Guías Docentes Electrónicas
1. General information
Course:
ALGEBRA
Code:
19500
Type:
BASIC
ECTS credits:
6
Degree:
384 - MINING AND ENERGY ENGINEERING DEGREE
Academic year:
2020-21
Center:
106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING
Group(s):
51 
Year:
1
Duration:
First quarter
Main language:
Spanish
Second language:
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer: DOROTEO VERASTEGUI RAYO - Group(s): 51 
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
6049
doroteo.verastegui@uclm.es

2. Pre-Requisites

Students will have to master the contents taught in the subject of Mathematics in the Bachelor's Degree in Science and Technology.

In particular, they must have achieved:

1. Basic knowledge of geometry, trigonometry, mathematical operations (powers, logarithms, fractions), polynomials, matrices, derivation, integration and graphical representation of functions.

2. Basic instrument handling skills: Basic computer handling (operating system).

Those students who have studied another modality should acquire, during the first weeks of the semester, a sufficient knowledge of the basic mathematical techniques. In this regard, it would be advisable to attend the so-called "Zero Courses" that the Centre will organise during the first four-month period.

3. Justification in the curriculum, relation to other subjects and to the profession

The Mining Engineer is the professional who uses the knowledge of the physical and mathematical sciences and engineering techniques to develop his professional activity in aspects such as the search for mining resources, the exploitation of mines, the extraction of elements of economic interest from their original minerals, the control, instrumentation and automation of processes and equipment, as well as the design, construction, operation and maintenance of extractive industrial processes, etc. This training allows him to successfully participate in the different branches that make up mining engineering, to adapt to changes in technology in these areas and, where appropriate, to generate them, thus responding to the needs that arise in the productive and service branches to achieve the welfare of the society to which it is due.
Within the mathematical knowledge necessary to carry out all the above, the methods developed in the subject of Algebra have proven to be the most appropriate for the modern treatment of many disciplines included in the Curriculum. Disciplines that, in the end, will allow the engineer to face the problems that will arise during the course of his career.
 
Therefore, it is necessary to take this course because it is an essential part of the basic training of a future engineer. Its purpose is to provide students with the basic algebraic resources necessary to follow up on other specific subjects of their degree, so that the student has sufficient algebraic ability and dexterity to solve problems related to engineering and mathematics. In addition, this subject helps to enhance the capacity for abstraction, rigour, analysis and synthesis that are characteristic of mathematics and necessary for any other scientific discipline or branch of engineering.


4. Degree competences achieved in this course
Course competences
Code Description
B01 Capacity to solve mathematical problems which might arise in the engineering field. Attitude to apply knowledge about: linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives; numerical methods, numeric algorithms, statistics and optimization.
C03 To know basic numerical calculus applied to the engineering field.
CB01 Prove that they have acquired and understood knowledge in a subject area that derives from general secondary education and is appropriate to a level based on advanced course books, and includes updated and cutting-edge aspects of their field of knowledge.
CB02 Apply their knowledge to their job or vocation in a professional manner and show that they have the competences to construct and justify arguments and solve problems within their subject area.
CB03 Be able to gather and process relevant information (usually within their subject area) to give opinions, including reflections on relevant social, scientific or ethical issues.
CB05 Have developed the necessary learning abilities to carry on studying autonomously
CT00 To promote respect and promotion of Human Rights as well as global access principles and design for everybody according to the 10th final order of the Law 51/2003 of December 2nd¿ about equal opportunities, non-discrimination and universal accessibility for people with disabilities.
CT02 To be acquainted with Information and Communication Technology ICT
CT03 Capacity for written and oral communication skills.
5. Objectives or Learning Outcomes
Course learning outcomes
Description
Capacity to express yourself correctly both in spoken and in written form , and particuarly, to know how to use mathematical language as well as to know how to express precisely quantities and operations which are present in the Mining engineering field
To know how to use and carry out basic calculations with complex numbers.
To know matrix theory and to know how to carry out the corresponding calculations.
Additional outcomes
Description
- To know the theory of linear equation systems and how to apply them to real situations.
. Know the fundamentals and applications of Vector Spaces and Linear Applications.
. Know the basic aspects of the Equations in Differences.
. To know the Euclidean Geometry and to know how to carry out the corresponding calculations.
. Know the main approaches to numerical resolution and apply them to solving real problems.
. Use, at the user level, some mathematical calculation and visualization software packages, analyze data and interpret results.
6. Units / Contents
  • Unit 1: Complex numbersº
  • Unit 2: Matrices and determinants
  • Unit 3: Linear Equation Systems
  • Unit 4: Vector Spaces
  • Unit 5: Linear applications
  • Unit 6: Diagonalization of endomorphisms
  • Unit 7: Euclidean vector space. Geometry
  • Unit 8: Introduction to Linear Equations in Differences
7. Activities, Units/Modules and Methodology

