Course  Mathematical methods 2 for Computer engineering  IMAG2021
IMAG2021  Mathematical methods 2 for Computer engineering
About
Examination arrangement
Examination arrangement: School exam and portfolio
Grade: Letters
Evaluation  Weighting  Duration  Grade deviation  Examination aids 

School exam  2/3  4 hours  D  
Portfolio  1/3 
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. Relations.
 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, relations 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.
 relations and 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 relations and graphs, including equivalence relations, 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 selfstudy 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.
Compulsory assignments
 Exercises
Further on evaluation
 There will be a digital exam at the end of the semester.
 A resit exam can be an oral exam if the conditions allow it.
 The exercises that make up the portfolio are decided at the beginning of the semester.
Specific conditions
Compulsory activities from previous semester may be approved by the department.
Admission to a programme of study is required:
Computer Science (BIDATA)
Geomatics (BIGEOMAT)
Recommended previous knowledge
Mathematical methods 1 or equivalent
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  
IMAA2021  10.0  AUTUMN 2019  
IMAT2021  10.0  AUTUMN 2019  
REA2091  10.0 
No
Version: 1
Credits:
10.0 SP
Study level: Intermediate course, level II
Term no.: 1
Teaching semester: SPRING 2022
Language of instruction: Norwegian
Location: Gjøvik
 Engineering
 Mathematics
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: School exam and portfolio
 Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
 Spring ORD School exam 2/3 D 20220513 09:00 INSPERA

Room Building Number of candidates  Spring ORD Portfolio 1/3

Room Building Number of candidates
 * 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.
For more information regarding registration for examination and examination procedures, see "Innsida  Exams"