MATHEMATICS-1

The Mathematics course is a compulsory course for all students and it is proposed as the first course of quantitative area: it takes place in fact 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 of study.

Due to the percistency of the current health emergency it is not possible to establish now the precise teaching method adopted for this course. We can expect that at least half of the activities will be delivered in distance (through video recordings and other teaching materials uploaded on the Moodle platform or via lectures held on Hangouts Meet). The description provided here below applies to lessons delivered both in presence or in distance.

The attendance and the effective participation in the teaching activities proposed in the lectures and practice lectures of the course, tutoring activities and to all the activities proposed via the Moodle platform during the course, along with the individual study, allow the student to acquire the ability to appropriately employ the tools of differential calculus and optimization related to problems that have been formalized in mathematical language. Through the study and discussion of examples and exercises the student is started to contextualize their knowledge in the field of managerial disciplines.

Expected learning outcomes.
A) Knowledge and understanding skills:
a.1) to understand the meaning of the concepts of function, derivative, integral
a.2) to know the main techniques of the calculation for functions of one and two variables
a.3) to understand the fundamentals of financial mathematics
a.4) to know the main operations between matrices and the matrix representation of a linear system

B) Ability to apply knowledge and understanding:
b.1) ability to calculate derivatives and simple integrals
b.2) ability to solve simple optimization problems in one or two variables, even with constraints
b.3) ability to solve simple exercises of classical financial mathematics
b.4) ability to set up and solve systems of linear equations
b.5) ability to apply the above knowledge in examples of economic/managerial vocation.

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.

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 be revised by the student, for example, by studying chapters 0, 1 and 2 of the reference textbook and by attending the Additional Learning Requirements of Mathematics courses
(ALR). Some of these topics are also reported in the syllabus of the CISIA tolc-E test for the access to the degree program (see www.cisiaonline.it).

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.

Knut Sydsæter - Peter Hammond - Arne Strøm, Metodi matematici per l'analisi economica e finanziaria con MyMathLab e eText, Pearson, Milano, 2015 (Chapters 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13).

book + MyMATHLAB
ISBN9788865189535

or

e-book + MyMATHLAB

Other teaching material will be made available on the Moodle platform of the course.
ISBN9788865189542

Grading is based on a final written exam.
The exam verifies that the students have acquired the concepts presented during the lectures, are familiar with the calculus techniques, have learned the theoretical results in order to use this knowledge and skills in solving assigned exercises.

The written exam consists of 8 exercises: 4 exercises are related to the first module of the course and 4 related to the second module. They are open-ended exercises. During the test, the 4 exercises related to the first part of the course (duration 45 minutes) are first assigned and then, after a 15-minute break, the 4 exercises related to the second part of the course (45 minutes). All problems carry equal number of marks (1/8 of the total score).
In the written exam only the use of your pen is allowed, instead electronic tools, notes or books are not allowed.
Registration for the written tests is mandatory.

Partial exams
A possibility of an intermediate evaluation of the students' preparation level (first partial exam) will be provided at the end of the first teaching period (first 5 weeks), provided that the students solved the exercises assigned weekly. The students with sufficient preparation level at this stage (with a score of at least 15/30) will be allowed to answer only to the questions concerning the second module of the course (second partial exam) at the first written exam (primo appello). The final evaluation in this case is obtained as the mean value of the two partial examinations.

The precise form of the final written exam will depend on the health situation and on the disposition of the national authority at the time. Detailed instructions will be given by the instructors in time to prepare for the exam.

In the two periods of teaching activity the course consists of 30 + 30 hours of face to face lectures 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 a rigorous reasoning, several examples and applications to economics are discussed during the lectures. Students are required to register for the course on the Moodle platform.

Depending on the health situation, updates concerning the activities and their scheduling will be made available on the Moodle platform (moodle.unive.it) and on the personal pages of the instructors.

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). Students are required to register for the course on the Moodle platform.

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.

written

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development