Unit MATHEMATICS FOR APPLICATIONS
- Course
- Biotechnology
- Study-unit Code
- GP000515
- Curriculum
- In all curricula
- Teacher
- Roberta Filippucci
- CFU
- 6
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Base
- Area
- Discipline matematiche, fisiche, informatiche e statistiche
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
MATHEMATICS FOR APPLICATIONS - Canale A
| Code | GP000515 |
|---|---|
| CFU | 6 |
| Teacher | Roberta Filippucci |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Discipline matematiche, fisiche, informatiche e statistiche |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Sequences and functions of a single variable. Examples of elementary functions and biological models. Limits, differentiability, monotonicity, concavity and convexity. Graphs of functions. Riemann integral, integral function. Integration techniques. Descriptive statistic. Elements of probability. Statistic tests (Chi quadro, t-Student..). Linear regression. |
| Reference texts | M. Bramanti C. Pagani & S. Salsa, ANALISI MATEMATICA 1, Zanichelli. S. Salsa & A. Squellati, ESERCIZI DI ANALISI MATEMATICA 1, Zanichelli. M. C. Withlock & D. Schluter, ANALISI STATISTICA DEI DATI BIOLOGICI, Zanichelli |
| Educational objectives | The student should acquire a basic knowledge in mathematical analysis, descriptive statistic and some notions of inferential statistics. The course matter is part of the contents of a standard reformed first level course for Italian three-year degrees in mathematics. Even the setting is reformed, and the textbooks used are rich of examples and counterexamples, and therefore seem to be optimal to achieve a good understanding of the topics starting from exercises, that is from applications. Main knowledge acquired will be: - To know the main topics of mathematical analysis and how to apply them to the natural sciences, - To know the theory of diagnostic tests and some statistical hypotheses tests, - To know several tools to solve elementary and basilar exercises, - To read and understand texts of Mathematical Analysis and Statistics, - To work in teams, but also in autonomy. The skills listed above are set out in the framework of the professions related to both a traditional Biotechnologist, and a Biotechnologist oriented to technical and/or industrial activities. Main competence (i.e. ability to apply the main knowledge acquired) will be: - To apply the theory to the resolution of exercises or problems based on models developed during lessons - To analyze and treat simple concrete statistical problems by choosing the right statical test to apply, - To solve some easy mathematical problems in the field of applied mathematics, indipendently. |
| Prerequisites | To better understand the topics covered in the course the student should be familiar with pre-university education notions such as decomposition of simple algebraic expressions, set theory (union, intersection, complement, difference, Venn diagram, algebra of sets), resolution of linear and quadratic equations and inequalities, manipolation of polynomials. In particular during the first 12 hours of the course, this part is called "corso di allineamento", a short review of the above topics together with a review of the main definitions and elementary functions (polynomial functions, exponential function, logarithm and circular functions) will be performed. Hence it is crucial for all students to attend this first part of the course. |
| Teaching methods | The course is split in theoretical lessons and practical lessons, in these latter several exercises are carried out in class. The course is organized as follows: the first 12 hours are called "corso di allineamento" and contain the prerequisites, then the remaining 45 hours are divided into 21 hours of theory, together with different examples and counterexamples and at least 24 hours of practical exercises. A tablet is used to project lessons for the mathematical analysis part , while for the statistics part a PowerPoint presentation will be used. In the tutorial service the students will be followed individually by the teacher. |
| Other information | The teacher makes available educational materials in UNISTUDIUM , useful for a better understanding of the course, in order to help and to let the students pass easily the exam. Furthermore all the previous written tests can be found in UNISTUDIUM, where you can also find the results of the written test and the date of the relative oral exam. |
| Learning verification modality | The exam is a written exam both with open answers and with multiple choice tests. In particular the written test consists of solving 4 or 5 exercises on topics which cover all the programme for the part of Mathematical Analysis (for the first 2 hours) and 3 exercises of Statistics (for 1 hour). Exercises assigned are modelled on those solved during the lessons. The written exam is designed to assess the ability of solving concrete or teoric problems. The written test is positively concluded if the grade is greater or equal to 18. Eventually the written test can be replaced by progress assessments. Furthermore, only under the request of the student, an oral exam can be performed after having concluded positively the written test. In this case the oral exam consists of a discussion on two or three topics on all the programme, mainly starting from exercises, and takes about 20 minutes. The oral test is designed to assess the level of knowledge attained by the student on the theoretical contents and on and counterexamples). Finally, the oral examination allows the teacher to verify the performance of the student and his/her ability to organize the presentation in autonomy. During the written test the student is allowed to use his/her notes and books. To solve the statistic exercises a calculator is useful. It not possible to use the cellular phone calculator. |
| Extended program | Sequences, converging sequences. Functions of a single variable. Examples of elementary functions and biological models. Limits, continuous functions, differentiability, Fermat's theorem, Rolle's theorem, Lagrange's theorem, increasing and decreasing functions, concave and convex functions. Graphs of functions. Riemann integral: definition and properties, integral function and its properties. The fundamental theorem of integral calculus, mean value theorem of integral calculus. Integration by parts. Change of variable in an integral. Introduction to Statistic, describing data sets, using statistics to summarize data sets (mean value, median, mode..). Elements of probability. Bayes' theorem. Discrete random variables and normal random variable. Estimation. Testing statistical hypotheses. Hypotheses test concerning two populations. Linear regression. |
