Ateneo - UPO

The aim of the course is to provide students with a mastery of basic knowledge in mathematics also applied to modelling problems of natural phenomena.

M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 1 con elementi di geometria e algebra lineare, Zanichelli, Bologna W. Dambrosio, Analisi Matematica. Fare e comprendere, Zanichelli C.B Boyer, Storia della matematica, Mondadori

To provide to the student the knowledge of the mathematical instruments and concepts necessary to face the problems along the degree course in Chemistry. They will be able to use the learned methods in the solution of mathematical problems. Communication skills: the students will be able to use a suitable mathematical language in relation to the course arguments and methods. Making judgements: stimulate the critical sense in the justification of the strategy adopted in the solution of the exercises.

Basic competencies in Mathematics achieved during the High School.

Interactive lectures, practical exercises, use of software to promote classroom participation and provide formative feedback, use of the university's Moodle platform and mathematical software. Workshop activities promoting cooperative learning and the development of problem-solving skills. Innovative teaching activities.

Learning monitoring: workshops and activities also supported by the use of the Moodle platform of the University. These activities have an educational goal: they are discussed and corrected with the students.During classroom discussions, the origin and evolution of mathematical ideas and theories is analysed, and their foundations, concepts and methods will be explored. The factors that influenced, favoured or hindered its development is also examined, along with the historical interactions of mathematics with other scientific disciplines.Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities. Students with disabilities, learning disabilities or special education needs, after they had contacted the university staff, can refer to the teacher in charge of the course to define the examination modalities.

The exam consists of a written test followed by an oral discussion. Access to the oral discussion is conditional upon passing the written test.

The written test lasts 90 minutes and consists of a minimum of 4 to a maximum of 7 questions. The score assigned to each question is indicated in the text of the test. The questions are designed to assess: knowledge and understanding of the mathematical concepts and methods presented in the course; the ability to identify and apply appropriate methods to solve problems; the ability to interpret the results obtained and to evaluate their consistency and plausibility; the ability to present the procedure followed and to develop arguments using clear, correct, and appropriate mathematical language. Answers must include the essential steps of the procedure and adequate justifications. Scoring takes into account conceptual and procedural correctness, completeness of the solution, appropriateness of the chosen method, consistency of the argument, and precision of notation. A correctly set up but incomplete procedure may receive partial credit. The overall score for the written test is obtained by summing the scores assigned to individual questions according to the criteria indicated above. The written test is passed with a score of not less than 18/30. Achieving a passing grade requires knowledge of the fundamental concepts and methods of the course and the ability to apply them substantially correctly to solve standard problems. Furthermore, the ability to illustrate the main steps of the procedure in an understandable manner and to provide an essential justification for the answers is required. Inaccuracies, non-substantial calculation errors, or limited incompletenesses are compatible with achieving a passing grade, provided they do not show significant gaps in the understanding of fundamental concepts. Grades progressively higher than the pass mark correspond to a broader, more solid, and in-depth knowledge of the content, greater accuracy and completeness in answering the questions, increasing autonomy in the choice and application of methods, and a more complete ability to argue and justify choices and statements. The highest grades are awarded in the presence of full mastery of the content and methods, correct, efficient, and adequately motivated procedures, as well as a rigorous, clear, and precise presentation. The oral discussion is aimed at delving deeper into aspects of the written test and verifying knowledge of the concepts and methods used. During the oral exam, theoretical concepts and mathematical methods learned during the course are discussed. The outcome of the oral discussion contributes to the overall evaluation and may confirm, increase, or decrease the grade obtained in the written test.

During the written test, only textbooks and paper notes are permitted, in addition to non-graphical scientific calculators (without internet access). Exchanging material or using other electronic devices is prohibited.

Self-assessment and formative assessment activities are made available on the DIR platform during the course.

Natural numbers, integers, rational numbers and real numbers: recalls structures and proprieties. Complex numbers: definitions and basic properties, polar form, algebraic operations and nth roots. Basic of Algebra. Outlines of historical-epistemological aspects related to the development of algebra. Real functions of one variable: domain, co-domain, properties. Limits and continuity: proprieties and theorems. Historical outline of calculus. Derivatives: definition and geometrical meaning. Maxima, minima, inflection points. Root-finding algorithms. Integrals: definite and indefinite integrals; main methods of integration. Fundamental theorem of calculus. Applications of integral calculus to areas computation. Sequences and series: a brief outline.

Knowledge and understanding: Knowledge of some basic mathematical concepts and methodologies. Specifically: knowledge of definitions related to complex numbers; knowledge of elementary functions; knowledge of the concepts of continuous and differentiable functions; knowledge of the concepts of definite and indefinite integrals.Applying knowledge and understanding: Ability to use complex numbers; ability to identify the properties of functions; ability to calculate derivatives and integrals; ability to apply the aforementioned concepts and methodologies to the interpretation of graphs.Making judgements: Ability to understand the potential and limitations of the concepts and methodologies adopted.Communication skills: The ability to communicate the description and rationale of one's problem-solving procedures in a clear and comprehensive manner.Lifelong learning skills: Ability to utilize the educational material for critical and well-reasoned study.