Kaleidoscope Mathematics
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WPMA18002 
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: 1. 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 analyse the dimensions of variables in a mathematical model; 5. to apply a dimensional analysis to reduce the number of variables; 6. to derive elementary models for melting snow balls, population growth, traffic flow etc.; 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: Balance equation can be used to model a variety of processes. We consider what variables play a role, perform dimension analysis, and make simple models for the growth of a population, the melting a snowball, the swinging of a pendulum, etc. 

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. C.A. Bertoglio ,dr. W.P. Krijnen ,prof. dr. J. Top  
Verplichte literatuur 


Entreevoorwaarden  The course builds on high school knowledge in mathematics.  
Opmerkingen  
Opgenomen in 