All training activities will be recoverable, in other words, there must be an alternative evaluation test that allows to reassess the acquisition of the same skills in the ordinary, extraordinary and special call for completion. If exceptionally, the evaluation of any of the training activities cannot be recovered, it must be specified in the description and be expressly authorized by the department.

Training Activity Methodology Related Competences ECTS Hours As Com Description
Class Attendance (theory) [ON-SITE] Lectures B01 CB01 CB02 CB03 CB05 CT00 CT03 1.1 27.5 N N Development of theoretical content in the classroom, using the participatory master lesson method
Problem solving and/or case studies [ON-SITE] Problem solving and exercises B01 CB01 CB02 CB03 CB05 CT00 CT03 0.6 15 Y N Participatory resolution of exercises and problems in the classroom
Computer room practice [ON-SITE] Practical or hands-on activities B01 CB01 CB02 CB03 CB05 CT02 0.3 7.5 Y N Laboratory practices in the computer classroom with the use and application of specific software
Writing of reports or projects [OFF-SITE] Problem solving and exercises B01 CB01 CB02 CB03 CB05 CT00 CT03 1.2 30 Y N Performance of academic work (exercises) carried out by the student outside or inside the classroom
Individual tutoring sessions [ON-SITE] Problem solving and exercises B01 CB01 CB02 CB03 CB05 CT00 CT03 0.2 5 N N Tutoring of academic work in the professor's office
Other off-site activity [OFF-SITE] Self-study B01 CB01 CB02 CB03 CB05 2.4 60 N N Personal study of the subject, especially on dates near the final exam
Final test [ON-SITE] Assessment tests B01 CB01 CB02 CB03 CB05 0.2 5 Y Y Final evaluation of the course by written test
Total: 6 150
Total credits of in-class work: 2.4 Total class time hours: 60
Total credits of out of class work: 3.6 Total hours of out of class work: 90

As: Assessable training activity
Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).

8. Evaluation criteria and Grading System
Evaluation System Continuous assessment Non-continuous evaluation * Description
Laboratory sessions 10.00% 10.00% For the evaluation of the practices in the computer room, with the application of specific software, the delivery of the work done in them will be assessed, and the work will have to be defended orally before the teacher.
Final test 70.00% 70.00% Finalmente se realizará una prueba escrita que constará de preguntas, cuestiones teóricas y problemas cuyos criterios de evaluación serán similares a los de los trabajos académicos antes descritos.
Assessment of problem solving and/or case studies 10.00% 10.00% For the evaluation of the academic work carried out by the students outside the classroom, tutored by the teacher individually or in small groups, a report should be submitted where the approach to the problem, the use of appropriate terminology and notation to express the ideas and mathematical relations used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleaning and presentation of the document will be assessed.
Assessment of problem solving and/or case studies 10.00% 10.00% For the evaluation of the academic work carried out by the students in class, a report should be submitted evaluating the approach to the problem, the use of appropriate terminology and notation to express the ideas and mathematical relations used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleanliness and presentation of the document.
Total: 100.00% 100.00%  
According to art. 6 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 13.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).

