Mathematics, First Cycle of Courses (WMI00501SO)(in Polish: Matematyka, stacjonarne pierwszego stopnia)  
firstcycle fulltime, 3 years Language: Polish  Jump to:
Opis ogólny
No description for the programme.

Qualification awarded:
(in Polish) Licencjat na matematyce
Access to further studies:
secondcycle programmes, postgraduate programmes
Professional status:
In compliance with the educational level the graduate has achieved
Access requirements
ATTENTION: this information may be not up to date. Valid admission requirements can be found on www.erk.uj.edu.pl
For candidates with old maturity exam diploma  test entrance exam, for these with the new one matura schoolleaving certificate
For candidates with old maturity exam diploma  test entrance exam, for these with the new one matura schoolleaving certificate
Teaching standards
ATTENTION: this information may be not up to date. Valid admission requirements can be found on www.erk.uj.edu.pl
Graduates who complete the programme of study have acquired the learning outcomes specified in Resolution No. 34/III/2012 adopted by the Senate of the Jagiellonian University on 28th March 2012 on the introduction of learning outcomes for particular fields of study conducted at the Jagiellonian University as of the 2012/2013 academic year, with later amendments. Graduates hold the following qualifications as regards knowledge, skills, and social competences: KNOWLEDGE Knowledge of the significance of mathematics and its applications in civilisation.  Appreciation of the role and significance of mathematical proofs, and also of the significance of mathematical assumptions.  Knowledge of the construction of selected mathematical theories; ability to apply mathematical formalism to construct and analyse simple mathematical models for application in other sciences.  Knowledge of the basic theorems of the branches of mathematics he/she has learned.  Knowledge of the basic examples to illustrate specific mathematical concepts, and to disprove erroneous hypotheses or unwarranted reasoning.  Knowledge of selected concepts and methods in mathematical logic and the theory of multiplicity applied in the foundations of other disciplines of mathematics.  Knowledge of the foundations of the differential and integral calculus of functions with one or more variables, and of the other branches of mathematics applied in it, with special consideration of linear algebra and topology.  Knowledge of the computational and programming techniques which assist the mathematician in his/her work, and an appreciation of their limitations.  A foundation knowledge of at least one utility software package. Knowledge of the basic concepts of the protection of intellectual property.  Knowledge of the basic principles of safety and hygiene at work. SKILLS  Ability to present mathematical reasoning and formulate theorems and definitions correctly and clearly, in speech and in writing.  Ability to use propositional calculus and first order predicate calculus; ability to apply quantifiers correctly, also in colloquial language.  Ability to define functions and relations.  Ability to conduct proofs using the complete induction method; ability to define functions and recurrence relations.  Ability to apply classical logic to formalise mathematical theories.  Ability to create new objects by constructing quotient structures or Cartesian products.  Ability to use the language of the theory of multiplicity to interpret issues from various branches of mathematics.  Comprehension of the issues associated with the various types of infinity and orders in sets.  Ability to use the concept of real numbers and perform real number operations; knowledge of examples of irrational and transcendental numbers.  Ability to perform complex number operations; knowledge of the elementary theorems of the arithmetic of complex numbers.  Ability to define functions, also with the use of limits including power series; and to describe their properties.  Ability to use the concepts of convergence and limits in various contexts; ability to calculate the limits of sequences and functions, and examine absolute and relative convergence in series.  Ability to interpret and explain functional dependencies in the form of formulae, tables, graphs, and schemata, and apply them in practical problems.  Ability to apply the differential calculus theorems and methods for a singlevariable function in problems involving the examination of function’s properties and to give grounds for the reasoning applied.  Ability to apply the differential calculus theorems and methods for a multivariable function in problems involving optimisation, the determination of local and global extremes, and the examination of function’s properties and to give grounds for the reasoning applied.  Ability to use the definition of the integral of a function with a single real variable, and to explain the analytical and geometrical meaning of this concept.  Ability to integrate singlevariable functions by parts and by substitution; ability to apply the Riemann integral in simple geometrical problems.  Ability to apply the definition of the integral of functions of several real variables, and to explain the analytical and geometrical meaning of this concept.  Ability to integrate multiplevariable functions; ability to change the order of integration; ability to apply the Riemann integral for multiplevariable functions in simple geometrical problems.  Ability to apply selected tools and numerical methods to solve selected problems in differential and integral calculus.  Ability to apply the concepts of linear space, vectors, linear transformations, and matrices.  Ability to recognise algebraic structures (groups, rings, fields, linear spaces) in various mathematical problems.  Ability to calculate determinants, and knowledge of their properties; ability to give the geometrical interpretation of determinants and comprehension of its connection with mathematical analysis.  