Admission requirements for Mathematics

It is generally expected that students understood the material taught in secondary school and continue to grasp these concepts.

General information
If you fulfil these requirements, you should have no trouble with the coursework during the Assessment Year. The required subject matter is listed below.

You should be both familiar with these terms and comfortable applying the skills in practice. In addition, elementary algebraic skills, in particular basic algebraic operations and dealing with fractions, are necessary.

1. Arithmetic and algebra

• Power with rational exponents (including calculation rules) 
• Basic rules for inequalities 
• Solution of linear systems of equations with a maximum of three variables 
• Solution of quadratic equations with one variable 
• Specific terms and the fundamental associated relationships: absolute value, sigma sign, factorial, binomial coefficients, notation of elementary set theory 2

2. Functions 

• Polynomial functions 
• Simple rational functions 
• Root functions 
• Exponential functions including calculation rules; the number e 
• Logarithmic function including calculation rules for logarithms 
• Trigonometric functions (degrees, radians, definition in the unit circle); addition theorems for cosine and sine; representation of periodic events 
• Concept of inverse function with concrete examples (square function/square root, exponent/logarithm)

The ability to sketch graphs and recognise functions based on their graphical representation are also requirements. When handling exponential and logarithmic functions as well as for trigonometric functions, knowledge of the most important function values is also a necessity.

3. Analysis 

• Limits and continuity of functions in the graphic sense 
• Concept of the derivative and its various terms 
• Recognition of various types of derivatives (tangent line, speed, etc.) 
• Meaning of the first derivative (growth behaviour of functions) 
• Derivative formulas for basic functions xr, cos, sin, tan, exp, ln 
• Product and quotient rule, chain rule 
• Determination of extrema 
• Determination of integrals 
• Calculation of integrals (according to the rules of derivation specified in 3.5 Special integration methods such as partial integration, integration by substitutions, partial fractions are not assumed to be known.)

Literature

The above concepts can be understood with the help of the following books: 

• Bachmann, Heinz. Einführung in die Analysis . Bände 1 bis 3. (Zürich: Sabe, 1975) 
• Deller, Henri; Peter Gebauer und Jörg Zinn. Algebra 1 Aufgaben. (Zürich: Orell Füssli, 2000) 
• Deller, Henri; Peter Gebauer und Jörg Zinn. Algebra 2 Aufgaben. (Zürich: Orell Füssli, 2000) 
• Keil, Karl-August; Johannes Kratz und Hans Müller. Die Infinitesimalrechnung. (München: Bayerische Verlagsanstalt, 1997)