# Matematica | INFORMATION THEORY

## Matematica INFORMATION THEORY

 0522200052 DIPARTIMENTO DI MATEMATICA EQF7 MATHEMATICS 2022/2023

 YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY INF/01 6 48 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 UGO VACCARO T
ExamDate
TEORIA DELL'INFORMAZIONE12/06/2023 - 09:00
TEORIA DELL'INFORMAZIONE03/07/2023 - 09:00
Objectives
THE MAIN OBJECTIVE OF THE COURSE IS TO SHOW
HOW THE CONCEPTS AND BASIC RESULTS OF INFORMATION THEORY CAN
TO CONTRIBUTE TO THE EFFICIENT RESOLUTION OF BASIC PROBLEMS THAT ARISE
IN VARIOUS FIELDS OF APPLIED AND PURE SCIENCES.

KNOWLEDGE AND UNDERSTANDING:
-KNOWLEDGE OF THE MOST USED QUANTITATIVE INFORMATION MEASURES;
-KNOWLEDGE OF THE MOST USED MEASURES OF INFORMATIONAL THEORETICAL DISTANCES;
-KNOWLEDGE OF BASIC METHODS FOR INFORMATION COMPRESSION;
-KNOWLEDGE OF THE BASIC METHODS FOR PROTECTING INFORMATION FROM OPPONENTS;
-KNOWLEDGE OF BASIC METHODS FOR PROTECTING INFORMATION AGAINST ERRORS.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
-CAPACITY TO ABSTRACT INFORMATION THEORETIC FORMAL MODELS FROM CONCRETE PROBLEM AND TO DESIGN FOR THEM EFFICIENT SOLUTIONS;
- ABILITY TO DESIGN DATA COMPRESSION ALGORITHMS;
- ABILITY TO DESIGN ALGORITHMS FOR THE PROTECTION OF INFORMATION;

INTERDISCIPLINARY COMPETENCES:
STUDENTS WILL ACQUIRY THE CAPABILITY OF SOLVING PROBLEMS ARISING IN ALGORITHMICS, MACHINE LEARNING, STATISTICAL PREDICTION, DATA SECURITY, BY USING INFORMATION THEORETIC TOOLS
Prerequisites
STUDENTS ARE REQUIRED TO HAVE ALREADY DEVELOPPED BASIC CAPABILITIES OF FORMAL DEDUCTIVE REASONING. STUDENTS ARE ALSO REQUIRED TO MASTER THE BASIC CONCEPTS OF AN INTRODUCTIVE CLAS IN PROBABILITY AND LINEAR ALGEBRA.
Contents
PART 0. BASIC INFORMATION THEORETIC CONCEPTS: ENTROPY, MUTUAL INFORMATION, THEIR MATHEMATICAL PROPERTIES, RELATIONS, AND MEANING.

PART 1. INFORMATION THEORY AND DATA SECURITY: SECRET SHARING, THEIR INFORMATION THEORETIC ANALYSIS AND RELATIVE ALGORITHMS; KEY DISTRIBUTIONS, THEIR INFORMATION THEORETIC ANALYSIS AND RELATIVE ALGORITHMS;

PART 3. INFORMATION THEORY AND DATA COMPRESSION: FUNDAMENTAL LIMITATIONS TO DATA COMPRESSION;ALGORITHMS FOR DATA COMPRESSION (LEMPEL &ZIV, ARITHMETIC ENCODING ...)

PART 3. INFORMATION THEORY IN FINANCE END ECONOMETRICS: OPTIMAL PORTFOLIO ALLOCATION VIA INFORMATION THEORETICAL TECHNIQUES, MEASURES OF ECONOMICAL INEQUALITY, ABSOLUTE AND RELATIVE; INFORMATION THEORETICAL ANALYSIS OF BETTING SCHEMATA.

PART 4. INFORMATION THEORY AND STATISTICS: INOFRMATION THEORETIC METHODS IN HYPOTHESIS TESTING.

PART 5. ERROR DATA PROTECTION. BASICS OF ALGEBRAIC ERROR CORRECTING CODES.
Teaching Methods
THE COURSE INCLUDES 32 HOURS OF THEORETICAL LESSONS AIMED AT LEARNING THE BASIC TECHNIQUES OF INFORMATION THEORY, AND 16 HOURS OF EXERCISES IN WHICH WE WILL ILLUSTRATE HOW TO DESIGN AND ANALYZE DATA COMPRESSION ALGORITHMS, HOW TO DESIGN AND ANALYZE ALGORITHMS FOR THE DATA SECURITY AND HOW TO DESIGN AND ANALYZE ALGORITHMS FOR ERROR CORRECTION.
Verification of learning
THE EXAMINATION TEST IS AIMED TO EVALUATE THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN THE LESSONS.
THE VERIFICATION AND EVALUATION OF THE LEARNING LEVEL OF THE STUDENT WILL BE VIA A FINAL EXAM, CONSISTING OF AN ORAL TEST. IN THIS TEST, THE
STUDENT IS REQUIRED TO ILLUSTRATE THE MAIN INFORMATION THEORETIC CONCEPTS PRESENTED DURING THE COURSE, AND THE APPLICATION OF THESE CONCEPTS TO CONCRETE EXAMPLES IN THE AREAS OF DATA COMPRESSION, DATA SECURITY AND ERROR CORRECTION.
Texts
1. THOMAS M. COVER, JOY A. THOMAS, ELEMENTS OF INFORMATION THEORY (2ND EDITION), WILEY-INTERSCIENCE.
2. ROBERT J. MCELIECE, THE THEORY OF INFORMATION AND CODING, CAMBRIDGE UNIVERSITY PRESS
3. NOTES PROVIDED BY THE TEACHER.