Mathematics I for EOR

Uitgebreide vaknaam	Mathematics I for EOR
Leerdoelen	Upon completion of this module the student is able to 1. Define different number systems. Use mathematical induction to define algebraic operations and prove propositions. 2. Understand all basic operations and prove algebraic laws in set theory. 3. Prove the convergence of a given sequence of real numbers using the epsilon-N definition and determine the limiting value. Find the supremum and infimum of a set of real numbers. 4. Define a function and distinguish different common real-valued functions based on the analytic expression as well as the function graph. 5. Define the function limit and prove continuity for a given real-valued function using the epsilon-delta definition. 6. Define differentiability for a real-valued function. Classify a given real-valued function as being continuous and/or differentiable. 7. Use various differentiation techniques, such as the power law, the product rule, the quotient rule and the chain rule. 8. Perform simple calculations with complex numbers, such as addition, multiplication, division and the transformation to and from polar coordinates. 9. Identify integrable functions. Use various integration techniques, such as integration by substitution, integration by parts, and partial fraction decomposition. 10. Solve a system of linear equations by Gaussian elimination, backward substitution and Cramer's rule. 11. Calculate the determination and the rank of a given matrix. Perform various matrix operations such as addition, multiplication, inversion and co-factor expansion.
Omschrijving	Main educational goal: Students will learn to formulate in a mathematically correct way and acquire understanding of the mathematics underlying economic models. Students obtain the skills to prove results, and to solve problems. Topics: Number systems, set theory, mathematical induction, calculus, analysis and introduction to linear algebra.
Uren per week	8
Onderwijsvorm	-hoorcollege ,  -werkcollege, practica (Lectures (2*2h) and tutorials (2*2h) every week)
Toetsvorm	-individuele opdracht,  -schriftelijk tentamen (open vragen) (Assignments (25%) and the final written exam (75%).)
Vaksoort	propedeuse
Coördinator	Dr. W. Zhu
Docent(en)	student-assistants ,Dr. W. Zhu
Verplichte literatuur	Titel Auteur ISBN Prijs Mathematics for Economists, 1st edition, 1994 (or any later edition), W.W. Norton and Company Simon, Carl P., Lawrence Blume 9780393117523 €  81,00 Analysis I, 3rd edition, 2016, Springer (not mandatory literature) Terence Tao 9789811017896 €  45,36
Entreevoorwaarden	Admittance to the BSc EOR (contact the programme coordinator for questions).
Opmerkingen	Info: Dr Wei Zhu, e-mail: w.zhu@rug.nl. Secr: Martine Geerlings-Koolman, phone: +31(0)50 36 37018, e-mail: m.a.koolman@rug.nl.
Opgenomen in	Opleiding Jaar Periode Type BSc Econometrics and Operations Research/EOR  (basisprogramma BSc EOR) 1 semester I a verplicht