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# 30062 - MATEMATICA - MODULO 1 (GENERALE) / MATHEMATICS - MODULE 1 (GENERAL)

Department of Decision Sciences

For the instruction language of the course see class group/s below

Go to class group/s: 21 - 22

BIEF (8 credits - I sem. - OBBC  |  SECS-S/06)
Course Director:
FABIO ANGELO MACCHERONI

Classes: 21 (I sem.) - 22 (I sem.)
Instructors:
Class 21: ELISA TACCONI, Class 22: SATOSHI FUKUDA

Class group/s taught in English

Class-group lessons delivered  on campus

Mission & Content Summary
MISSION

The aim of this course is to give students the basic mathematical knowledge and instruments that are necessary to cope with the quantitative study of problems in Economics, Finance and Management. In order to reach this aim, it is first of all necessary that students understand which are the internal structures and the essential procedures of Mathematics, and that they get to comprehend the nature of Mathematics as an axiomatic-deductive system.

CONTENT SUMMARY
• Structures. The set R: real numbers, operations, properties. The set R^n: vectors, operations, properties.
• Functions. Composite function, inverse function. Real functions of one real variable: domain, maxima/minima, convexity, other properties. Real functions of n real variables: domain, maxima/minima, convexity, other properties.
• Sequences of real numbers: definition and properties. Limits of sequences and their computation.
• Number series. Series with non-negative terms, series with terms of indefinite sign.
• Limits and continuity for functions of one or n real variables.
• One-variable differential calculus. Difference quotient, derivative. Differentiability. Differentiation rules. Fermat's and Lagrange's Theorems. Higher-order derivatives. Taylor formula. Optimization and convexity conditions.
• N-variable differential calculus. Partial derivatives and gradient. Differentiability. Unconstrained extrema, optimization conditions. Constrained extrema, Lagrangean function.
• Linear algebra. Subspaces. Linear dependence and independence. Basis and dimension of a subspace. Matrices and their operations. Linear functions and applications: definition, properties, representation. Determinant, rank and inverse matrix. Linear systems: discussion and structure of the solutions, solution.

Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
• Know the fundamental notions of mathematical analysis, of differential calculus, and of linear algebra.
• Articulate these notions in a conceptually and formally correct way, using adequate definitions, theorems, and proofs.
• Understand the nature of mathematics as an axiomatic-deductive system.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
• Apply the fundamental theoretical results of mathematical analysis, of differential calculus and of linear algebra to the solution of problems and exercises.
• Actively search for deductive ideas and chains that are fit to prove possible links between the properties of mathematical objects and to solve assigned problems.

Teaching methods
• Face-to-face lectures
• Exercises (exercises, database, software etc.)
DETAILS

Exercise sessions are dedicated to the application of the main theoretical results obtained to problems and exercises of various nature.

Assessment methods
Continuous assessment Partial exams General exam
• x x x
ATTENDING AND NOT ATTENDING STUDENTS

Students are evaluated on the basis of a written exam, which can be taken in one of the two following ways.

• It can be split in four partial exams (September, October, November, and January). The second and fourth partial exams are the main ones: each one contains a large part of open-answer questions and some multiple-choice ones; each one weighs for one-third of the final mark. The first and third partials are multiple-choice tests and each one weighs for one-sixth of the final mark. Each type of questions contributes in a specific way to the assessment of the students' acquired knowledge. In particular, multiple-choice questions mainly aim at evaluating the knowledge of the fundamental mathematical notions and the ability to apply these notions to the solution of simple problems and exercises. While open-answer questions mainly aim at evaluating:
• The ability to articulate the knowledge of mathematical notions in a conceptually and formally correct way, adequately using definitions, theorems and proofs.
• The ability to actively search for deductive ideas and chains that are fit to prove possible links between the properties of mathematical objects.
• The ability to apply mathematical notions to the solution of more complex problems and exercises.
• It can be taken as a single general exam, which contains both open-answer questions and multiple-choice ones. The general exam covers the whole syllabus of the course and it can be taken in one of the four general sessions scheduled in the academic year (the two regular sessions in January and February, or the two make-up sessions in June and August/September). This way is mainly meant for students who have withdrawn from the four partials procedure or could not follow it. Each type of questions contributes in a specific way to the assessment of the students' acquired knowledge. In particular, multiple-choice questions mainly aim at evaluating the knowledge of the fundamental mathematical notions and the ability to apply these notions to the solution of simple problems and exercises. While open-answer questions mainly aim at evaluating:
• The ability to articulate the knowledge of mathematical notions in a conceptually and formally correct way, adequately using definitions, theorems and proofs.
• The ability to actively search for deductive ideas and chains that are fit to prove possible links between the properties of mathematical objects.
• The ability to apply mathematical notions to the solution of more complex problems and exercises.

We take a special care to adjust the raw grades assigned in each exam, to obtain final grades whose distribution follows as closely as possible the normal distribution of grades that is recommended by Università Bocconi.

Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
• S. CERREIA VIOGLIO, M. MARINACCI, E. VIGNA, Principles of Mathematics and Economics, Milano (draft version available as a pdf file).
• Integrative teaching materials.
Last change 27/05/2019 08:48