Preparatory Course in Mathematics (University-wide)
in partnership with the Munich Adult Education Centre
The Munich Adult Education Centre, in collaboration with the Hochschule München, offers a 10-day preparatory maths course for first-year students. It is aimed at beginners in all technical and business-related subjects.
In this course, you can fill any gaps in your school-leaving knowledge or refresh your understanding, thereby making it easier for you to get started in this important foundation subject. You will revise the relevant mathematics material from the upper secondary school curriculum without getting ahead of the topics covered in the foundation year. At the same time, you will become familiar with the standard methods of teaching used at university (lectures in large groups and tutorials in small groups).
The lecturers are experienced teaching staff at Hochschule München who, thanks to their many years of experience, are well aware of the difficulties students face when starting their studies. The small-group sessions are led by students in later semesters who have relevant teaching experience and can also offer valuable advice on studies in general.
The lecture, which takes place daily from 9 am to 12 noon, covers the material that is then practised in small-group sessions (from 1 pm to 4 pm).
Contents
Basic concepts of mathematical logic and set theory
- Statements, truth tables, forms of statements
- Definition of a set, subset, set operations, pair set
- Combinatorics, department, binomial coefficient
Elementary arithmetic
- Rules for performing arithmetic with real numbers
- Powers, roots, logarithms,
- Sum and product symbols, the binomial theorem
Equations and Inequalities
- Quadratic and Radical Equations
- Equations and inequalities involving absolute value
- Systems of equations
Elementary Geometry and Trigonometry
- Ray theorems, similarity
- Sine, cosine, tangent
- The Sine and Cosine Theorems
Vector calculus and analytical geometry
- Vectors in the plane and in space
- Calculations with vectors, scalar product, cross product
- Straight lines and planes in space
Functions of a real variable
- Definition of a function, graph, elementary properties
- rational functions, power functions and exponential functions
- trigonometric functions
Convergence
- Limits of functions, elementary limit theorems
- Limits of functions, continuity, the intermediate value theorem
Differential Calculus
- Derivative, Tangent, Rules of differentiation
- Law of Mean Values, Analysis of Graphs
Integral calculus
- Introduction to the concept of integration; the fundamental theorem of calculus
- Integration rules, applications
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