Part 1: Basic Concepts - Axioms
• Introduction
• Sets and set algebra
• Sample space, events, operations with events
• Probabilistic models, statistical regularity
• Properties of relative frequency
• Mathematical probability, axioms of probability, properties
• Conditional probability and multiplication rule
• Total probability and Bayes' rule
• Independence
• Elements of combinatorial analysis and sampling Part 2: Discrete Random Variables
• Definition of a random variable (r.v.)
• Probability mass function
• Discrete distributions: Uniform, Bernoulli, Binomial, Geometric, Poisson
• Functions of random variables
• Mean, variance, moments
• Multidimensional random variables, joint distributions
• Conditional probability function, multiplication rule, independent random variables Part 3: Continuous Random Variables
• Probability density function
• Cumulative distribution function
• Continuous distributions: Uniform, Exponential, Gaussian
• Multidimensional continuous random variables
• Conditional distributions and conditional moments
• Bayes' rule and signal detection
• Calculating the probability density function of a function g(X) of the random variable X
• Covariance and correlation coefficient Part 4: Limit Theorems
• Moment generating functions
• The weak law of large numbers
• The central limit theorem
• Basic concepts of stochastic processes
Learning Outcomes
Knowledge: Having attended and successfully completed the course, the student has acquired a comprehensive mathematical foundation in Probability Theory, which is essential for the analysis and study of random phenomena and is one of the key components of Data Science. Understanding: Having attended and successfully completed the course, the student has understood the fundamental concepts of probabilities (probabilistic laws, conditional probability, multiplication rule, total probability, Bayes' theorem, independence), as well as discrete and continuous random variables and distributions. Application: Having attended and successfully completed the course, the student is capable of understanding and applying innovative techniques to practical problems in detection, classification, and decision-making across various engineering fields such as data analysis, acoustics, biomedical engineering, satellite remote sensing, telecommunications, image, sound, and video analysis, and astrophysics. Analysis: Having attended and successfully completed the course, the student is capable of performing probabilistic analysis and modeling of data originating from various sources (scientific instruments, social networks, economic measurements, etc.). Synthesis: Having attended and successfully completed the course, the student is capable of integrating data processing techniques and designing statistical methods based on probabilistic models to extract information from scientific measurements. Evaluation: Having attended and successfully completed the course, the student is capable of attending advanced data analysis courses, comparing the performance of different signal processing methods using measurable performance criteria, and evaluating the efficiency of state-of-the-art algorithms.
Student Performance Evaluation
Specific details on grading can be found on the course’ s website
The courses of the Computer Science Department are designated with the letters "CS" followed by three decimal digits. The first digit denotes the year of study during which students are expected to enroll in the course; the second digit denotes the area of computer science to which the course belongs.
First Digit
Advised Year of Enrollment
1,2,3,4
First, Second, Third and Fourth year
5,6
Graduate courses
7,8,9
Specialized topics
Second Digit
Computer Science Area
0
Introductory - General
1
Background (Mathematics, Physics)
2
Hardware Systems
3
Networks and Telecommunication
4,5
Software Systems
6
Information Systems
7
Computer Vision and Robotics
8
Algorithms and Theory of Computation
9
Special Projects
The following pages contain tables (one for each course category) summarizing courses offered by the undergraduate studies program of the Computer Science Department at the University of Crete. Courses with code-names beginning with "MATH" or "PHYS" are taught by the Mathematics Department and Physics Department respectively at the University of Crete.
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