Available courses

Students will acquire knowledge in advanced algorithmic concepts. They will become familiar with designing efficient algorithms and precise analysis of their complexity.

Learning outcomes - a student will be able to:

- apply studied material for the development of new algorithms and calculate complexity of these algorithms
- analyze each algorithm and analyze its basic properties (input, output, efficiency, …)
- argue the importance of sorting algorithms, reproduce and compare sorting algorithms
- argue advantages and disadvantages of greedy algorithms, support claims on solving optimization problems (minimum spanning tree, ...)
- distinguish which method of constructing algorithms should be used for solving particular problems, compare the chosen method with other methods

Students acquire the ability to establish a clear bidirectional communication between 3D objects in space and an architectural drawing on a 2D background, to identify the underlying principles of specific projection methods and apply them in construction assignments, regardless of the tools used for visualization; furthermore, employ orthogonal axonometry in constructing some dome-vaulted structures.

Learning outcomes - a student will be able to:

  • identify, classify and construct conics using perspective collineation and affinity;
  • solve 2D and 3D problems using Monge's projection;
  • construct 3D images of objects given by Monge's projection using axonometric projection;
  • construct intersections of surfaces and planes;
  • recognize, analyze and comment the intersection curve of a surface and a plane;
  • distinguish various conics as intersection curves;
  • use and apply projection methods to solve architectural problems.

Course content allows students to fully master spatial vision as a basis for presenting spatial 3D objects on a 2D background and vice versa. This visual communication between three-dimensional and two-dimensional spaces is achieved by various projection methods used in the modern technical profession. The basic quality of acquired knowledge and competencies is knowledge and use of existing laws in the application of certain projection methods in engineering practice.

Learning outcomes - a student will be able to:

  • solve 2D and 3D problems using Monge's projection;
  • construct 3D images of objects given by Monge's projection using axonometric projection;
  • solve roof structures (simple roofs and roofs with external/internal barriers) of the building using the roof planes method;
  • describe the orthogonal projection and solve 2D problems;
  • analyze topographic maps and by orthogonal projection draw cuts and fills along a level or grade road;
  • recognize the laws of projections and apply them accordingly to solve civil engineering problems;
  • draw and solve constructive tasks using computer programs of dynamic geometry.

Computer geometry precedes professional courses that use constructed, spatial, or virtual drawing as a basis in communication. Presentation of interactive teaching content with the support of computer graphics is also included in the performance of the program.

Learning outcomes - a student will be able to:

  • identify, classify and construct conics using perspective collineation and affinity;
  • solve 2D and 3D problems using Monge's projection;
  • solve 2D and 3D problems using the orthogonal projection;
  • recognize, analyze and comment the intersection curve of a surface and a plane;
  • distinguish various conics as intersection curves;
  • analyze topographic maps and by orthogonal projection draw cuts and fills along a level or grade road;
  • recognize the laws of projections and apply them accordingly to solve problems in geodesy;
  • draw and solve constructive tasks using computer programs of dynamic geometry.

The aim of the module is to provide students with mathematical knowledge from the part about the functions (as a special mapping), how a function is given. 

To provide with the knowledge about the limit of a function and other properties as a derivatives of a function, to find the integral of a function etc. Also the aim is to solve and apply some problems from the part of linear algebra. 

OBJECTIVES: By the end of this module students should: 

  • To define different functions among two numerical sets. 
  • To represent functions in different forms (tabular, diagram, analytical form. Graphical form etc.) 
  • To understand the different types of functions. 
  • To find limit of a function. 
  • To understand the concept of continuity 
  • To find the derivative of a function, integral of a function and to apply these knowledge for solving different practical problems. 
  •  To sketch the graph of a function using the mentioned topics

The aim of the module is to provide students with mathematical knowledge from the part about the matrices, their properties, operation both binary and unary operation with matrices. To provide with the knowledge about the determinant of a matrix. Systems of linear equations and their solutions. Different matrix factorization and their application as well as the basic concepts of linear transformations. 

OBJECTIVES: By the end of this module students should: 4 To define the concept of matrix and matrix operations. 

  • To apply matrix theory 
  • To find the determinant of a function 
  • To discuss about existence of solution of systems of linear equations 
  • To solve systems of linear equations by different methods 
  • To define the linear transformation concept and discuss about its applications.

