Graduate university study programme Mathematics, specialisation in Pure Mathematics - Prirodoslovno-matematički fakultet Sveučilišta u Splitu

The graduate study programme Mathematics, specialisation in Pure Mathematics has the goal of offering students appropriate fundaments for the scientific postgraduate doctoral study programme in mathematics. This study programme is directed towards further autonomous research and scientific work. This specialisation, based on the syllabus, enables students to adopt fundamental knowledge and understand results in the area of algebra, mathematical analysis, probability, geometry and topology, including applied mathematics. Though the study programme is primarily directed to further researchers, the programme also provides a good education for all jobs seeking abilities in mathematical modelling, programming, analytical thinking and applied ICT techniques.

I semester

LIST OF COURSES
Year of study: 1.
Semester: 1.
STATUS	CODE	COURSE	COURSES IN SEMESTER				ECTS
STATUS	CODE	COURSE	L	S	E	T	ECTS
Mandatory	PMM912	Metric Spaces	45	15			6
	PMM811	Vector Spaces II	30	15			5
	PMM216	Algebra I	30	15			5
	PMM913	Measure and Integral	30		30		6
	PMM914	Vector Analysis	45		15		6
	Total mandatory		180	45	45		28
Elective	PMM009	History of Mathematics	30				3
	PMM810	Diophantine Equations	30	15			5
	PMM205	Cryptography	30	15	15		5
	PMM217	Algebraic Number Theory	45		15		5
	PMM204	Mathematical Theory of Computation	45		15		5
	PMM922	Optimization	30	15			5
	PMM014	Constructive Methods in Geometry	30		30		5
	PMP106	Fundamental Concepts in Physics	30	15			3
	PMII10	Introduction to Artificial Intelligence	30		30		5
	The students select at least 3 ECTS (1 course).

II semester

LIST OF COURSES
Year of study: 1.
Semester: 2.
STATUS	CODE	COURSE	COURSES IN SEMESTER				ECTS
STATUS	CODE	COURSE	L	S	E	T	ECTS
Mandatory	PMM228	Probability I	30		30		6
	PMM215	Normed Spaces	45	15			6
	PMM813	Algebra II	30	15			5
	PMM915	Partial Differential Equations	30		30		6
	PMM120	Introduction to Differential Geometry	30		30		6
	Total mandatory		165	30	90		29

III semester

LIST OF COURSES
Year of study: 2.
Semester: 3.
STATUS	CODE	COURSE	COURSES IN SEMESTER				ECTS
STATUS	CODE	COURSE	L	S	E	T	ECTS
Mandatory	PMM230	Statistics	30		30		6
	PMM219	Stochastic Processes	30		30		6
	PMM916	Operators on Normed Spaces	45	15			6
	PMM812	Foundations of Geometry ( if the student HAD passed the course at the undergraduate level, the course is substituted with the prescribed course from the group of elective courses MAThEMATIcs	45		30		6
	Total mandatory		150	15	90		24
Elective	Elective courses: group Mathematics
	PMM218	Topics in Topology	45	15			6
	PMM810	Diophantine Equations	30	15			5
	PMM205	Cryptography	30	15	15		5
	PMM217	Algebraic Number Theory	45		15		5
	PMM204	Mathematical Foundation of Computing	45		15		5
	PMM922	Optimization	30	15			5
	PMM014	Constructive Methods in Geometry	30		30		5
	PMM919	Introduction to Lie Groups and Lie Algebras	45	15			5
	PMM710	Mathematics in Action					5
	Elective courses: Informatics and Physics
	PMP106	Fundamental Concepts in Physics	30	15			3
	PMII10	Introduction to Artificial Intelligence	30		30		5
	Minimum 6 ECTS, or 8 ECTS is selected from elective courses (depending on the selected ECTS from elective courses for 1. semester). One or two elective courses is selected for 3. and 4. semester together (minimum one elective course from group Mathematics).

IV semester

LIST OF COURSES
Year of study: 2.
Semester: 4.
STATUS	CODE	COURSE	COURSES IN SEMESTER				ECTS
STATUS	CODE	COURSE	L	S	E	T	ECTS
Mandatory	PMM918	Topics in Applied Mathematics	30		30		6
	PMM991	Diploma Thesis		30			22
	Total mandatory		30	30	30		28
Elective	Elective courses: group Mathematics
	PMM118	Numerical Analysis	30		30		5
	PMM121	Introduction to Projective Geometry	30		30		5
	PMM232	Probability II	30		30		6
	PMM129	Computability	30		15		5
	PMM710	Mathematics in Action					5
	PMM502	COMPLEX NETWORKS ANALYSIS	30		30		5
	PMM504	STATISTICS IN BIOMEDICINE	30		30		5
	Elective courses: group Informatics and Physics
	PMPN01	Physics	30	15	30		6
	PMP009	History of classical physics	30				3
	PMP11C	Fundamental Concepts in Quantum Physics	30	15			4
	PMID30	Object Oriented Programming	30		30		6
	PMIH20	Data Minning	30		30		5
	Minimum 6 ECTS, or 8 ECTS is selected from elective courses (depending on the ECTS from elective courses for 1. semester). One or two elective courses is selected for 3. and 4. semester together (minimum one elective course from group Mathematics).

CONDITIONS OF ENROLLMENT AND POTENTIAL DIFFERENTIAL COURSES:	ANY UNDERGRADUATE STUDY OF MATHEMATICS OR MATHEMATICS AND OTHER FIELD WITH AT LEAST 115 ECTS IN MATHEMATICAL COURSES. TOTAL DIFFERENTIAL COURSES CAN NOT EXCEED 30 ECTS.