasible for the students to acquire those courses of the social sciences and Humanities they take interest in.
Description of Programmes
The studies for a baccalaureate at the University of Latvia were opened in 1990. The studies programme has been developed on the basis of up to that time existing studies programmes of the speciality of Mathematics at the faculty of Physics and Mathematics and has been modified in compliance with the corresponding studies programmes of the leading European universities, taking into consideration the historical traditions characteristic of the University of Latvia and the peculiarities of the development of Mathematics in Latvia.
The baccalaureate’s programme in mathematics is the leading studies programme in Mathematics in Latvia’s higher educational establishments.
The studies programmes determinates the subject and the syllabus of the studies, specific requirements for the assessment of the studies and successful fulfilment of the programmes, secured by academic and financial resources as well as by the required material and informative bases. The programme and their courses are added in the supplement.
Successful mastering of the baccalaureate’s programme makes it possible to continue studies for a master’s degree in Latvia and abroad.
Mastering of the baccalaureate’s programme makes it possible to compete successfully in the multinational labour market.
Length of Studies and Score of Subject Matters
The total score of the baccalaureate’s programme in mathematics is 161 credit points and the length of the studies for full time form studies is 4 years.
The course of the programme are divided into three parts:
part A – the compulsory courses (94 credit points, 58% of the common score of studies programme);
part B – the optional courses (52 credit points, 32% of the common score of studies programme);
part C – the free optional courses of studies (15 credit points, 10% common score of studies programme);
Immatriculation Terms
The candidates for the baccalaureate’s studies programme in mathematics are subject to the general immatriculation terms of the University of Latvia and to the orders of the UL Studies Vice–Rector.
In addition to the requirements mentioned in the General Terms in 1998, there was an entrance examination in mathematics (in a written form) at the bachelor’s studies programme in Mathematics. In case of an equal assessment, a candidate took a higher position in the competition with higher average mark in geometry and algebra from the secondary education document (certificate). Without the entrance examinations for the studies at the bachelor’s degree programme in mathematics could register the following candidates: the first three price winners of LR and international mathematics and computer science olympiads; students with an honours diploma of A.Liepa Correspondence Mathematics School; and, in the competition order, the students whose final examination mark of mathematics in the secondary education document (certificate) is not less than 8.
Requirements in Assessment of Studies and Assessment Order
The students of the bachelor’s studies programme in Mathematics are subject to the UL assessment requirements and assessment order.
Syllabus of Studies
The planning of the bachelor’s studies programme in mathematics is shown in the following table
A: Compulsory courses / 1.sem / 2.sem / 3.sem / 4.sem / 5.sem / 6.sem / 7.sem / 8.semProgramming and Computer Science I / 4
Algebra I / 4
Analytical Geometry / 4
Mathematical Logic / 2
Calculus I / 8
Programming and Computer Science II / 4
Algebra II / 8
Calculus II / 8
Programming and Computer Science III / 2
Calculus III / 8
Differential Equations I / 4
Numerical Methods I / 2
Probability Theory / 4
Calculus IV / 4
Numerical Methods II / 2
Mathematical Statistics / 4
Numerical Methods III / 4
Function Theory of Complex Variable / 4
Course Paper / 4
Bachelor’s Work / 10
94 / 22 / 20 / 16 / 10 / 12 / 4 / 10
B: Optional Courses / 1.sem / 2.sem / 3.sem / 4.sem / 5.sem / 6.sem / 7.sem / 8.sem
Foreign Language / 1 / 1
Natural Sciences / 4 / 2 / 3
Special courses in Mathematics / 2 / 2 / 4 / 4 / 15 / 8 / 6
52 / 1 / 3 / 2 / 4 / 8 / 17 / 11 / 6
C: Free Optional Courses / 1.sem / 2.sem / 3.sem / 4.sem / 5.sem / 6.sem / 7.sem / 8.sem
15 / 3 / 3 / 3 / 3 / 3
Total Score of Credit Points / 1.sem / 2.sem / 3.sem / 4.sem / 5.sem / 6.sem / 7.sem / 8.sem
161 / 23 / 23 / 21 / 17 / 23 / 20 / 18 / 16
Subject of Curriculum Studies Programme
The subject of the bachelor’s degree programme is shown in the following table:
No. / Name of course / Credit points / Testing MethodPart A (94 credit points)
Algebra I / 4 / Exam
Algebra II / 8 / Exam
Analytical Geometry / 4 / Exam
Differential Equations I / 4 / Exam
Complex Variable Function Theory / 4 / Exam
Calculus I / 8 / Exam
Calculus II / 8 / Exam
Calculus III / 8 / Exam
Calculus IV / 4 / Exam
Mathematical Logic / 2 / Test
Mathematical Statistics / 4 / Exam
Numerical Methods I / 2 / Test
Numerical Methods II / 2 / Test
Numerical Methods III / 4 / Exam
Programming and Computer Science I / 4 / Test
Programming and Computer Science II / 4 / Test
Programming and Computer Science III / 2 / Test
Probability Theory / 4 / Test
Course Paper / 4 / Defence
Bachelor’s Work / 10 / Defence
Courses in Natural Sciences (9 credit points)
Natural Sciences I / 4 / Test
Natural Sciences II / 2 / Test
Natural Sciences III / 3 / Exam
Optional Courses in Mathematics (41 credit points)
Analytical Solutions / 2 / Exam
Applications of Numerical Methods for Solution of Mathematical Physics and Hydrodynamics Problems / 2 / Exam
Calculus of Variations / 4 / Test
Correctness of Problems / 2 / Exam
Differential Equations II / 4 / Exam
Differential Geometry / 4 / Exam
Discrete Mathematics / 2 / Exam
Elements of Combinatorics / 3 / Exam
Equations of Mathematical Physics / 4 / Exam
Fixed Point Method / 2 / Exam
Functional Analysis / 4 / Test
Fundamentals of Actuarial Mathematics / 4 / Test
Fundamentals of Geometry / 2 / Exam
Fuzzy Sets and Systems I / 4 / Exam
Fuzzy Sets and Systems II / 4 / Exam
General Theory of Optimal Algorithms / 4 / Test
Integral Equations / 4 / Exam
Integral Splines and their Applications / 2 / Exam
Introduction to Algorithm Theory / 2 / Exam
Introduction to Number Theory / 3 / Exam
Lebesque Integrals / 4 / Exam
Mathematical Models in Differential Equations / 2 / Test
Mathematical Models of Chemical Reactors Theory / 2 / Exam
Mathematical Models of Continuous Medium Mechanics / 2 / Test
Mathematical Principles of Economic Models / 2 / Test
Mathematical, Statistical and Special Software Products / 4 / Test
Methods of Mathematical Physics / 4 / Exam
Methods of Optimisation / 4 / Exam
Microeconomics of Insurance / 4 / Test
Non-linear Boundary Value Problems in Applications / 2 / Exam
Numerical Methods IV / 3 / Exam
Numerical Methods of Optimisation / 4 / Test
Open - Key Criptography / 2 / Test
Operational Research / 4 / Exam
Optimal Control of Processes / 4 / Exam
Portfolios of Securities and their Management / 4 / Test
Practical Logic I / 2 / Test
Practical Logic II / 2 / Test
Principles of Mathematical Modelling / 2 / Exam
Regression analysis / 2 / Exam
Seminar on Program Packages / 2 / Test
Seminar for Data Handling of Continuous Process / 2 / Test
Solution of Boundary Value Problems in Layered Media / 2 / Exam
Special Numerical Methods / 2 / Exam
Supplementary Chapters of Mathematical Statistics / 4 / Exam
Survey Sampling / 4 / Exam
Topology I / 2 / Exam
Topology II / 2 / Exam
Studies module in Technomathematics
Motivation of Necessity of Studies module. The European Consortium for Mathematics in Industry (ECMI) has worked out and henceforth, in most leading European universities, carried out an educational conception of mathematicians for the needs of industry and other branches of economy. The Latvian Academy of Sciences and the UL Institute of Mathematics are members of the above mentioned organisation, therefore since 1995 the higher education and science integration project supported financially by the RL Education and Science Ministry, Development of Studies Programme Orientated to Technomathematics, has been made (project director doc. J.Cepitis). As a result, for a baccalaureate’s studies programme in mathematics a supplementary module in technomathematics is opened, which after having mastered it, could serve the students as a basis being awarded a certificate issued by the ECMI Board for a performance of its requirements in the ECMI training centres.
Description of Studies module. At the supplementary module of technomathematics studies the main emphasis is laid upon the analytical and numerical methods of differential equations, the problems of non-linear analysis and optimisation as well as the analysis of regression and the elements of discrete mathematics. An essential studies component is seminars in mathematical modelling, which provide for the students’ active participation in the working out the process of mathematical modelling, in its analysis, in solving a mathematical problem, making a written report and giving its verbal presentation.
Subject of Supplementary module. A supplementary module in technomathematics studies records the optional courses of the bachelor’s programme in mathematics, part B, with the common score of 44 credit points, leaving a selection relevant to the specialisation with the score of 8 credit points. A course paper is substituted by seminars in mathematical modelling (e.g. Seminar in Programme Packages, Seminar in Continuous Data Processing) envisaged for performance.
Compulsory courses, part B (44 credit points)Natural Sciences I / 4 / Test
Natural Sciences II / 2 / Test
Natural Sciences III / 3 / Exam
Differential Equations II / 4 / Exam
Discrete Mathematics / 2 / Exam
Functional Analysis / 4 / Test
Equations of Mathematical Physics / 4 / Exam
Principles of Mathematical Modelling / 2 / Exam
Operations Research / 4 / Exam
Methods of Optimisation / 4 / Exam
Regressions analysis / 2 / Exam
Numerical methods IV / 3 / Exam
Applications of Numerical Methods for Solution of Mathematical Physics and Hydrodynamics Problems / 2 / Exam
Topology I / 2 / Exam
Optional courses, part B (8 credit points)
Analytical Solutions / 2 / Exam
Integral Splines and their Applications / 2 / Exam
Correctness of Problems / 2 / Exam
Solution of Boundary Value Problems in Layered Media / 2 / Exam
Mathematical Models of Mechanics in Continuous Environment / 2 / Test
Non-linear boundary Value Problems in Applications / 2 / Exam
Note. The optional courses of the technomathematics supplementary module from part B can be substituted by the relevant master’s degree studies courses.