Calculus

A.Y. 2015/2016
12
Max ECTS
130
Overall hours
SSD
INF/01 MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09 SECS-S/02
Language
Italian
Learning objectives
The course is splitted in three units with the aim of providing the basic elements of Mathematics, Statistics and Computer Science.
Expected learning outcomes
Undefined
Course syllabus and organization

A-L

Responsible
Lesson period
year
modulo: Matematica generale
Course syllabus
Unit: Calculus:
Numbers: natural, rational and real numbers. The field R and its operations. The simbols of infinity. Inequalities in R.
Functions: 1:1, onto and bijective functions; composition and invertibility. Real functions of one real variable, graphics, monotonicity. Elementary functions (powers, logarithms, exponentials, ...).
Linear Algebra: vectors, matrices and their operations. Determinants, inversion, and ranks. Linear systems. Cramer's and Rouché's theorems.
Limits: definitions and basic properties; uniqueness; monotonicity. Limits for elementary functions. Uncertainties. Asymptotics and comparison results. Eulero's number "e" and some fundamental limits. Divergent and vanishing functions. Continuity and related proprties: Darboux and Weierstrass' results.
Differential calculus: first derivative, geometric and mechanical meaning, tangent line. Operations with derivatives: chain rule. Differentiation of elementary functions. Optimization and the classical theorems (Fermat, Rolle, Lagrange), monotonicity. Convexity. Hopital's rule. Qualitative study for the graph of a real valued function. Antiderivatives and some methods to compute indefinite integrals.
Integral calculus: definite integrals and their main properties. The Fundamental Theorem of Integral Calculus. Area of plane regions.

Formal prerequisites
None

Suggested textbook:
P. Marcellini, C. Sbordone, Calcolo - edizione aggiornata per i nuovi corsi di laurea, Liguori editore (2004).
Online course "Matematica Assistita", http://ariel.unimi.it/User/

Previous knowledge and exam
Knowledge of elementary algebra and plane trigonometry, use of logarithms in the real field.
Written and oral exam, being possible to replace the written final exam with medium term exams. Attendance is highly recommended.

Teaching methods:
Traditional

Teaching language
Italian

Web page http://users.mat.unimi.it/users/paleari
modulo: Laboratorio di Metodi Matematici e Statistici
Course syllabus
Unit: Mathematical and Statistical methods
Descriptive Statistics.
18) Population, sample, parameter, statistics. Types of data and variables. Sampling.
19) Graphs and tables. Frequency tables. Histograms/bar graphs.
20) Mean, modal value, median, midrange and their relations. Range, standard deviation, variance and their relations. Percentiles, quartiles and outliers. Boxplot. Weighted mean.
Probability and random variables.
21) Introduction.Events and space of events; probability o fan event.
22) Probability of the union and the intersection. Complemento of an event. Independence. Conditional probability. Bayes Theorem.
23) Random Variables. Expected value, variance and deviation standard of discrete r.v.s.
24) Discrete r.v.s: Binomial and Poisson. Continuous r.v.s: Uniform and Normal.
25) Sample distributions. Centrale Limit Theorem. Normal approximation of the binomial distribution.
Confidence intervals and Hypothesis tests.
26) Confidence interval for a proportion.
27) Confidence interval for the mean, and known/unknown variance. T-Student Distribution.
28) Confidence interval for the variance of a population normally distributed. Chi-square distribution.
29) Hypothesis tests:general concepts. Null and alternative hypothesis, test statistic, critical region, level of significance, critical values, one/two tails test, P-value, errors of the first/second kind, power of a test.
30) Hypothesis test for a proportion. Hypothesis test for one sample: test on the mean (known/unknown variance), test on the variance or on the standard deviation.
31) Inference for two independent samples: inference on two proportions. Inference on two means, either for independent samples or for coupled samples.
Linear dependence.
32) Linear correlation and hypothesi test on the correlation coefficient.
33) Linear regression.
34) Test of independence.
35)


Teaching resources:
1) Book: Triola M.M. e Triola M.F., Statistica per le discipline biosanitarie, Pearson, 2009.
2) Self-evaluation test: can be found on Ariel.

