## Mathematics modules in the first academic year

The modules and courses in the first academic year give students the essential foundation for successfully completing their degree in mathematics.

They take traditional basic courses in analysis, linear algebra and discrete structures so that they can master the basic principles of mathematics. In the introductory stage, we also pay special attention to sustainable and networked learning, knowledge of interconnections between individual subject areas and the targeted and intensive introduction to the way of working, writing and thinking in mathematics.

- Analysis 1 and Analysis 2:

Lectures, large-group exercises, small-group exercises - Linear Algebra 1 and Linear Algebra 2 and Discrete Mathematics

Lectures, large-group exercises, small-group exercises - Mathematical Studies:

Courses for practical exercises in analysis, linear algebra and discrete structures & a mathematics presentation (workshop), plus the course offerings: Sessions for answering questions, assistance with homework and how to write down mathematics correctly - Principles of Mathematics:

Self-study module (no classes), office hours possible

Comprehensive knowledge of the essential fundamentals is indispensable for additional specialized training in mathematics. For this reason, sufficient knowledge must be demonstrated in the Fundamentals and Orientation Examinations (GOP)

As of the Winter Semester 2019/20, all students in the bachelor’s degree program in mathematics must pass the Fundamentals and Orientation Examinations (GOP) in the first year of their studies.

The GOP gives all students the opportunity togain academic orientation based on the discipline-specific content of the initial modules of the mathematics program. To pass the examinations, students must demonstrate that they are familiar with the essential principles of mathematics, which is required to continue studying in the mathematics program at TUM. The Fundamentals and Orientation Examinations (GOP) are also considered an excellent indicator for the student’s future academic success. The GOP helps students get a clear understanding of the program’s requirements during the first year of their studies. Students who do not pass the GOP must leave the degree program.

**The GOP (FPSO 2023, program start Winter Semester 2023/24) encompasses**

- obligatory modules in Analysis (written):
- MA0001 Analysis 1
- MA0002 Analysis 2

- obligatory modules in Linear Algebra (written):
- MA0004 Linear Algebra 1
- CIT1130005 Linear Algebra 2

- the module MA0007 Principles of Mathematics (oral).

By **the end of the second semester of enrollment in the degree program,** students must pass at least **one of the Analysis modules** (MA0001, MA0002), at least **one of the Linear Algebra module**s (MA0004, CIT1130005) **and **the oral examination in **Principles of Mathematics**. Two introductory modules from Analysis and Linear Algebra may be passed later on in their studies. If a student is not present for an examination and does not demonstrate a valid reason for their absence, this will be considered a failed attempt for this examination.

**The GOP (FPSO 2019, program start up to Winters Semester 2022/23) encompasses**

- the four introductory modules (written):

- MA0001 Analysis 1
- MA0004 Linear Algebra 1
- MA0002 Analysis 2 and
- MA0005 Linear Algebra 2 and Discrete Structures, and

- the module MA0007 Principles of Mathematics (oral).

By **the end of the second semester of enrollment in the degree program,** students must pass at least **two of the written introductory modules** **and **the oral examination in **Principles of Mathematics**. Students have **two attempts **to pass each of these modules. Two introductory modules can be taken later on in their studies. If a student is not present for an examination and does not have a valid reason for their absence, they will fail the examination.

The module Mathematical Studies is one component of the (math) coursework and consists of five different elements:

**1. Courses for practical exercises in analysis, linear algebra and discrete structures**

In these courses, students complete written exercises (homework) independently or in small groups. The instructors for the exercises are responsible for the organization of the courses and are also the contact person for questions about this component. To pass this component of the module, students must complete three of the four possible practical exercise courses in the basic modules “Analysis 1”, “Analysis 2”, “Linear Algebra 1” and “Linear Algebra 2”.

**2. Question & answer sessions**

In the basic modules “Analysis 1”, “Analysis 2”, “Linear Algebra 1” and “Linear Algebra 2”, the instructors of the respective lecture offer a session for answering questions equivalent to 1 weekly hour per semester (SWS).

Registration for this session is not required.

**3. Homework assistance**

In the basic modules “Analysis 1”, “Analysis 2”, “Linear Algebra 1” and “Linear Algebra 2”, we offer assistance with homework. In the curriculum, homework assistance equivalent to 1 weekly hour per semester is planned for each student. You can make use of this assistance more or less often, depending on your needs.

Registration for this session is not required.

**4. Writing down mathematics properly**

In the first semester, we offer the course “Writing Down Mathematics Properly”, which is the equivalent to 1 weekly hour per semester and is held in small groups. In these groups, the techniques for writing down mathematical texts correctly and providing proof using the right mathematical terminology are discussed in depth; these techniques are required in the practical courses and written exam.

Students can register via TUMonline.

**5. Mathematical presentation (workshop)**

Workshops on different topics are held at the beginning of the second semester. To pass the module, you must take one of these workshops equivalent to 1 weekly hours per semester and give an oral mathematics presentation.

You will be informed of the title of the workshops in the middle of the first semester; students register for the workshops during the first semester. Students usually receive the topic of their oral presentation at the end of the semester.

**Important remarks:**

**You must register yourself for the examinations of this module. **

For the homework sessions in the 1st semester, they are the examinations MA0006A1 and MA0006L1, and in the 2nd semester, they are examinations MA0006A2 and MA0006L2. For the workshops (MA0006P), students register using the matching system; observe the notifications via e-mail.

If you are **not registered** for the examination, your **credits** in the program will **not be recognized**.

In mathematics, it is essential to think long-term and holistically, to recognize interconnections between different fields and be able to communicate mathematical terminology and content clearly in a conversation.

We have included the module “Principles of Mathematics” as a required module in the curriculum so that students have time to gain competencies in the two key areas of analysis, as well as linear algebra and discrete structures. This module is a self-study module, which means there are no lessons. This module spans the first two semesters.

More information is also available in the module description.

**Examination**

The 30-minute oral examination takes place at the end of the second semester. In this examination, students demonstrate that they understand the fundamentals of analysis as well as linear algebra and discrete structures in a confident and integrated manner. Our questions are designed to assess if you can make connections within an individual area of mathematics and between different areas, as well as to assess whether you identify ways in which individual areas of mathematics can be applied to solve mathematical problems. In a direct interview with the examiner, students demonstrate whether they can present, explain and justify their solution approaches in a structured manner.

## Module paths and tracks

In our overview, you can find unbinding suggestions about when you should take certain elective modules. This overview is structured according to semesters and takes the selected area of specialization in the last academic year into consideration. Please follow the recommended prerequisites indicated in the module descriptions.