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Code MATH 203
Term 201602
Title Introduction to Probability
Faculty Faculty of Engineering and Natural Sciences
Subject Mathematics(MATH)
SU Credit 3
ECTS Credit 6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Instructor(s) Semih Onur Sezer -sezer@sabanciuniv.edu,
Language of Instruction English
Level of Course Undergraduate
Type of Course Click here to view.
Prerequisites
(only for SU students)
MATH102
Mode of Delivery Formal lecture,Recitation
Planned Learning Activities Task based learning
Content

Counting techniques, combinatorial methods, random experiments, sample spaces, events, probability axioms, some rules of probability, conditional probability, independence, Bayes' theorem, random variables (r.v.'s), probability distributions, discrete and continuous r.v.'s, probability density functions, multivariate distributions, marginal and conditional distributions, expected values, moments, Chebyshev's theorem, product moments, moments of linear combinations of r.v.'s, special discrete distributions, uniform, Bernouilli, binomial, negative binomial, geometric, hypergeoemtric and Poisson distributions, special probability densities, uniform, gamma, exponential and normal densities, normal approximation to binomial, distribution of functions of r.v.'s, distribution function and moment-generating function techniques, distribution of the mean, law of large numbers, the central limit theorem.

Objective

- To give an understanding of uncertainty and randomness
- To teach the fundemantal concepts and defintions of probability
- To equip the students with the tools and techniques of probability theory

Learning Outcome

Upon completing this course students should be able to:

Use the basic principles of counting, permutations, combinations, and multinomial coefficients.

Perform set operations and compute elementary (conditional) probabilities.
Use the concept of random variables and their distributions, cumulative distribution functions.
Compute marginal distributions, conditional distributions and conditional expectations.
Evaluate mathematical expectations, moments, variances, co-variances, conditional expectations, and moment-generating functions.
Investigate the basic properties of important discrete and continuous random variables such as Bernouilli, binomial, hypergeometric, Poisson, uniform, exponential, gamma and normal.
Standardize means and sums of independent random variables and apply the Law of Large Numbers and the Central Limit Theorem.
Implement different techniques such as the distribution function technique, the moment generating function technique, the transformation technique to evaluate the distribution of functions of random variables.
Investigate the properties of various statistics (sample mean, sample variance, order statistics) taken from a population.

