Probability Theory (PRO) Syllabus

Fall Semester, Academic Year 2008-2009

**T 10:30 - 11:15am, W 10:15am - 12:00, Room 104**

**Office hour: T 11:15am - 12:00, Room 104**

Márton Balázs | ||

Email: | balazs@math.bme.hu | |

Tel: | 463 1111, ext. 5904 | |

Office outside BSM: | Budapest University of Technology and Economics (BME) | |

(just in case) | Office 3a, fifth floor, Building H, 1 Egry József u., 1111 Budapest | |

Text is: | A First Course in Probability, Seventh Edition by S. Ross | |

Final Exam: | 2:15pm, Thursday December 11, room 105. |

**Prerequisite:** A calculus sequence.

**Course Description:** This is a first course on the mathematical phenomenon of uncertainty and techniques used to handle them. Not only being challenging itself, this field is of increasing interest in many areas of engineering, economical, physical, biological and sociological sciences as well. In this course we cover the basic notions and methods of probability theory, also giving emphasize on examples, applications and problem solving. Briefly, the topics include probability in discrete sample spaces, methods of enumeration (combinatorics), conditional probability and independence, random variables, properties of expectations, the Weak Law of Large Numbers, and the Central Limit Theorem. A detailed course schedule can be downloaded from here.

Probability is a conceptually difficult field, although it might seem easy and straightforward at first. One has to distinguish between very different mathematical objects, and find their connection to real-life situations within the same problem. Therefore it is very important to follow classes and deeply understand the material during the semester.

**Grading and assignments:** There will be two in-class exams, weekly homeworks to be handed in during the semester, and a final exam.

**The in-class exams**are on**Tuesdays October 7 and November 18, at 10:30am**.**Please let me know immediately if later you will have a conflict with these dates.**The first exam will be on Chapters 1, 2 and 3, the second one will be on Chapters 4, 5 and 6.**Each**worth**160 points**(each 20% of the total possible points).Weekly

**homework sets**will be assigned during the semester, they can be downloaded from here. Please notice their due dates.**Each**worth**20 points**, but the worst one will be dropped. In this way, a**total**of**240 points**(30% of the total possible points) can be earned from these assignments. Solving the homework problems by no means guarantees that you have the necessary level of practice. Please do other exercises (and check the answers in the back of the book*after*solving them) until you feel safe with problems on the topics in question.**The final exam**is at**10:15am, Tuesday December 16**. Half of it will cover Chapters 1 to 6, the other half is on Chapters 7 and 8 of the book. It worth**240 points**(30 % of the total possible points).**Bonus questions**are also to be found in the homework sets. While a total of 800 points can be earned by the exams and homeworks, an additional**4 points**can be given for a solution of each bonus problem.

Grades will be based on the total of 800 points approximating the following standards:

Grade | Points |
---|---|

A^{+} | ≥775 |

A | ∈[745, 775) |

A^{-} | ∈[720, 745) |

B^{+} | ∈[695, 720) |

B | ∈[665, 695) |

B^{-} | ∈[640, 665) |

C^{+} | ∈[615, 640) |

C | ∈[585, 615) |

C^{-} | ∈[560, 585) |

D | ∈[480, 560) |

F | <480 |

Because of this standard, you are not in competition with your classmates nor does their performance influence positively or negatively your performance. You are encouraged to form study/problem groups with your classmates; things not clear to you may become obvious when you try to explain them to others or when you hear other points of view. Sometimes just verbalizing your mathematical thoughts can deepen your understanding. However, if you discuss with others the exercises, each person should write up her/his own version of the solution. Please note that much less can be learned by just understanding and writing up someone else's solution than by coming up (or even just trying to come up) with original ideas and solving the problem.

**Please feel free to contact me** any time outside class via e-mail, phone, or in person if you have questions or suggestions about this course.

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