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Mathematics (ECO-CO-MATH)

ECO-CO-MATH

Purpose

Prerequisites.
Students are supposed to be familiar with the topics usually taught in basic course on Calculus and Linear Algebra. Those topics are covered in either of the following sets of books and notes: 1. Apostol, T. M., (1967), Calculus, Volume 1, 2nd edition, John Wiley & Sons, New York, NY: Chapters 1-7 included, 9-10. Clark, C., (1982), Elementary Mathematical Analysis, 2nd edition, Wadsworth Publisher of Canada, Ltd., Belmont, CA. Appendix 1. Villanacci, A., (2014), Basic Linear Algebra, Metric Spaces, Di§erential Calculus and Nonlinear Programming, available on line: Chapters 1, 2 and 3; Sections 5.1 and 5.2 2. Spivak, M., (1980), Calculus, 2nd ed., Publish or Perish, Inc., Houston,TX: all but chapters16, 20, from 23 to 29, included. Clark, C., (1982), Elementary Mathematical Analysis, 2nd edition, Wadsworth Publisher of Canada, Ltd., Belmont, CA. Appendix 1 and Appendix 2. Villanacci, A., (2016), Basic Linear Algebra, Metric Spaces, Di§erential Calculus and Nonlinear Programming, Chapters 1, 2 and 3; Sections 5.1 and 5.2.

Description

Content of the course
Linear algebra. Some topology in metric spaces. Differential calculus in Euclidean spaces. Nonlinear programming.

Reading material
Mandatory. Villanacci, A., (2016), Basic Linear Algebra, Metric Spaces, Differential Calculus and Nonlinear Programming, Class Notes. !!
tudents are supposed to have read and understood the content of Chapters 1, 2 and 3 and Sections 5.1, 5.2 before the beginning of the course.

Exercises
Students are strongly advised to do a large part of the following exercises; all the exercises are solved in some detail in the Öle listed below. a. exercises inserted at the end of almost all chapters or parts of the Notes; they are taken from Lipscutz (1991), Lipschutz (1965), handwritten Öle by Tito Pietra. b. Problem sets at the end of the Notes; c. past Önal exams.

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 Pennsylvania, Philadelphia, PA, mimeo. Ok. E. A., (2007), Real Analysis with Economic Applications, Princeton University Press, Princeton NJ. Simmons, G. F., (1963), Introduction to Topology and Modern Analysis, McGraw-Hill, New York. III Differential 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.

Teaching and Review Sessions
The course is organized on 12 lectures and 5 review sessions. Review sessions will be devoted to the discussion and solutions of exercises. Class time will be organized as follows: 1 hour and 15 minutes class; 15 minutes break; 1 hour class.

Exam Requirements
There will be a final exam and 3 homework assignments. The final grade will be based on the final exam (90 per cent of the final grade) and on the problem sets (10 per cent of the final grade). The final exam will be open notes-open books

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