- Code: DT0654
- Unit Coordinator: Matthias Schulte
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 2
- Year: 1
- Campus: Hamburg University of Technology
- Language: English
- Aims:
This course provides an introduction to probability theory and stochastic processes with special emphasis on applications and examples. The first part covers some important concepts from measure theory, stochastic convergence and conditional expectation, while the second part deals with some important classes of stochastic processes.
- Content:
- Measure and probability spaces
- Integration and expectation
- Radon-Nikodym theorem
- Fubini’s theorem and independence
- Types of stochastic convergence
- Law of large numbers
- Characteristic functions and central limit theorem
- Conditional expectation
- Martingales
- Markov chains
- Pre-requisites:
Familiarity with the basic concepts of probability
- Reading list:
- H. Bauer, Probability theory and elements of measure theory, second edition, Academic Press, 1981.
- A. Klenke, Probability Theory: A Comprehensive Course, second edition, Springer, 2014.
- G. F. Lawler, Introduction to Stochastic Processes, second edition, Chapman & Hall/CRC, 2006.
- A. N. Shiryaev, Probability, second edition, Springer, 1996.
- Unit Coordinator: Ramon Anton Piera Eroles
- ECTS Credits: 3
- Semester: 1
- Year: 2
- Campus: Autonomous University of Barcelona
- Language: English
- Aims:
To introduce students to the knowledge, processes, skills, tools and techniques suitable for project management, such that the application of them satisfy the requirements specified for project development, and may have a significant impact on its success. Specifically: learning the terminology and basic concepts of project management area and understanding the relationship between logistics and supply chain management and project management.
- Content:
- Introduction to Project Management
- System Development Cycle
- Feasibility Study
- Project Planning
- Graphs-based Programming Methods
- Cost Analysis
- Risk Management
- Project Control
- Reading list:
- Heagney, Joseph. Fundamentals of Project Management, 5th edition. 2016.
- Martinelli, Russ, et al. Program Management for Improved Business Results, 2nd edition, 2014.
- Nicholas, John M. Project management for business and technology: principles and practice , 2nd edition. Prentice Hall, 2001.
- Nicholas, John M., Steyn, H. Project management for business and technology: principles and practice, 3rd edition. Elsevier, 2008.
- Nicholas, John M. and Steyn, H. Project management for engineering, business, and technology, 4th edition. Routledge, 2012.
- A Guide to the project management body of knowledge: (PMBOK® Guide), 6th edition. Project Management Institute, 2017.
- Lewis, James P. Fundamentals of project management: developing core competencies to help outperform the competition. Amacom, 2002.
- ECTS Credits: 10
- Semester: 1
- Year: 2
- Campus: Leibniz University Hannover
- Language: English
- Code: DT0708
- Unit Coordinator: Simone Fagioli, Emanuela Radici
- Programme: Pre Master's Foundation
- ECTS Credits: 6
- Taught hours: 36
- Campus: University of L'Aquila
- Language: English
- Delivery: Online
- Content:
Sets, operations with sets, subsets, power set, Cartesian product. Sets of numbers, integers, rational numbers, gentle introduction to real numbers.
A resume of the algebraic properties of rational numbers, ordering in rational numbers. Definition of real numbers through decimal alignment. Absolute value. Intervals. A non-rigorous definition of the separation property or real numbers.
Introduction to functions on arbitrary sets. Image and pre-image. Surjective and injective functions. Composition of functions. The identical function on a set. Invertible functions and their inverse.
Power laws, exponentials, and logarithms in the set of real numbers.
Cardinality of infinite sets. Countable sets. Cardinality of real numbers.
More on functions of real numbers. Domain of a function. Examples. Operations on the graph of a functions through translations, dilations, and absolute values. Examples of elementary functions. Bounded functions, monotone functions, even and odd functions, periodic functions. Trigonometric functions and their inverse.
Upper bounds and lower bounds. Bounded and unbounded subsets of the real line. Maxima and minima. Supremum and infimum. Examples.
Complex numbers. Cartesian form, real and imaginary part, conjugacy, modulus, operations with complex numbers. Representation on the complex plane. Trigonometric form. De Moivres' formulas. Roots of a complex number. Algebraic equations on complex numbers. Fundamental theorem of algebra.
Polynomials on real numbers. Algebraic and transcendental equations. Trigonometric equations, exponential equations, logarithmic equations. Exercises.
The Cartesian plane. Geometric loci on the plane: straight lines, parabolas, circles, ellipses, hyperboles. Exercises. Solution of nonlinear systems and intersection of geometric loci in the plane.
Solution of algebraic and transcendental inequalities on the real line. Exercises.
Introduction to the study of the graph of a functions of real variables. Domain, zeroes, sign. Exercises
