• Understanding and applying mathematical and logical notations (k1, k2, k3)
• Comprehending and appropriately applying mathematical proof techniques (k2, k3, k4)
• Recognizing, representing, and solving set theory problems (k2, k3, k4)
• Knowing, understanding, and applying the properties and differences of various number sets, their operations, and representation (k1, k2, k3)
• Determine solution sets of equations and inequalities (k3, k4, k5)

From the area of vector and matrix calculations, as well as linear equation systems:

• Knowing vector calculus and methods of analytical geometry and applying them in the analysis and solution of practical problems (k1, k2, k3, k4)
• Knowing and performing matrix operations, determining the inverse and determinant of a matrix, knowing and applying properties of matrices and determinants (k1, k2, k3, k4)
• Setting up linear equation systems and solving them using Gaussian elimination; knowing, understanding, and applying the solvability conditions for linear equation systems (k1, k2, k3, k4)

From the area of real functions and number sequences:

• Knowing, recognizing, analyzing, and applying fundamental properties of real functions and sequences, as well as certain function classes (polynomials, rational functions, exponential functions, logarithmic functions, hyperbolic and trigonometric functions) (k1, k2, k3, k4)
• Analyzing the convergence and limit behavior of real sequences and functions (k3, k4, k5)

From the area of one-dimensional differential and integral calculus:

• Knowing and understanding the basics of one-dimensional differential and integral calculus (k1, k2)
• Knowing and applying basic techniques of differential calculus (e.g., local approximation, determination of extrema, curve sketching, limit behavior of functions, iterative approximation methods for solving equations) (k2, k3, k4, k5)
• Knowing basic techniques of integral calculus and their meaning and applying them (e.g., functions defined by integrals, geometric applications) (k2, k3, k4, k5)

• Basic notations and definitions from logic and the covered mathematical sub-areas, such as logical connectives and quantifiers, set operations, summation and product symbols, binomial coefficients, vector products, limit notations, notations of differential and integral calculus
• Basic knowledge of various proof techniques (direct, indirect, contradiction, proof by induction)
• Basic knowledge of set theory: set operations, set relations, cardinalities of sets, interval notation, Cartesian products
• Representations of complex numbers, de Moivre's formula, exponentiation and root extraction of complex numbers; modeling of harmonic oscillations with complex numbers
• Analytic geometry: representations for lines and planes
• Matrix calculus: multiplication, rank of a matrix, Gauss-Jordan method for determining the inverse, expansion and multiplication theorem for determinants
• Linear equation systems: classifications, Gaussian elimination algorithm, solvability criteria, solution cases, modeling with matrices
• Properties of functions: monotonicity, boundedness, invertibility, continuity
• Limit properties, criteria, and theorems for sequences and functions
• Properties of continuous functions: intermediate value theorem, extreme value theorem
• Polynomial functions: fundamental theorem of algebra, polynomial interpolation
• Rational functions: partial fraction decomposition
• Properties of exponential, logarithmic, and hyperbolic functions
• Trigonometric functions in the triangle and unit circle, addition theorems, modeling o harmonic oscillations
• Basic terms and techniques of differential calculus: differentiation rules, linear approximation, mean value theorem of differential calculus, l'Hôpital's rule, iterative approximation methods (Newton's method, direct fixed-point iteration)
• Basic terms and techniques of one-dimensional integral calculus: Riemann integral, definite, indefinite, improper integral, integration methods (integration by parts, substitution, numerical integration), fundamental theorem of calculus