Kaleidoscope Mathematics

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 two-sided 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 power-series 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 real-life 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 power-series 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 ode-modelling.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Werkcollege (T)
Toetsvorm	Schriftelijk tentamen (WE) (The assessment consists of three sub-exams held during the quarter. Each sub-exam 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 sub-exam 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	Titel Auteur ISBN Prijs Reader: Statistics and Probability E.C. Wit Modular Arithmetic: A reader for the other parts of the course will made available Applied mathematics: Calculus. Early transcendentals. Newest (9th) Edition (International Student Edition), London: Thomson Learning James Stewart Applied mathematics: Handouts R. Luppes
Entreevoorwaarden	The course builds on high school knowledge in mathematics.
Opmerkingen	This course was registered last year with course code WPMA18002
Opgenomen in	Opleiding Jaar Periode Type BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I a BSc Mathematics and Physics (double degree) 1 semester I a verplicht BSc Mathematics: General Mathematics  ( Major track General Mathematics) 1 semester I a verplicht BSc Mathematics: Probability and Statistics 1 semester I a verplicht BSc Technische Wiskunde 1 semester I a verplicht