MATHEMATICS FOR APPLICATIONS - Canale B
| Code | GP000515 |
|---|---|
| CFU | 6 |
| Teacher | Roberta Filippucci |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Discipline matematiche, fisiche, informatiche e statistiche |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Sequences and functions of a single variable. Examples of elementary functions and biological models. Limits, differentiability, monotonicity, concavity and convexity. Graphs of functions. Riemann integral, integral function. Integration techniques. Descriptive statistic. Elements of probability. Statistic tests (Chi quadro, t-Student..). Linear regression. |
| Reference texts | M. Bramanti C. Pagani & S. Salsa, ANALISI MATEMATICA 1, Zanichelli. S. Salsa & A. Squellati, ESERCIZI DI ANALISI MATEMATICA 1, Zanichelli. M. C. Withlock & D. Schluter, ANALISI STATISTICA DEI DATI BIOLOGICI, Zanichelli |
| Educational objectives | The student should acquire a basic knowledge in mathematical analysis, descriptive statistic and some notions of inferential statistics. The course matter is part of the contents of a standard reformed first level course for Italian three-year degrees in mathematics. Even the setting is reformed, and the textbooks used are rich of examples and counterexamples, and therefore seem to be optimal to achieve a good understanding of the topics starting from exercises, that is from applications. Main knowledge acquired will be: - To know the main topics of mathematical analysis and how to apply them to the natural sciences, - To know the theory of diagnostic tests and some statistical hypotheses tests, - To know several tools to solve elementary and basilar exercises, - To read and understand texts of Mathematical Analysis and Statistics, - To work in teams, but also in autonomy. The skills listed above are set out in the framework of the professions related to both a traditional Biotechnologist, and a Biotechnologist oriented to technical and/or industrial activities. Main competence (i.e. ability to apply the main knowledge acquired) will be: - To apply the theory to the resolution of exercises or problems based on models developed during lessons - To analyze and treat simple concrete statistical problems by choosing the right statical test to apply, - To solve some easy mathematical problems in the field of applied mathematics, indipendently. |
| Prerequisites | To better understand the topics covered in the course the student should be familiar with pre-university education notions such as decomposition of simple algebraic expressions, set theory (union, intersection, complement, difference, Venn diagram, algebra of sets), resolution of linear and quadratic equations and inequalities, manipolation of polynomials. In particular during the first 12 hours of the course, this part is called "corso di allineamento", a short review of the above topics together with a review of the main definitions and elementary functions (polynomial functions, exponential function, logarithm and circular functions) will be performed. Hence it is crucial for all students to attend this first part of the course. |
| Teaching methods | The course is split in theoretical lessons and practical lessons, in these latter several exercises are carried out in class. The course is organized as follows: the first 12 hours are called "corso di allineamento" and contain the prerequisites, then the remaining 45 hours are divided into 21 hours of theory, together with different examples and counterexamples and at least 24 hours of practical exercises. A tablet is used to project lessons for the mathematical analysis part , while for the statistics part a PowerPoint presentation will be used. In the tutorial service the students will be followed individually by the teacher. |
| Other information | The teacher makes available educational materials in UNISTUDIUM , useful for a better understanding of the course, in order to help and to let the students pass easily the exam. Furthermore all the previous written tests can be found in UNISTUDIUM, where you can also find the results of the written test and the date of the relative oral exam. |
| Learning verification modality | The exam is a written exam both with open answers and with multiple choice tests. In particular the written test consists of solving 4 or 5 exercises on topics which cover all the programme for the part of Mathematical Analysis (for the first 2 hours) and 3 exercises of Statistics (for 1 hour). Exercises assigned are modelled on those solved during the lessons. The written exam is designed to assess the ability of solving concrete or teoric problems. The written test is positively concluded if the grade is greater or equal to 18. Eventually the written test can be replaced by progress assessments. Furthermore, only under the request of the student, an oral exam can be performed after having concluded positively the written test. In this case the oral exam consists of a discussion on two or three topics on all the programme, mainly starting from exercises, and takes about 20 minutes. The oral test is designed to assess the level of knowledge attained by the student on the theoretical contents and on and counterexamples). Finally, the oral examination allows the teacher to verify the performance of the student and his/her ability to organize the presentation in autonomy. During the written test the student is allowed to use his/her notes and books. To solve the statistic exercises a calculator is useful. It not possible to use the cellular phone calculator. |
| Extended program | Sequences, converging sequences. Functions of a single variable. Examples of elementary functions and biological models. Limits, continuous functions, differentiability, Fermat's theorem, Rolle's theorem, Lagrange's theorem, increasing and decreasing functions, concave and convex functions. Graphs of functions. Riemann integral: definition and properties, integral function and its properties. The fundamental theorem of integral calculus, mean value theorem of integral calculus. Integration by parts. Change of variable in an integral. Introduction to Statistic, describing data sets, using statistics to summarize data sets (mean value, median, mode..). Elements of probability. Bayes' theorem. Discrete random variables and normal random variable. Estimation. Testing statistical hypotheses. Hypotheses test concerning two populations. Linear regression. |