The course Applied Statistics introduces the statistical methods and techniques as tools for decision making in economics, business, and finance. It is designed to introduce basic methods of statistics, and its use in everyday life and in the context of economics and business research. The course introduces the descriptive statistics and graphical methods to summarize data accurately, as well as inferential statistics to make valid judgments based on the data. The course provides a broad range of practical business exercises. Students will also learn to utilize the results of regression analysis for prediction purposes and make sound business decisions.  Interpretation of the results and implications are also essential to the learning process.

Course Objectives and Outcomes:

By the end of the course, students should be able to:

  • Master graphical, tabular, and numerical methods of describing statistical data.
  • Apply descriptive statistics to probability distributions and understand that these distributions allow businesses to assign probabilities to several possible outcomes.
  • Explore methods of gathering samples from a larger population.
  • Develop null and alternative hypotheses for the purposes of hypothesis test and use sampling distributions to draw statistical inference for the population.
  • Use the statistical techniques to build regression models and analyse managerial, economics and business problems.
  • Show an advanced level of critical thinking and quantitative reasoning capabilities.

The course introduces the basic notions of linear models, number sequences and their applications, arithmetic and geometric progressions, numerical series, proportion and percentage, interest and mortgages calculation, deposits and rents, loans and loan amortization plan, other ways of amortization of loans. Also, the course provides various applications of financial mathematics in the context of business and economics.

Learning objectives and outcomes:

By the end of the course, students should be able to:

  • Apply the accumulated knowledge on linear models, arithmetic and geometric progression, number sequences, and numerical series for solving various problems from the field of business and economics.
  • Demonstrate pronounced knowledge related to financial mathematics: calculating the percentage, interest, deposits, rents, loans, compiling the plan of amortization as well as other methods of loan amortization.
  • Apply the linear models as well as financial mathematics for business and financial decision-making in certain market conditions.


Course Description

Notions, techniques and algorithms of discrete mathematics are studied, with special interest on parts of it involving algebra: number theory, algebraic structures and cryptography. A student will get the crucial knowledge from elementary number theory, founding structural properties of groups, rings and finite fields, and will be introduced and learn to analize some most common cryptosystems.

General Competencies

Learning how to use techniques and ways of thinking in discrete mathematics, particularly in algebraic combinatorics, and applying that knowledge to specific examples.

Learning Outcomes

  1. use the basic facts in elementary number theory
  2. solve linear and some particular non-linear congruences
  3. solve the basic diophantine equations
  4. identify the basic algebraic structures; groups, rings and fields
  5. understand the basic concepts in Cryptography
  6. use the algorithms for some Public-Key Cryptosystems

In this course, students are introduced to the basics of combinatorics. Permutations, variations and combinations.
Then we teach probability where students learn the basics of probability, geometric probability, total probability
formula and the Bayes formula.
The third chapter is Descriptive Statistics. Here, students are introduced to various tabular and
graphical representations of statistical data, then to the parameters of statistical data and
dispersion measures.
We continue with the two-dimensional statistical feature and the Pearson correlation
coefficient.
The next chapter covers discrete and continuous random variables, we teach basic discrete distributions
(binomial, hypergeometric, Poisson) and continuous distributions (continuous uniform distribution,
exponential distribution, normal distribution, t-distribution, F-distribution, χ2-distribution).
We continue with point estimates of the parameters of mean, proportion and variance and reliable intervals
for the parameter of mean and proportion.
The course ends with the testing of statistical hypotheses (t-test, F-test, χ2 - test).


Students are introduced with basic numerical methods, so they can apply them in professional courses.

Calculation of the value of some elementary functions by using the Taylor's polynomial. Calculation the value of some elementary functions by using Taylor's polynomial with the help of the
Mathematica software package.

Discrete case. Continuous case. Trigonometric polynomial; Fourier polynomial. Computer implementation with the help of the
Mathematica software package.

Lagrange's form of interpolation polynomial. Aitken interpolation scheme. The general Newton's form of interpolation polynomial. Calculate the interpolation polynomial with the
Mathematica software package.

