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Mathematics (first cycle)

Study program cycle and type:

First cycle academic study program.

Anticipated academic title:

In Slovenian: diplomirani matematik (UN), diplomirana matematičarka (UN), abbreviated to dipl. mat. (UN).

Duration:

3 full years (6 terms) based on 180 ECTS credits.

Basic goals:

The principal goal of the academic study program in Mathematics is to qualify its graduates for solving hard mathematical problems arising in industry, in the public sector, and in sciences. At the same time, graduates of the program are equipped with the core knowledge necessary for studies in the second cycle.

Generic competences developed by the student:

Subject specific competences developed by the student:

Mathematics is the link between natural sciences, engineering, social sciences and computer sciences. Therefore, a graduate of the academic study program in Mathematics should be able to:

Employment possibilities:

Graduates of the academic study program in Mathematics can find employment in:

Admission requirements and admission limitation measures

Admission to the study program is open to the following:

a) Holders of the matura certificate.

b) Holders of the vocational matura certificate obtained in any of the four-year high school programs. In this case, an additional examination in one of the general matura subjects different from those of the vocational matura is required. Either one of the vocational matura subjects or the additional one must be mathematics.

c) Holders of the final examination certificate obtained in any of the four-year high school programs prior to 1 June 1995.

In case the number of applicants exceeds the maximum availability, the applicants are selected according to their final matura (or vocational matura) grade, their mathematics matura (or vocational matura) grade, their grade point average (GPA) in the last two years of high school, and their final mathematics grades in the last two years of high school. These are weighted in the following way.

Applicants under a)

Applicants under b)

Applicants under c)

Enrollment requirements

Enrollment in the first study year is granted upon admission.

For enrollment in the next study year it is necessary to earn 50 ECTS credits from courses and exams in the current study year.

In addition to the credit quota, the completions of the following exams are obligatory:

Re-enrollment requirements

For re-enrollment in the same study year, a student needs to earn:

a) at least half of all possible credits of the current study year (30 ECTS credits), and

b) all credits from the previous study years.

Re-enrollment is only possible once in the course of studies. A change of the study program as result of disability of enrollment in the next study year is automatically counted as re-enrollment.

Finishing requirements

To finish the program, students need to complete all exams.

Validation of competences, knowledge, and skills acquired prior to admission to the study program

Students may apply for validation of their competences acquired previously by means of various forms of education if their competences match those of one or more courses offered within this study program. In a formal written request submitted to the mathematics department at the FMF, the applicant must specify the course(s) whose competences he or she had already mastered, and attach accredited transcripts proving it. When considering the possible validation of competences corresponding to a particular course, the department study committee bases its decision on a comparison of

If the study committee decides to validate the previously acquired competences, the student is awarded all ECTS credits that correspond to the respective course(s). In the validation process, the study committee follows The rules and guidelines for validation of informally acquired knowledge and skills, accepted by the Senate of The University of Ljubljana on 29 May 2007 (http://www.uni-lj.si/o_univerzi_v_ljubljani/statut_in_pravilniki.aspx).

Grading system

The methods for testing the competences, knowledge, and skills are described in the courses syllabi. The basic knowledge testing rules are explained in the Exam guidelines of the FMF. Course examinations are either written or oral or both. They can have the form of midterm exams, oral defense of midterm exams, written exams, oral exams, seminar or project work and oral defense of seminar and project work. Grading is based on the grading scale determined in the Statute of The University of Ljubljana. All forms of examinations are graded by grades 1-10, out of which 6-10 are passing grades, and 1-5 are failing grades. The following grading scale is most commonly used for grading the score of a written course examination:

Score (in %) grade
50 - 59 % 6
60 - 69 % 7
70 - 79 % 8
80 - 89 % 9
90 - 100 % 10

Curriculum

The spreadsheet data are given for both the winter and the summer term.
Each term comprises 15 weeks of classes.

Abbreviations:
L = lectures per week (in hours),
P = problem sessions per week (in hours),
Lab = lab classes per week (in hours),
S = seminars per week (in hours),
ECTS = ECTS credits worth,
TSW = estimated total student workload (in hours).

