# IMAA2021 - Mathematical methods 2 for Computer engineering

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

### Course content

Numerical methods in all parts where applicable.

• Complex numbers,
• Eigenvalues and eigenvectors.
• Power series, geometric series, Taylor series. series for exponential and trigonometric functions.
• Function of two and more variables, partial differentiation, extreme value problems.
• Logics: Statements, arguments, basic proof theory. Mathematical induction.
• Set theory and discrete functions.
• Number theory: Divisibility and congruence, RSA as application.
• Graph theory: Important types of graphs, graph isomorphy, trees. Graph theoretical algorithms, such as Prim's and Dijkstra's algorithms.
• Combinatorics: Counting results related to quantities, functions, and graphs.

### Learning outcome

Knowledge: The candidate should demonstrate knowledge of the following

• complex numbers.
• eigenvalues ​​and eigenvectors for square matrices.
• transformations in two dimensions.
• the concepts of series and convergence in general and geometric series in particular.
• Taylor series of important function types.
• functions of several variable and partial derivation.
• concepts in logic of statements.
• common forms of mathematical proofs, including mathematical induction.
• basic set theory.
• discrete functions.
• concepts and algorithms related to graphs, including trees and graphisomorphism.
• concepts, methods and results in number theory, modular calculus and cryptography.

Skills: The candidate can

• do calculations with complex numbers in normal and polar forms and can apply Euler's formula.
• apply characteristic polynomials in finding eigenvalues ​​and eigenvectors of a square matrix.
• use matrix multiplication to combine transformations in the plane
• apply eigenvalues ​​in practical applications
• use power series in approximations, knows Taylor's formula with residual term and can use the residual term to estimate the error in calculations
• derive partial derivatives and total differential and use them to linearize functions and to find stationary points of functions of two variables
• apply basic concepts, results and methods from the theory of statements and arguments, for example determine whether an argument is valid or invalid and determine whether two statements are equivalent
• construct simple mathematical proofs, including inductive proofs
• apply basic concepts and results related to set theory, discrete functions and can represent these in different ways
• apply basic concepts and results related to graphs, including paths in graphs and graphisomorphism
• apply algorithms to smaller examples,
• apply basic concepts and methods from number theory related to divisibility, including Euclid's method
• apply congruences calculations and perform RSA encryption and decryption

General competence: The candidate

• can use mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.
• The candidate can use computational and analytical tools to visualize and solve mathematical problems.

### Learning methods and activities

Lectures and exercises. Exercises will be based on assignments in a digital assessment system. Use of Python will also be included. Exercises and learning videos for self-study will be available as a supplement to the lectures.

Compulsory work: at least 75% of the exercises must be approved for admission to the exam. The number of obligatory assignments and weighting will be announced at the start of the semester.

• Exercises

### Further on evaluation

• There will be a school exam (in a digital examination system) at the end of the semester.
• Retake of examination may be given as an oral examination.

### Specific conditions

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

Admission to a programme of study is required:
Computer Science (BIDATA)

### Required previous knowledge

You must have been admitted to a technology study this subject is related to at the NTNU

### Course materials

• A specially compiled course book comprising chapters of Adams and Essex: Calculus, and Lay, Lay and McDonald: Linear Algebra and its Applications, available as the semester begins.
• Discrete Mathematics With Applications, (International Edition) Susanna S. Epp

Eventual notes will be released on the Blackboard page.

### Credit reductions

Course code Reduction From To
TDAT2002 10.0 AUTUMN 2019
IMAG2021 10.0 AUTUMN 2019
IMAT2021 10.0 AUTUMN 2019
More on the course

No

Facts

Version: 1
Credits:  10.0 SP
Study level: Intermediate course, level II

Coursework

Term no.: 1
Teaching semester:  SPRING 2023

Language of instruction: Norwegian

Location: Ålesund

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

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 100/100
Summer UTS School exam 100/100
• * 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.
Examination

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

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