## Introduction to Mathematics

 Faculteit Science and Engineering Jaar 2017/18 Vakcode WIOW-10 Vaknaam Introduction to Mathematics Niveau(s) propedeuse Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Introduction to 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 two-sided 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 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: 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 written exam is assessed via three sub-exams during the quarter. 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. E.C. Wit
Docent(en) prof. dr. J. Top ,prof. dr. ir. R.W.C.P. Verstappen ,prof. dr. E.C. Wit
Verplichte literatuur
Titel Auteur ISBN Prijs
a reader for the other parts of the course will be made available various
Reader: Statistics and Probability E.C. Wit
Entreevoorwaarden
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
BSc Applied Mathematics 1 semester I a verplicht
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: Statistics and Econometrics 1 semester I a verplicht