1st year

 Winter termSummer termTotal
CourseLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Analysis 1 4 4 0 0 9 270 4 4 0 0 9 270 18 540
Algebra 1 3 3 0 0 7 210 3 3 0 0 7 210 14 420
Logic and sets 2 2 0 0 6 180 0 0 0 0 0 0 6 180
Computer lab 1 0 3 0 6 180 0 0 0 0 0 0 6 180
Introduction to programming 0 0 0 0 0 0 2 0 2 0 6 180 6 180
Physics 1 0 0 0 0 0 0 3 3 0 0 6 180 6 180
Elective 1 2 0 0 2 60 1 2 0 0 2 60 4 120
Weekly total 11 11 3 0 30 900 13 12 2 0 30 900 60 1800
Term total 165 165 45 0     195 180 30 0        

Electives

 Winter termSummer termTotal
CourseLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Proseminar A 2 2 0 0 2 60 0 2 0 0 2 60 4 120
Proseminar B 0 2 0 0 2 60 2 2 0 0 2 60 4 120

Remark: Proseminars A and B are electives. Proseminar A is intended as a review of selected high school topics in mathematics, while Proseminar B should be chosen by students with strong mathematical background. Problem sessions for both Proseminars are a supplement to the other courses in the first year's curriculum.

2nd year

 Winter termSummer termTotal
CourseLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Analysis 2 4 3 0 0 8 240 4 3 0 0 6 180 14 420
Physics 2 3 3 0 0 6 180 0 0 0 0 0 0 6 180
Algebra 2 3 2 0 0 6 180 0 0 0 0 0 0 6 180
Algebra 3 0 0 0 0 0 0 3 2 0 0 6 180 6 180
Programming 1 2 0 2 0 5 150 0 0 0 0 0 0 5 150
Point-set topology 2 2 0 0 5 150 0 0 0 0 0 0 5 150
Seminar 1 0 0 0 0 0 0 0 0 0 2 3 90 3 90
Elective 1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Elective 2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Elective 3 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Weekly total 14 10 2 0 30 900 13 11 0 3 30 900 60 1800
Term total 210 150 30 0     195 165 0 30        

Electives

  Winter termSummer termTotal
CourseGroupLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Discrete mathematics 1 B1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Programming 2 B1 0 0 0 0 0 0 2 0 2 0 5 150 5 150
Algebraic curves B2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Introduction to geometric topology B2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Affine and projective geometry B 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Coding theory and cryptography B 0 0 0 0 0 0 2 2 0 0 5 150 5 150

Remark: Electives are divided into groups B1, B2, and B. Each student opts for three electives. Of those, at least one must belong to group B1, and at least one to group B2.

3rd year

 Winter termSummer termTotal
CourseLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Analysis 3 3 3 0 0 6 180 0 0 0 0 0 0 6 180
Analysis 4 0 0 0 0 0 0 3 3 0 0 6 180 6 180
Introduction to numerical methods 3 3 0 0 6 180 0 0 0 0 0 0 6 180
Probability and statistics 2 2 0 0 5 150 2 2 0 0 5 150 10 300
Seminar 2 0 0 0 2 3 90 0 0 0 1 1 30 4 120
Mechanics 1 2 2 0 0 5 150 0 0 0 0 0 0 5 150
Specific elective 1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Specific elective 2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Specific elective 3 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Specific elective 4 2 2 0 0 5 150 0 0 0 0 0 0 5 150
General elective 0 0 0 0 0 0 2 0 0 0 3 90 3 90
Weekly total 12 12 0 2 30 900 13 11 0 1 30 900 60 1800
Term total 180 180 0 30     195 165 0 15        

Specific electives

  Winter termSummer termTotal
CourseGroupLPLabSECTSTSWLPLabSECTSTSWECTSTSW
Numerical linear algebra B1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Mechanics 2 B1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Mathematical modelling B1 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Data structures and algorithms 1 B2 2 1 1 0 5 150 0 0 0 0 0 0 5 150
Data structures and algorithms 2 B2 0 0 0 0 0 0 2 1 1 0 5 150 5 150
Coding theory and cryptography B2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Discrete mathematics 2 B2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Optimization 1 B2 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Database basics B 0 0 0 0 0 0 2 0 2 0 5 150 5 150
Financial mathematics 1 B 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Game theory B 3 3 0 0 6 180 0 0 0 0 0 0 6 180
Affine and projective geometry B 0 0 0 0 0 0 2 2 0 0 5 150 5 150
Introduction to differential geometry B 2 2 0 0 5 150 0 0 0 0 0 0 5 150

Remarks: