MATHEMATICS

Single discipline educational activity

Course Sheet

Academic Year of enrolment:

2015/2016

Type of Course:

Basic

Optional/Mandatory:

Compulsory

Degree:

Bachelor's Degree Programme in NATURAL SCIENCES

Disciplinary Sector:

MATHEMATICAL ANALYSIS

Credits:

Programme Year:

Professor and Collaborators:

PENSAVALLE Carlo Andrea

Hours of classroom activity:

Prerequisites:

Algebra and Trigonometry acquired in high school: simplifying exponents, radicals, logarithms, fractions, factoring polynomials, solving equations and inequalities. Graph points in the plane. Read information from graphs, translating verbal information into math symbols. The Pythagorean Theorem.

AF code:

40000691

Assessment Methods

Verification of learning:

The course score will be determined by the following weighted average: Written Exams 60%, Final Oral Exam 40%.

Teaching period

First semester

Objectives

Fundamentals of linear algebra, calculus, probability and statistics. The common thread is the function concept and its role in the mathematical modeling to solve problems. One of the major goals of college – level Mathematics Education is to move students from computational processes to conceptual thinking and communication. Mathematics is more than a bag of tricks! The goal in class is to prepare students to deal with problems that must be solved and not just show them how it's done. The real learning happens when they move autonomously and explore unknown territories.

Contents

Scalar and vector valued functions of real variables. Algebraic and geometric transformations of elementary functions. Linear, bilinear and quadratic forms. Eighenvalues and eighenvectors. The Differential and Anti-Differential Operators. Derivatives and Definite Integrals. The Fundamental Theorem of Calculus. The gradient vector, the Jacobian matrix. Ordinary differential equations with separable variables. Linear ordinary differential equations of the first order. The Cauchy problem. Random variables and main probability density functions. The maximum likelihood method for estimating statistical parameters.

Recommended Bibliography

For Italian readers:
Marco Abate. Matematica e Statistica. Le basi per le scienze della vita. McGraw-Hill. This textbook promotes the idea of mathematics as the science of patterns. It is rich of many examples inspired by natural, physical and biological phenomena. – Handouts and teacher prepared materials.
For English readers:
Larissa Fradkin.Elementary Algebra and Calculus. Bookboon.com
Leif Mejlbro. Introduction to Probability. Bookboon.com
David Brink. Essential of Statistics. Bookboon.com

Teaching Methods

Lecture sessions meet three times a week for two sessions of 45 minutes each class period. In addition, weekly lectures are supported by a recitation session per week, which will also meet for two sessions of 45 minutes in one afternoon. Every student is urged to participate at the recitations associated to the lectures.

Contacts/More Information

Readiness to offer individual assistance in a foreign language to incoming students (English): YES
Availability of supporting material and bibliographic references also in a foreign language (English): YES
Serge Lang. A First Course in Calculus. Springer – Verlag. This textbook covers all the topics taught in the course in a simple but complete way.
Readiness to accept examination of incoming students also in a foreign language (English) : YES

Other courses

Course year: 1

GENERAL ZOOLOGY
9 credits
BASIC CHEMISTRY
9 credits - Base
MATHEMATICS
6 credits - Base
PHYSICAL GEOGRAPHY
10 credits - Base
PHYSICS
6 credits - Base
GENERAL BOTANY
6 credits - Caratterizzante
SYSTEMATIC BOTANY
7 credits - Caratterizzante
APPLICAZIONI MINERO-PETROGRAFICHE AI BENI CULTURALI
3 credits - A scelta dello studente
ENVIRONMENTAL RISKS
3 credits - A scelta dello studente
ETHOLOGY
3 credits - A scelta dello studente
COMPUTER SKILLS
4 credits - Altro
FURTHER LANGUAGE KNOWLEDGE
4 credits - Altro

Course year: 2

METODI MATEMATICI APPLICATI ALLE SCIENZE NATURALI
6 credits - Base
ORGANIC CHEMISTRY
6 credits - Base
GENETICS
9 credits - Caratterizzante
PETROGRAPHY AND MINEROLOGY
10 credits - Caratterizzante
SYSTEMATICS AND ANIMAL PHYLOGENIS
10 credits - Caratterizzante
VERTEBRATE ZOOLOGY
6 credits - Caratterizzante
ENVIRONMENTAL RISKS
3 credits - A scelta dello studente
PLANT BIOACTIVE MOLECULES
3 credits - A scelta dello studente
ENGLISH LANGUAGE ABILITY
4 credits - Lingua/Prova Finale

Course year: 3

ECOLOGY
12 credits
GEOLOGY
10 credits - Caratterizzante
PLANT ECOLOGY
6 credits - Caratterizzante
SOIL SCIENCES
6 credits - Caratterizzante
BIOCHEMISTRY
6 credits - Affine/Integrativa
ECONOMY AND MANAGEMENT OF THE ENVIRONMENT AND RESOURCES
6 credits - Affine/Integrativa
FINAL TEST
6 credits - Lingua/Prova Finale
FURTHER HOURS OF TRAINEESHIP
4 credits - Altro
TRAINING
8 credits - Altro

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MATHEMATICS