Home » Departments and Centres » Academic catalogue » Course detail

Open sidebar menu

Mathematics (ECO-CO-MATH)

ECO-CO-MATH

Purpose

Prerequisites
Students are supposed to be familiar with the topics usually taught in basic courses on Calculus and Linear Algebra. Those topics are covered in the following 3 sets of books or notes.
1. Either Clark, C., (1982), Elementary Mathematical Analysis, 2nd edition, Wadsworth Publisher of Canada, Ltd., Belmont, CA. Appendix 1, or
Villanacci, A., (2020), Mathematics for Economics 1, Class Notes, Chapter 1.
2.Either Apostol, T. M., (1967), Calculus, Volume 1, 2nd edition, John Wiley & Sons, New York, NY: Chapters 1-7 included, 9-10, or Spivak, M., (1980), Calculus, 2nd ed., Publish or Perish, Inc., Houston,TX: all but chapters16, 20, from 23 to 29, included.
3.Villanacci, A., (2024), Basic Linear Algebra, Metric Spaces, Di¤erential Calculus and Nonlinear Pro-gramming: Chapters 1, 2 and 3; Sections 5.1 and 5.2.
If you studied those topics in your undergraduate courses, just send me information about the books you used and I will tell you if they are suitable to cover the needed prerequisites. Students are supposed to be familiar with the topics usually taught in basic courses on Calculus and Linear Algebra. Those topics are covered in the following 3 sets of books or notes.
1.
Either Clark, C., (1982), Elementary Mathematical Analysis, 2nd edition, Wadsworth Publisher of Canada, Ltd.,
Belmont, CA. Appendix 1, or
Villanacci, A., (2020), Mathematics for Economics 1, Class Notes, Chapter 1.
2.Either Apostol, T. M., (1967), Calculus, Volume 1, 2nd edition, John Wiley & Sons, New York, NY: Chapters 1-7 included, 9-10, or Spivak, M., (1980), Calculus, 2nd ed., Publish or Perish, Inc., Houston,TX: all but chapters16, 20, from
23 to 29, included.
3. Villanacci, A., (2024), Basic Linear Algebra, Metric Spaces, Di¤erential Calculus and Nonlinear Pro-gramming: Chapters 1, 2 and 3; Sections 5.1 and 5.2.
If you studied those topics in your undergraduate courses, just send me information about the books you used and I will tell you if they are suitable to cover the needed prerequisites.

Description

Content of the course
Linear algebra. Some topology in metric spaces. Di¤erential calculus in Euclidean spaces. Nonlinear programming. An introduction to Dynamic Programming.
Reading material
Mandatory.
Villanacci, A., (2024), Basic Linear Algebra, Metric Spaces, Di¤erential Calculus and Nonlinear Pro-gramming, Class Notes.
!! Students are supposed to have read and understood the contents of Chapters 1, 2 and 3 and Sections
5.1, 5.2 in Villanacci (2024) before the beginning of the course.   ¿
2
Exercises
Students are strongly advised to do a large part of the following exercises (all the exercises are solved in some detail in the ¿le listed below.
a. exercises inserted at the end of almost all chapters or parts of the Notes; they are taken from Lipschutz(1991), Lipschutz (1965), handwritten ¿le by Tito Pietra (I will give further information about these exercises in class);
b. Problem sets at the end of the Notes;
c. past ¿nal exams.
How to study
1. Come to class, try to understand, take notes; ask questions if you do not understand. On the website of the course, you will ¿nd a .pdf ¿le of what I wrote on the blackboard during the lecture.
2. Before coming to the next class, study your handwritten notes and compare them with mine and with the Class Notes.
3. Do exercises.
4. After the end of the course, just review everything: a week will be enough.
Main sources of the Notes.
I. Linear algebra Lang S. (1971), Linear Algebra, second edition, Addison Wesley, Reading. Lipschutz, S., (1991), Linear Algebra, 2nd edition, McGraw-Hill, New York, NY.
II Some topology in metric spaces. Lipschutz, S., (1965), General Topology, McGraw-Hill, New York, NY.McLean, R., (1985), Class notes for the course of Mathematical Economics (708), University of Pennsylva-nia, Philadelphia, PA, mimeo.
Ok. E. A., (2007), Real Analysis with Economic Applications, Princeton University Press, Princeton NJ.
III Di¤erential calculus in Euclidean spaces Apostol, T.M., (1974), Mathematical Analysis, 2nd edition, Addison-Wesley Publishing Company, Reading, MA.
IV Nonlinear programming. Cass D., (1991), Nonlinear Programming for Economists, University of Pennsylvania, Class Notes.
V Basic Dynamic Programming Cugno, F., and Montrucchio, L., (1998), Scelte intertemporali; Teoria e modelli, (in Italian), Carocci, Roma. Stokey, N. L., and Lucas, R.E., (1989), Recursive Methods in Economic Dynamics, Harvard University Press, Cambridge, MA.
Lectures and Review Sessions
The course is organized on 16 lectures and 5 review sessions. Review sessions will be devoted to the
discussion and solutions of exercises.
Exam Requirements
There will be a ¿nal exam and 3 or 4 homework assignments. The ¿nal grade will be based on the ¿nal
exam (90 percent of the ¿nal grade) and the problem sets (10 percent of the ¿nal grade). The ¿nal exam
will be open notes and open books.

Register for this course