## MATHEMATICS

Algebra and Trigonometry acquired in high school: simplifying exponents, radicals, logarithms, fractions, factoring polynomials, solving equations and inequalities. Graphing points in the plane. Reading 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%.

In this course the foundations of calculus, probability and statistics are presented. One of the major goals of college – level mathematics education is to move students from computational processes to conceptual thinking and communication. That is the biggest difference between this course and a high school course. Mathematics is more than a bag of tricks and there are not a limited number of types of problems that can be asked! The goal in class is to prepare students to do their homework and not necessarily to show them how to do it. The learning occurs when students can move themself into the unknown territory.

Understand what a function is and how it can be represented geometrically as a graph. Learn some standard function manipulations (algebraic combinations, composition, inverses, etc.) focusing on how such manipulations affect the shape of the graph. Learn algebraic and geometric properties of classic functions (polynomial, rational, exponential, logarithmic, trigonometric, etc.), emphasizing the relationship between them. Explore the basic two ideas for nearly all mathematical formulas in science: the derivative, which measures the instantaneous rate of change of a function and the definite integral, which measures the total accumulation of a function over an interval. The rules by which we can compute the derivative and the integral of any function are called calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. Finally, the course offers an introduction to probability and statistics, approaching the study of discrete random variables (geometric, hyper-geometric, Bernoulli, binomial, Poisson), statistical variables, measures of central tendency, measure of dispersion, the Pearson correlation coefficient, the coefficient of determination, linear regression.

For Italian readers:

- Benedetto, Degli Esposti, Maffei. Matematica per le Scienze della Vita. Ambrosiana.

- Marco Abate. Matematica e Statistica. Le basi per le scienze della vita. McGraw-Hill.

These textbooks promote the idea of mathematics as the science of patterns. They are 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 once a week for three sessions of 45 minutes each class period in the morning. In addition, week lectures are supported by a recitation session per week, which will meet for two sessions of 45 minutes in one afternoon. Every student is urged to participate at the recitations associated to the lectures.

A graphing calculator is encouraged for class discussion and for homework, but not allowed for exams or quizzes. No specific calculator is endorsed, if you have one already continue to use that one. In order to pursue a deeper acquaintance with the topics presented in the course, it is strongly recommended the use of the following math site: https://www.khanacademy.org/