Mathematics BSc
Courses
2013. Mathematics BSc — Courses
How to use the tables below?

In the cells, the notation k + n means: k hours of lectures and n hours of practice classes per week (a contact hour lasts 45 minutes). By clicking on these numbers you can read a detailed description (syllabus, literature, prerequisites, requirements, number of credits) of the given course. One semester consists of 13 study weeks and an examination period.

Compulsory and optional courses
• White cell: compulsory course.
• Yellow cell: optional course (you are required to collect a certain amount of credits from these).
• Green cell: recommended course (free credits can be used for these).
Types of prerequisites
• Course X is a strong prerequisite of course Y, if X must be completed before enrolling in Y.
• Course X is a weak prerequisite of course Y, if X must be completed successfully before completing course Y, but you can enroll in them during the same semester. For example, the practice class of each course is a weak prerequisite of the lecture of the same course (you have to get a passing grade from the practice class in order to take the exam).
 Core courses Semester 1 Semester 2 hourslect+pc creditslect+pc hourslect+pc creditslect+pc Elementary mathematics 1 0 + 2 0 + 3 Analysis 1, 2ac 3 + 4 3 + 5 3 + 3 3 + 4 Calculus 1, 2ac 2 + 4 2 + 4 2 + 2 2 + 2 Foundations of analysisac 3 + 2 3 + 2 Algebra 1, 2 2 + 2 2 + 3 2 + 2 2 + 3 Number theory 1 2 + 2 2 + 3 Geometry 1 3 + 2 3 + 3 Discrete mathematics 1, 2 2 + 2 2 + 3 2 + 2 2 + 3 Programming fundamentals 2 + 2 2 + 3
Requirements

Compulsory: 11/12 courses, 54 credits.

Remarks

ac) You have to take exactly one of the following two equivalent sets of courses:

• {Analysis 1, Analysis 2}
• {Calculus 1, Calculus 2, Foundations of analysis}
 Pure mathematics Semester 3 Semester 4 Semester 5 Semester 6 hourslect+pc creditslect+pc hourslect+pc creditslect+pc hourslect+pc creditslect+pc hourslect+pc creditslect+pc Analysis 3, 4 4 + 3 4 + 4 4 + 2 4 + 3 Algebra 3, 4 2 + 2 2 + 3 2 + 2 2 + 3 Number theory 2 2 + 0 2 + 0 Geometry 2, 3 2 + 2 2 + 3 3 + 2 3 + 3 Introduction to differential geometry 2 + 2 2 + 3 Differential geometry of manifolds 2 + 2 2 + 3 Introduction to topology 2 + 2 2 + 3 Algebraic topology 2 + 2 2 + 3 Set theory 2 + 0 2 + 0 Mathematical logic 2 + 2 2 + 3 Probability theory 1, 2pt 2 + 2 2 + 3 3 + 2 3 + 2 Mathematical statistics 2 + 2 2 + 3 Differential equations 2 + 2 2 + 3 Partial differential equations 2 + 2 2 + 3 Functional analysis 2 + 2 2 + 3 Function series 2 + 0 2 + 0 Complex analysis 2 + 2 2 + 3 Complex analysis, extensionce 1 + 0 1 + 0 Fourier integral 2 + 2 2 + 3 Operations research 1, 2 2 + 2 2 + 3 2 + 2 2 + 3 Numerical analysis 2 + 2 2 + 3 Computer science 2 + 2 2 + 3 Programming language (JAVA, C++) 2 + 2 2 + 3 2 + 2 5 Symbolic mathematical programs 0 + 2 0 + 2 Computer methods of applied analysiscm 0 + 1 0 + 1 Total number of courses: 6 4 6 3 1 4 0 2 1 0 1 4 Total number of hours and credits: 14 + 13 33 11 + 6 20 13 + 12 30 6 + 4 12 0 + 2 2 8 + 6 17 0 0 4 + 4 10 2 + 2 5 0 0 1 + 0 1 6 + 7 16
Requirements

For a BSc degree in Pure Mathematics, 180 credits have to be completed.

• Compulsory: 149 credits. The core courses yield 54 credits, the rest is listed in the table above (19 courses, 44+35=79 contact hours, 95 credits).
• Optional: 12 credits. These have to be chosen from the courses indicated by yellow cells.
• 10 credits.
• Free: 9 credits.
Remarks

ce) Complex analysis, extension is a recommended extension of Complex analysis, taught in parallel.

cm) The course Computer methods of applied analysis is designed for applied mathematicians, but it is recommended for pure mathematicians, too. They are advised to take it in semester 6, and take Numerical analysis (mm1c1na5m) first.

 Applied mathematics Semester 3 Semester 4 Semester 5 Semester 6 hourslect+pc creditslect+pc hourslect+pc creditslect+pc hourslect+pc creditslect+pc hourslect+pc creditslect+pc Algebra 3 2 + 2 2 + 3 Analysis 3, 4, 5 4 + 3 4 + 4 2 + 2 2 + 3 2 + 0 2 + 0 Differential geometry 2 + 2 2 + 3 Foundations of mathematics 2 + 2 2 + 3 Design and analysis of algorithms 1, 2 2 + 2 2 + 3 2 + 2 2 + 3 Probability theory 1, 2pt 2 + 2 2 + 3 2 + 2 2 + 3 Mathematical statistics 2 + 2 2 + 3 Differential equations 2 + 2 2 + 3 Partial differential equations 2 + 2 2 + 3 Functional analysis 2 + 2 2 + 3 Complex analysis 2 + 2 2 + 3 Operations research 1,2 2 + 2 2 + 3 2 + 2 2 + 3 Numerical analysis 1, 2, 3 2 + 2 2 + 3 2 + 2 2 + 3 2 + 2 2 + 3 Computer science 2 + 2 2 + 3 Programming language (JAVA, C++) 2 + 2 2 + 3 2 + 2 5 Symbolic mathematical programs 0 + 2 0 + 2 Computer packages in numerical mathematics 0 + 1 0 + 1 Basics of CAD 0 + 2 0 + 3 Computer methods of applied analysis 1, 2cm 0 + 1 0 + 1 0 + 1 0 + 2 AMam Programming 2 + 2 5 AMam Applications of geometric transformations 2 + 2 2 + 3 AMam Optimization 2 + 2 2 + 3 AMam Probabilistic models 0 + 3 0 + 5 Applied linear algebra 2 + 2 2 + 3 Algebraic coding theory 2 + 0 2 + 0 Applied geometry 2 + 2 2 + 3 Elementary mathematics 2 0 + 2 0 + 3 Elementary mathematics 3 0 + 2 0 + 3 Total number of courses: 5 5 6 3 3 4 3 3 0 2 2 1 Total number of hours and credits: 10 + 11 25 8 + 9 21 12 + 12 30 6 + 6 15 4 + 6 13 6 + 7 16 4 + 3 9 4 + 7 15 0 + 0 0 2 + 4 8 2 + 4 8 2 + 0 2
Requirements

For a BSc degree in Applied Mathematics, 180 credits have to be completed.

• Compulsory: 145 credits. The core courses yield 54 credits, the rest is listed in the table above (19 courses, 36+38=74 contact hours, 91 credits).
• Optional: 15 credits. These have to be chosen from the courses indicated by yellow cells.
• 10 credits.
• Free: 10 credits.

It is recommended to choose the topic of the thesis in an applied area, possibly by taking part in a computer project aimed at a practical application.

Remarks

pt) Both pure and applied mathematics students can choose whether to take the applied or pure mathematics version of Probability theory 2 (it is compulsory to take one of these two courses). The pure mathematics version covers more material.

am) AM means: applied module.