Mathematics Lab II

Code:

M2036

Acronym:

M2036

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Web Page:	https://moodle2425.up.pt/course/view.php?id=6020
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Applied Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:MA	39	Official Study Plan	2	-	3	24	81

Teaching language

Portuguese
Obs.: Poderá ser feito em inglês o esclarecimento de dúvidas de estudantes que não dominem o português.

Objectives

Acquaint students with computational problem-solving in mathematics applications to other fields of knowledge or the mathematics itself, using graphic visualization techniques and implementation of numerical algorithms.

Learning outcomes and competences

Upon completing this curricular unit, the student should be able to use computer algebra systems to deal with mathematical application problems.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Co-requirements: knowledge of the subjects studied in other curricular units in the 1st and 2nd years.

Program

An introduction to the SageMath computer algebra system aiming to apply mathematical concepts and results, particularly those studied in other subjects in the 1st and 2nd years.
The illustration of applications is made at the level of analytical and numerical treatment of mathematical models in other branches of knowledge. The models in question will involve, in particular, the topics listed below, which will also be study studied:

• solving nonlinear equations (numerically);


• interpolation (namely polynomial interpolation);


• ordinary differential equations, including numerical methods.

Mandatory literature

Paul Zimmermann et al.; Computational Mathematics with SageMath, SIAM, 2018. ISBN: 978-1-611975-45-1 (https://www.sagemath.org/sagebook/english.html)

Complementary Bibliography

George A. Anastassiou , Razvan A. Mezei; Numerical Analysis Using Sage, Springer, 2015. ISBN: 978-3-319-16739-8 (https://doi.org/10.1007/978-3-319-16739-8)
Gregory V. Bard; Sage for Undergraduates, American Mathematical Society, 2015. ISBN: 978-1470411114 (Freely available in the internet: http://gregorybard.com/sage_for_undergraduates_color.pdf.zip)
Vários autores; Documentação disponibilizada na página do sagemath (https://doc.sagemath.org/)

Teaching methods and learning activities

Contact hours consist of laboratory classes, which are based on the use of the Sagemath computer system. 
In these classes are introduced symbolic/numerical manipulation and graphic visualization techniques on various topics, and students are instructed to apply these techniques, solving and interpreting exercises directly on the computer terminal.
Support is provided to students in clarifying doubts both in the content and in solving exercises.

Software

SageMath (https://www.sagemath.org/)

keywords

Physical sciences > Mathematics > Computational mathematics > Computing systems

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	57,00
Frequência das aulas	24,00
Total:	81,00

Eligibility for exams

There is no requirement.

Calculation formula of final grade

In the classes, four sets of exercises will be carried out on dates to be announced.
The first three sets of exercises each weigh 3 points, and the two best-ranked ones contribute to the final grade.
The fourth set of exercises weighs 5 points, which can contribute towards the final grade.
The classifications obtained in the exercises can be used in the exam, as described below.

Approval of the curricular unit is obtained in the final exam.

The final exam will have three parts.
The first part corresponds to the first three sets of exercises, weighing 6 points.
The second corresponds to the fourth set of exercises, weighing 5 points.
The student may choose not to solve one or both of these exam parts. Each unsolved part is assigned the classification obtained by the student in the corresponding sets of exercises.
The third part of the exam weighs 9 points.

Special assessment (TE, DA, ...)

Special assessments are done in the form of an exam.

Classification improvement

All students will be able to improve their classification in the exam of the appeal season.