MA-443 Algebra and Number Theory

The course is connected to the following study programs

• Subject didactics in Teacher Education Level 5-10, 2-year Master’s Programme
• Master's 5-Year Programme in Teacher Education, level 5-10

Teaching language

Norwegian

Prerequisites

Completed 60 ECTS credits in mathematics

Course contents

Elementary algebra. Mathematical proofs. Number sequences. Arithmetic and geometric series. Elementary topics in number theory.

The subject in practice
During the 5 days in teaching practice, it will be arranged for the student to gain experience with the use of various teaching resources in mathematics and student-active teaching methods.

Learning outcomes

The student

• can use the language of algebra to describe situations and to solve practical problems

• can expand and factor quadratic expressions in different contexts and, especially, solve the quadratic equation by completing the square

• can explain and use general principles for solving equations and inequalities, and can solve different types of equations as rational, logarithmic and exponential

• can solve linear, and some non-linear, systems of equations with several unknown, and can solve optimization problems using linear programming (two variables)

• have knowlegde about multiplication and division of polynomials

• have knowledge about number sequences and series

• can use the summation sign to represent series, and can use finite series in practical situations

• can explain, justify and prove theorems in algebra and number theory, and is able to use different types of proofs

• have knowledge about prime numbers, prime factorization and the distribution of primes

• have knowledge about division with a remainder and divisibility

• can solve linear Diophantine equations

 

Examination requirements

The teacher education students

• approved attendance in the course

• approved required assignments. (see Canvas for more information)

• approved practice

Other students

• approved attendance in the course

• approved portfolio collection of mathematical tasks.(see Canvas for more information)

• approved didactic work of similar scope as practice

Teaching methods

Joint teaching, work in small groups, compulsory assignments, oral presentations. Digital software is used where appropriate.

Requirements for minimum 70% compulsory participation.

The course has an expected scope of work of 267 hours.

It is included 5 days practice for the teacher education students. This is a preparation for the teaching practice in the 8th semester.

Other students will perform a didactic work of similar scope as practice.

Evaluation

The person responsible for the course, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.

Assessment methods and criteria

6-hour written eksamination. Graded assessment.

Reduction of Credits

This course’s contents overlap with the following courses. A reduction of credits will occur if one of these courses is taken in addition:

Course	Reduction of Credits
MA-419 – Number Theory	7.5
MA-164 – Algebra	2.5