General Information

Programme Coordinator: doc. RNDr. Ondřej Čepek, Ph.D.

Study specializations

The Bachelor of Computer Science programme has a common first year of study and is divided into three specializations starting in the second year of study:

General Computer Science
Databases and Web
Artificial Intelligence.

Students select their specialization during the second year of their study in accordance with the study regulations.

Degree plans

The course of study in the individual specializations is regulated by the relevant degree plan, which specifies the obligatory and elective courses, the requirements for the State Final Exam, and a recommended course of study. The elective courses are in each specialization divided into several groups. A minimum number of credits should be obtained from elective courses overall; in addition, a minimum total number of credits is also required for certain groups of elective courses. Besides obligatory courses and the required number of elective courses, each student may sign up for additional courses taught at our faculty or at other faculties of Charles University (these are called ``optional courses").

All three specializations share a large part in common, containing obligatory courses that cover the foundations of mathematics, theoretical computer science, programming, and software systems. Most of these subjects are recommended for the first year in the entire Computer Science programme. The recommended course of study for the first year specified below consists of obligatory courses (in boldface) and several optional courses (in italics). Of course, other optional courses may be selected instead of those that are recommended, provided that a total of at least 60 credits is achieved within the first academic year.

Recommended Course of Study for the First Year

NPRG062Introduction to Algorithms 42/1 C+Ex
NPRG030Programming 1 52/2 C
NSWI120Principles of Computers 32/0 Ex
NSWI141Introduction to Networking 32/0 MC
NDMI002Discrete Mathematics 52/2 C+Ex
NMAI057Linear Algebra 1 52/2 C+Ex
NMAI069Mathematical skills120/2 C
NTVY014Physical Education I210/2 C
ASE500129Czech Language Course 1330/2 C
NTIN060Algorithms and Data Structures 1 52/2 C+Ex
NPRG031Programming 2 52/2 C+Ex
NSWI170Computer Systems 52/2 C+Ex
NSWI177Introduction to Linux 41/2 MC
NMAI054Mathematical Analysis 1 52/2 C+Ex
NMAI058Linear Algebra 2 52/2 C+Ex
NTVY015Physical Education II210/2 C
ASE500130Czech Language Course 2330/2 C

1 The course NMAI069 Mathematical Skills is designed for students who wish to gain and practice the fundamental mathematical skills needed for the more mathematically oriented courses given at our faculty. Emphasis is put on the ability to use precise and correct mathematical formulations and on basic proof techniques.

2 The Physical Education courses are obligatory for students on the programme taught in Czech, while they are elective for students on the programme taught in English. If you like sports, this may be a course for you, but there is no obligation to take it.

3 The Czech Language Courses are optional, offered as a counterpart to the elective English Language Courses recommended for students studying in the programme taught in Czech. Since these courses are elective, they may naturally be replaced by any other course while maintaining the minimum of 30 credits per semester.

Some obligatory courses common to all specializations are taught in the second and third year of study. They are listed below.

Common obligatory courses in the second and third year of study

NTIN061Algorithms and Data Structures 2 52/2 C+Ex
NDBI025Database Systems 52/2 C+Ex
NDMI011Combinatorics and Graph Theory 1 52/2 C+Ex
NAIL062Propositional and Predicate Logic 52/2 C+Ex
NTIN071Automata and Grammars 52/2 C+Ex
NMAI059Probability and Statistics 1 52/2 C+Ex
NPRG045Individual Software Project440/1 C
NSZZ031Bachelor Thesis 60/4 C

4 It is possible to sign up for the course NPRG045 both in the winter semester and in the summer semester; the standard period is the summer semester.

Each individual specialization requires additional obligatory courses and groups of elective courses. A detailed degree plan for each specialization is given later in this text.

Recommended course of study for the second and third year

The recommended course of study is prepared for each specialization in such a way that the obligatory courses are scheduled in the required order, the student obtains in time the credits needed for enrolment in the next year of study, and the student fulfils in time all the prerequisites needed in order to take the State Final Exam. A recommended course of study for each specialization is given later in this text.

Branches within specializations

Some specializations are further divided into branches. Individual branches within the same specialization differ only in one area of prerequisites for the State Final Exam. Students should adjust their choice of elective and optional courses according to the branch in which they intend to take the State Final Exam. The choice of a particular branch within the student's specialization is declared only when signing up for the State Final Exam.

State Final Exam

The State Final Exam consists of two parts:

Defence of Bachelor Thesis
Exam in Mathematics and Computer Science

Each part of the State Final Exam is graded. The final grade for the State Final Exam is determined by the grades obtained for each part. The student can sign up for each part of the State Final Exam separately. Bachelor studies are successfully concluded only upon passing both parts of the State Final Exam. In case of failure, the student retakes those parts of the State Final Exam which he or she failed. Each part of the State Final Exam can be retaken at most twice.

Necessary conditions for signing up for either part of the State Final Exam are the following:
passing all the obligatory courses of a given specialization,
obtaining the required number of credits for elective courses,
submitting a completed bachelor thesis by the specified deadline (necessary for signing up for the bachelor thesis defence),
obtaining at least 180 credits (necessary for signing up for the last part of the State Final Exam).

A bachelor thesis topic is typically assigned at the beginning of the third year. The bachelor thesis usually consists of either a software package, which may be a continuation of the Individual Software Project (see degree plans above), or a piece of theoretical work. We recommend choosing a topic offered by the department which is connected with the selected specialization. In case another topic (offered by another department or suggested by the student) is to be selected, we strongly recommend consulting the relevant Specialization Coordinator before doing so.