Programme Outcomes
 
Common Outcomes For All Programs
1 Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 2
2 Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4
3 Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects. 4
4 Communicate effectively in Turkish and English by oral, written, graphical and technological means. 3
5 Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 3
Common Outcomes ForFaculty of Arts & Social Sci.
1 Develop a thorough knowledge of theories, concepts, and research methods in the field and apply them in research design and data analysis. 1
2 Assess the impact of the economic, social, and political environment from a global, national and regional level. 1
3 Know how to access written and visual, primary and secondary sources of information, interpret concepts and data from a variety of sources in developing disciplinary and interdisciplinary analyses. 1
Common Outcomes ForFaculty of Eng. & Natural Sci.
1 Possess sufficient knowledge of mathematics, science and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4
2 Identify, define, formulate and solve complex engineering problems; choose and apply suitable analysis and modeling methods for this purpose. 3
3 Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; possess knowledge of standards used in engineering applications; use information technologies effectively. 2
4 Ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling specified needs; apply modern design techniques for this purpose. 2
5 Design and conduct experiments, collect data, analyze and interpret the results to investigate complex engineering problems or program-specific research areas. 2
6 Knowledge of business practices such as project management, risk management and change management; awareness on innovation; knowledge of sustainable development. 1
7 Knowledge of impact of engineering solutions in a global, economic, environmental, health and societal context; knowledge of contemporary issues; awareness on legal outcomes of engineering solutions; understanding of professional and ethical responsibility. 1
Common Outcomes ForSchool of Management
1 Demonstrate an understanding of economics, and main functional areas of management. 1
2 Assess the impact of the economic, social, and political environment from a global, national and regional level. 1
Electronics Engineering Program Outcomes Required Courses
1 Use mathematics (including derivative and integral calculations, probability and statistics), basic sciences, computer and programming, and electronics engineering knowledge to design and analyze complex electronic circuits, instruments, software and electronics systems with hardware/software. 2
2 Analyze and design communication networks and systems, signal processing algorithms or software using advanced knowledge on differential equations, linear algebra, complex variables and discrete mathematics. 1
Industrial Engineering Program Outcomes Required Courses
1 Formulate and analyze problems in complex manufacturing and service systems by comprehending and applying the basic tools of industrial engineering such as modeling and optimization, stochastics, statistics. 2
2 Design and develop appropriate analytical solution strategies for problems in integrated production and service systems involving human capital, materials, information, equipment, and energy. 2
3 Implement solution strategies on a computer platform for decision-support purposes by employing effective computational and experimental tools. 1
Economics Program Outcomes Required Courses
1 Provide constructive analysis of economic phenomena at the national and international level, and interactions between the two. 1
2 Develop an understanding of organizations and institutions in the society as well as their influence on the economy. 1
3 Recognize how incentives shape the behavior of individuals and organizations. 1
4 Identify ?economic? problems and propose alternative models and/or design and conduct research to provide viable solutions using theoretical tools and/or quantitative methods. 1
5 Communicate problems and solutions to managerial and policy decision-making units as well as to lay audiences. 1
Computer Science and Engineering Program Outcomes Required Courses
1 Design, implement, test, and evaluate a computer system, component, or algorithm to meet desired needs and to solve a computational problem. 1
2 Demonstrate knowledge of discrete mathematics and data structures. 1
3 Demonstrate knowledge of probability and statistics, including applications appropriate to computer science and engineering. 3
Management Program Outcomes Required Courses
1 Pursue open minded inquiry and appreciate the importance of research as an input into management practice. 1
2 Know how to access, interpret and analyze data and information and use them to make informed decisions. 1
3 Work effectively in environments characterized by people of diverse educational, social and cultural backgrounds. 1
4 Identify, select, and justify strategies and courses of action at the divisional, business, and corporate levels of analysis and to develop effective plans for the implementation of selected strategies. 1
Molecular Biology, Genetics and Bioengineering Program Outcomes Core Electives
1 Comprehend key concepts in biology and physiology, with emphasis on molecular genetics, biochemistry and molecular and cell biology as well as advanced mathematics and statistics. 1
2 Develop conceptual background for interfacing of biology with engineering for a professional awareness of contemporary biological research questions and the experimental and theoretical methods used to address them. 1
Materials Science and Nano Engineering Program Outcomes Core Electives
1 Applying fundamental and advanced knowledge of natural sciences as well as engineering principles to develop and design new materials and establish the relation between internal structure and physical properties using experimental, computational and theoretical tools. 1
2 Merging the existing knowledge on physical properties, design limits and fabrication methods in materials selection for a particular application or to resolve material performance related problems. 1
3 Predicting and understanding the behavior of a material under use in a specific environment knowing the internal structure or vice versa. 1
International Studies Program Outcomes Core Electives I (Economics and Quantitative Methods)
1 Analyze global affairs from international relations and economics perspectives. 1
2 Demonstrate theoretical and practical knowledge of the international affairs. 1
3 Compete for increasing opportunities in careers within the newly emerging global institutions. 1
4 Evaluate the international political events and present their views and positions on international affairs with advanced oral and written skills. 1
Political Science Program Outcomes Core Electives IV
1 Understand and follow changes in patterns of political behavior, ideas and structures. 1
2 Develop the ability to make logical inferences about social and political issues on the basis of comparative and historical knowledge. 1
Mechatronics Engineering Program Outcomes Area Electives
1 Familiarity with concepts in statistics and optimization, knowledge in basic differential and integral calculus, linear algebra, differential equations, complex variables, multi-variable calculus, as well as physics and computer science, and ability to use this knowledge in modeling, design and analysis of complex dynamical systems containing hardware and software components. 2
2 Ability to work in design, implementation and integration of engineering applications, such as electronic, mechanical, electromechanical, control and computer systems that contain software and hardware components, including sensors, actuators and controllers. 1
Assessment Methods and Criteria
  Percentage (%)
Exam 100
Recommended or Required Reading
Textbook

John Freund's Mathematical Statistics with Applications, 8th Edition, Pearson-
Prentice Hall, 2004

Optional Readings

Supplementary Texts :
1) S. Ross: A First Course in Probability, 7th Edition, Pearson- Prentice Hall, 2006.
2) S. Lipschutz: Schaum?s Outline of Theory and Problems of Probability, Mc
Graw-Hill, 2000.

Course Web https://sucourse.sabanciuniv.edu/portal/site/MATH203-201401