Teaching plan for the course unit



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General information


Course unit name: Logic and Algebra

Course unit code: 568194

Academic year: 2021-2022

Coordinator: Joan Gispert Braso

Department: Department of Mathematics and Computer Science

Credits: 6

Single program: S



Estimated learning time

Total number of hours 150


Face-to-face and/or online activities



-  Lecture





-  Lecture with practical component





-  Other class types




Supervised project


Independent learning




Competences to be gained during study


—Originality in the development and/or application of ideas, often in a research context, facilitated by a sufficient base of knowledge.
— Capacity to apply acquired knowledge and solve problems in new or unfamiliar environments within broader or multidisciplinary contexts related to the area of study.
— Capacity to integrate knowledge and tackle the complexity of making judgments based on information that, despite being incomplete or limited, includes reflection on social and ethical responsibilities linked to the application of knowledge and judgments.
— Ability to communicate findings, knowledge and the most recent supporting arguments to specialized and non-specialized audiences clearly and concisely.
— Skills to enable lifelong self-directed and independent learning.


— Capacity for time and resource management in the application of acquired knowledge and skills.
— Ability to access specialized bibliographic databases using new technologies.
— Ability to gather and synthesize the information needed to address a problem.
— Capacity for teamwork.


— Understanding of the concepts and rigorous proofs of the fundamental theorems of crosscutting areas of mathematics.
— Understanding of the concepts and rigorous proofs of the fundamental theorems of a specific area of mathematics.
— Capacity for the application of results and techniques learned to solve complex problems in an area of mathematics within academic or professional contexts.
— Capacity to prepare and develop logical-mathematical reasoning and identify errors in incorrect arguments.
— Ability to construct, interpret, analyse and verify advanced mathematical models that simulate real situations.
— Ability to state and verify propositions in an area of mathematics and to convey acquired mathematical knowledge orally and in writing.





Learning objectives


Referring to knowledge

— To learn to associate a language to an algebraic or relational structure
— To understand the notion of semantics of a deductive system
— To identify the algebraic semantics of certain deductive systems
— To distinguish different logics by their semantical and syntactical properties



Teaching blocks


1. Structures

*   Signatures, examples and constructions

2. First order language

*  Syntax, semantics, Theories and Models

3. Completeness Theorem

*  First order Hilbert calculus. Completeness theorem.

4. Compactness and Lowenheim-Skolem Theorems

5. Definable classes and preservation theorems

6. Algebraic structures

*   Universal algebra: model theory for algebraic structures

7. Varieties and quasivarieties

8. Propositional logics and matrix semantics



Teaching methods and general organization


The classes will be mostly theoretical and practical in which we explain the theory required to develop and solve the exercises. It is intended that the problem solving is the basis for learning the subject and we encourage the active participation of students in class. In class there will be a proposed list of small exercises that need to be solved  to help  the everyday learning. Every four weeks approximately,  the teacher will propose more complex exercises that require the review of all the material taught.

In the case of virtual teaching required by the health situation, the time ranges are maintained and teaching will be carried out in a non-contact format. Theoretical and practical hours will be face-to-face and / or non-face-to-face asynchronous. Throughout the course various material will be delivered with the main definitions and results of the course. The main objective of the face-to-face part will be to help students with the material uploaded to the virtual campus. The distribution of this part will be as follows: Part of the time will be used to comment on the theoretical results, give examples and answer and clarify doubts. The second practical part will be dedicated to  on-site resolution of exercises to help understand the theoretical results and solutions to the proposed problems.






Official assessment of learning outcomes


It consist of two activities:

Activity 1: Solving exercises in class and work commissioned

Activity 2: Final exam 

The grade will be obtained with the weighting of 65% for activity 1 and 35%  of the activity  2.



• It consists of a single examination.

• There are no minimum requirements to apply for repeat assessment.

• Any grade obtained through repeat assessment stands as the final grade.



Examination-based assessment

The final grade for single assessment is obtained through a single final examination.




• It consists of a single examination.

• There are no minimum requirements to be eligible take the reassessment.

• Any grade obtained through repeat assessment stands as the final grade.