The prerequisites for the State Final Exam are divided into two parts, one common to all specializations and the other specific to the given specialization. The list of common prerequisites is given below this paragraph; the prerequisites specific to the various specializations are listed after their degree plans given further below.

Knowledge requirements for the State Final Exam common to all specializations


1. Fundamentals of Differential and Integral Calculus
Sequences and series of numbers and their properties. Real functions of one variable. Continuity, limit of a function. Derivatives: definition and basic rules, behaviour of functions, Taylor polynomial with remainder. Primitive functions: definition, uniqueness, existence, methods of calculation.

Relevant courses:

Mathematical Analysis 1 (NMAI054)

2. Algebra and Linear Algebra
Groups and subgroups, fields. Vector spaces and subspaces. Scalar product, norm. Orthogonality, othonormal basis. Systems of linear equations, Gauss and Gauss–Jordan elimination. Matrices, operations with matrices, matrix rank. Eigenvalues and eigenvectors of a matrix. Characteristic polynomial, relationship between eigenvalues and roots of polynomials.

Relevant courses:

Linear Algebra 1 (NMAI057)
Linear Algebra 2 (NMAI058)

3. Discrete Mathematics
Relations, properties of binary relations. Equivalence relation, equivalence classes. Partial orders. Functions, types of functions. Permutations and their basic properties. Binomial coefficients, binomial theorem. Principle of inclusion and exclusion. Hall's theorem on systems of distinct representatives, matchings in a bipartite graph.

Relevant courses:

Discrete Mathematics (NDMI002)
Combinatorics and Graph Theory 1 (NDMI011)

4. Graph Theory
Basic concepts, basic examples of graphs. Connected graphs, connected components. Trees, their properties, equivalent characterizations of trees. Planar graphs, Euler's formula and the maximum number of edges in a planar graph. Graph colourings, chromatic number and clique number. Edge- and vertex-connectivity, Menger's theorem. Directed graphs, weak and strong connectivity. Network flows.

Relevant courses:

Discrete Mathematics (NDMI002)
Combinatorics and Graph Theory 1 (NDMI011)

5. Probability and Statistics
Random events, conditional probability, independence of random events, Bayes' formula, applications. Random variables, mean (expectation), distribution of random variables, geometric, binomial, and normal distribution. Linear combination of random variables, linearity of expectation. Point estimates, confidence intervals, hypothesis testing.

Relevant courses:

Discrete Mathematics (NDMI002)
Probability and Statistics 1 (NMAI059)

6. Logic
Syntax – language, open and closed formulas. Normal forms of propositional formulas, prenex forms of predicate logic formulas, converting to normal form, applications in algorithms (SAT, resolution). Semantics, truth, falsity, independence of a formula with respect to a theory, satisfiability, tautologies, logical consequence, the notion of a model of a theory, extensions of theories.

Relevant courses:

Propositional and Predicate Logic (NAIL062)

Computer Science

1. Automata and Languages
Regular languages, finite automaton (deterministic, nondeterministic), Kleene's theorem, iteration lemma, regular grammars. Context-free languages, push-down automaton, context-free grammar. Turing machine, type 0 grammar, diagonal language, universal language. Chomsky hierarchy.

Relevant courses:

Automata and Grammars (NTIN071)

2. Algorithms and Data Structures
Time and space complexity of algorithms, asymptotic notation. Complexity classes P and NP, NP-hardness and NP-completeness. ``Divide and conquer" algorithms, complexity computation for these algorithms, examples. Binary search trees, AVL trees. Binary heaps. Hashing with buckets and open addressing. Sorting algorithms. DFS, BFS and their applications. Shortest paths. Minimum spanning trees. Network flows. Euclid's algorithm.

Relevant courses:

Algorithms and Data Structures 1 (NTIN060)
Algorithms and Data Structures 2 (NTIN061)

3. Programming Languages
Concepts for abstraction, encapsulation, and polymorphism. Primitive and object types and their representation. Generic types and functional elements. Working with resources and mechanisms for error handling. Object lifecycle and memory management. Threads and support for synchronization. Implementation of basic elements of object-oriented languages. Native and interpreted execution, compilation and linking.

Relevant courses:

Programming 1 (NPRG030)
Programming 2 (NPRG031)
Principles of Computers (NSWI120)
Based on the choice of the programming language: Programming in C# Language (NPRG035) or Programming in C++ (NPRG041) or Programming in Java Language (NPRG013)

4. Computer Architecture and Operating Systems
Computer organization, data and program representation. Instruction set architecture as a hardware/software interface, connection to elements of high-level programming languages. Support for operating system execution. Peripheral device interface and handling. Fundamental OS abstractions, interfaces, and mechanisms for program execution, resource sharing, and input/output. Parallelism, threads and interfaces for thread management, thread synchronization.

Relevant courses:

Principles of Computers (NSWI120)
Computer Systems (NSWI170)
Introduction to Networking (NSWI141)
Introduction to Linux (NSWI177)
Based on the choice of the programming language: Programming in C# Language (NPRG035) or Programming in C++ (NPRG041) or Programming in Java Language (NPRG013)

Charles University, Faculty of Mathematics and Physics
Ke Karlovu 3, 121 16 Praha 2, Czech Republic
VAT ID: CZ00216208

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