Insegnamento a.a. 2022-2023

30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)

Department of Decision Sciences

Course taught in English
Go to class group/s: 25
BEMACS (8 credits - I sem. - OB  |  SECS-S/06)
Course Director:
EMANUELE BORGONOVO

Classes: 25 (I sem.)
Instructors:
Class 25: EMANUELE BORGONOVO


Mission & Content Summary

MISSION

This course covers the fundamentals of Real Mathematical Analysis (univariate and multivariate calculus) and Linear Algebra .

CONTENT SUMMARY

  • Mathematical Logic.
  • Set theory.
  • Topology.
  • Fundamentals of Calculus:
    • Univariate Calculus: Continuity, Differentiability, Riemann Integral.
    • Multivariate Calculus
    • Linear Algebra: Vector Spaces, Matrices, Determinant, Rank.

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Explain the theoretical foundations of mathematics: axioms, definitions, theorems, proofs.
  • Explain in detail, through definitions, theorems and proofs, some selected topics of Real Analysis and Linear Algebra
  • Illustrate the structure of a mathematical reasoning through the description of the steps in a proof.

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Use selected basic computational techniques (limits, derivatives (ordinary and partial) and antiderivatives, series expansions, integrals, matrix theory tools).
  • Formulate definitions, theorems and their proofs as presented in the course.
  • Use the theorems, definitions and techniques learnt in class to analyze the correctness of new statements.
  • Perform corresponding calculations and solve problems posed in the form of exercises.

Teaching methods

  • Face-to-face lectures
  • Online lectures
  • Exercises (exercises, database, software etc.)

DETAILS

  • Exercises: the course material includes a collection of exercises, some of them taken from past exam papers, that help students improve their performances.
  • Every week the class is assigned a homework consisting of some selected exercises, some theorems/statements to be proved and additional "multiple choice" and "true or false" questions. Homework assignments is not graded but they are possibly discussed in class in the following week.

Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
     x
  • Individual assignment (report, exercise, presentation, project work etc.)
 x    

ATTENDING AND NOT ATTENDING STUDENTS

  • Assignments and general exams consist of open ended questions. All types of questions contribute to the assessment of the students' acquired knowledge. Questions are aimed at verifying the knowledge of specific facts and properties about mathematical objects in order to assess students' ability to correctly apply theorems and other mathematical statements in solving dedicated problems.

Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

  • S. CERREIA VIOGLIO, M. MARINACCI, E. VIGNA, Principles of Mathematics for Economics, Springer.
  • Lecture notes, homework assignments and exercises, available online.
Last change 09/05/2022 15:03