Code

ΜΥ0204

Category

Compulsory

Semester

2nd Semester

Thematic field(s)

C7-Mathematics - Information Technology

Hours (weakly)

4

ECTS

5

Workload (h)

125

Instructor(s)

**General objectives – General learning outcomes**

- Providing and acquiring knowledge of basic mathematical and statistical principles and concepts, as well as techniques of analytical geometry and geometry of space and their application in solving specific problems in space analysis.
- Acquiring theoretical knowledge of statistical hypothesis testing and basic data analysis methods in conjunction with laboratory application exercises – in particular spatial data – is intended to provide knowledge of specific statistical and data analysis methods both theoretically and in the handling of statistical software.
- Expanding understanding of space and an in-depth understanding of the spatial analysis officer concepts that serve to study space, location and distance.
- Providing students with advanced knowledge of statistical data analysis and in particular their applicability to spatial data.
- Gain basic knowledge of the concepts and methods of Multivariable Function Calculation and their application in solving problems of space and regional economics.

- Acquiring the required background so that the student can meet the requirements of the respective courses of the Department.

**How they specialize in the following categories**

**Knowledges **

Students have assimilated the basic concepts and theories of mathematics and statistics related to the general content of their studies, as shown by the successful final examination.

**Skills**

Students at the end of the course have the ability to apply their knowledge in understanding mathematical and statistical subjects, as well as applying mathematics and statistics to solve real-world problems.

**Abilities**

Concerning the general abilities that students should have acquired in this course, these are as follows:

- Ability to analyze basic problems of space that require quantitative analysis and include mathematical and statistical concepts.
- Ability to approach problems and meet future “challenges” in spatial development.

The general abilities that students should have acquired in the course concerns the development of creative and inductive thinking, through the analysis of mathematical and statistical problems related to the field and the general subject of their studies.

The course provides advanced mathematics and data analysis knowledge in order to obtain the required cognitive supplies from the learners for their use in space analysis and economic analysis problems. In this context, the course content includes the following sections:

*Infinitesimal calculus Elements: Analyzes the concepts of the function of one and many variables, its scope, its graph, boundary, continuity, monotony, and describes the types (linear, exponential, trigonometric), their inverse, as well as basic theorems.**Matrix Calculus Elements: Knowledge of matrix calculus is provided, such as matrix formats (simple, complex, inverse tables, function tables), their operations and properties, a table definition, and expanded by teaching tables with elements of real functions.**Topology Elements: Basic knowledge is provided from a mathematical understanding of the concepts of space, set, topology, metric function and distance, in order to broaden and deepen the corresponding concepts dealt with in Spatial Analysis.**Analytical Geometry Elements: Emphasis is placed on 2D and 3D Euclidean coordinate systems (Cartesian, polar, cylindrical and spherical), on the conversion of coordinates between systems and on finding distances therein, in order to understand and extend the concept and the corresponding problems dealt with in Spatial Analysis.**Vector Calculus: Basic principles of vector algebra (vector dimension, measure, vector angle, internal and external product) are taught, with emphasis on positional properties that practice students’ perceptions of space.**Differential Calculation: Basic principles of calculating functions of one or more variables with emphasis on derivation and partial derivation (derivative by definition, using derivative rules, derivative properties, some derivatives and total differentials).**Integral Calculus: Basic principles of integral calculation of functions of one, two and three variables (definite and indefinite integral of a variable, integration rules, calculation of encompassing area functions, double and triple integrals, volume calculation).**Analysis of the methodology of statistical hypotheses and basic sampling methods such as probability sampling, simple random sampling, stratified sampling and systematic random sampling.*- Regression analysis ie determination of linear regression coefficients, linear regression study, parabolic regression, exponential regression application and multiple regression.
- Analysis of main components ie standardization of the original data matrix, creation of the correlation matrix, finding of the eigenvalues and eigenvectors of the correlation matrix, calculation of the inertia (dispersion) of the point clouds in each of the new factor axes and calculation of the coordinates of the points on the new axes
- Clustering methods, ie hierarchical methods such as the nearest-neighbor method, the Lance and Williams flexible method, and non-hierarchical methods such as the K-Means method. Laboratory exercises and applications in virtual and / or real data will be performed using the statistical data processing software S.P.S.S.

Specified evaluation criteria |
Determination of weight |

Understanding concepts | 25% |

Use of theories and methods | 25% |

Applying theories and methodologies to problems solving | 25% |

Problem-solving speed | 25% |

The evaluation criteria used are linked to the learning outcomes, since the students’ ability to show their knowledge and depth of understanding of the core content of the course is indirectly assessed.

The assessment system and criteria are familiar to the students, and they are considered sufficient to reflect the degree of understanding of the course and in-depth knowledge of its content.

The examination process is assessed indirectly, since students are asked to comment after the exams are over. In addition students can view their writing if they wish and find out what mistakes they have made and to comment on them.

- Μυλωνάς, Ν., Χατζαράκης, Γ., (2016) Εφαρμοσμένα Μαθηματικά, Θεσσαλονίκη, Εκδόσεις Τζιόλα., Εύδοξος [77106816]
- Μυλωνάς, Ν., Σχοινάς, Χ., Παπασχοινόπουλος, Γαρ., (2016) Λογισμός Συναρτήσεων Πολλών Μεταβλητών & Εισαγωγή στις Διαφορικές Εξισώσεις, Θεσσαλονίκη, Εκδόσεις Τζιόλα.
- Πολύζος, Σ., Τσιώτας, Δ. (2017), Εφαρμοσμένα Μαθηματικά, Πανεπιστημιακές Εκδόσεις Θεσσαλίας, Βόλος.
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- 1. Bronson R., Kosta G. (2009), Matrix Methods, Apllied Linear Algebra, Elsevier, N.Y.
- 2. Halmos P. (1995), Linear Algebra Problem Book, Mathematical Association of America, Washington.
- 3. Horn P., Johnson C. (2013), Matrix Analysis, Cambridge, N.Y.
- 4. Kijowski, J., Tulczyjew, W., (1979) A Symplectic Framework for Field Theories, Heidelberg, Springer-Verlag Publications.
- 5. Lancaster P., Tismenetsky M. (1985), The Theory of Matrices, Academic Press, London.
- 6. Lay D. (2012), Linear Algebra and its Applications, Addison-Wesley, N.Y.
- 7. Leon S. (2010), Linear Algebra with Applications, Pearson, Boston.
- 8. Marsden, J., Tromba, A., (2005) Διανυσματικός Λογισμός, Γιαννόπουλος, Α., (επ) Ηράκλειο, Πανεπιστημιακές Εκδόσεις Κρήτης.
- 9. Nicholson W. (1995), Linear Algebra with Applications, PWS Publishing Company, Boston MA.
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- 14. Stein, E., Shakarchi, R., (2011) Functional Analysis, An introduction to further topics in analysis, Princeton, New Jersey, Princeton University Press.
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- Scientific journals: Advances in Mathematics, Econometric Theory , Journal of Physics A , Linear Algebra and its Applications , Operations Research , Studies in Applied Mathematics

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