Evaluation criteria for the final exam:
  • Continuous assessment:
    In order to obtain the final grade, the 4 evaluation systems described above are calculated, with the specified weights, and a grade of 4 out of 10 or higher must be obtained in the final written test. If the grade obtained in this test is less than 4 points, it will be given as the final grade of the course.
  • Non-continuous evaluation:
    Evaluation criteria not defined

Specifications for the resit/retake exam:
In order to obtain the final grade, the grades obtained in the first 3 evaluation systems described above will be kept and a new written Final Exam will be taken, calculating the final grade of the course combining the 4 grades as specified above. Likewise, in the final written test, a grade equal to or higher than 4 points out of 10 must be obtained. If the grade obtained in this test is less than 4 points, this will be the final grade of the course. If the 4 evaluation systems are calculated as described in the previous paragraph, and the final grade is lower than the grade obtained in the written Final Exam, the grade obtained in the Final Exam will be recorded as the final grade of the course.
Specifications for the second resit / retake exam:
A final written test will be taken, weighing 100 % of the overall grade of the subject and consisting of questions, theoretical questions and problems where the approach to the topic or problem will be assessed, the use of appropriate terminology and notation to express the ideas and mathematical relations used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleaning and presentation of the document.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours
Computer room practice [PRESENCIAL][Practical or hands-on activities] 7.5
Individual tutoring sessions [PRESENCIAL][Problem solving and exercises] 5
Final test [PRESENCIAL][Assessment tests] 5

Unit 1 (de 8): Complex numbersº
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 2
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 2
Other off-site activity [AUTÓNOMA][Self-study] 6

Unit 2 (de 8): Matrices and determinants
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 3
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 3
Other off-site activity [AUTÓNOMA][Self-study] 9

Unit 3 (de 8): Linear Equation Systems
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 4
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2.5
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 4
Other off-site activity [AUTÓNOMA][Self-study] 8

Unit 4 (de 8): Vector Spaces
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 4.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 3
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 6
Other off-site activity [AUTÓNOMA][Self-study] 9

Unit 5 (de 8): Linear applications
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 4.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 3
Other off-site activity [AUTÓNOMA][Self-study] 7

Unit 6 (de 8): Diagonalization of endomorphisms
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 3.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2.5
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 3
Other off-site activity [AUTÓNOMA][Self-study] 6

Unit 7 (de 8): Euclidean vector space. Geometry
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 4
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 5
Other off-site activity [AUTÓNOMA][Self-study] 9

Unit 8 (de 8): Introduction to Linear Equations in Differences
Activities Hours
Class Attendance (theory) [PRESENCIAL][Lectures] 2
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2
Writing of reports or projects [AUTÓNOMA][Problem solving and exercises] 4
Other off-site activity [AUTÓNOMA][Self-study] 6

Global activity
Activities hours
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
David C. Lay Álgebra lineal y sus aplicaciones Álgebra lineal y sus aplicaciones 978-607-32-1398-1 2012  
David C. Lay , Steven R. Lay, Judi J. McDonald Linear Algebra and Its Applications (5th Edition) 032198238X 2015  
Dionisio Pérez Esteban Álgebra lineal enfocada a la ingeniería Garceta 978-84-1622-864-5 2016  
Gilbert Strang Introduction to Linear Algebra - Fifth Edition Edition 0980232775 2016  
Gutiérrez Gómez, Andrés Geometría Pirámide 84-368-0236-5 1983 Ficha de la biblioteca
López Guerrero, M.A.; Verastegui Rayo, D. Ejercicios de Álgebra Lineal Almadén Copy-Expres 1992  
Serge Lang Linear Algebra 0387964126 2013  
Seymour Lipschutz, Marc Lipson Schaum's Outline of Linear Algebra, 5th Edition 0071794565 2012  
Vicent Estruch Fuster, Valentín Gregori Gregori, Bernardino Roig Sala Álgebra matricial Universidad Politécnica de Valencia 978-84-9048-644-3 2017  



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