Course  Mathematics for Computer Science  DCST1004
DCST1004  Mathematics for Computer Science
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
Evaluation  Weighting  Duration  Grade deviation  Examination aids 

School exam  100/100  4 hours  C 
Course content
 Matrices: Basic matrix arithmetic  Equation systems and Gaussian elimination  Least squares method  Transformations in 2 dimensions.
 Logics: Statements, arguments, basic proof theory. Mathematical induction.
 Set theory and discrete functions. Relations.
 Number theory: Divisibility and congruence, Euclid's algorithm, 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. Four standard formulas.
Learning outcome
The course will give students knowledge of how mathematics is used in solving problems in computer science. It will also provide a foundation for further specialisation in mathematics and computer science. The course emphasises applications.
Knowledge: The candidate should demonstrate knowledge of the following
 matrices, basic matrix operations and linear systems
 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 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
 The candidate can use computational and analytical tools to visualize and solve mathematical problems.
 can use mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.
Learning methods and activities
Lectures and exercises. Exercises will be based on assignments in a digital assessment system. 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
 xxx
Further on evaluation
 There will be a school exam (in a digital examination system) at the end of the semester.
 A resit exam can be changed to oral exam
Specific conditions
Admission to a programme of study is required:
Digital Infrastructure and Cyber Security (BDIGSEC)
Recommended previous knowledge
Mathematics from secondary education
Course materials
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 

BMA1010  7.5  AUTUMN 2019 
No
Version: 1
Credits:
7.5 SP
Study level: Foundation courses, level I
Term no.: 1
Teaching semester: AUTUMN 2022
Language of instruction: Norwegian
Location: Trondheim
 Computer Science
 Information Security
 Mathematics
Department with academic responsibility
Department of Computer Science
Examination
Examination arrangement: School exam
 Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
 Autumn ORD School exam 100/100 C 20221220 09:00 INSPERA

Room Building Number of candidates SL228 Sluppenvegen 14 1 SL274 Sluppenvegen 14 2 SL120 blå sone Sluppenvegen 14 4 SL310 blå sone Sluppenvegen 14 43  Summer UTS School exam 100/100 C INSPERA

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"