Ability to find the solution to a system of linear equations with constant coefficients, and to interpret the solution.  Ability to find the matrices of linear transformations with respect to various bases; ability to calculate the eigenvalues and eigenvectors of matrices and to explain the geometrical meaning of these concepts.  Ability to reduce matrices to the canonical form; ability to apply this skill in the solution of linear differential equations with constant coefficients.  Ability to solve simple ordinary differential equations and a system of linear differential equations with constant coefficients.  Ability to identify and determine the principal topological properties of subsets in Euclidean space and in metric spaces.  Ability to apply the topological properties of sets and functions (including the Darboux property and Weierstrass’ extreme value theorem.  Ability to identify problems which may be solved algorithmically.  Ability to design and analyse a simple algorithm.  Ability to compile, instal, and test a simple computer program on his/her own.  Ability to use computer software for data analysis.  Ability to model and find solutions to simple practical problems.  Ability to apply the concept of probability space; ability to design and analyse a mathematical model for a random experiment.  Ability to apply the basic properties of probability theory (including the formula for total probability and Bayes’ formula).  Ability to give various examples of discrete and continuous probability distributions and discuss selected random experiments and the mathematical models in which these distributions occur; knowledge of the practical applications of the basic distributions.  Ability to determine the parameters for the random variable in a discrete distribution and in a continuous distribution; ability to apply the limit theorems and the laws of large numbers to estimate probabilities.  Ability to apply the statistical characteristics of a population and their sample counterparts.  Ability to conduct simple statistical reasoning, also with the use of computer tools.  Ability to speak on mathematical issues in a simple, clear manner.  Capacity for independent study.  Proficiency in at least one foreign language at the B2 intermediate level. SOCIAL COMPETENCES  Awareness of the shortcomings of his/her knowledge and appreciation of the need for continuing education.  Appreciation of the need to formulate statements and questions precisely, to help him/her understand the issue under discussion better or to retrieve the missing components in the reasoning.  Appreciation of the need for teamwork; appreciation of the need for systematic work on a project.  Appreciation for intellectual integrity in his/her own and other people’s work; adherence to the ethical code.  Appreciation for the need to present selected issues in higher mathematics in an accessible manner to the nonspecialist general public.  Ability to conduct an independent search for information in the literature, including foreignlanguage publications.  A critical attitude with respect to theorems, observations, and conclusions, particularly those which are not based on logical grounds.  Appreciation of the need for critical analysis of information, including statistical and financial data, and of decisionmaking on the basis of an appropriate analysis of the data available.  Appreciation of the need to formulate objective opinions on issues which are described in the language of mathematics.
Graduates who complete the programme of study have acquired the learning outcomes specified in Resolution No. 34/III/2012 adopted by the Senate of the Jagiellonian University on 28th March 2012 on the introduction of learning outcomes for particular fields of study conducted at the Jagiellonian University as of the 2012/2013 academic year, with later amendments. Graduates hold the following qualifications as regards knowledge, skills, and social competences: KNOWLEDGE Knowledge of the significance of mathematics and its applications in civilisation.  Appreciation of the role and significance of mathematical proofs, and also of the significance of mathematical assumptions.  Knowledge of the construction of selected mathematical theories; ability to apply mathematical formalism to construct and analyse simple mathematical models for application in other sciences.  Knowledge of the basic theorems of the branches of mathematics he/she has learned.  Knowledge of the basic examples to illustrate specific mathematical concepts, and to disprove erroneous hypotheses or unwarranted reasoning.  Knowledge of selected concepts and methods in mathematical logic and the theory of multiplicity applied in the foundations of other disciplines of mathematics.  Knowledge of the foundations of the differential and integral calculus of functions with one or more variables, and of the other branches of mathematics applied in it, with special consideration of linear algebra and topology.  Knowledge of the computational and programming techniques which assist the mathematician in his/her work, and an appreciation of their limitations.  A foundation knowledge of at least one utility software package. Knowledge of the basic concepts of the protection of intellectual property.  Knowledge of the basic principles of safety and hygiene at work. SKILLS  Ability to present mathematical reasoning and formulate theorems and definitions correctly and clearly, in speech and in writing.  Ability to use propositional calculus and first order predicate calculus; ability to apply quantifiers correctly, also in colloquial language.  Ability to define functions and relations.  Ability to conduct proofs using the complete induction method; ability to define functions and recurrence relations.  Ability to apply classical logic to formalise mathematical theories.  Ability to create new objects by constructing quotient structures or Cartesian products.  Ability to use the language of the theory of multiplicity to interpret issues from various branches of mathematics.  