Teaching plan for the course unit

 

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General information

 

Course unit name: Advanced Methodology in Mathematics

Course unit code: 568174

Academic year: 2018-2019

Coordinator: Carlos Antonio D'Andrea

Department: Department of Mathematics and Computer Science

Credits: 3

Single program: S

 

 

Estimated learning time

Total number of hours 75

 

Face-to-face learning activities

30

 

-  Lecture

 

15

 

-  Lecture with practical component

 

15

Supervised project

10

Independent learning

35

 

 

Competences to be gained during study

 


CB6: Students should acquire knowledge and understanding to provide a basis or opportunity for originality in developing and/or applying ideas, often within a research context.

 


CB7: Students should be able to apply their knowledge and ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

 


CB8: Students should be able to integrate knowledge and handle complexity, and formulate judgements based on information that was incomplete or limited, including the reflection on social and ethical responsibilities linked to the application of their knowledge and judgements.

 


CB9: Students should be able to communicate their conclusions and the knowledge and reasoning derived from these to specialist and non-specialist audiences in a clear and unambiguous way.

 


CB10: Students should have the learning skills to allow them to continue studying in an independent way.

 


CG1: Students should apply their acquired knowledge and skills by planning their own timing and available resources.

 


CG2: Students should be able to access specialized bibliographic data bases using new technologies.

 


CG3: Students should be able to gather the information needed to address a problem and synthesize it.

 


CG4: Students should be able to work in groups.

 


CE4: Students should have the ability to design and develop logical-mathematical reasoning and identify errors in incorrect reasoning.

 


CE6: Students should possess the ability to state and verify statements in various areas of mathematics, and to transmit the acquired mathematical knowledge, orally and in writing.

 


CE7: Students should be able to understand by themselves research and/or expository articles in any area of mathematics.

 


CE8: Students should be able to summarize the content of seminars and conferences in several areas in mathematics.

 


CE9: Students should be able to choose and use suitable computational technology to address problems related to mathematical research and applications.

 

 

 

 

Learning objectives

 

Referring to abilities, skills


To learn to search for bibliography and mathematical information online.

 


To acquire the ability to make oral and written presentations in mathematics.

 


To acquire the ability to understand mathematical lectures, colloquiums and seminars.

 

 

Teaching blocks

 

1. TeX and LaTeX

1.1. Introduction to Tex

1.2. Introduction to LaTeX: Papers, books

1.3. Beamer: Presentations, posters

1.4. Graphics: TikZ, PGF, XY-pic, jPicEdt

1.5. Interaction with other programs: Mathematica, MATLAB

1.6. Writing mathematics on the web: MathJax

2. Reference sources in mathematics

2.1. Interactive mathematics websites: MathOverflow, nLab, StackExchangeNetwork.

2.2. Mathematical reviews on the web: Mathscinet and Zentralblatt.

2.3. Mathematic Subject Classification and keywords

2.4. Resources online: arxiv, Project Euclid, etc.

3. Oral presentations

3.1. Sharing Maths background and interests with the rest of the class

3.2. Designing a class for undergraduate or graduate students

3.3. Presentating current research/professional work to a specialized audience

3.4. Actively participating as part of the audience with questions and comments

4. Mathematical activities

4.1. Attending conferences, seminars and/or colloquiums in the field

4.2. Introduction to research in mathematics and its specialized applications

4.3. Reporting progress in final projects to the rest of the class

 

 

Teaching methods and general organization

 

This course will have a part devoted to some sessions on TeX and LaTeX. In this section, students will be introduced to and evaluated in the use of LaTeX as a tool for writing texts and presentations in mathematics.
The other part of the course will focus on introducing them to the world of professional mathematics. Students are expected to attend to talks, seminars and/or colloquiums in the field, to search bibliography on the Internet, to prepare and present written reports and oral presentations on elementary and more advanced topics in mathematics, and also to participate in group discussions on how to give talks in the field.
 

 

 

Official assessment of learning outcomes

 

Active participation in class will be worth 40% of the final grade for continuous evaluation. Students are expected to give short talks in basic mathematics, and also presentations on academic resources. They should also engage in group discussions about how to present their research/innovation results and the possible applications of them.

Written reports are also mandatory. They will be worth 20% of the final grade for continuous evaluation.

The TeX/LaTeX section will be worth 20% of the final grade of the continuous evaluation.


At the end of the semester, students must present a report with the state of the art of their Final Master Project, and  give a presentation of the project of this in the Master Students’ Seminar. This will award them the remaining 20% of the final grade.

The Reevaluation will consist of the written and oral presentation of the Final Master Project, following suggestions for improvement. The final grade will be the maximum between  the grades obtained in the Reevaluation and the continuous evaluation.


Students who do not reach a minimum grade of 3 (over 10) during the continuous evaluation cannot apply for Reevaluation.

 

 

Examination-based assessment

The single evaluation option will consist of exercise-solving problems in TeX/LaTeX and delivering 3 oral presentations on topics to be determined by the instructors. In addition, the student must present a written report on their Final Master Project, and deliver a 20-minute talk about it. All these activities must be completed before the semester is over.

The reevaluation will consist of the written and oral presentation of the final project, following suggestions for improvement. The final grade will be the highest of the grades obtained in the reevaluation and the continuous or single evaluation.

Students who do not reach a minimum grade of 3 (out of 10) during the single evaluation cannot apply for Reevaluation.