## MATHEMATICS

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.

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

Fundamentals of calculus, probability and statistics. The common thread is the function concept and its role in the mathematical modeling to solve deterministic, probabilistic and statistical 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.

Functions and their graphs. Algebraic combinations, compositions, inversions of functions and their graph manipulations. Algebraic and geometric properties of polynomial, rational, exponential, logarithmic, trigonometric functions. Homographic, Gaussian and Sigmoid functions. The basic two ideas for nearly all mathematical formulas in science: the derivative, and the definite integral. The Fundamental Theorem of Calculus. Approach to one of the central objects of mathematical modeling: Ordinary Differential Equations. They arise in many different contexts throughout mathematics and science, governing dynamical phenomena. The Cauchy Problem. The separable ordinary differential equations and the linear equations of first and second order.

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

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.

Face to face lessons and recitation sessions.

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