Previous knowledge and exam
Elements of algebra and basic use of the scientific calculator.
Written multiple choice exam.

Teaching methods: frontal lectures, attendante is hgihly suggested

Language: italian

Fromal prerequisites: none

Further information and WEB page: all the information concerning the course will be published on the Ariel webpage
modulo: Laboratorio di informatica
Course syllabus
PART I - Introduction to Computer Science
G.1. Introduction to Computer Science
G.2. Data representation
G.3. Computer hardware
G.4. Software
G.5. Computer networks

PART II - Data analysis using spreadsheets
F.1. Spreadsheets
F.2. Mathematical functions in Excel
F.3. Statistical functions in Excel
F.4. Graphics in Excel

PART III - Data management and databases
B.1. Data management
B.2. Storing data in databases
B.3. Data models
B.4. Relational databases
B.5. Creation of databases using Access
B.6. Query in Access
B.7. Databases on the web

PART IV - Internet and the Web
I.1. Internet
I.2. Web architecture
I.3. Standard for the Web
I.4. Markup languages
I.5. Client-side applications
I.6. Search engines

PART V - Computer Science and Biology
1. Use of PubMed and UNIMI Library Network for bibliographic search
2. Biological databases
3. Notions of Bioinformatics: sequence alignment, protein folding, molecular docking, bio-inspired algorithms

Teaching resources
Teaching resources consist in lecture notes, slides and spreadsheets exercises, all available through the online software platform.

Previous knowledge and exam
Before taking the examination, students are required to compile the self-assessment questionnaires that are available through the online software platform. The examination consists in a multiple answer test.
modulo: Laboratorio di informatica
INF/01 - INFORMATICS - University credits: 3
Basic computer skills: 18 hours
modulo: Laboratorio di Metodi Matematici e Statistici
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH - University credits: 0
Laboratories: 32 hours
Lessons: 8 hours
Professors: Cogliati Alberto, Maggis Marco
modulo: Matematica generale
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 48 hours
Lessons: 24 hours

M-Z

Responsible
Lesson period
year
modulo: Matematica generale
Course syllabus
Numbers: natural, rational and real numbers. The field R and its operations. The simbols of infinity. Inequalities in R.
Functions: 1:1, onto and bijective functions; composition and invertibility. Real functions of one real variable, graphics, monotonicity. Elementary functions (powers, logarithms, exponentials, ...).
Linear Algebra: vectors, matrices and their operations. Determinants, inversion, and ranks. Linear systems. Cramer's and Rouché's theorems.
Limits: definitions and basic properties; uniqueness; monotonicity. Limits for elementary functions. Uncertainties. Asymptotics and comparison results. Eulero's number "e" and some fundamental limits. Divergent and vanishing functions. Continuity and related proprties: Darboux and Weierstrass' results.
Differential calculus: first derivative, geometric and mechanical meaning, tangent line. Operations with derivatives: chain rule. Differentiation of elementary functions. Optimization and the classical theorems (Fermat, Rolle, Lagrange), monotonicity. Convexity. Hopital's rule. Qualitative study for the graph of a real valued function. Antiderivatives and some methods to compute indefinite integrals.
Integral calculus: definite integrals and their main properties. The Fundamental Theorem of Integral Calculus. Area of plane regions.

Formal prerequisites
None

Suggested textbook:
P. Marcellini, C. Sbordone, Calcolo - edizione aggiornata per i nuovi corsi di laurea, Liguori editore (2004).
Online course "Matematica Assistita", http://ariel.unimi.it/User/

Previous knowledge and exam
Knowledge of elementary algebra and plane trigonometry, use of logarithms in the real field.
Written and oral exam, being possible to replace the written final exam with medium term exams. Attendance is highly recommended.

