## Mathematics, advanced syllabus (MAA)

**Mathematics, advanced syllabus (MAA)**

The compulsory courses are studied in numerical order. Course xLmaa12 is offered in the spring term of the second year. Courses xLmaa11, xLmaa13, xLmaa14 and xLmaa15 are offered in the third year. xLmaa17 is offered at the same time as xLmab06. Course xLmaa18 begins in the second year.

When students switch from the advanced to the basic syllabus the advanced courses compensate for the following basic courses: xLmaa02 → xLmab02, xLmaa03 → xLmab03, xLmaa06 → xLmab07 and xLmaa08 → xLmaa04 and xLmaa10 → xLmab05.

**Compulsory courses**

**xLmay01 Numbers and Number Sequences**

The course topics includes: real numbers, basic and percentage calculations, the graphing and interpretation of functions, numbers sequences and their sums and the link between logarithms and powers. Graded assessment.

**xLmaa02 Polynomial functions and Equations**

Students learn to solve polynomial equations and inequalities. Additionally, students explore the number of solutions of a quadratic equation and examine the binomial formula and how to factorize polynomials using the roots of the equation. Graded assessment.

**xLmaa03 Geometry**

The course contents are: similarity of figures and objects; sine and cosine rules; geometry of a circle, its parts and straight lines related to it; calculating lengths, angles, areas and volumes related to figures and objects. Graded assessment.

**xLmaa04 Vectors**

The course includes studies on vectors and their properties and calculation rules, points, distances and angles in two- and three-dimensional coordinate systems by means of vectors. Simultaneous equations are also covered in this course. Graded assessment.

**xLmaa05 Analytic Geometry**

Students examine: equations of set points; for example, equations of straight lines, circles and parabolas as well as the distance from point to a straight line. Students also get practice in solving absolute value equations and inequalities and equation systems. Graded assessment.

**xLmaa06 Derivative**

Investigate, for example, rational equations and inequalities, function limit value, continuity and derivation. Consider derivations of simple polynomial functions, derivations of function inputs and partial numbers, as well as their use in the study of function flow and determination of extremes, the maximum and minimum value of a function relating to application problems. Graded assessment.

**xLmaa07 Trigonometric Functions**

The course examines the properties, equations and derivatives of trigonometric functions. Graded assessment.

**xLmaa08 Roots and Logarithmic Functions**

The course examines, among others, the roots of a function, exponential, logarithmic functions their solutions as well as the derivatives. Graded assessment.

**xLmaa09 Integral Calculations**

The course deals with definition of the integral and integrating functions. The course examines the area and volume of shapes using the definition of integration. Graded assessment.

**xLmaa10 Probability and Statistics**

The course examines various statistical distributions (discrete and continuous), their statistical numbers, classical and statistical probability, combinatorial, probability distribution rules, probability distributions, expectation and normal distribution. Graded assessment.

**National Advanced Courses**

**xLmaa11 Number Theory and Proof**

The course examines, among others, principles of logic, different evidence principles, the concepts of number theory: the properties of prime numbers and the divisibility of integers. Graded assessment.

**xLmaa12 Algorithms in Mathematics**

The course examines, among other things, numerical solution of equations by iteration, polynomial divisibility, numerically determining the rate of change and surface area. Graded assessment.

**xLmaa13 Advanced Course in Differential and Integral Calculus**

The course deepens and supplements the skills of differential and integral calculations, for example: examines, among other things, the limit values of functions at infinity, improper integrals, inverse functions, their series and sums. Graded assessment.

**School Based Advanced Degree Courses**

**xLmaa14 Review Course 1**

The course covers numbers and mathematical operations, equations and inequalities, geometry and analytical geometry. Graded assessment. A grade of 4 does not affect the overall assessment.

**xLmaa15 Review Course 2**

The course covers vectors, probability calculations, continuity, derivatives, integral calculations and number sequences. Graded assessment. A grade of 4 does not affect the overall assessment.

**xLmaa16 Postgraduate studies in Mathematics**

The course studies mathematics at the university / technical university level. The course prepares the student and postgraduate studies in both. The subjects studied in the course can be differential equations, complex numbers, vector input, scalar triple product, matrix computational algorithms and geometry. The content of the course is affected by the students' wishes. This is suitable for 3rd year students. The grade is a pass/fail.

**xLmaa17 Economic Mathematics (= xLmab06)**

The course introduces the concepts of business life and develops mathematical skills in the planning personal finances. The course teaches how to calculate index numbers, costs (expenses), monetary transactions, loans and taxes. The course will and deepen the understanding of percentages and solutions of equations to model economic phenomena by means of number sequences and sums. The course provides a good foundation for postgraduate studies, such as entrepreneurship and economics. The course studies will use of technical aids for calculating and solving practical applications. Graded assessment.

**xLmaa18 Mathematics Tutor Course**

The 2nd year student works as a tutor for the 1st year students in high school using this time to review material that has previously been learned. The course is done independently. The grade is a pass/fail.