In this lesson we will recall some in important concepts the theory of games, starting with strategy, payoffs, payoffs matrix. Beside them this lesson covers the two most basic concepts of the games, dominance and best response. Finally the most popular solution concepts in all of game theory called Nash Equilibrium will be introduced with some very well-known examples as Prisoner's Dilemma 

By the end of the lesson  students will be  able to:

1.     Find the Nash Equilibrium of a game

2.     Appraise the application of Prisoner’s Dilemma to a different real-word problems

3.     Identify Nash Equilibrium in various daily life problems

4.     Recognize the economic theory exemplified by the Prisoner’s Dilemma


In this lesson we will deal with the games which do not have pure strategy Nash Equilibrium. The idea behind this topic is to randomize your pure strategies called mixed strategies. So the other player can not be sure of what I will do. This is the main idea of mixed strategy Nash Equilibrium. The Nash Equilibrium of some games will be found by using partial derivative and algebraically.

By the end of the lesson  students should be able to:

1.     Determine the mixed strategy not only by algebraically but also by using partial derivatives

2.     Find the Nash Equilibrium of a game (mixed or pure)

3.     Describe the difference between pure and mixed strategies


 


Students will know that many different growth curves exist for populations in our daily lives. In exponential growth populations per individual growth rate stays the same regardless of population size and makes the population grow faster and faster as it gets larger. In nature, populations grow exponentially for some period but at the end they will be limited by source. The students will understand that modeling helps to describe and also predict population growth over time. Specially if the population has limited resources we will talk about logistic function and logistic population model. In logistic growth, population’s per individual growth rate gets smaller and smaller as population size approach a maximum imposed by limited resources.

By the end of the lesson some students should be able to:

1. Identify whether a growth curve describes exponential, logarithmic or logistic population model

2. Solve an equation or inequality involving a logistic function and construct  the logistic model

3.  Graph the logistic function by using some software programs (desmos)




Scientists use many different mathematical methods to model population dynamics (how population change in size and composition over time). Some of these models represent growth without constraints but some of the models have limited resources, known as the carrying capacity.In this lesson students will learn by different kind of examples that we can apply logistic functions by logistic population models  in ecology, statistics, neural networks , medicine chemistry, agriculture, economy, sociology, biology and political science. 

By the end of the lesson students should be able to:

1.     Solve an equation or inequality involving a logistic population model

2.     Find a logistic population model that best fits the given data

3.     Student will understand real-world applications of scientific models

4.     Graph the logistic population model by using some software programs (desmos)

5.     Determine whether a relation described graphically or symbolically represents a logistic population model

6.     Explain the influence of carrying capacity



Generally various differential equations types are used to express mathematical models explaining real life problems on the disciplines such as physics, engineering, astronomy, economy and statistics. While these mathematical models are generated variables changing depending on each other and rate of change of one quantity according to the other quantity (derivative) are needed. Besides it is easier solving the connection between derivatives using differential equation models and interpreting counterparts of these on real life. 

 

In this course, the concept of first-order linear differential equation will be introduced.. By integrating factor, the algorithm of the equation and solution will be presented. On the other hand, applications of the first order differential equation in verbal problems will be made.

By the end of the lesson all students should be able to:

1.       Recognize first order linear differential equations.

2.       Shows whether a given function is a general solution or a particular solution of a given linear differential equation.

3.       Finds integrating factor of a linear differential equation.

4.       Makes geometric interpretation of solutions of the first order linear differential equations and search singular solutions.

By the end of the lesson some students should be able to:

1.   Explains the ralationship between a linear differential equation and a one parameter family of curves.

2.   Finds singular solution of a linear differential equation. 

3.   Makes applications of the first order linear differential equations on oral problems.



A daily life problem will be presented to students in the context of mathematical modeling activity.

Preparatory questions and class discussions will be held to understand the problem. Then students will be divided into two groups and will try to model the problem mathematically. In this process, students' suggestions for solution will be evaluated, software such as Excel, Maple will be discussed by creating visualizations for solution suggestions of groups and guidance for solution will be provided. At the end of the process, mathematical models created by the groups for the solution of the problem will be discussed in the classroom.


By the end of the lesson all students should be able to:

 

1.        Understands the applications of mathematical concepts in other fields of science.

2.       Makes the solution of linear differential equations for some special values.

  1. Interpret the solution of linear differential equations in accordance with the real-life problem.

 

By the end of the lesson some students should be able to:

 

1.       Express a daily life problem with mathematical concepts such as rate of change, integral factor, linear differential equations.

 

        2. Have the ability to create mathematical models for real life problems.