Mathematics for IT 1

Mathematics for IT

Matrices:

• Introduction to matrices and the order of matrices
• Types of (square) matrices: symmetric, diagonal, identity
• Adding, subtracting and multiplying matrices
• Transpose of a matrix
• The determinant and inverse of 2 x 2 and 3 x 3 matrices

Relations:

• (Binary) relations (as a set of ordered pairs), digraphs
• Reflexive, symmetric, antisymmetric, transitive, and closures
• Equivalence relations, equivalence classes, partitions

Functions:

• Introduction to (finite discrete) functions as a special case of relations
• Domain, codomain, image (range)
• Expressing a function as a mapping diagram and in “domain-codomain-rule" notation
• Types of functions: injective, surjective, bijective
• Inverse of a function, domain restriction
• Composition of functions
• Exploring some non-finite and continuous functions (e.g. linear on an interval or the Reals, modulo)

Trigonometry:

• Degrees and Radians
• Pythagoras' theorem
• Trigonometric ratios: sin, cos and tan, and the inverses of these
• Sine rule and cosine rule
• Compound angle formula

Algebra:

• Factorization and roots, solving quadratics and cubics
• Solving simultaneous equations
• Solving inequalities which involve intersections/unions, quadratics, absolute values

Coordinate Geometry:

• Points as ordered pairs and expressed on the Cartesian plane
• Distance between two points, slope
• Equation of a line, and construction of such from two points or the slope and a point or y-intercept, calculating a y value from an x value or an x value from a y value
• Perpendicular and parallel lines
• 3-dimensional Cartesian coordinate system