Preparatory Courses for Students with Vocational Qualifications

Studying without A-Levels / Abitur: The TUM School of Computation, Information and Technology offers a preparatory course for students with vocational qualifications (as defined in §88(6) BayHIG) in order to be eligible for university admission. 

You have vocational qualifications and would like to be eligible for subject-specific university admission? Then you will have to prove your knowledge of mathematics at TUM by taking a written exam. We support you in preparing for the exam – with a free course and a tutorial on a voluntary basis.

Current information

The next preparation course will take place in summer 2024. It will be similar to last year's, hence the following information for reference.

Lecture

Date:
Monday to Friday,
July 24 to 28, 2023

Time:
9:00 to 12:00 with breaks

Place: Room MI 00.09.022

Tutorial

Date:
Monday to Thursday,
July 24 to 27, 2023

Time: 
13:30 to 15:30

Place: Room MI 00.09.022

Mathematics Exam

Date:
Friday, August 28, 2023

Time:
13:00
Duration: 180 minutes

Place: Room MI 00.09.022

Mathematics exam for university admission

The mathematics admission exam is obligatory to qualify for subject-specific university admissions and is a written test.  

Registration

Please register via email to Prof. Dr. Johann Hartl: hartl@ma.tum.de

Permitted aids

During the exam, you are permitted to use a formula collection booklet of your choice and all your course documents, such as scripts and exercise papers with the sample solutions.

Preparatory course

The preparatory course for vocationally qualified applicants lasts a week (5 workdays). It includes a lecture and a tutorial. In addition, you will be given exercises to solve on your own.

Please note: The teaching language is German. 

Content of the course

  • Numbers and quantities
  • Graphs
  • Vectors
  • Analytical geometry
  • Real functions
  • Limits and continuity 
  • Basics of differential and integral calculations

Material

If you want to prepare for the course, you can, for example, look at one of the following books:

  • Wilfried Scharlau: Schulwissen Mathematik
    Various editions published by different publishers.
  • Jan van de Craats, Rob Bosch: Grundwissen Mathematik 
    Ein Vorkurs für Fachhochschule und Universität 
    Heidelberg: Springer-Verlag 2010, 324 Seiten, 19.95 EUR
    ISBN 978-3-642-13500-2

All textbooks for the upper level of the Gymnasium (secondary level = grades 11 to 13 (in case of G9) or grades 11 to 12 (in case of G8)) are suitable – even older ones, they do not have to be the latest.

12./13. Schuljahr 

Friedrich Barth, Gert Krumbacher:
Analysis anschaulich 1
Schülerbuch, 240 Seiten, ISBN 978-3-637-11401-2, Bestell-Nr. 11401-2, Preis 24.95 €.

Inhalt: 

1. Funktion und Graph / 2. Polynomfunktion / 3. Ableitung der Polynomfunktion / 4. Anwendungen / 5. Scharen / 6. Technik des Ableitens / 7. Stetigkeit und Grenzwert / 8. Differenzierbarkeit

12./13. Schuljahr 

Marianne Baierlein, Friedrich Barth, Ulrich Greifenegger, Gert Krumbacher: 
Anschauliche Analysis 2 – Grundkurs
Schülerbuch, 168 Seiten, ISBN 978-3-637-02291-1, Best.-Nr. 02291-1, 25.95 €.

Inhalt: 

1. Stammfunktion und unbestimmtes Integral / 2. Das bestimmte Integral bei positiven Funktionen / 3. Das bestimmte Integral, die Integralfunktion / 4. Die Exponentialfunktion / 5. Die Ableitung der Umkehrfunktion / 6. Die Logarithmusfunktion / 7. Rationale Funktionen

Elisabeth Barth, Friedrich Barth, Gert Krumbacher: 
Anschauliche Analytische Geometrie
Schülerbuch, 304 Seiten, ISBN 978-3-637-03500-3, Best.-Nr. 03500-3, 28.95 €.

Inhalt: 

1. Was ist Analytische Geometrie? / 2. Lineare Gleichungssysteme / 3. Punkte und Vektoren im Raum / 4. Elementare Vektorrechnung / 5. Lineare Abhängigkeit / 6. Der abstrakte Vektorraum / 7. Geraden im Raum / 8. Ebenen / 9. Skalarprodukt / 10. Vektorprodukt / 11. Normalformen / 12. Kugel

Formel-Sammlungen

Friedrich Barth, Paul Mühlbauer, Friedrich Nikol, Karl Wörle: 
Mathematische Formeln und Definitionen
118 Seiten, ISBN 978-3-7627-3272-3, Best.-Nr. 3272-3, 11.50 €.

Inhalt:

Grundbegriffe – Algebra – Geometrie – Analysis - Komplexe Zahlen – Vektoren – Analytische Geometrie im R² – Analytische Geometrie im R³ – Abbildungen im R² – Inzidenzgeometrie – Aus-sagenalgebra – Stochastik

  • graph paper
  • a pencil (H, 2H)
  • coloured pencils
  • ruler/set square
  • compass
  • calculator (may not be used during the exam)