OVERVIEW

The course Principles of Mathematics consists of the modules Elements of Mathematics  (cod. 72565, 1st semester) and Elements of Mathematics 2 (cod. 72566, 2nd semester). The course covers the study of real-valued functions of one and two real variables, their differential calculus and the integral calculus, and the complex numbers.

This section provides information that is common to the two modules; the specific information can be found in the modules sheets.

AIMS AND CONTENT

LEARNING OUTCOMES

The course covers the study of real functions with one or two real variables, and their differential and integral calculus. The aim of the course is to give students the tools to use these essential notions in the subsequent courses of physical and chemical character.

AIMS AND LEARNING OUTCOMES

Acquisition of a correct methodological approach to learning of scientific disciplines, based on the use of language and mathematical reasoning as useful  tools for the interpretation of the real world and not as mere abstract notions.

PREREQUISITES

• Algebraic calculus, polynomial and fractional equations and inequations
• Analytical geometry elements (Cartesian coordinate system in the plane, equations of lines and the canonical form of conics in the plane)
• Definition of a matrix, determinant of 2x2 and 3x3 matrices
• Absolute value, definition and basic properties, simple equations and inequations
• Roots, definition and basic properties, simple equations and inequations
• Powers, exponentials, logarithms, definition and basic properties
• Basics on exponential and logarithmic functions
• Basic elements of trigonometry

TEACHING METHODS

The course is organized in theoretical and exercises lectures, which are based on teaching methods that aim to encourage students to take an active role in the development of the learning process.

The course also provides classroom and online instructional tutorials, which are based on a workshop approach and make it possible to implement flexible learning pathways adapted to the needs of individual students.

The material course is made available on the Aulaweb site of the course: handouts of lectures, exercises sheets, texts and solutions of guided exercises, texts and solutions of written exams from previous years.

SYLLABUS/CONTENT

The detailed programs of the two modules are described in the modules sheets.

RECOMMENDED READING/BIBLIOGRAPHY

Istituzioni di Matematica , M.Bertsch, Ed. Bollati Boringhieri
Analisi Matematica 1 e 2, M.Bramanti, C.D. Pagani, S.Salsa Ed. Zanichelli

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

For the start date of the lectures, please refer to the following link https://corsi.unige.it/corsi/11894/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The course Istituzioni di Matematiche (“Principles of Mathematics”) is divided into two modules: Elementi di Matematica (“Elements of Mathematics”, first semester) and Elementi di Matematica 2 (“Elements of Mathematics 2”, second semester).

The individual modules do not have separate final examinations; instead, each module includes only a partial test, which may contribute to the final assessment of the course.

The final examination for Istituzioni di Matematiche consists of a written examination and an oral examination, both covering the material taught in the two modules of the course.

The written examination may be replaced by passing two partial tests. The partial test corresponding to the module Elementi di Matematica, taught during the first semester, may only be taken during the first exam session of the winter examination period, scheduled in January. The partial test corresponding to the module Elementi di Matematica 2, taught during the second semester, may only be taken during the first exam session of the summer examination period, scheduled in June.

Students may access the oral examination if they obtain a grade of at least 18/30 in the written examination, or at least 18/30 in both partial tests. The oral examination may be made compulsory if the outcome of the written examination reveals significant gaps in substantial parts of the syllabus, or whenever the instructors deem an additional assessment of the student’s preparation necessary. All other students admitted to the oral examination may choose not to take it.

If the oral examination is not taken, the final recorded grade cannot exceed 24/30 and will coincide with the grade obtained in the written examination, or with the average grade of the two partial tests if this value is below 24/30.

The oral examination, when required or chosen by the student, must be taken within the same exam session as the written examination or, in the case of the partial tests, together with the second partial test.

Students with disabilities or specific learning disorders (DSA/SLD) are referred to the section Further Information.

ASSESSMENT METHODS

The examination is aimed at assessing:

• the acquisition of the concepts and technical content covered in the course;
• the ability to apply such concepts to problem solving;
• the student’s reasoning skills, with particular emphasis on the development and analysis of solution strategies;
• the command of appropriate mathematical language.

The written examination consists of several questions of progressively increasing difficulty, in order to allow an accurate assessment of the extent to which the learning objectives have been achieved. The examination board establishes assessment criteria providing for the assignment of partial scores to the different answers, also taking into account the complexity of the proposed topics. The overall score therefore makes it possible to evaluate the degree of achievement of the intended learning outcomes.

The oral examination is conducted by two instructors with expertise in the subject and is intended to further assess the achievement of the course learning objectives. If such objectives are deemed to have been achieved, the final grade is determined taking into account both the evaluation of the written examination (or the partial tests) and the outcome of the oral examination..

The examination is not passed if the learning objectives are not considered to have been achieved. In such cases, the student is encouraged to strengthen their preparation and to seek further clarification from the instructor, both with regard to the course content and to the study methods to be adopted.

FURTHER INFORMATION

For CTC the course of Institutions of Mathematics is a prerequisite to the 2nd-year course of Physical Chemistry 2, and to all the 3rd-year courses.

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 Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.