Week |
Subject |
Related Preparation |
1) |
Review of probability, conditional probabilities and expectations. |
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2) |
Basic ideas about stochastic processes. Discrete time Markov chains, transition probabilities, classification of states, limiting probabilities. |
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3) |
Applications of Markov Chains, branching processes and Markov decision processes. |
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4) |
The exponential distribution and the Poisson process. Interrarival and waiting time distributions, nonhomogeneous and compound Poisson processes. |
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5) |
Continuous time Markov chains, birth and death processes, the Kolmogorov differential equations. |
|
6) |
Limiting probabilities, time reversibility. Examples. |
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7) |
Renewal theory and its applications. |
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8) |
Martingales; definition, examples, the Optional Sampling Theorem and its applications. |
|
9) |
Brownian motion, hitting times, the Gambler's ruin problem. |
|
10) |
Geometric brownian motion and its application to finance. Pricing stock options, the arbitrage theorem. |
|
11) |
The Black Scholes option pricing formula, gaussian processes. |
|
12) |
Stationary and diffusion processes, examples. |
|
13) |
The Ito Stochastic integral and the Ito formula and other stochastic integrals. |
|
14) |
Monte Carlo Simulation. |
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other. |
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
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3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
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4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
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6) |
Ability to use mathematical knowledge in technology. |
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7) |
To apply mathematical principles to real world problems. |
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8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
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10) |
To apply mathematical principles to real world problems. |
|
11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
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12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
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