Teaching methods:
Traditional

Teaching language
Italian

Web page http://users.mat.unimi.it/users/zanco
modulo: Laboratorio di Metodi Matematici e Statistici
Course syllabus
Descriptive Statistics.
18) Population, sample, parameter, statistics. Types of data and variables. Sampling.
19) Graphs and tables. Frequency tables. Histograms/bar graphs.
20) Mean, modal value, median, midrange and their relations. Range, standard deviation, variance and their relations. Percentiles, quartiles and outliers. Boxplot. Weighted mean.
Probability and random variables.
21) Introduction.Events and space of events; probability o fan event.
22) Probability of the union and the intersection. Complemento of an event. Independence. Conditional probability. Bayes Theorem.
23) Random Variables. Expected value, variance and deviation standard of discrete r.v.s.
24) Discrete r.v.s: Binomial and Poisson. Continuous r.v.s: Uniform and Normal.
25) Sample distributions. Centrale Limit Theorem. Normal approximation of the binomial distribution.
Confidence intervals and Hypothesis tests.
26) Confidence interval for a proportion.
27) Confidence interval for the mean, and known/unknown variance. T-Student Distribution.
28) Confidence interval for the variance of a population normally distributed. Chi-square distribution.
29) Hypothesis tests:general concepts. Null and alternative hypothesis, test statistic, critical region, level of significance, critical values, one/two tails test, P-value, errors of the first/second kind, power of a test.
30) Hypothesis test for a proportion. Hypothesis test for one sample: test on the mean (known/unknown variance), test on the variance or on the standard deviation.
31) Inference for two independent samples: inference on two proportions. Inference on two means, either for independent samples or for coupled samples.
Linear dependence.
32) Linear correlation and hypothesi test on the correlation coefficient.
33) Linear regression.
34) Test of independence.
35)

Teaching resources:
1) Book: Triola M.M. e Triola M.F., Statistica per le discipline biosanitarie, Pearson, 2009.
2) Self-evaluation test: can be found on Ariel.

Previous knowledge and exam
Elements of algebra and basic use of the scientific calculator
Written multiple choice exam.


Teaching methods
Frontal lectures, attendante is hgihly suggested

Language
Italian

Fromal prerequisites
None

Further information and WEB page
All the information concerning the course will be published on the Ariel webpage.
modulo: Laboratorio di informatica
Course syllabus
PART I - Introduction to Computer Science
G.1. Introduction to Computer Science
G.2. Data representation
G.3. Computer hardware
G.4. Software
G.5. Computer networks

PART II - Data analysis using spreadsheets
F.1. Spreadsheets
F.2. Mathematical functions in Excel
F.3. Statistical functions in Excel
F.4. Graphics in Excel

PART III - Data management and databases
B.1. Data management
B.2. Storing data in databases
B.3. Data models
B.4. Relational databases
B.5. Creation of databases using Access
B.6. Query in Access
B.7. Databases on the web

PART IV - Internet and the Web
I.1. Internet
I.2. Web architecture
I.3. Standard for the Web
I.4. Markup languages
I.5. Client-side applications
I.6. Search engines

PART V - Computer Science and Biology
1. Use of PubMed and UNIMI Library Network for bibliographic search
2. Biological databases
3. Notions of Bioinformatics: sequence alignment, protein folding, molecular docking, bio-inspired algorithms

Teaching resources
Teaching resources consist in lecture notes, slides and spreadsheets exercises, all available through the online software platform.

Previous knowledge and exam
Before taking the examination, students are required to compile the self-assessment questionnaires that are available through the online software platform. The examination consists in a multiple answer test.
modulo: Laboratorio di informatica
INF/01 - INFORMATICS - University credits: 3
Basic computer skills: 18 hours
modulo: Laboratorio di Metodi Matematici e Statistici
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
SECS-S/02 - STATISTICS FOR EXPERIMENTAL AND TECHNOLOGICAL RESEARCH - University credits: 0
Laboratories: 32 hours
Lessons: 8 hours
modulo: Matematica generale
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 48 hours
Lessons: 24 hours