Topics of Mathematics and Statistics

Topics in Mathematics and Statistics is a curricular unit of fundamental Mathematics of the 1st year and 1st semester of the study plan of the Bachelor Degree in Solicitorship and Administration, which aims to harmonize and adjust the level of mathematical knowledge of students in this course. Thus, the basic knowledge is the one common to the various programs of the Mathematics disciplines in Portugal, in the components of Algebra, Functions and Statistics, in the different branches of compulsory education in Portugal (http://www.dge.mec.pt/).

The classes are, according to what is determined in the curriculum plan, both theoretical and practical, planned and prepared to involve students actively in various moments or throughout the entire class.

In the theoretical part of the lesson, the expository method will be frequently used to introduce concepts, fundamental results, and methods, interspersed with tasks that encourage active participation by all students (interactive lectures). Thus, it  will included posing questions to and by students, orally and/or on a platform, as well as proposing debates/discussions in small groups on certain exposed aspects/topics.

The practical part will be designed for the comprehensive development of the listed skills, through commented exemplification of procedures and/or problem-solving under the guidance/tutoring of the teacher. Autonomous work or work in small groups will be encouraged. There will be a strong interaction between theory and practice, with a central focus on visualizing and dealing with actual real scenarios.

It is assumed that the student attends classes regularly and is available for continued involvement beyond the classroom, including initiating or completing tasks agreed upon during class.

All supporting materials are available on the InforEstudante|Nonio platform. Other platforms that allow for interaction may also be used.

Objectives

This UC aims to provide students with knowledge and fundamental technical skills to understand, select and apply mathematical or statistical base methods necessary to solve real problems inherent to the profession they propose to pursue.

Competencies

It is intended that the student be able to:

• recognize application contexts, in the professional areas of the course, in which fundamental mathematical and statistical concepts and techniques can be applied;
• select mathematical and statistical methods for solving real problems;
• obtain the mathematical formulation of problems, in the form of equations and inequalities, if necessary, using functions;
• identify and apply the fundamental mathematical techniques necessary for its resolution;
• analyze data sets using distribution tables, graphing, and statistical measures;
• apply correlation and regression techniques to data analysis and prediction;
• interpret and communicate mathematical and statistical results clearly and accurately.

0. Review
    Approximate value and rounding
    Absolute variation and relative/percentage variation
    Sets
    Polynomial equations and inequalities

1. Mathematics
    Functions
    1. Generalities. Graphics.
    2. Some special functions: polynomial functions – linear function and quadratic function; exponential function and logarithmic function.
    3. Derivative: geometric notion of derivative; interpretation; derivation rules; applications.

2. Statistics
    Descriptive statistics
    1. Introduction and terminology. Data organization.
    2. Measures of central tendency. Dispersion measures. Shape features.
    Correlation and Linear Regression
    1. Motivation. Nature of the relationship between variables. Correlation.
    2. Linear regression and the least squares line. Coefficient of determination. Forecast.

NAO

Fundamental:

• Harshbarger, R., Reynolds, J. (2006). Matemática Aplicada: Administração, Economia e Ciências Sociais e Biológicas, 7.ª edição. McGraw Hill.
• Webster, A. (2006). Estatística Aplicada à Administração e Economia. McGraw-Hill.
• Slides and worksheets available at InforEstudante|Nonio.

Complementary:

• Caraça, B.J. (1998). Conceitos Fundamentais de Matemática. Gradiva.
• Curto, J.D. (2019). Potenciar os Negócios? A Estatística Dá uma Ajuda! (Muitas Aplicações em Excel e poucas fórmulas…), 3.ª Edição. Edição do Autor.
• Garcia, R., Rosa, M.J.V., Barbosa, L. (2017). Que número é este? Um guia sobre estatísticas para jornalistas. Pordata, Fundação Francisco Manuel dos Santos. https://www.ffms.pt/publicacoes/detalhe/1963/que-numero-e-este
• Khan Academy Portugal: Matemática. https://pt-pt.khanacademy.org/math/
• Sydsæter, K., Hammond, P., Strøm, A., Carvajal, A. (2020). Essential Mathematics for Economic Analysis, 6th Edition. Pearson.