Mathematical Laboratory

Code:

M1025

Acronym:

M1025

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

Active?	Yes
Web Page:	https://moodle2324.up.pt/course/view.php?id=2228
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	76	Official Study Plan	1	-	3	24	81
L:MA	56	Official Study Plan	1	-	3	24	81

Teaching language

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

Objectives

Use the computer algebra system Sagemath to treat problems on real analysis, linear algebra and analytic geometry, and some elementary mathematics topics. Particular attention is given to the consolidation, through the development and analysis of algorithms and geometric interpretation, of the concepts and problems covered in the courses Linear Algebra and Analytic Geometry I (M1010), Real Analysis I (M1011) and Topics in Elementary Mathematics (M1024).

Learning outcomes and competences

Upon completing this curricular unit, the student should be able to use sagemath to deal with problems stemming from real analysis to linear algebra and analytic geometry: solving them, graphing and interpreting their solutions.

Working method

Presencial

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

Co-Requirements. Syllabus of the curricular units: Linear Algebra and Analytic Geometry I (M1010), Real Analysis I (M1011) and Topics in Elementary Mathematics (M1024).

Program

• Introduction to Sagemath: using the documentation; variables; functions; programming structure; ploting functions.


• Computational treatment of topics whose interest is pointed out by the teachers of the remaining curricular units of the same school year.


• Illustration of elementary mathematics applications, particularly in the field of cryptography.


• Graphical representation and interpretation of solutions of equations and inequalities in R and R^2.


• Properties and geometric interpretation of real functions of a real variable.


• Properties and geometric interpretation of limits of sequences.


• Systems of linear equations: numerical resolution, graphical representation and interpretation of the solution.

Mandatory literature

Gregory V. Bard; Sage for Undergraduates, Mathematical Society, 2015. ISBN: 978-1470411114 (Freely available in the internet: http://gregorybard.com/sage_for_undergraduates_color.pdf.zip)

Complementary Bibliography

P. Zimmermann, A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. M. Thiéry, E. Bray, J. Cremona, M. Forets, A. Ghitza, and H. Thomas; Computational Mathematics with SageMath, 2018 (Freely available in: http://dl.lateralis.org/public/sagebook/sagebook-ba6596d.pdf)
George A. Anastassiou , Razvan A. Mezei; Numerical Analysis Using Sage, Springer, 2015. ISBN: ISBN: 978-3-319-16739-8 (https://doi.org/10.1007/978-3-319-16739-8)
Vários autores; Documentação disponibilizada na página do sagemath (https://doc.sagemath.org/)

Teaching methods and learning activities

The contact hours consist of laboratory classes. They will proceed to the resolution, with discussion by the teacher and the students, of exercises proposed in the exercise sheets or class.
Some supporting material will be made available to the classes, as well as the resolution of some of the proposed exercises.
Support will be provided to students in clarifying doubts both in terms of content and in solving exercises.

Software

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

keywords

Physical sciences > Mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Teste	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

No requirement.

Calculation formula of final grade

Tests
Approval to the curricular unit can be obtained by carrying out two tests.
The first test takes place roughly in the middle of the semester, and the second at the end of the semester. Each of the tests is classified for 20 points.

• A classification greater than or equal to 5 values is required in each test.

The final classification is obtained using the following formula

0.5x(T1+T2),

where T1 and T2 are, respectively, the ratings of the first and second tests.

Examination of the appeal period
Students who have not passed tests will be able to pass the exam at the time of appeal.
Upon application, students who have passed may use the resource exam for grade improvement.
The appeal exam consists of two parts, each corresponding to one of the modules.

Observation
The evaluation moments may include a computer test with a written or oral component.

Examinations or Special Assignments

The exams required under special conditions will consist of a computer test with a written or oral component, which can be preceded by an oral eliminatory exam.

Special assessment (TE, DA, ...)

The exams required under special conditions will consist of a computer test with a written or oral component which can be preceded by an oral eliminatory exam.

Classification improvement

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