# Mathematics modules in the 1st academic year

The information on this page is about the modules for the 1st year of studies for the Bachelor in Mathematics, with the Subject Examination and Study Regulations from 2019.

## The 1st year of studies

The modules and teaching events in the 1st year of studies provide you with a fundamental basis for successful math studies.

So that you gain command over these skills, you visit the classic basic lectures in analysis, as well as linear algebra and discrete structures. During this introductory phase, we also offer a particular focus on networked learning, awareness for connections between individual subject fields, and a guided and intensive introduction into the very special methods of working, writing and thinking in mathematics.

### Modules and their teaching methods

- Analysis 1 and Analysis 2:

Lectures, central practice units and small practice groups. - Linear Algebra 1 and Linear Algebra 2 and Discrete Structures:

Lectures, central practice units and small practice groups. - Studying Mathematics:

Practice units in Analysis, Linear Algebra and Discrete Structures and a mathematics presentation (Workshop)

Furthermore, the teaching units: Question Hour, Homework Help and How to write Math. - Foundations in Mathematics:

Self-study module (no teaching events), consultation hours are possible.

For your future math education, the comprehensive understanding of these elementary foundations is essential. It is therefore necessary to prove your knowledge through the passing of the Foundations and Orientation Exam (GOP) - see below.

### Contact

#### Linear Algebra and Discrete Structures

**Lecturer WS19/20**

Prof. Christian Liedtke

**Practice Tutor WS19/20**

David Mundelius, M. Sc.

## Foundations and Orientation Exam (GOP)

With the **Grundlagen- und Orientierungsprüfung (GOP)** students have the opportunity to attain basic knowledge of the diverse subject content of the Bachelor program and therefore to orientate themselves for their further studies in mathematics. The course gives students in their first year of study a realistic insight into the demands of mathematical studies. By passing the exam, students demonstrate that they have mastered the essential mathematics foundations, which are prerequisite for the continuation of their mathematical studies. The GOP is also an excellent indicator of the success of each individual's studies. Those students who do not pass the GOP must withdraw from the program.

**The GOP comprises**

- the four foundation modules (written exams):
*Analysis 1*,*Linear Algebra 1*,*Analysis 2*and*Linear Algebra 2 and Discrete Structures*and - the module
*Foundations in Mathematics*(oral exam)*.*

By the end of the second semester, all students must have passed **at least two of the four written exam modules**, as well as the oral exam "Foundations in Mathematics". For each exam, you have two chances to attain a pass. The two remaining written exams must be passed during the further study program. Not attending the exam without good, documented reasons will count as if you have attended the exam and failed.

## Studying Mathematics

The module Studying Mathematics counts as one of the (mathematical) study attainments and consists of 5 different blocks:

**1. Practice attainments in Analysis, Linear Algebra and Discrete Structures**

For these teaching units you submit written practice exercises individually or in a group. The organization takes places through the practice tutors of each unit, who are also your contact persons, should you have any questions regarding this unit. In order to pass this part of the module, you must complete 3 of the 4 possible practice attainments in the basic modules "Analysis 1", "Analysis 2", "Linear Algebra 1" and "Linear Algebra 2 and Discrete Structures".

**2. Question Hour**

Within the basic modules "Analysis 1", "Analysis 2", "Linear Algebra 1" and "Linear Algebra 2 and Discrete Structures", the lecturer offers a Question Hour of 1 semester-week hour (SWS) for each course. It is not necessary to register for the question hour.

**3. Homework Help**

For the basic modules "Analysis 1", "Analysis 2", "Linear Algebra 1" and "Linear Algebra 2 and Discrete Structures" we also offer homework help. In the study plan, the attendance at homework help hours for each student is planned with 1 SWS. However, you can use this assistance more or less often, as you require. Registration is not necessary.

**4. How to write math**

In the first semester, the teaching unit "How to write math" takes place in small groups for 1 SWS. In these groups, we present techniques for the correct notation of mathematical texts and proofs, as well as correct terminology, as required in the practice groups and examinations.

Registration is possible via TUMonline.

**5. Mathematics Presentation (Workshop)**

At the beginning of the second semester a variety of workshops take place. In order to pass the module, each student must visit one of these workshops with a duration of 1SWS and successfully present mathematical talk.

The titles of the workshops are published in the middle of the 1st semester. The theme for your talk is generally issued at the end of the lecture period in the first semester.

### Contact

**General Information**

Dr. Florian Lindemann

**Practice attainments, Question Hour and Homework Help**

Contacts for Analysis and Linear Algebra and Discrete Structures

**How to write Math**

**Mathematics Presentation (Workshop)**

Maria Präßl, Dr. Kathrin Ruf

## Foundations in Mathematics

In Mathematics it is essential, to think in a networked and sustained manner, to recognize the connections between the separate subject fields and to be able to communicate mathematical terms and facts in an understandable manner.

In order for students to have time to gain these competences in the two central fields of analysis, as well as linear algebra and discrete structures, we have established "Foundations of Mathematics" as an obligatory module in the curriculum. This is a self-study module, which means that there are no taught units, and the module is part of both the first and second semesters.

Further information can be found in the Module Description.

### Examination

The 30-minute oral examination takes place at the end of the second semester. Here you are expected to prove how intrinsically and interlinked you understand the foundations of analysis, linear algebra and discrete structures. With various questions, we test whether you can establish connections within one, as well as between the subject fields, and can implement the knowledge from single fields in order to contribute to solving mathematical problems, also in other fields. In direct conversation with the examiner, the students are tested whether they can present their ideas to solve problems in a structured manner, and how well they can explain and justify their approach to solving a problem.