Advanced Mathematics for Economics
Universidad Carlos III de Madrid
Area of Study
Business, Business Administration, Economics, International Business, International Economics, Mathematics
Taught In English
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
OverviewThis subject provides the quantitative instruments that are needed to pose and analyze economic problems with the aid of a formal model.In working toward the above goal the student will acquire the following competences and skills.Regarding the contents of the course, the student will be able to:- Understand basic concepts of matrices and algebra of matrices.- Analyze dynamic economic models.- Pose and solve differential and difference equations and systems, and styudy in detail the qualitative behavior of the solutions.- Understand elementary techniques of dynamic programming in discrete time.- Apply all the above concepts to economic problems.Pertaining the general competences or skills, in the class the student will develop:- The ability to address economic problems by means of abstract models.- The ability to solve the above formal models.- The ability to interpret and classify the different solutions and apply the appropriate conclusions to social contexts.- The ability to use the basic tools that are need in the modern analysis of economic problems.Through out the course, the student should maintain:- An inquisitive attitude when developing logical reasoning, being able to tell apart a proof from an example.- An entrepreneurial and imaginative attitude towards the cases studied.- A critical attitude towards the formal results and their applicability in social contexts.The course has three parts: (I) Matrix algebra and matrix diagonalization, (II) Differential and difference equations and systems, and (III) Introduction to dynamic programming in discrete time.(I) Matrix algebra and matrix diagonalization: After a brief review of the elementary operations with matrices, some fundamental concepts for obtaining the canonical form of a matrix are given.(II) Differential and difference equations and systems: definition and illustration of these concepts with examples coming mainly from economics. The main tools of resolution are given, and special emphasis on the analysis of the qualitative behavior of the solutions is done. The techniques are applied to some classical economic models.(III) Introduction to dynamic programming in discrete time: Definition of the sequenctial decision problem and study of the optimality principle and the Bellman equation. Application of the results to some economic models.The course lectures will be based on combining theoretical explanations with several practical exercises. The students should attempt to solve the exercises by themselves, before they are addressed in class.Student participation is considered very important in order to acquire the skills needed to pose and solve economic models.The final grade is the weighted average of the final exam and the class grade. The final exam is the same for all the Mathematics for Economics II groups and consists of practical exercises and theoretical questions. The class grade is determined by each professor and is based on quizzes done in the classes.Ordinary exam: The final grade is the weighted average of 60% the grade in the final exam and 40% the class grade.Extraordinary exam: The final grade is the maximum of the following grades:a) A weighted average consisting of 60% the grade in the final exam and 40% the class grade.b) The grade in the final exam.
Please note that there are no beginning level Spanish courses offered in this program.
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.
ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.
Please reference fall and spring course lists as not all courses are taught during both semesters.
Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations
Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.