Learning Mathematics Through Real-World Applications SYLLABUS AN INTRODUCTION TO Probability and Statistics MAT 134, ID3345/ MAT 133, ID3346 FALL 2014 Lecturers: Elmira Musuraliyeva, Professor, elmiratm@mail.auca.kg Enver Atamanov, Acting Professor, sevenver@mail.ru Class meetings: classes per week, 15 working weeks Consultations: according to faculty schedules Office: 314/1, phone:… Course description: When a weather forecaster predicts the weather, when a coach evaluates the team’s chances of winning, or when a businessperson projects the success of the big clearance sale, an element of uncertainty exists Often in our daily lives we would like to measure the likelihood of an event or of an outcome of an activity This course will introduce you to basic theory of probability tools with applications in the social sciences and business The course consists of the following themes: counting techniques; basic probability concepts and theorems; discrete and continuous probability distributions; statistical inference and sampling, the central limit theorem, statistical conclusions for the normal distribution Prerequisites: secondary school mathematics Textbooks: W.H Freeman and Company, New York For All Practical Purposes: Mathematical Literacy in Today's World 2009 Alan H Kvanli Introduction to business statistics.1989 Mario Triola Elementary statistics 2002 Alan Hoenig Applied finite mathematics 1986 Amir D Azel Complete Business Statistics 1986 Lawrence L Lapin Statistics for modern business 1978 Howard L Rolf Finite mathematics Baylor University Inc 2005 All materials are presented on electronic resource of AUCA: H:\Courses Information Support\Natural Sciences and Information Technologies\MAT 228 An Introduction to Contemporary Mathematics II Objectives: The primary objectives of this course are: students will focus on basic theory of probability and discuss statistical analysis techniques for applications in social problem solving, to develop abstract and logical (probative) thinking, to appreciate the value of further mathematical study for the major Expected outcomes: After completing MAT … the student will be able: to use a general principle of counting, the multiplication principle, permutations, combinations; to understand the relationship between a question that arises in the natural, computer, and social sciences and the numerical data that are needed in order to provide an answer to the question; to formulate the question in a mathematical context, set up the required mathematical procedure and carry out the required calculations, appropriately using a calculator, to answer questions to use a general principles of statistics in social science research Method of Evaluating Outcomes: Grading Tests are graded by a team of faculty To ensure consistency each team member grades the same question(s) on each test Students may appeal the grading of a test question on a designated appeal day (time and room to be announced) Students may discuss any problem with the faculty member who graded their work and state the reason for the appeal Only the grader determines whether any adjustment to the grade should be made Students should discuss the appeal with the course instructor who will then make any necessary adjustment to the record and return the paper to the department office Grades will be based on a total of 100 points, coming from: Quiz The lecturer sets day and time Midterm The lecturer sets exam day and time Quiz The lecturer sets day and time Final exam The lecturer sets day and time Home works Every class The total grade of the student is as follows: 10 points 25 points 10 points 35 points 20 points F 40 D 45 C- 50 C 60 C+ 65 B- 70 B 80 B+ 85 A- 90 A100 Make-up Exams and Quizzes If the reason for missing the midterm exam is valid, the student’s final exam will be worth up to 50 points In this case extra tasks will be included in the final test If the reason for missing the Final Exam is valid, a student can apply for the grade of “I” If the reason for missing the Final Exam is not valid, a grade of will be given If a student misses both exams, he/she will not be attested for the course If a student has missed Quiz for a valid reason, the student may take Quiz at the time specified by the lecturer before Midterm Exam If a student misses the Quiz for a valid reason, the student may take Quiz at the time specified by the lecturer before Final Exam Attendance Requirements It is important to attend classes to master the materials in the course Attendance affects grades: students lose point for any unexcused absence Academic Honesty The Mathematics and Natural Sciences Department has a zero tolerance policy for cheating Students who have questions or concerns about academic honesty should ask their professors or refer to the