Sets and Numbers
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA05105 
Vaknaam  Sets and Numbers 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Sets and Numbers  
Leerdoelen  At the end of the course, the student is able to: 1. Understand and use notations from set theory that indicate “is element of”, “subset”, “union”, “intersection”, “complement”, “cartesian product”, “power sets”; 2. Understand and apply the definitions of functions between sets, and the notions “injective”, “surjective”, “bijective”; 3. Recognize “equivalence relations” and use them to divide a given set into a union of pairwise disjoint subsets; 4. Understand the difference between countable and uncountable sets; 5. The student is able to read and write simple proofs in set theory. 6. Formulate correct arguments proving divisibility properties of integers; 7. Perform the extended Euclidean algorithm on a pair of integers and use this in calculating modular inverses; 8. Formulate, prove, and use the fundamental theorem of arithmetic; 9. Apply modular arithmetic to verify divisibility properties of integers, and to compute with concrete examples of Hill ciphers and RSA cryptosystems. 

Omschrijving  The course consists of two parts. First, the notations of elementary set theory are introduced, and we study functions on sets, the image and inverse image of a subset under a function, and equivalence relations. The notions finite, countable, and uncountable are explained and illustrated. The second part of the course begins with a study of divisibility properties of integers, the greatest common divisor, and factorization into a product of prime numbers. Next, this is applied to modular arithmetic;, in particular addition, subtraction, multiplication, division, exponentiation modulo a number. Besides theory, we also discuss two applications to data security namely Hill ciphers and the RSA cryptosystem. Throughout the course there is an emphasis on structuring and writing mathematically sound arguments. 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC), Werkcollege (T)
((The final grade is determined by the formula 0.50*WE1+0.50*WE2. A student fails the course if this is less than 5.5 and also if one of WE1, WE2 is below 4.5. The student passes in all other cases.)) 

Toetsvorm  Schriftelijk tentamen (WE)  
Vaksoort  bachelor  
Coördinator  prof. dr. J. Top  
Docent(en)  prof. dr. J. Top ,dr. R.I. van der Veen  
Verplichte literatuur 


Entreevoorwaarden  
Opmerkingen  
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