Linear Algebra and Analytic Geometry

Code:

M1002

Acronym:

M1002

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Web Page:	https://moodle2324.up.pt/course/view.php?id=1956
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Computer Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	1	Official Study Plan	3	-	6	48	162
L:BIOINF	34	Official Study Plan	1	-	6	48	162
L:CC	101	study plan from 2021/22	1	-	6	48	162
			2
L:G	3	study plan from 2017/18	2	-	6	48	162
			3
L:IACD	95	study plan from 2021/22	1	-	6	48	162
L:Q	4	study plan from 2016/17	3	-	6	48	162

Teaching language

Suitable for English-speaking students

Objectives

Upon completing this course, the student should master the main concepts of Linear Algebra and Analytic Geometry. Namely, he must understand, be able to work with and use the main properties of the concepts of matrix, determinant, real vector space and linear function.

Learning outcomes and competences

Upon completing this course, the student should be able to: make the main matrix operations; solve systems of linear equations using matrices; using matrices to discuss systems of linear equations; calculate determinants; apply the properties of determinants; recognize real vector subspaces; determine bases for real vector spaces; calculate the dimension of vector spaces; recognize linear functions, and their main properties; determine or justify why there are no linear functions satisfying certain conditions; work with matrices associated with linear functions; determine eigenvectors and eigenvalues ​​of matrices; diagonalize a matrix (if possible); using some properties of matrix diagonalization. Identify conic sections.

Working method

Presencial

Program

1. Linear systems and matrices


2. Matrices


3. Determinants of square matrices


4. Real vector spaces


5. Linear functions


6. Eigenvectors and eigenvalues and diagonalization of matrices


7. Conic sections

Mandatory literature

Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Edwards jr. C. H.; Elementary linear algebra. ISBN: 0-13-258245-7
Monteiro António; Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
Mansfield Larry E.; Linear algebra with geometric applications. ISBN: 0-8247-6321-1

Teaching methods and learning activities

Contact hours are divided into theoretical and practical classes. In the first, the contents of the course are presented using examples to illustrate them and to guide the students. In the practical classes, previously announced exercises and problems are solved. Support materials are available on the course webpage. In addition to the classes, the students can schedule presencial or online sessions to clarify their questions.

Evaluation Type

Distributed evaluation without 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	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

Not applicable

Calculation formula of final grade

The content of this course will be divided into two parts, each evaluated separately, on the scale of 0 to 10 points. It is a necessary condition to obtain approval to have a minimum of 2,5 points in the second part. If the previous condition is met, the final grade will be the sum of the points of the two parts.

Regular Season:

• The first part will be evaluated by test during the semester. The date will be announced later.
• The second part will be evaluated on the date set for the examination of this UC during the regular season. It should be noted that the first part will not be evaluated on the date set for the examination of this UC during the regular season.

Second examination season (except for classification improvement exams):

• The exam of the second examination season will be divided into two parts.
• Students may choose not to do one of the parts. In that case, the grade of that part will be the one obtained in the regular season.
• If a part is solved in the second examination season exam, its grade is calculated as follows (CN - regular season grade; CR - second examination season exam grade):
• If CR>=CN-2, the final grade of that part will be the maximum{CN,CR};
• If CR<CN-2, the final grade of that part will be the mean{CN,CR}.

Special assessment (TE, DA, ...)

Any examination required under special statutes consist of a written exam that can be preceded by an oral or written evaluation.

Classification improvement

• Students wishing to take a grade improvement examination in the regular season will have to follow the rules indicated above for the evaluation of the remaining students during the regular season.


• Students who want to improve their grades at the second examination season will have to do both parts on the day scheduled for the second season exam and the final grade will be the one obtained in that exam. Thus, the grades obtained in the regular season do not count in the second examination season for the purpose of grade improvement.

Observations

Article 13 of the General Regulation for the Assessment of Students in First Cycles, Integrated Masters Studies Cycles and Second Cycles of the U.Porto, approved on 19 May 2010 (cf. http://www.fc.up. pt/fcup/documentos/documentos.php?ap=3&ano=2011): "Fraud committed in taking a test, in any form, implies its annulment and communication to the statutorily competent body for possible disciplinary proceedings. "

Any student may be required to take an oral test to clarify doubts that may have arisen in relation to the applicable tests or assessment work.