Algebra

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Credits
6
Types
Compulsory
Requirements
This subject has not requirements, but it has got previous capacities
Department
MAT
Complex numbers. Matrices, determinants and linear systems of equations. Vector spaces and euclidean spaces. Linear transformations.

Teachers

Person in charge

  • Jaume Marti Farre ( )
  • Jose Luis Ruiz Muñoz ( )

Weekly hours

Theory
2
Problems
2
Laboratory
0
Guided learning
0
Autonomous learning
6

Competences

Transversal Competences

Transversals

  • CT6 [Avaluable] - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.

Basic

  • CB2 - That the students know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and problem solving within their area of ??study.
  • CB5 - That the students have developed those learning skills necessary to undertake later studies with a high degree of autonomy

Technical Competences

Especifics

  • CE01 - To be able to solve the mathematical problems that may arise in the field of artificial intelligence. Apply knowledge from: algebra, differential and integral calculus and numerical methods; statistics and optimization.
  • CE02 - To master the basic concepts of discrete mathematics, logic, algorithmic and computational complexity, and its application to the automatic processing of information through computer systems . To be able to apply all these for solving problems.

Generic Technical Competences

Generic

  • CG2 - To use the fundamental knowledge and solid work methodologies acquired during the studies to adapt to the new technological scenarios of the future.
  • CG4 - Reasoning, analyzing reality and designing algorithms and formulations that model it. To identify problems and construct valid algorithmic or mathematical solutions, eventually new, integrating the necessary multidisciplinary knowledge, evaluating different alternatives with a critical spirit, justifying the decisions taken, interpreting and synthesizing the results in the context of the application domain and establishing methodological generalizations based on specific applications.

Objectives

  1. Acquisition of the basic knowledge of complex numbers.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,
  2. Acquisition of basic knowledge of linear algebra.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,
  3. Recognize concepts of complex numbers and linear algebra within interdisciplinary problems.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,
  4. Learn how to use complex numbers and linear algebra in solving problems in data analysis and artificial intelligence.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,
  5. Using tools from linear algebra and complex numbers in solving mathematical problems.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,
  6. Understanding the notions of matrix decomposition, its geometric interpretation and its applications in problem solving.
    Related competences: CG2, CG4, CT6, CB2, CB5, CE01, CE02,

Contents

  1. Complex numbers.
    The imaginary unit. Ordered pair and binomial form. The conjugate. Module and argument. Trigonometric and polar expressions. Powers and roots. Exponential and matrix expressions.
  2. Matrices. Determinants. Linear systems of equations.
    Matrices. Operacions with matrices. Elementary transformations by rows and by columns. Row echelon form. Gauss method. Rank. Determinants. Linear systems of equations. Inverse matrix.
  3. The real and complex n-dimensional vector spaces.
    Vector structure of n-dimensional real and complex spaces. Vector subspaces. Euclidean structure of real n-dimensional space.
  4. Linear transformations. Diagonalitation.
    Linear transformations of the n-dimensional space. Associated matrix of linear trnasformation. Equivalent and similar matrices. Matrix diagonalization. Singular value decomposition.

Activities

Activity Evaluation act


Development of topic 1

Theoretical classes and problem sessions on topic 1.
Objectives: 1
Contents:
Theory
2h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
6h

Development of topic 2.

Theoretical classes and problem sessions on topic 2.
Objectives: 2 3 4 5
Contents:
Theory
6h
Problems
6h
Laboratory
0h
Guided learning
0h
Autonomous learning
18h

Development of topic 3.

Theoretical classes and problem sessions on topic 3.
Objectives: 2 3 4 5
Contents:
Theory
10h
Problems
10h
Laboratory
0h
Guided learning
0h
Autonomous learning
20h

Development of topic 4.

Theoretical classes and problem sessions on topic 4.
Objectives: 2 3 4 5 6
Contents:
Theory
12h
Problems
10h
Laboratory
0h
Guided learning
0h
Autonomous learning
25h

Partial exam

Partial exam
Objectives: 1 2 3 4 5
Week: 9 (Outside class hours)
Type: problems exam
Theory
0h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Final exam

Final exam
Objectives: 1 2 3 4 5 6
Week: 15 (Outside class hours)
Type: theory exam
Theory
3h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
5h

Problem delivery

Problem delivery
Objectives: 1 2 3 4 5
Week: 12 (Outside class hours)
Type: assigment
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h

Teaching methodology

Different methodologies will be considered for theory classes and problems. Theory classes will consist mainly of master classes, based on presentations and explanations on the board; problem classes will consist of solving exercises and practicing concepts learned in theory sessions.

Evaluation methodology

Subject assessment consists of three parts: P, F, T.

Grade P comes from a midterm partial exam.
Grade F comes from a final exam.
Grade T comes from the resolution and delivery of problems throughout the course.

Final grade is computed as:

FinalGrade = max(0.50F + 0.30P, 0.80F) + 0.20T

Transversal Competence (Self Learning) assessment will be done according to the final grade as following:

A: 8.5 - 10
B: 7 - 8.4
C: 5 - 6.9
D: 0 - 4.9
NA: NP

Bibliography

Basic:

Complementary:

Web links

Previous capacities

Students must master high school mathematics and have skills in solving high school level math problems.