Course Objectives: |
The aim of the course is to gain basic knowledge and abilities to the students about Combinatorial methods; product rule, permutation, combination. Probability; probability axioms, conditional probability, Bayes formula. Random variable; distribution function, probability function, Chebyshev inequality. Discrete and continuous distributions; uniform, Bernoulli, Poisson, geometric, hypergeometric, normal, exponential, gamma and beta distributions. Generating functions. |
Course Content: |
Combinatorial methods; product rule, permutation, combination. Probability; probability axioms, conditional probability, Bayes formula. Random variable; distribution function, probability function, Chebyshev inequality. Discrete and continuous distributions; uniform, Bernoulli, Poisson, geometric, hypergeometric, normal, exponential, gamma and beta distributions. Generating functions. |
Week |
Subject |
Related Preparation |
1) |
Discrete Random Variables
Continuous & General Random Variables
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Read the relevant section of the textbook.
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2) |
Random Vectors
Function of Random Variables
Expectation, Variance, Conditional Expectation
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Read the relevant section of the textbook. |
3) |
Bounds: Jensen, Markov, Chebyshev, Chernoff
Law of Large Numbers, Central Limit Theorem
Random Graphs
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Read the relevant section of the textbook. |
4) |
**Mini-Lab**: Introduction to Python, Phase Transitions in Random Graphs, Auctions
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Read the relevant section of the textbook. |
5) |
Discrete-Time Markov Chains (e.g., PageRank)
Law of Large Numbers for Markov Chains
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Read the relevant section of the textbook. |
6) |
Poisson Process
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Read the relevant section of the textbook. |
7) |
Continuous-Time Markov Chains & Queues
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Read the relevant section of the textbook.
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8) |
**Mini-Lab & Project**: Search Engines (PageRank), Digital Communication, Markov Decision Processes (e.g., Settlers of Catan)
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Read the relevant section of the textbook.
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9) |
Statistical Inference
Hypothesis Testing
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Read the relevant section of the textbook.
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10) |
Maximum Likelihood Estimation
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Read the relevant section of the textbook.
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11) |
Bayesian Inference
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Read the relevant section of the textbook.
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12) |
Confidence Intervals
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Read the relevant section of the textbook.
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13) |
**Mini-Lab & Project**: Real-world applications (e.g., Signal Processing, Communication Systems)
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Read the relevant section of the textbook.
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14) |
Review |
Review |
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Program Outcomes |
Level of Contribution |
1) |
Reaches the information in the field of power electronics and clean energy systems in depth through scientific researches; evaluates the knowledge, interprets and implements. |
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2) |
Has the extensive information about current techniques and their constraints in the field of Power Electronics . |
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3) |
Using limited or missing data, completes the information through scientific methods and applies; integrates the information from different disciplines. |
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4) |
Aware of new and emerging applications of his/her profession; learn and examine them if needed. |
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5) |
Builds the Power Electronics problems, develops methods to solve and implements innovative ways for solution. |
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6) |
Develops new and/or original ideas and methods; develops innovative solutions for the design of a process, system or component. |
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7) |
Designs and implements the analytical, modeling and experimental-based researches; resolves the complex situations encountered in this process and interprets. |
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8) |
Leads multi-disciplinary teams, develops solution approaches to complex situations and takes responsibility. |
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9) |
Uses at least one foreign language at the general level of European Language Portfolio B2 and communicates effectively in oral and written language. |
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10) |
Presents the process and results of the work in national and international media systematically and clearly in written or oral language. |
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11) |
Describe the social and environmental dimensions of Power Electronics Engineering applications. |
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12) |
In the stages of data collection, interpretation and publication as well as all professional activities, he/she considers the social, scientific and ethical values. |
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