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Mathematics and statistics - term 1
Code: G250NA
Teacher:  Daniela Poggioli
Year: 
Term: 
CFU: 
CFU subdivision: Lectures: 3,5
Practices in classroom: 2,5
Basic aims:  Knowledge of the basics of Maths, in particular, of elementary Calculus (real functions in one variable, limits, derivatives, integrals).
Knowledge of descriptive statistics. Position and variability indices. Acquisition of the principles and the techniques of regression and correlation between variables. Knowledge of inferential statistics. Analysis of Variance.
Acquired skills:  Possibility of exploiting the basic tools of Maths in any context.
Describe phenomena using main statistical indicators. Plan sampling surveys. Using the one and two-ways analysis of variance. Objective assessment of statistical surveys results.
Course contents:  Numerical sets. The coordinate plane: straight lines,
parabolas, circles. Elementary functions. Equations,
inequalities and system of algebraic and irrational
inequalities. Generalities about real funcion. Limits.
Continuity. Asymptotes. Differential calculus.
Monotonicity. Global maxima and minima. Convexity and
concavity. Integral calculus.
Program:  Numerical sets.: N, Z, Q e R. The coordinate plane:
straight lines, parabolas, circles. Outline of trigonometry.
Elementary functions and their graph. Equations,
inequalities and system of algebraic and irrational
inequalities. Generalities about real funcion: domain,
range, injective and surjective functions, composed
functions, inverse functions, geometric transforms of
elementary functions. Limits: computing limits,
comparison of infinites and infinitesimals, indeterminate
forms. Continuity. Asymptotes: vertical, horizontal and
slant. Differential calculus: first derivative, tangent line,
monotonicity, global and local maxima and minima.
Second derivative: convexity and concavity, inflection
points. Integral calculus. Computation of plane areas.
Prerequisites:  Integers, rational and real numbers. Literal Calculus.
Equations and inequalities. Eponential and logarithm.
Outline of Analytic geometry (Coordinates and lines)
Preparatory instructions:  None.
Learning materials:  agrimat and matematica assistita: free download at
http://ariel.ctu.unimi.it/corsi/mateassistita
Other info:  The final mark is the outcome of a written and an oral
exam that are both compulsory. The written exam
(whose mark is at most 30/30) is made of two part, A
and B that take place the same day. Part A takes half
an hour and it focuses on the prerequisities. It consists
in 10 problems to be solved quickly. Only if the student
answers correctly at least 8 questions, his part B will
be evaluated. Part B takes two hours and consists of a
few open-ended question regarding the exam program.
The oral examination consists of a short conversation
about the topics of the program, which aims to
establish definitively what tools the student has
acquired in the study of mathematics.
DOWNLOAD
Program of Mathematics and statistics - term 1 (pdf version)
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