It is a subject of the second semester of the first year (part of the Basic Training Module). It introduces the foundations and methods of non-deterministic analysis applied to engineering problems.



Algebra and Calculus are the key subjects that are required to take this course. Also, it is needed some knowledge available in Foundations of Computer Science, because it will allow a more fluently handle of the software tool to be used in computer practices. Moreover, it will prepare for the study of other subjects such as Production Systems and Manufacturing (second year), Economics and Business Administration (second year), Production Organization (fourth year), ...



The following prerequisite skills are strongly recommended to successfully complete the course: express ideas with order, clarity, conciseness and correction making appropriate use of the mathematical symbolic language; have sufficient mastery of numeracy, basic geometry and fluid performing of mental calculations (how to interpret and geometrically represent abstract results; master certain calculations: operations with matrices and determinants, solving systems of linear equations, obtaining primitive functions of elementary functions, resolution of definite and indefinite integrals of simple functions); ability to read, understand and assimilate mathematical texts; have aptitude and attitude for group work; develop good study skills based on proper note-taking, literature search and reading comprehension and, finally, to have motivation, responsibility, involvement and requirement to carry out the daily work demand of a continuous assessment.

The knowledge that students will face include:



SPECIFIC COMPETENCIES:



(1) To derive and to infer the value of population parameters with a given confidence level using different inductive statistics tools, through the use of commercial scientific software, from the information obtained of a significant random sample (simple problems in engineering and applied sciences) using descriptive statistics.



(2) To develop knowledge of basic concepts of optimization problems to precisely design solutions to engineering problems according to various benchmarks.



TRANSVERSAL COMPETENCIES:



(3) To develop written and oral presentations which critically argue valid conclusions (reasoned and justified), based on an efficient management of the information acquired from the results produced.



(4) To develop working group (from the cooperation and positive interdependence) for coherently planning a simple research on an engineering problem.



(5) To defend learning evidences to demonstrate and justify the acquisition of strategies and mechanisms for working, encouraging the continued need for improvement using computer management through ICTs.



As a result the following learning outcomes will be achieved:



LO1: To define and to accurately handle the basics of the statistics.



LO2: To efficiently manage searching for information by providing the appropriate references.



LO3: To design and to plan the steps needed to solve a problematic situation, reasonably justifying with the appropriate working language.



LO4: To give results accurately and precisely using appropriate units.



LO5: To acquire the habit of critically analyzing all the results, that are obtained, are consistent with the input data and the reality of the posed problem to be solved.



LO6: To deduce correct conclusions, reasoning the answer with the appropiate language, relating the results obtained with the theoretical content involved.



LO7: To use any statistical program easy and fluently to analyze the information involved and to present the findings, validating the results with the expected values.



LO8: To present (orally and written) the results of a statistical research, that will be conducted on a working group under the Project/Problem Based Learning active methodology.

The contents included in the subject are:



THEORY OF PROBABILITY



The fundamental concepts of a random experiment are identified. The combinatorial analysis is used to characterize the sample space, analyzing the situations in which the classical probability model fails. The probability laws are set up to calculate the probability of a given event. Finally, the most usual (discrete and continuous) probability models are discussed, describing its fundamental characteristics, analyzing typical use environments, and establishing the conditions that allow approximations between the existing approaches.



DESCRIPTIVE STATISTICS



From a significant random sample (namely, s.r.s or statistical series) the data needed for its numerical and graphical description are obtained, both qualitatively and quantitatively. In this sense, the results are extended to two statistical samples to analyze the relationships between the existing information: marginal probability, covariance, correlation, association, ...



THEORY OF SAMPLING



The characteristics that the information (to be validated for statistical study) must possess are discussed. The available methods to select a statistical series are described and analyzed. Also, the fundamental theorems of statistics are studied and applied to generate sampling distributions, fundamental for inferential statistics.



INDUCTIVE STATISTICS



Estimation problems and hypothesis testing with parametric and nonparametric methods are analyzed, and the results are applied to fields such as: quality control, linear regression and correlation theory, and the analysis of variance. Examples of engineering are considered in the applied problems.



INTRODUCTION TO LINEAR PROGRAMMING



The linear programming problem is defined from a basic point of view and their geometric resolution in two/three dimensions are envisioned, and a user-level resolution using a computer application is provided.

The lectures develop the key theoretical concepts from simple reference examples using cooperative learning to involve students' participation (LO1-6).



The planning and the resolution of more elaborate situations are worked in the classroom practices and computer practices by Problem Based Learning techniques (LO1-7).



In Computer Practice sessions, simple problems (that collect all the competences of the subject using the statistical method) are designed and solve individually or in pairs (LO1-8).



Students' and teachers' reflection and self-assessment will be constant throughout the course. The learning outcomes mentioned, and the minimum levels to be achieved, will be taken as a reference, so that the student will know in advance.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 50
  • Realization of Practical Work (exercises, cases or problems) (%): 25
  • Individual written evidences (%): 25

The evaluation will be mixed (continuous and final) to gradually measure the achievements of the student in each competence. The weighted sum of the marks obtained in the various activities performed by the student will apply.



