## Available courses

- Teacher: Elske Ammenwerth
- Teacher: Ivan Chorbev
- Teacher: Renate Nantschev
- Teacher: Konstantinos Petridis

**Course program goals (competencies):**

In this course you will learn the concepts and methods of linear algebra, and how to use them to think about problems arising in computer science

**Course program content:**

Linear geometry: Vectors in R2 and R3, dot product, angel between two vectors, cross product in R3, lines and planes and applications. Linear equations and matrices: Matrix operations and properties, special types of matrices, transpose of a matrix symmetric matrices, diagonal matrices, inverse of a matrix. Solution of system of linear equations: Gaussian elimination, geometric interpretation of solution set. Elimination with matrices: elementary matrices, elimination and permutation matrices. LU – factorization. Reduced echelon form of a matrix. Real vector spaces: Definition of a vector spaces and subspaces, linear independence, basis and dimension of a vector space. Vector spaces and homogeneous systems, rank of a matrix and applications. Coordinates and change of basis. Applications. Orthogonal basis in Rn and orthogonal complement. Linear transformations, definition and examples. The kernel and range of a linear transformation, The matrix of a linear transformation. Orthogonal projection and applications. Determinants and properties. Eigenvalues and eigenvectors, diagonalization, diagonalization of symmetric matrices and applications. SV decomposition of matrices.

- Teacher: Ivan Chorbev
- Teacher: Vesna Dimitrova
- Teacher: Alexandra Mitrovikj

**Course program goals (competencies):**

This course is a support course that is essential for introducing the terms of a function, limits, derivate and integrals. These terms are important for almost all courses in the following years.

**Course program content:**

(1) Function definition. Function properties. Operations with functions. (2) Lines. Families of functions. (1) Limits. Computing limits. Continuity. (2) Definition of derivative. Techniques of differentiation. Derivative of a composite function. (1) L'Hôpital's rule. (1) Application of derivatives: monotonicity of functions, concave and convex functions, relative extrema. (1) Analysis of properties and sketching the graph of a function. Absolute extrema. (1) Integration: indefinite integral, integration by substitution. (1) Definite integral. Fundamental theorem of calculus

- Teacher: Ivan Chorbev
- Teacher: Vesna Dimitrova
- Teacher: Alexandra Mitrovikj

**Abstract: **

**Learning Outcomes:**

- Teacher: Maria Zakinthinaki

**An Abstract:** Randomness, finite probability space, probability measure, events; conditional probability, independence, Bayes’ theorem; discrete random variables; binomial and Poisson distributions; concepts of mean and variance; continuous random variables; exponential and normal distribution, probability density functions, calculation of mean and variance; central limit theorem and the implications for the normal distribution; purpose and the nature of sampling; nature of estimates, point estimates, interval estimates; maximum likelihood principle approach, least-squares approach; confidence intervals; estimates for one or two samples; development of models and associated hypotheses; nature of hypothesis formulation, null and alternate hypotheses, testing hypotheses; criteria for acceptance of hypothesis t-test, chi-squared test; correlation and regression.

**Learning Outcomes:**

Successful completion of the course, students will be able to:

**•** Use basic counting techniques (multiplication rule, combinations, permutations) to compute probability and odds.

• Use R to run basic simulations of probabilistic scenarios.

• Compute conditional probabilities directly and using Bayes' theorem, and check for independence of events.

• Set up and work with discrete random variables. In particular, understand the Bernoulli, binomial, geometric and Poisson distributions.

• Work with continuous randam variables. In particular, know the properties of uniform, normal and exponential distributions.

• Know what expectation and variance mean and be able to compute them.

• Use available resources (the internet or books) to learn about and use other distributions as they arise.

• Create and interpret scatter plots and histograms.

• Understand the difference between probability and likelihood functions, and find the maximum likelihood estimate for a model parameter.

• Use null hypothesis significance testing (NHST) to test the significance of results, and understand and compute the p-value for these tests.

• Use specific significance tests including, z-test, t-test (one and two sample), chi-squared test.

• Find confidence intervals for parameter estimates.

