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) |
By carrying out scientific research in their field, graduates evaluate and interpret deeply and broadly, their findings and apply their findings. |
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2) |
Graduates have extensive knowledge about current techniques and methods applied in engineering and their limitations. |
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3) |
Graduates can complet and implement knowledge using scientific methods using limited or incomplete data; can use the information of different disciplines together. |
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4) |
Graduates are aware of new and evolving practices of their profession, examinining new knowledge and learning as necessary |
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5) |
Graduates can define and formulate problems related to the field, develop methods to solve them and apply innovative methods in solutions. |
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6) |
Graduates develop new and/or original ideas and methods; design complex systems or processes and develop innovative / alternative solutions in their designs. |
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7) |
Graduates design and apply theoretical, experimental and model-based research; analyze and investigate the complex problems encountered in this process. |
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8) |
Lead in multidisciplinary teams, develop solution approaches in complex situations, work independently and take responsibility. |
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9) |
A foreign language communicates verbally and in writing using at least the European Language Portfolio B2 General Level. |
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10) |
Transfers the processes and outcomes of their work in a systematic and explicit manner, either written or verbally, in the national or international contexts of that area. |
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11) |
Recognize the social, environmental, health, safety, legal aspects of engineering applications, as well as project management and business life practices, and are aware of the limitations they place on engineering applications. |
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12) |
Consider social, scientific and ethical values in the collection, interpretation, announcement of data and in all professional activities. |
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