# About

### Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Home exam 80/100 4 hours
Semester test 20/100 A

### Course content

This course gives an introduction to elementary number theory. Topics included are: greatest common divisor, Euclidean algorithm, linear diophantine equations, elementary prime number theory, linear congruences, Chinese remainder theorem, Fermat's little theorem, Euler's phi-function, Euler's theorem with application to cryptography. Additional topics that may change from year to year may include number theoretical functions, Fermat's last theorem for n = 4, continued fractions, rational approximations, Pell's equations, and quadratic reciprocity.

### Learning outcome

1. Knowledge. The student is familiar with basic concepts in elementary number theory as specified under "Academic content".

2. Skills. The student is able to apply the theoretical knowledge to solve concrete problems. This includes being able to apply Euclid's division algorithm, solve diophantine equations and (systems of) linear congruences, encryption and decryption of messages in given RSA-systems. The student is able to write simple mathematical proofs.

### Learning methods and activities

Lectures, compulsory exercises and mid-semester examination. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and the mid-semester examination (20%). The mid-semester examination only counts if it has a positive effect on the final grade. The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. The re-sit examination may be given as an oral examination.

• Exercises

### Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation, see «Teaching methods and activities».

### Specific conditions

Compulsory activities from previous semester may be approved by the department.

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
MNFMA104 6.0
MA6301 7.5 01.09.2007
TMA4155 3.0 01.09.2009
More on the course

Facts

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2020

Language of instruction: -

Location: Trondheim

Subject area(s)
• Mathematics
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences

# Examination

#### Examination arrangement: Portfolio assessment

Term Status code Evaluation Weighting Examination aids Date Time Digital exam
Autumn ORD Semester test 20/100
Autumn ORD Home exam (1) 80/100

Release
2020-11-25

Submission
2020-11-25

09:00

13:00

Summer UTS Home exam 80/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
• 1) Merk at eksamensform er endret som et smittevernstiltak i den pågående koronasituasjonen. Please note that the exam form has changed as a preventive measure in the ongoing corona situation.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

More on examinations at NTNU