• Compute and interpret simple linear regression between two variables

** **

- Teacher: Faton Merovci

**Abstract: **A course designed to prepare computer science for a background in abstraction, notation, and critical thinking for the mathematics most directly related to computer science. Topics include: logic, set theory, relations, functions, Induction, and Recursion. Countability and counting arguments. Graphs. Trees. Boolean Algebra. Modeling Computations. Languages recognitions. Turing Machine. Basic meanings of codification theory

**Learning Outcomes: **

Upon Successful completion of the course, students will be able to:

• understand and construct mathematical arguments using logical connectives and quantifiers.

• verify the correctness of an argument using propositional and predicate logic and truth tables.

• develop recursive algorithms based on mathematical induction

• know the basic properties of relations

• solve problems using counting techniques and combinatorics

• use graphs and trees as tools to visualize and simplify situations.

• understand basic concepts in formal languages and computability

• apply knowledge about discrete mathematics in problem-solving

- Teacher: Faton Merovci

The student should be able to apply the knowledge gained through this course as an auxiliary device in the studies of electrical engineering and computer engineering subjects

The learning outcomes of the course are:

- Understand the concept of indefinite and definite integral as well as their application in the measurement of various measures in Geometry, Electrotechnics, Telecommunication, Informatics and other fields;
- Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
- Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions, and integration by parts.
- Generalize concepts related to functions with one variable into multivariable functions and in particular into those with two variables. Also, be able to apply every concept related to the differential calculation for the one variable function in the case of two-variable functions;
- Sketch a slope field of a differential equation and find a particular solution
- Use an exponential function to model growth and decay
- Use separation of variables to solve a differential equation
- Think logically about various differential equations; solve concrete examples step by step and model different practical problems through differential equations.

- Teacher: Isak Shabani

Students should be trained so that the knowledge gained through this course can be applied as a supplementary tool in electrical and computer engineering studies.

The learning outcomes of the course are:

- Describe, solve and design various problems in the field of his profession when dealing with complex number operations, through matrices and determinants;
- Describe and solve problems related to systems of linear equations;
- Find the functional connections of the magnitudes of various electrical problems and then with differential calculations, describe and examine those functional connections;
- Understand the concept of the derivative and is able to apply it to many problems in Geometry, Electronics, Telecommunication, Informatics and other areas;
- Sketch the graph of a function using asymptotes, critical points, the derivatives test for increasing/decreasing functions, and concavity.
- Apply differentiation to solve applied max/min problems.
- Apply differentiation to solve related rates problems.

- Teacher: Isak Shabani

This is the 1st Course in Mathematics the 1st year students of the ULL follows.

The envisioned learning outcomes are the following:

- Provide a wider panoramic view of resources available for the use of ICTs at math classrooms.
- Deduce strategies and examples for the use of ICTs in teaching and problem-solving.
- Identify good practices and initiatives on innovation in maths teaching by using ICT.

- Teacher: Rodrigo Gonzalez

This is the Calculus I modules as runs in the University of Mitrovica. Prof. Faton Merovci is the teacher and the module also exists in a local installed Moodle Platform (http://213.163.104.219/moodle/)

**Course Description**

Functions of Single Variable, Limit, and Continuity, Differentiation of Functions. Derivative as Slope of Tangent to a Curve and as Rate of Change, Application to Tangent and Normal, Linearization, Maxima/Minima and Point of Inflexion, Taylor and Maclaurin Expansions and their convergence. Integral as Anti-derivative, Indefinite Integration of Simple Functions. Methods of Integration: Integration by Substitution, by Parts, and by Partial Fractions, Definite Integral as Limit of a Sum, Application to Area, Arc Length, Volume and Surface of Revolution. function of several real variables. Differential Equations. First-order and second-order differential equations

**Objectives of the Course**

The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of one variable

**Learning Outcomes**

Upon successful completion of the course, students will be able to:

•Use both the limit definition and rules of differentiation to differentiate functions.

•Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.

•Apply differentiation to solve applied max/min problems.

•Apply differentiation to solve related rates problems.

•Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.

•Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.

•Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions, and integration by parts.

•Use L'Hospital's rule to evaluate certain indefinite forms.

•Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.

•Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.

•Sketch a slope field of a differential equation and find a particular solution

•Use an exponential function to model growth and decay

•Use separation of variables to solve a differential equation

- Teacher: Faton Merovci

This is the module in Mathematics I that mainly deals with Linear Algebra. The module is run using the iTEM principles and tools of the iTEM project

**Course Description: **Mathematical Logic. Sets of Real and Complex Numbers. Matrices, operation with matrices and some special type of matrices. Vector spaces and subspaces, linear independence, bases, and dimension. Determinants and their properties. Linear Equation Systems and Their Solutions using Cramer’s Method, Gauss elimination method and inverse matrix. Vector algebra. Equations of Lines and Planes in Space. Relative Positions of Lines and Planes. Distances Between Points, Lines, and Planes. Quadratic surfaces

**Objectives of the Course: **

**•**to provide students with a good understanding of the concepts and methods of linear algebra, described in detail in the syllabus.