The student will need to score at least 3.5 of 10 points in the last exercise that continuous evaluation mark to be taken into account. Anyway, the student will be "FAIL" considered.



Practical work (exercises, cases or problems), weighted at 20%, relates exclusively to computer practices. Similarly, individual written evidences, weighted at 25%, include the theoretical and practical exercises to be carried out throughout the semester.



In this call, a student will be considered "NOT PRESENTED" if the final exercise is not performed and less than 40 % of the continuous assessment activities and tasks are done (otherwise, the continuous assessment qualification will be considered).



Special cases referred to in Article 64.2.b of the Student Regulations of the UPV/EHU (General Provision 3521, by agreement of the Governing Council of June 21, 2012, BOPV number 148, July 31, 2012) must be requested and credited to the Secretariat of the Centre within the fixed administrative term. That evaluation will be conducted by an exercise to ensure the adequacy of the subject competence according to the following scale: theoretical and practical test, 80%; computer test, 20%.

Unless otherwise specified, explicit and written, to the teacher responsible for the group, and only for the extraordinary call, the continuous assessment mark will be saved if the weighted average is 50% or greater (i.e., the equivalent of 5 out of 10 points). The request must be made not later than seven calendar days before the resit exam. The document for this application is available in the teaching platform of the UPV/EHU from the very start of the course.



Who keeps the continuous assessment mark will be weighted as in the ordinary call. Who does not hold, will perform a single test (which will account for 100% of the assessment), and which may include a computer session.



Who was not present at the final exercise of this call will be rated as "NOT PRESENTED".



Special cases will follow those rules in the ordinary call.

Each teacher implements a course guide where develops the teaching planning for the course. It will be available with all the teaching material in the educational platform of the UPV/EHU. The faculty group will supply the materials and the precise activities to develop the competences that will lead to the achievement of the learning outcomes with appropriate safeguards. Also, in the literature various alternatives are provided, that can be useful for obtaining additional information sources.

Basic bibliography

G.D. Eppen, C.P. Schimdt y F.J. Gould (2000): "Investigación de operaciones en la ciencia administrativa". México: PrenticeHall

J. E. Freund, I. Miller y M. Miller (2000): "Estadística matemática con aplicaciones". México: Pearson Educación (Prentice Hall)

L. Gocking y W. Smith (2002): "La estadística en cómic". Barcelona: Ed. Zendrera Zariquiey

W. Mendenhall y T. Sincich (1997): "Probabilidad y Estadística para Ingeniería y Ciencias". México: Prentice-Hall Hispano Americana, S.A.

D. C. Montgomery y G. C. Runger (1999): "Applied Statistics and Probability for Engineers". Nueva York: John Wiley & Sons, Inc.

d. Peña (2001): "Fundamentos de Estadística". Madrid: Alianza Editorial

S. M. Ross (2005): "Introducción a la Estadística". Barcelona: Ed. Reverté

R. E. Walpole, R. H. Myers y S. L. Myers (1999): "Probabilidad y estadística para ingenieros". México: Prentice Hall

E. Agirre (2006): "Estatistikaren oinarriak. Ariketak". Bilbao: Udako Euskal Unibertsitatea.

K. Fernandez (1996): "Estatistikarako Sarrera". Bilbao: Udako Euskal Unibertsitatea.

J. M. Eguzkitza (2014): "Laboratorio de Estadística y Probabilidad con R". Granada: Gami Editorial.

In-depth bibliography

M.S. Bazaraa y C.M. Shetty (1979): "Nonlinear Programming. Theory and Algorithms".Nueva Cork: John Wiley
C. L. Chiang (2003): "Statistical Methods of Analysis". New Jersey: World Scientific Pub. Co. Inc.
N. Dokuchaev (2015): "Probability Theory". New Jersey: World Scientific Pub. Co. Inc.
F. Escudero Laureano (1976): "Programación Lineal". Bilbao: Deusto
J. García, L. Fernández y P. Tejera del Pozo (1990): "Técnicas de I.O.". Madrid: Paraninfo
A. Gómez Mellado y L.M. Marín Trechera (2000): "Estadística para ingenieros técnicos". Cádiz: Servicio de Publicaciones, Universidad de Cádiz
S. Lipschutz y J. Schiller (2000): "Introducción a la probabilidad y estadistica". Madrid: McGraw-Hill
M. R. Spiegel (1997): "Estadística". Madrid: McGraw-Hill

Journals

MAGAZINES/JOURNALS

Web addresses

www.kuleuven.ac.be/ucs/java/index.htm
www.ucm.es/BUCM/est/05.htm
www.statistics.com
www.eustat.es/prodserv/seminario_c.html
www.ine.es
www.amstat.org/publications/jse/
www.statsoftinc.com/textbook/stathome.html
www.uoc.edu/in3/e-math/