Quantitative Research Methods I

COURSE OBJECTIVE
This course is the first in the line of our academic core, teaching you mathematical thinking and working (Academic Skills). During this course you will get acquainted with a number of important mathematical topics and some basic quantitative tools for business and economics. These tools are not only relevant in an academic research setting, but also help to solve business and economics problems (Bridging Theory and Practice – Knowledge). You will not only learn the techniques as such, but you will also learn the art of abstraction from a real-world problem to a formal problem, and back from a formal answer to a real-world answer (Bridging Theory and Practice – Application).

After successfully completing this course you are able to:
• properly use mathematical notation (both passively and actively);
• use the summation operator and product operator;
• calculate and interpret descriptive statistics (mean, variance, covariance, correlation);
• work with the elementary principles of probability theory (random variables, probability, distribution function, expectation, variance);
• differentiate functions of one or more variables;
• visualize implicit functions through level curves and differentiate such functions;
• integrate simple functions;
• determine when you need derivatives and integrals;
• use vectors and matrices;
• calculate from a function the elasticity;
• find extreme values of functions of one or two variables;
• find extreme values of functions of one or two variables under a
constraint, using the Lagrange method;
• apply operations (transpose, inner product) on vectors and matrices;
• use and calculate the inverse of a matrix;
• solve systems of linear equations;
• formulate a linear programming problem;
• type formulas in Microsoft Word;
• use Microsoft Excel, including the Solver add-in, for modelling mathematical problems.

COURSE CONTENT
Mathematics is a challenging, but highly relevant topic for any student in economics. The process of market and price equilibrium is a good example. In the business and economics literature we see many mathematical models, for instance for assessing risks and optimizing option portfolios. Using such models requires a basic understanding of mathematical principles related to multi-variable calculus, optimization, and expectation. Further, today’s simple calculations require basic skills in setting up and handling spreadsheets and typesetting formulas. This course therefore also addresses such general skills.

Moreover, mathematics is more than just calculations and numbers, it is language. A language that is essential to understand if you want to develop and acquire an analytical way of thinking that is not only at the core of any academic, but also the successful economics or business professional. It is a first step on the path of understanding the power of quantitative and mathematical approaches to problems you will face as a business and economics student.

FORM OF TUITION
Lectures
Tutorials
Computer tutorials

TYPE OF ASSESSMENT
Entry exam
Digital exams
Written exam
Surprise questions

RECOMMENDED BACKGROUND KNOWLEDGE 
Active command of mathematics at high school level. It can be helpful to refresh your skills in advance. The Vrije Universiteit offers an online summer school for this (see http://sbe.prep-campus.nl/).

REMARKS
You will work with the software packages Word (including the equation editor) and Excel (including the Solver add-in). These programs are available on computers at the VU campus. You may wish to purchases a cheap license for home use at http://www.surfspot.nl/. At the intermediate tests we use the English language versions for Windows.