# Mathematics and Mathematics Teaching I

30 ECTS credits

Module 1 The basics of mathematics and problem-solving, 9 ECTS cr

Patterns and generalisations, arithmetic and geometric series and sums. Set theory notation set theory operations, Venn diagrams and the sets normal numbers, integers, rational numbers, real numbers and complex numbers. Basic logic with truth tables and quantifiers as implication and equivalence. Different number bases and transformations between them. Divisibility, prime numbers, the greatest common divisor, diophantine equations, congruence arithmetic. Direct proof, indirect proof, proof by contradiction and proof by induction.

Curricula and syllabi in mathematics. Teaching methods in school and analysis of teaching material. Different aspects of problem-solving and its central role in the teaching of mathematics are studied, as are different strategies and common learner reactions to problem-solving. Pupils' basic perception of numbers and the arithmetic of positive and negative integers and rational numbers as fractions and decimals. Different number systems, including those of some early cultures. Performing and assessing mathematical reasoning and proofs in school.

Module 2 Basic algebra, 6 ECTS cr

Vectors in the plane and space, scalar and vector products. Equations of lines and planes, distance between points, lines and planes. Complex numbers in cartesian form, polar form and exponential form. Polynomial long division, the division algorithm, the factor theorem and the fundamental theorem of algebra. Polynomial equations and binomic equations.

Matrices and matrix arithmetics, matrix transpose, systems of linear equations in matrix form linear equation, and matrix inverse. Determinants and determinant arithmetics.

Didatic tratment of algebra and equations in a school perspective. Visualisations and investigating activities using dynamic mathematics software and related teaching and learning issues.

Module 3 Mathematical relationships and change in one variable, 15 ECTS cr

The concept of function and ways to introduce it. Function domain, function range, injectivity, surjectivity, bijectivity and invertability. Combination of functions and calculation of function inverse, The elementary functions; polynomial function, power function, exponential function, logarithm function, and corresponding equations and ineqalities. Trigonometric functions and the inverse trigonometric functions, hyperbolic functions, and the corresponding equations.

Limit, continuity, derivative and derivation rules. Curve construction, extreme value problems and Taylor's formula. Primitive function, integral and integration methods and generalised integrals.

Number sequences and series, and basic convergence criteria. Applications, modelling and problem-solving using one variable analysis, also with the help of dynamic mathematics software.

The historical development of the area of mathematical analysis. Some module components are also treated with a more advanced mathematics teaching perspective. Visualisations and investigating activities using dynamic mathematics software, and related teaching and learning issues.

Patterns and generalisations, arithmetic and geometric series and sums. Set theory notation set theory operations, Venn diagrams and the sets normal numbers, integers, rational numbers, real numbers and complex numbers. Basic logic with truth tables and quantifiers as implication and equivalence. Different number bases and transformations between them. Divisibility, prime numbers, the greatest common divisor, diophantine equations, congruence arithmetic. Direct proof, indirect proof, proof by contradiction and proof by induction.

Curricula and syllabi in mathematics. Teaching methods in school and analysis of teaching material. Different aspects of problem-solving and its central role in the teaching of mathematics are studied, as are different strategies and common learner reactions to problem-solving. Pupils' basic perception of numbers and the arithmetic of positive and negative integers and rational numbers as fractions and decimals. Different number systems, including those of some early cultures. Performing and assessing mathematical reasoning and proofs in school.

Module 2 Basic algebra, 6 ECTS cr

Vectors in the plane and space, scalar and vector products. Equations of lines and planes, distance between points, lines and planes. Complex numbers in cartesian form, polar form and exponential form. Polynomial long division, the division algorithm, the factor theorem and the fundamental theorem of algebra. Polynomial equations and binomic equations.

Matrices and matrix arithmetics, matrix transpose, systems of linear equations in matrix form linear equation, and matrix inverse. Determinants and determinant arithmetics.

Didatic tratment of algebra and equations in a school perspective. Visualisations and investigating activities using dynamic mathematics software and related teaching and learning issues.

Module 3 Mathematical relationships and change in one variable, 15 ECTS cr

The concept of function and ways to introduce it. Function domain, function range, injectivity, surjectivity, bijectivity and invertability. Combination of functions and calculation of function inverse, The elementary functions; polynomial function, power function, exponential function, logarithm function, and corresponding equations and ineqalities. Trigonometric functions and the inverse trigonometric functions, hyperbolic functions, and the corresponding equations.

Limit, continuity, derivative and derivation rules. Curve construction, extreme value problems and Taylor's formula. Primitive function, integral and integration methods and generalised integrals.

Number sequences and series, and basic convergence criteria. Applications, modelling and problem-solving using one variable analysis, also with the help of dynamic mathematics software.

The historical development of the area of mathematical analysis. Some module components are also treated with a more advanced mathematics teaching perspective. Visualisations and investigating activities using dynamic mathematics software, and related teaching and learning issues.

Progressive specialisation:
G1N (has only upper‐secondary level entry requirements)

Education level:
Undergraduate level

Admission requirements:
General admission requirements plus upper secondary level English 6, Social Science 1b or 1a1 + 1a2, Mathematics 4, or English B, Social science A, Mathematics D, or equivalent

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Secondary Education Programme: Upper-Secondary School: Mathematics (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics - Physics (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics - Technolog (studied during year 1)
- Secondary Education Programme: Upper Secondary Education Programme: Mathematics (studied during year 1)

### More information

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Campus, 100%
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- Start Autumn 2019
- Mode of study Campus
- Language Swedish
- Course code MAGL11
- Application code KAU-32782
- Study pace 100% (Day)
- Study period week 35–3