Kaleidoscope Mathematics
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WBMA00605 
Vaknaam  Kaleidoscope Mathematics 
Niveau(s)  propedeuse 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Kaleidoscope Mathematics  
Leerdoelen  The aim of this course is that: students get an overview of three areas of mathematics in order to see both the diversity and unity of the discipline. The student is able: 1. to calculate with probabilities; 2. to perform twosided hypothesis tests; 3. to define a transition matrix of a Markov Chain and be able to calculate a stationary distribution; 4. to solve a number of types of ode's analytically using basic methods like separation of variables, e^lambda method, integrating factor and variation of constants; 5. to employ a powerseries method and/or a numerical method (Euler) to solve an ode approximately; 6. to interpret the (approximate) solution in relation to the underlying problem; 7. to perform the extended Euclidean algorithm on a pair of integers and use this in calculating modular inverses; 8. to formulate complete arguments proving divisibility properties of integers; 9. to apply modular arithmetic to examples of the cryptographic applications discussed in class. 

Omschrijving  Students who want to study mathematics in Groningen have the choice of specializing in three different areas: statistics & probability, pure and applied mathematics. This course introduces these three areas to the student: 1. Introduction to algebra: we cover `modular arithmetic', in particular addition, subtraction, multiplication, division, exponentiation modulo a number. Besides theory, we also discuss an application to data security. There is an emphasis on structuring and writing mathematical proofs. 2. Statistics and probability theory: Probabilities play a vital role in modeling many reallife processes. In this part, we define what we mean by a probability, how to calculate with it, and how you can use it for data analysis. 3. Applied mathematics: (Ordinary) Differential Equations (o.d.e.) can be used to model a variety of processes in the 'outside world'. These are often derived following a balance equation (force, mass, value, ...). We consider a number of types of ode's and learn how to solve these analytically. When the ode cannot be solved exactly, a powerseries method or a numerical method can be used to yield an approximate solution. Interpretation of the (approximate) solution, in relation to the underlying problem, is an important element of odemodelling. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Schriftelijk tentamen (WE)
(The assessment consists of three subexams held during the quarter. Each subexam covers one of the three topics of the course. The final grade is calculated as the average of the three individual exam grades. Students pass the course if they have an average of at least 5.5, having no subexam with a grade lower than 4.5.) 

Vaksoort  propedeuse  
Coördinator  prof. dr. J. Top  
Docent(en)  dr. ir. R. Luppes ,prof. dr. D. Rodrigues Valesin ,prof. dr. J. Top  
Verplichte literatuur 


Entreevoorwaarden  The course builds on high school knowledge in mathematics.  
Opmerkingen  This course was registered last year with course code WPMA18002  
Opgenomen in 