University Catalog for more information Workbooks Each student must maintain a math workbook with a clear record of completed homework Workbooks will be assessed from time to time Students should bring their workbooks to all classes as they are necessary for their class work Workbooks must be submitted for assessment immediately upon request of the instructor or full credit for homework may not be earned The workbook must contain calculations completed by the student Photo-copies of answers will not be accepted nor will answers that have been copied from the back of the text book or transcribed from the solution manual We highly recommend working jointly with your fellow students on homework problems Calculators Students will be advised whether calculators are needed for specific assignments Graphic calculators may not be used during quizzes and exams Cell phones We ask students to turn off their cell phones during math classes Use of cell phones is entirely prohibited during the exams Syllabus change Instructors reserve the right to change or modify this syllabus as needed; any changes will be announced in class 10.Tentative Academic Calendar: Weeks 1,2 The Language of Sets cl cose terms The foundation of set theory was laid by the eminent German mathematician Georg Cantor during the latter part of the 19th century In this chapter we present the language of sets We introduce the concept of a set, the various ways of describing a set and of constructing new sets from known sets The concept of a set Operations with sets: union, intersection, difference and complement Sets and probability: Space of events Elementary events Operations above random events [3]: Ch 3.2, [4]: Ch.6.1 Weeks 3-5 Combinatorial analysis Combinatorics is a fascinating branch of discrete mathematics, which deals with the art of counting Very often we ask the question: “In how many ways can a certain task be done?” Usually combinatorics comes to our rescue In most cases, listing the possibilities and counting them is the least desirable way of finding the answer to such a problem Permutations, rearrangement, combinations [2] ch 4.6, [3] ch 3.6, [4] ch 5.45.6 Weeks 6-9 Introduction to Probability The groundwork for probability theory was laid by chance in 1654 when an aristocratic gambler, Chevalier de Mere, asked Blaise Pascal the following question: If two players of equal skill are forced to quit a game before it is over, how should the stakes be divided? The problem sounds simple, and the stakes should be divided so that the person who had the greater chance to win the game when they stopped playing gets more than his opponent But how much more? Pascal communicated the problem to Pierre de Fermat, and they solved it independently Thus began probability theory A probability model is a mathematical representation of a random phenomenon It is defined by its sample space, the events within the sample space, and the probabilities associated with each event Random events Definition of probability [1] p 247, [2] p 245 Conditional probability Addition and multiplication rules [2] ch 4, 1-4.5, [3] ch 3.1-3.5, [4] ch 6.2-6.4 Law of total probability Bernulyes’ and Bayes’ theorems [3] ch 3.4, [4] ch 6.5 Weeks 10-15 Introduction to Statistics We are surrounded by data A fundamental knowledge of statistics will allow us to deal with data in a transparent and skillful manner The basics of data collection and analysis will be studied Descriptive Statistics [3] ch Random variables Discrete and continuous random variables [3] ch Distribution function of random variables [3] ch Features of probability distributions of random variables The normal and related distribution [3] ch 5, 5.2, 5.3 The central limit theorem [3] ch 5.6 Introduction to regression Statistical hypothesis testing [3] ch Out-of class assignments Hypothesis testing on the mean of a normal population: small sample Inference for the variance and standard deviation of a normal population [2]: Ch.8.4, [5]: Ch 6.4 Distribution function of discrete random variables [5]: Ch 2.2, [6]: Ch 6.4 Distribution function of continuous variables [4]: Ch 2.6 Distribution function of continuous random variables [5]: Ch 2.6, [6]: Ch 6.5 ... combinations; to understand the relationship between a question that arises in the natural, computer, and social sciences and the numerical data that are needed in order to provide an answer to the... adjustment to the grade should be made Students should discuss the appeal with the course instructor who will then make any necessary adjustment to the record and return the paper to the department... on a total of 100 points, coming from: Quiz The lecturer sets day and time Midterm The lecturer sets exam day and time Quiz The lecturer sets day and time Final exam The lecturer sets day and