Applied mathematics & statistics

Lesson Code: 2.3

Semester: 2nd Semester

Category: Compulsory

Hours: 2h Theory + 2h Lab

ECTS credits: 5

 

LEARNING RESULTS

After completing the course, students are expected to:

• Understand basic concepts and principles of mathematics and apply them in solving exercises and problems related to the field of oenology
• Cultivate and strengthen their critical and analytical thinking through the verification of results
• Utilize their knowledge both in their professional field and in wider applications of Biostatistics, which are necessary in the context of the study of nutrition, health and well-being life problems

 

General Skills

• Search, analysis and synthesis of data and information, also using the necessary technologies
• Group & independent work
• Generating new research ideas
• Project planning and management
• Work in an interdisciplinary environment

 

COURSE CONTENT

Theoretical part

1. Elements of vector calculus: definition and properties of vectors, products of vectors, applications
2. Linear algebra: matrix definition, matrix algebra, determinants, Systems of Linear Equations
3. Functions: function of a real variable definition, classes of functions, periodic function, graph, Limit value and continuity of a function: definitions, basic theorems, applications
4. Derivative of a function: definition, lateral derivatives, geometric meaning, higher order derivatives, differential of a function, rules of differentiation
5. Integral: definite integral, properties, antiderivative, indefinite integral, integrals of basic functions, applications of integrals
6. Differential equations: definition, elements, form and categories of differential equations, 1st order differential equation with constant coefficients.

 

Laboratory Part

The laboratory part of the course includes laboratory exercises referred to in Statistics, they will be carried out in a computer laboratory equipped with special software, they will be accompanied by relevant theory and will include the Laboratory thematic units:

1. In descriptive statistics
2. In the presentation of results
3. Confidence Intervals
4. In Hypothesis Testing (t-test, Case of independent samples)
5. In Case Control (Case of non-independent samples)
6. In the Control of Cases (percentages)
7. In non-parametric procedures (chi-square – Kruskal-Wallis, etc.)
8. Non-Parametric Procedures (Case of independent samples – Mann-Whitney or Wilcoxon test etc.)
9. In the Analysis of Variance (ANOVA, MANCOVA etc.)
10. In Linear Regression
11. In Accounting Regression

 

RECOMMENDED BIBLIOGRAPHY

APPLIED MATHEMATICS

1. Καρτσακλής A., Γενικά Μαθηματικά, 2005, Πανεπιστημιακές Εκδόσεις Αράκυνθος, ISBN: 960- 91034-3-X
2. Μπράτσου, Α., Ανώτερα Μαθηματικά, Εκδόσεις Α. Σταμούλη, Αθήνα 2003, ISBN 9603514535.
3. Thomas, G. και Russel, Ι., Απειροστικός Λογισμός 1-11, Πανεπιστημιακές Εκδόσεις Κρήτης, 2004, ISBN 9605241838 – 9605241846
4. Murray R. Spiegel, Ανώτερα Μαθηματικά, Schaum’s Outline Series 1982, ΕΣΠΙ, ISBN 070602298.
5. Frank Ayres, Jr., Γενικά Μαθηματικά, Schaum’s Outline Series, ΕΣΠΙ, Αθήνα 1983, ISBN 0700226531.
6. O’ Neil, P., Advanced Engineering Mathematics, International ed, Cengage Learning, 2006
7. Weir M, Hass J., Giordano Thomas’ Calculus 11th edition Pearson, Addison Wesley 2005

STATISTICS

1. Παπαγεωργίου Έφη (2017).Βιοστατιστική και Εφαρμογές, 2η Έκδοση, ΕΚΔΟΣΕΙΣ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΜΟΝ. ΕΠΕ.
2. Παπαγεωργίου Έφη (2015).Βιοστατιστική και Εφαρμογές, ΕΚΔΟΣΕΙΣ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΜΟΝ. ΕΠΕ.
3. Τριχόπουλος Δ, Τζώνου Α, Κατσουγιάννη Κ. (2000) Βιοστατιστική. Εκδόσεις Παρισιάνος. Αθήνα.
4. Τζώνου Α, Κατσουγιάννη Κ. (1997) Ασκήσεις Βιοστατιστικής. Εκδόσεις Αθανασοπούλου- Σ.Αθανασόπουλος Ο.Ε. Αθήνα, 1997.
5. PetrieAviva,SabinCaroline, (2008) Ιατρική Στατιστική με μια ματιά. Εκδόσεις Παρισιάνος. Αθήνα.
6. PaganoMarcello, GauvreauKimberlee (2002) Αρχές Βιοστατιστικής Γ.ΠΑΡΙΚΟΣ & ΣΙΑ ΕΕ.
7. Κατσουγιαννόπουλος Βασίλειος, (2009) Βασική Ιατρική στατιστική ΕΚΔΟΤΙΚΟΣ ΟΙΚΟΣ ΑΔΕΛΦΩΝ ΚΥΡΙΑΚΙΔΗ Α.Ε.
8. Σταυρινός Βασίλης Γ., Παναγιωτάκος Δημοσθένης Β. Βιοστατιστική, Εκδόσεις Γ. Δαρδάνος – Κ. Δαρδάνος Ο.Ε.
9. Bland (1995): An Introduction to Medical Statistics. Second Edition. Oxford University Press.
10. H. Katz (1999): Multivariable Analysis. A Practical Guide for Clinicians. Cambridge University Press.
11. D. Fisher and G. van Belle (1993): Biostatistics – Methodology for the Health Sciences. Wiley, New York.
12. Holm (1979): A Simple Sequentially Rejective Multiple Test Procedure. Scandinavian Journal of Statistics, 6, 65-70.
13. C. Hsu (1996): Multiple Comparisons. Theory and methods. Chapman and Hall