•to help the students develop the ability to solve problems using linear algebra.

•to connect linear algebra to other fields both within and without mathematics.

•to develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to linear algebra

**Learning Outcomes**

Upon successful completion of the course, students will be able to:

•Analyze arguments via the rules of logic.

•Formulate mathematical proofs by using the rules of logic.

•Perform operations with complex numbers.

•Perform basic matrix operations.

•Use Gaussian elimination to solve systems of linear equations.

•Find the determinant of square matrices.

•Find the cofactor matrix and use it to find the inverse of a matrix.

•Solve a system of equations by making use of determinant.

•Define a vector and perform basic vector operations (addition, scalar multiplication, length of a vector).

•Find the dot product and cross-product of two vectors.

•Give geometrical applications of the dot product of 3-dimensional vectors.

•Find the symmetric and parametric equations of a line.

•Find distance between skew lines.

•Find the equation of a plane and the distance between a point and a plane.

It can be found as well in a local run Moodle platform in the University of Mitrovica by Prof. Faton Merovci. Please check the link: http://213.163.104.219/moodle/

- Teacher: Faton Merovci

This is a first-year mathematics module in the Department of Electronic Engineering of the Hellenic Mediterranean University (ex. Technological Educational Institute of Crete).

The module offers fundamental knowledge to basic functions, trigonometry, complex numbers, vectors, differentiation, integration, and matrices. The module on the frame of the iTEM will be enriched with (a) real-life problems that can be linked with the taught terms; (b) frequent assessment tests; (c) pre-calculus modules for those that need to review prior knowledge

- Teacher: Evangelos Kokkinos
- Teacher: Konstantinos Petridis
- Teacher: Maria Zakinthinaki

*This intensive course envisions to provide an introduction to the participants about the (a) principles of the Problem Based Learning (PBL)& Project-oriented Based Learning Teaching techniques, and (b) learn how to apply them.*

*The participants should study prior to the event follow the suggested modules, which include both reading and learning activities. During the event, the participants will participate in group hand-ons activities with the aim to apply their knowledge on PBL to locally run modules in Calculus I and Linear Algebra I. During these activities, t**he participants will be guided by PBL experts and will have the opportunity to discuss their developed scenarios with the other participants. *

- Teacher: Christie Anne Jeannine Laurent
- Teacher: Olga Timcenko
- Teacher: Evangelia Triantafilou

This is a pilot Module in Linear Algebra I. Its curriculum extracted after studying the respective modules within the iTEM consortium. Inputs have been accepted also from successful courses in top Math Schools in the world

All the real-life problems, frequent testing exercises and simulations will be integrated into this module.

Any stakeholder can use it as he or she wishes.

- Teacher: Elske Ammenwerth
- Teacher: Sadullaev Azimbay
- Teacher: Laure Barthel
- Teacher: Armend Berisha
- Teacher: Mirela Bernhoff
- Teacher: Ivan Chorbev
- Teacher: Vesna Dimitrova
- Teacher: Alibek Eshev
- Teacher: Eva Feuerstein
- Teacher: Eva Feuerstein
- Teacher: Rodrigo Gonzalez
- Teacher: Nissim Harel
- Teacher: Javlon Karimov
- Teacher: Ronnie Karsenty
- Teacher: Boris Koichu
- Teacher: Evangelos Kokkinos
- Teacher: Renate Nantschev
- Teacher: Isak Shabani
- Teacher: Evangelia Triantafilou
- Teacher: Nargiza Usmanova
- Teacher: Maria Zakinthinaki

This course **has been build as a result of the curricula of the respective courses** in the iTEM test Institutions (HMU, FINKI, NUUz, TUIT, HAC, HIT, UC, UoP, UoM, KEEI)

It will work as **a pilot module** where all the proposed examples from other sciences and real life. Moreover, the frequent test quizzes will be first integrated within this module.

- Teacher: Rodrigo Gonzalez

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