Ateneo - UPO

The course aims at providing students with basic mathematical knowledge also applied to biological problems.

Villani, Gentili: Matematica. Comprendere e interpretare fenomeni delle scienze della vita, Mc Graw Hill. Benedetto, Degli Esposti, Maffei: Matematica per le scienze della vita, C.Ed. Ambrosiana.Materiali didattici disponibili sulla piattaforma Moodle dell’Università.

Getting students to learn some elementary concepts and methods of mathematics useful to deal with the typical topics of the applications of mathematics to empirical science. Developing competences in order to solve simple math problems and to be able to effectively communicate the obtained results.

Basic competencies in Mathematics achieved during the High School.

Interactive lectures, on-going exercises, use of software to foster classroom interaction and provide formative feedback, use of the university's Moodle platform and mathematical software. Development of 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-disabilitiesStudents with disabilities, learning disabilities or special education needs, after they 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 and, in the cases specified below, a possible subsequent oral discussion. The written test lasts 75 minutes and consists of a minimum of 5 to a maximum of 7 questions. The maximum 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 may be requested by the examination board if it is necessary to clarify aspects of the written test or to verify more thoroughly the understanding of the concepts and methods used. The oral discussion focuses mainly on the solutions proposed in the written exam and on the theoretical concepts related to them. 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.During the course special online self-assessment tests are carried out on Moodle platform.

1. Number systems. Approximations. Percentages. Equations and inequalities. 2. Analytic geometry: Cartesian coordiante system, straight lines and conics. Linear systems. 3. Real functions, graphs, links between graphs and formulas. Trigonometric functions and examples of periodic phenomena. Examples of exponential and logarithmic growth. Function composition. Curves intersections. Limits and continuity. 4. Derivatives. Continuity and differentiability. Derivatives of elementary functions and their graphical representation. Increasing and decreasing functions, maxima and minima of a function. Study of function. Applications of differential calculus. 5. Primitives. Integrals. Fundamental theorem of calculus. Applications of integration.

Knowledge and understanding: Knowledge of some basic mathematical concepts and methodologies, specifically: real numbers and their representations, main elementary functions, the derivative and its geometric meaning, simple integrals, and area calculation.Applying knowledge and understanding: Ability to apply the aforementioned concepts and methodologies to the modeling of simple mathematics problems and 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.