
Teaching plan for the course unit


Course unit name: Logic and Algebra
Course unit code: 568194
Academic year: 20182019
Coordinator: Joan Gispert Braso
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time

Total number of hours 150

Facetoface learning activities

60


 Lecture


28


 Lecture with practical component


28


 Other class types


4

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 nonspecialized audiences clearly and concisely. — Skills to enable lifelong selfdirected 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 logicalmathematical 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.

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

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 LowenheimSkolem 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. It is considered that for each hour taught in the classroom, students need between 1.5 and 2 hours to study new concepts and solve exercises.

Official assessment of learning outcomes

It consist of two activities:
Activity 1: Solving exercises in class and work commissioned
Activity 2: Exams (1 or 2 throughout the course)
The grade will be obtained with the weighting of 65% for activity 1 and 35% of the activity 2.
Reassessment:
• 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.
Examinationbased assessment
The final grade for single assessment is obtained through a single final examination.
Reassessment
• 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.

Reading and study resources

Consulteu la disponibilitat a CERCABIB
Book
Bergman, C. Universal algebra : fundamentals and selected topics. Boca Raton : CRC Press, 2012.
Burris, S. ; Sankappanavar, H. P. A course in universal algebra : the millenium edition. Ontario : S. Burris and H.P. Sankappanavar, 2012.
Accés lliure a text complet
Chang, C.C. ; Keisler, H.J. Model theory. Amsterdam [etc.] : NorthHolland, 1990.
Czelakoowski, J. Protoalgebraic logics. Dordrecht [etc.] : Kluwer Academic, 2001.
Rothmaler, P. Introduction to model theory. New York : Taylor & Francis, 2000.