Learning Mathematics
Through Real-World Applications
SYLLABUS
AN INTRODUCTION TO Probability and Statistics
FALL 2015
1. Lecturer:
Enver Atamanov, Acting Professor,
2. Class meetings: 3 classes per week, 15 working weeks.
3. Consultations: according to faculty schedules. Office: 415
4. 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.
5. Prerequisites: secondary school mathematics.
6. Textbooks:
1. W.H. Freeman and Company, New York. For All Practical Purposes: Mathematical Literacy in Today's World. 2009.
2. Alan H. Kvanli. Introduction to business statistics.1989.
3. Mario Triola. Elementary statistics. 2002.
4. Alan Hoenig. Applied finite mathematics. 1986.
5. Amir D. Azel. Complete Business Statistics. 1986.
6. Lawrence L. Lapin. Statistics for modern business. 1978.
7. Howard L. Rolf. Finite mathematics. Baylor University. Inc. 2005.
8. Maura Mast and Ethan Bolker. Common Sense Mathematics. 2013
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
7. 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.
8. Expected outcomes:
After completing the course 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
A lecturer grades tests. 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 lecturer. Only the lecture 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 1 / The lecturer sets day and time / 10 pointsMidterm exam / The lecturer sets day and time / 25 points
Quiz 2 / The lecturer sets day and time / 10 points
Final exam / The lecturer sets day and time / 35 points
Home works / Every class / 20 points
The total grade of the student is as follows:
0 £ F £ 40 D £ 45 C- £ 50 C £60 C+ £65 B- £70 B £ 80 B+ £ 85 A- £ 90 A£100.
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 0 will be given.
· If a student misses both exams, he/she will not be attested for the course.
· If a student has missed Quiz 1 for a valid reason, the student may take Quiz 1 at the time specified by the lecturer before Midterm Exam. If a student misses the Quiz 2 for a valid reason, the student may take Quiz 2 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 1 point for any unexcused absence.
Academic Honesty
General Education 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:
Week / Mathematical foundations / Real life applications1-2 / The Language of Sets
The foundation of set theory was laid by the eminent German mathematician Georg Cantor during the latter part of the 19th century. During two weeks, we will learn 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. Methods of defining sets.
· Venn diagrams.
· Operations with sets: union, intersection, difference and complement.
· The laws of set theory: associative, commutative, distributive, De Morgan's Laws, at alias.
· Inclusion-Exclusion Principle.
[3]: Ch. 3.2, [4]: Ch.6.1. / Sets of numbers and sets of letters.
Computer representation of sets, the bit string of length “n”
Who can catch the flu, different sorts of coffee (Venn diagrams applications)
Boys’ and girls’ names in the UK
Groups of students and the problem of choosing courses for registration
3-5 / Combinatorics
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, permutations with repetitions, permutation with constants.
[2] ch. 4.6, [3] ch. 3.6, [4] ch. 5.4-5.6. / Biology (transcript of the DNA code)
Arranging crops on different fields
Geography (coloring of maps)
Choice in the restaurant
Optimize walking
Mixing different colors
Manufacturing (distribution of several types of work between workers)
6-9 / Introduction to probability
This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling. Today, the theory of probability has found many applications in science and engineering. In this course, you will learn the basic terminology and concepts of probability theory.
· Random events. Definition of probability [1] p. 247, [2] p. 245. [8] ch.11
· 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. / Probability versus odds
State lotteries
The Monty Hall problem
The prosecutor’s fallacy
Killer football
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 (mean, median, mode, standard deviation, histograms, frequency polygon) [3] ch. 2.
· Random variables. Discrete and continuous random variables [3] ch. 2.
· Distribution function of random variables [3] ch. 4.
· 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
· Correlation coefficient / Histograms (Tornados in the USA, Ebola……)
Measuring poverty in Kyrgyzstan (representative surveys)
Authors identified
Missing data
Relationship between economic development, mortality and fertility
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.