Comprehension of the issues associated with the various types of infinity and orders in sets.  Ability to use the concept of real numbers and perform real number operations; knowledge of examples of irrational and transcendental numbers.  Ability to perform complex number operations; knowledge of the elementary theorems of the arithmetic of complex numbers.  Ability to define functions, also with the use of limits including power series; and to describe their properties.  Ability to use the concepts of convergence and limits in various contexts; ability to calculate the limits of sequences and functions, and examine absolute and relative convergence in series.  Ability to interpret and explain functional dependencies in the form of formulae, tables, graphs, and schemata, and apply them in practical problems.  Ability to apply the differential calculus theorems and methods for a singlevariable function in problems involving the examination of function’s properties and to give grounds for the reasoning applied.  Ability to apply the differential calculus theorems and methods for a multivariable function in problems involving optimisation, the determination of local and global extremes, and the examination of function’s properties and to give grounds for the reasoning applied.  Ability to use the definition of the integral of a function with a single real variable, and to explain the analytical and geometrical meaning of this concept.  Ability to integrate singlevariable functions by parts and by substitution; ability to apply the Riemann integral in simple geometrical problems.  Ability to apply the definition of the integral of functions of several real variables, and to explain the analytical and geometrical meaning of this concept.  Ability to integrate multiplevariable functions; ability to change the order of integration; ability to apply the Riemann integral for multiplevariable functions in simple geometrical problems.  Ability to apply selected tools and numerical methods to solve selected problems in differential and integral calculus.  Ability to apply the concepts of linear space, vectors, linear transformations, and matrices.  Ability to recognise algebraic structures (groups, rings, fields, linear spaces) in various mathematical problems.  Ability to calculate determinants, and knowledge of their properties; ability to give the geometrical interpretation of determinants and comprehension of its connection with mathematical analysis.  Ability to find the solution to a system of linear equations with constant coefficients, and to interpret the solution.  Ability to find the matrices of linear transformations with respect to various bases; ability to calculate the eigenvalues and eigenvectors of matrices and to explain the geometrical meaning of these concepts.  Ability to reduce matrices to the canonical form; ability to apply this skill in the solution of linear differential equations with constant coefficients.  Ability to solve simple ordinary differential equations and a system of linear differential equations with constant coefficients.  Ability to identify and determine the principal topological properties of subsets in Euclidean space and in metric spaces.  Ability to apply the topological properties of sets and functions (including the Darboux property and Weierstrass’ extreme value theorem.  Ability to identify problems which may be solved algorithmically.  Ability to design and analyse a simple algorithm.  Ability to compile, instal, and test a simple computer program on his/her own.  Ability to use computer software for data analysis.  Ability to model and find solutions to simple practical problems.  Ability to apply the concept of probability space; ability to design and analyse a mathematical model for a random experiment.  Ability to apply the basic properties of probability theory (including the formula for total probability and Bayes’ formula).  Ability to give various examples of discrete and continuous probability distributions and discuss selected random experiments and the mathematical models in which these distributions occur; knowledge of the practical applications of the basic distributions.  Ability to determine the parameters for the random variable in a discrete distribution and in a continuous distribution; ability to apply the limit theorems and the laws of large numbers to estimate probabilities.  Ability to apply the statistical characteristics of a population and their sample counterparts.  Ability to conduct simple statistical reasoning, also with the use of computer tools.  Ability to speak on mathematical issues in a simple, clear manner.  Capacity for independent study.  Proficiency in at least one foreign language at the B2 intermediate level. SOCIAL COMPETENCES  Awareness of the shortcomings of his/her knowledge and appreciation of the need for continuing education.  Appreciation of the need to formulate statements and questions precisely, to help him/her understand the issue under discussion better or to retrieve the missing components in the reasoning.  Appreciation of the need for teamwork; appreciation of the need for systematic work on a project.  Appreciation for intellectual integrity in his/her own and other people’s work; adherence to the ethical code.  Appreciation for the need to present selected issues in higher mathematics in an accessible manner to the nonspecialist general public.  Ability to conduct an independent search for information in the literature, including foreignlanguage publications.  A critical attitude with respect to theorems, observations, and conclusions, particularly those which are not based on logical grounds.  Appreciation of the need for critical analysis of information, including statistical and financial data, and of decisionmaking on the basis of an appropriate analysis of the data available.  Appreciation of the need to formulate objective opinions on issues which are described in the language of mathematics.