MATHEMATICS - 2

The Mathematics course is a compulsory course for all students. It is the first course in the quantitative area: it takes place in the first two periods of the first year of the course of study, the first module (Mathematics 1) in the first period and the second module (Mathematics 2) in the second period. The aim is to provide a common language of a logical-mathematical type as well as the essential notions of calculus, financial mathematics, and linear algebra. These contents are analytical tools necessary to face the theoretical contents and to solve the managerial problems that are proposed in the following courses of business administration, economics, and quantitative aspects of the course study.

At the end of “Mathematics I” students should have acquired the fundamentals of calculus in one variable. Specifically, students should have acquired the following skills.

a) Knowledge and understanding
a.1) Knowledge of basic definitions in calculus in one variable, such as: derivatives, limits, integrals;
a.2) Interpretation of the above definitions in terms of geometric properties, supported by a span of crucial examples.

b) Ability to apply knowledge and understanding
b.1) Ability to compute, for functions of one variable: derivatives, limits, integrals (elementary, by parts, by substitution);
b.2) Ability to analyse properties of functions of one variable, such as monotonicity, convexity, behaviour in the long run;
b.3) Ability to compute stationary and inflection points; ability to maximize/minimize a quantity described by a one variable function, particularly when it describes an economic variable;
b.3) Ability to interpret all above properties in economic/managerial examples.

c) (Lifelong) learning skills
c.1) Improved ability to handle a formal language, to make logic deductions; enhance rigorous rational thinking;
c.2) Improved ability to translate a problem into formal terms, solve it and interpret the solution in terms of the original problem.

Students must be clear of didactic debts (Additional Learning Requirements, ALR).

Topics usually taught in undergraduate courses are assumed to be well known, in particular: set theory notation, real numbers; algebraic rules; fractions; powers; inequalities; absolute value; single variable elementary functions, linear, power, exponential, logarithmic and their graphs; graphs obtained by translation from graphs of elementary functions; equations and inequalities (also parametric), first and second degree, fractional, exponential and logarithmic; analytical geometry: cartesian coordinates, distance between two points, equation of a straight line, parabola and circumference and their graphic representation; symbol of summation.
These topics can also be revised by the student, for example, by studying chapters 0, 1, and 2 of the reference textbook and by attending the ALR class.

The program of the whole course (12 cfu, 60 hours of lectures) is the following:

FIRST MODULE (Mathematics 1)
Domain, limits and derivative of single variable functions.
Single variable optimization.
Integrals.
Present and future values in financial mathematics, streams of cash flow.

SECOND MODULE (Mathematics 2)
Functions of several variables.
Unconstrained and constrained optimization with several variables.
Matrix algebra and linear equations systems.

K. Sydsaeter, P. Hammond and A. Strom, Essential Mathematics for Economic Analysis (Fifth Edition), Pearson, 2016.

ISBN:
978-1-292-07461-0 (print);
978-1-292-07465-8 (pdf);
978-1-292-07470-2 (epub).

The evaluation is based on a written exam, accompanied by ongoing assessments, particularly with reference to asynchronous classes (the course is delivered in a blended mode). The ongoing activities are presented in the form of Moodle quizzes. Students must successfully complete the activities labelled as "mandatory". They do not contribute to the final grade, but passing these activities is a prerequisite for admission to the written exam.
The final exam is divided into two parts. The first part, called Part 0, aims to assess basic but essential skills. It is based on three simple exercises and is a prerequisite for access to the second part of the exam, which covers knowledge and skills from the entire course. For convenience, this second part is divided into two sections. Each section consists of two exercises that aim to assess the knowledge and the ability to apply the knowledge acquired during the lessons, both synchronous and asynchronous.
Exercises similar to those proposed in the final exam are available on the e-learning platform, either as weekly exercise sheets or as past exam papers or written exam simulations.
Regarding the grading scale (how grades will be assigned):
A. Scores in the range of 18-22 will be awarded for:
- sufficient knowledge and applied understanding of the program;
- sufficient ability to solve the proposed problems;
- limited ability to explain the mathematical procedures underlying the solution of the proposed exercises.

B. Scores in the range of 23-26 will be awarded for:
- fair knowledge and applied understanding of the program;
- fair ability to solve the proposed problems;
- fair ability to explain the mathematical procedures underlying the solution of the proposed exercises.

C. Scores in the range of 27-30 will be awarded for:
- good or excellent knowledge and applied understanding of the program;
- good or excellent ability to solve the proposed problems;
- good or excellent ability to explain the mathematical procedures underlying the solution of the proposed exercises.
D. Honors will be awarded for:
- excellent knowledge and applied understanding of the program, and an outstanding ability to present and explain the solution of the exercises.

In the two periods of teaching activity, the course consists of 30 + 30 hours of face-to-face lectures (unless the Ministry and/or the University dispose otherwise) during which the teacher describes the topics of the course, proposes, analyzes and solves examples and exercises. Other 10 + 10 hours are held by a teaching assistant proposing further exercises in the two modules.
The students in their individual work are required to understand and assimilate the basic concepts of the theory, comparing the personal notes of the course with the recommended texts, so as to be able to face and identify the solution of exercises and problems.
In order to develop language precision and rigorous reasoning, several examples and applications to economics are discussed during the lectures.

Detailed information on the program and study materials will be communicated at the beginning of the course on the e-learning page of the course (moodle.unive.it).

Accessibility, Disability and Inclusion
Accommodation and support services for students with disabilities and students with specific learning impairments
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support
services and accommodation available to students with disabilities. This includes students with
mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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