Both mathematics and statistics are essential courses for economists. Economists specify, analyse and quantify relationships among economic variables. Think for example about the relationship between prices and quantities, or between national income and consumption. In doing so, economists use verbal, graphical, mathematical and statistical tools. Mathematics will focus on the third tool. Together with verbal ability, an economist should possess all these tools, which are essential in all of the followup courses. The knowledge gathered in this course will form the basis for many other courses, including Microeconomics (basic and intermediate), Macroeconomics (basic and intermediate), International Economics and Finance and Organisation.
The central issue in Mathematics is constrained optimisation. Specific applications of this type of problems are utility maximising behaviour of consumers or minimising cost by producers. To be able to solve these problems, you have to know how to solve systems of equations, how to differentiate (partial and higher order) and how to simplify complex functions and equations. Besides this you get an introduction to growth and dynamics, matrices and integration because these techniques are often used in economics. Applications for mathematics will be found mainly in economics.
Learning objectives
At the end of the course the student is able to:
 Understand, control and apply elementary notions of mathematics;
 Use mathematics to specify, analyse and quantify relationships among economic variables;
 Recognise the economic meaning from mathematical notions and models;
 Describe clear and structured solutions of mathematical problems;
 Solve unconstrained optimization problems of multivariate functions;
 Solve constrained optimization problems of multivariate functions (the Lagrange multiplier method);
 Use introductory knowledge of growth models, dynamics and integration.
Academic skills
This course focuses on the following academic skills:
 Analytical skills:
 Problem solving (identifying the problem, devising a path towards the solution, following this path, verifying the outcome) for specific questions.
Format
Two hours of lecture and two tutorials of two hours (group size 30 students) per week. The problems for both tutorials will have to be prepared in advance by the students. Each week at the first tutorial some specific problems will be worked through. In the second tutorials the remaining prepared exercises will be discussed. Furthermore, you need to hand in online exercises each week (see effort requirement). In the first tutorial the digital environment DWO will be introduced. During the tutorials students will get feedback on their work and have the opportunity to hand in additional exercises/problems (see course manual).
The academic skill problem solving at level one will be dealt with explicitly from the first week on by practicing exercises in both the tutorials and the online environment DWO. This skill will also be part of several followup courses.
Based on the score for the Entry test Mathematics in the introduction week students are assigned to tutorials. Especially for those students who have received an insufficient score for the Entry Test an extra digital practicum will be supplied; during the first four weeks these practica deal with preuniversity mathematics which will be supervised by student assistants.
In the introduction week a mandatory lecture will deal with a.o. the logistics of the digital environment DWO that will be used for the weekly (and extra) tests.
For Dutch students only, each week a socalled Q&A session (Questions & Answers) will be organised to help you with the conversion of the mathematics language from Dutch to English. These sessions are not a replacement for the regular tutorials. Language of instruction during these sessions will be Dutch.
Assessment method
 Mid term exam, open questions (50%);
 End term exam, open questions (50%).
See the course manual for information on the supplementary and replacement retake exam.
All exams are closedbook examinations but a graphical calculator may be used if the memory is cleared at the start of the exam.
The assessments of both the tests and all problems worked on is partly focused on the results, but mostly on the academic skill problem solving. The justification of the method chosen, the systematically presentation of both the steps in the problem solving stage, the solution, and the interpretation of the results are all aspects that count heavily. This means that solutions using the problem solving skill extensively but with calculating errors can be assessed sufficient. But on the other hand only giving the result will be judged insufficient.
Effort requirements
 Weekly handing in worked out exercises online using the digital test environment DWO (5 out of 7 weeks; see the course manual for more details);
 Participation in the Entry test in the introduction week and in the Mathematical Skills test in the midterm exam week;
Course Repeaters
Students who signed up for the course in (one or more of the) previous years, and did not drop the course in time, or failed the course, may participate in the course repeaters programme. Repeaters are not entitled to follow the regular tutorials.
With respect to the teaching format, this implies that course repeaters:
 Can follow the regular lectures;
 Can subscribe for special repeaters tutorials (group size 50). The precise conditions are described below;
 Don’t have special tutorials just before each exam;
 And don’t have to full fill the effort requirements (apart from the UU requirement to pass with a grade of 4 or higher (not rounded off); see the course manual for more details).
For all repeaters it is necessary that they have to register for the course to be able to do the exams.
Participation in the special repeaters tutorials is only possible if:
 You have registered yourself in time in Osiris student for this course. Only then you are entitled to do the exams.
 You have registered yourself in time for the special repeaters tutorials via a reply on the mail of the student desk.
 You show commitment by doing your homework every week. We will check it at the start of every tutorial.
 You show commitment by preparing yourself for each tutorial. If not, you will be excluded immediately of participation in the special repeaters tutorials. A hardship clause is provided.
 You show commitment to devote enough time to this course. U.S.E. advises you strongly not to follow three courses in the first period.
 Work is no reason to dismiss classes.
Given these rules, you are entitled to full commitment of the teacher, including support by email.
With respect to the assessment method, this implies that course repeaters:
 Have a midterm exam (50%) and an endterm exam (50%);
 Can do a supplementary or replacement exam.
Course materials
 Knut Sydsaeter & Peter Hammond with Arne Strøm, Essential Mathematics for Economic Analysis, Pearson Education Limited, fourth edition, ISBN 9780273760689
NB ISBN 9781292074610 is the version with a code for the digital environment MyMathLab Global (MyLabsPlus), This digital environment offers more material to practice with and the ebook version. The code is not necessary to follow the course.
 For the extra practicum: Yolanda Grift, Luuk Rietvelt, Refreshing Mathematics A, Pearson, ISBN 9781780164069
 Digital environment DWO (www.dwo.nl/ec/student)
 Course manual Mathematics 2017/2018. The course manual will be published via Blackboard.
Language of instruction
English.
Students are expected to have knowledge of:
Preuniversity mathematics: algebra, equations, calculus (differentiation).
The summer school Refreshing Mathematics A addresses the required prior knowledge; see for more information:
https://www.utrechtsummerschool.nl/courses/laweconomics/refreshingmathematicsa
Courses that build on Mathematics
 Microeconomics, Institutions and Welfare (ECB1MI)
 Statistics (ECB1STAT)
 Macroeconomics, A European Perspective (ECB1MACR)
 Advanced Mathematics (ECB2VWIS)
 Economics of the Public Sector (ECB2EPS)
 Intermediate Microeconomics, Games and Behaviour (ECB2VMI)
 Intermediate Macroeconomics: International Financial Relations (ECB2IMAE)
 Intermediate Macroeconomics: Output and Time (ECB2VMAE)
 Corporate Finance and Behaviour (ECB2FIN)
 Financial Markets and Institutions (ECB3FMI)
 Growth and Development
 Politics, Philosophy and Economics (ECB3CMEPC)
 Econometrics (ECB2METRIE)
