OVERVIEW

Mathematics is the language of Science.  Even in Chemistry and Physics, foundamental for the understanding of nature, formulas are expressed in mathematical language.

This course presents the basics of Mathematics which are necessary for the young scientist.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of this course is to establish the essential mathematical foundations necessary for the language of science.
More specifically, this course presents the basic concepts and methods of linear algebra, geometry and calculus.

AIMS AND LEARNING OUTCOMES

In order to apply Mathematics to the sciences in a mature and critical way, this course puts high emphasis on verifying all results: for each topic, on top of learning the essential formulae, the sudent will learn how to verify the correctness, or at least the coherence, of the performed computations.

PREREQUISITES

Logical capabilities and basics of the mathematical knowledge (first years of high school).

TEACHING METHODS

48 hours theory; 32 hours exercises; 18 hours laboratory.

A laboratory is a monthly self-evaluation test.  It is done in class with the help of teachers and tutors.

Innovative teaching methods:

On aulaweb we offer many quizzes  specific for all topics.  They may be repeated many times (with changing questions) for self-evaluation and for admittance to the exam.

"Correzione tra pari" (peer evaluation): emphasis on critical thinking, evaluation of exercises done by classmates (anonymously)

"Dibattito matematico" (debate): emphasis on logical arguing and team work

"Matematica in ascensore" (elevator pitch): emphasis on creativity and illustration of the personal point of view on a topic

DSA

"Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sara Ferrando (sara.ferrando@unige.it), the Department’s disability liaison.”

COVID-19

All activities are performed respecting all legal limits defined for COVID emergency.  See Aulaweb for specific rules at the time of teaching.

SYLLABUS/CONTENT

• Overview of elementary set theory.
• Brief introduction to vectors and analytic geometry in 2 and 3 dimensions.
• Overview of complex numbers and polynomials (divisibility and roots).
• Functions. Graphs of elementary functions. Function composition. Inverse functions.
• Concept of limit. Continuous functions.
• Concept of the derivative, and rules for finding the derivative. Higher derivatives and their geometrical interpretation. Real-valued functions and their graphs.
• Definite integrals and the area of planar regions. Brief introduction to differential equations. The indefinite integral of a function. Integrals of elementary functions.
• Matrices and their operations; determinants and matrix inverse.
• Linear systems; gaussian reduction. Overview of numerical stability.
• Overview of combinatorics.

RECOMMENDED READING/BIBLIOGRAPHY

Theory: Anna M. Bigatti, Lorenzo Robbiano Matematica di base (CEA-Zanichelli) (prima o seconda edizione)

Exercises with solutions: Anna M. Bigatti, Grazia Tamone Matematica di base: Esercizi svolti, testi d'esame, richiami di teoria  (Esculapio)  (first or second edition)

For students with weak basic knowledge: Anna M. Bigatti, Grazia Tamone Matematica zero (CEA-Zanichelli)

TEACHERS AND EXAM BOARD

LESSONS

Class schedule

ELEMENTS OF MATHEMATIC

EXAMS

EXAM DESCRIPTION

Quizzes, written and oral exam

ASSESSMENT METHODS

Detailed description on Aulaweb