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) |
Knowledge and ability to apply the interdisciplinary synergetic approach of mechatronics to the solution of engineering problems |
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2) |
Ability to design mechatronic products and systems using the mechatronics approach |
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3) |
Knowledge and ability to analyze and develop existing products or processes with a mechatronics approach |
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4) |
Ability to communicate effectively and teamwork with other disciplines |
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5) |
Understanding of performing engineering in accordance with ethical principles |
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6) |
Understanding of using technology with awareness of local and global socioeconomic impacts |
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7) |
Approach to knowing and fulfilling the necessity of lifelong learning |
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