Mathematics For Social Sciences Learning Objectives: In

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MATHEMATICS FOR SOCIAL SCIENCES Learning Objectives: in addition to shape a proper sense of the use of applied mathematics, the study of mathematics for social sciences teaches the student how to choose different mathematical concepts that are useful to solve social problems Acquired skills: the student who passes the examination will be able to apply rigor and systematic approach of the different mathematical concepts. Acquired competences: the student who passes the examination will be able to focus on ideas and insights rather than on mathematical calculation techniques, understanding at the same time the operating rules of these latter. Syllabus Mathematics for social sciences Professor Maria Rita Scarpitti The foundations of mathematics for social sciences                 Definition of mathematical sign, symbol and model Concept of proposition, theorem, lemma and corollary Natural and negative integer numbers Rational and irrational numbers Real numbers Operations and comparison between real numbers The nth arithmetic roots of a real number Powers of real exponent The module or absolute value Mathematical equations Summation sign Elements of set theory, the biunivoc correspondence Cartesian product Intervals as subsets of the real line Plane analytical geometry Cartesian orthogonal coordinate system Functions of one variable        Concept of real function of real variable Graph of a function Linear and quadratic functions Logarithmic and exponential functions An intuitive idea of continuity for a real function of real variable The limit of a real function of real variable Differential calculus in one variable: the derivative Linear Algebra            Definition of vector and operations on vectors Scalar product of a vector Vector spaces Rⁿ Linear combination of vectors Linearly independent and dependent vectors Bases and dimensions of a vector space Rⁿ Matrices and operations on matrices Conformability for matrix multiplication The determinant of a matrix Rank of a matrix Systems of linear equations Reference text: Simon, C. P., and L. Blume (1994): Mathematics for Economists. W.W. Norton, New York, NY, (2007):