SF/0010 - BASIC MATHEMATICS
Academic Year 2019/2020
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HECTOR CARLOS FREYTES (Tit.)
- Teaching style
- Lingua Insegnamento
|[30/46] PRIMARY TEACHER EDUCATION||[46/00 - Ord. 2011] PERCORSO COMUNE||12||90|
Knowledge and understanding
The main objective of the course is devoted to provide students with the key tools for dealing with different kind mathematical problems of various types (arithmetic, geometry, set theory, logic etc ...).
The student have to acquire an autonomous and critical reflection on the course’s issues.
At the end of the course, the student will be able to communicate information regarding to the basic mathematic topics.
Finally, the student must be able to find sources to update and deepen autonomously and constantly knowledges and professional competencies
Only basic notions on arithmetic and geometry are required
The initial purpose of the course is to give the theoretical, conceptual and methodological fundamental issues in mathematic and logic. Application of the theoretical concept are considered.
Lesson 1) Natural language, formal language, sentences
Lesson 2) Logical conective, recursive grammar.
Lesson 3) Truth tables.
Lesson 4) Tautology, contradiction, contingency
Lesson 5) Propositional arguments, valid argument forms.
Lesson 6) Inference rules
Lesson 7) Natural deduction
Lesson 8) Natural deduction with equivalence.
Lesson 9) Introduction to 1st order logic
Lesson 10) Axiomatic theories
Lesson 11) Naive set theory.
Lesson 12) Russel paradox, Zermelo axiom.
Lesson 13) Axiom of specification
Lesson 14) Inclusion, Union, Intersection, Complement.
Lesson 15) Cartesian products, power set.
Lesson 16) Binary Relations.
Lesson 17) Equivalence relations, partitions, quotiente set.
Lesson 18) Ordering.
Lesson 19) Functions, domain, co-domain, image.
Lesson 20) Injective, surjective and bijective functions.
Lesson 21) Plane Geometry
Lesson 22) Angles, deg, rad
Lesson 23) Right triangles, Pitagora theorem
Lesson 24) Sine, Cosine, Tangent.
Lesson 25) Equation of a Straight Line
Lesson 26) Trigonometric functions
Lesson 27) Inverse Trigonometric functions
Lesson 28) Sinusoidal waves, frequence and period, maximum and efective values.
Lesson 29) Stationary sinusoidal Regime
Lesson 30) Sound waves
Verification of learning
The exam is expressed in thirtieths. In order to pass the exam that is with a minimum score of 18/30 the student must show a sufficient knowledge of all the addressed topics, with a proper use of the language. In order to achieve the maximum score of 30/30 cum laude, the student must show an excellent knowledge of all the dealt topics.
1)Introduction to Logic, Irving Copi (Ed Pearson 2010)
2) Naive Set Theory, Paul halmos (Martino Publishing 2011)
For an appointment send an e-mail to firstname.lastname@example.org
Not frequenting students are invited to refer to the website and to email the lecturer in order to clarify any doubts regarding their self-study
Students with special needs may benefit from a Disabled Office (http://people.unica.it/disabilita/) that certifies their difficulties in order to arrange individualized programs and exams.