Faculty of Economics and Business
BACHELOR IN ECONOMICS FIRST YEAR Course
Mathematics II
Code
802349
Module
Basic Formation
Area
Mathematics
Nature
Basic
Attendance
2,7
Non Attendance
3,3
Semester
2
Credits
6
Year
1
COORDINATION DEPARTMENT Fundamentos del Análisis Económico II
COORDINATOR AND CONTACT Marcos Bujosa;
[email protected]
% OF TOTAL CREDITS
ATTENDANCE
Lectures
30%
100%
Classes
10%
50%
Tutorials
6%
100%
Assessment activities
4%
100%
Homeworks and class assignments
20%
0%
Time to study
30%
0%
TEACHING ACTIVITIES
Faculty of Economics and Business
SYNOPSIS BRIEF DESCRIPTION This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in economics, including systems of equations, vector spaces, orthogonality, determinants, eigenvalues, definite matrices and quadratic forms.
PRE-REQUISITES None
OBJECTIVES Provide students with a good understanding of the concepts and methods of linear algebra. Help students to develop the ability to solve problems using linear algebra. Connect linear algebra to other fields. Develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to linear algebra.
COMPETENCES General: CG1, CG2 Transversal: CT1 Specific: CE8, CE9
LEARNING METHODOLOGY A mixed methodology of teaching and learning will be used in all educational activities with the aim of encouraging students to develop a collaborative and cooperative attitude in the pursuit of knowledge.
TOPICS COVERED (Syllabus) The goals are to use matrices and to understand them. Here are key computations and some of the ideas behind them: Solving Ax = b for square systems by elimination (pivots, multipliers, invertibility of A). Complete solution to Ax = b (column space containing b, rank of A, nullspace of A and solutions to Ax = 0). Basis and dimension (bases for the four fundamental subspaces) Least squares solutions (closest line by understanding projections). Properties of determinants (leading to the cofactor formula, applications to inv(A) and linear systems (Cramer)). Eigenvalues and eigenvectors (diagonalizing A, computing powers of A). Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications).
ASSESSMENT Exams
% Share of Final Grade
60%
% Share of Final
40%
Final Exam
Other Activities
Faculty of Economics and Business Grade Exams (not final). Active participation in the classroom and/or exercises
EVALUATION CRITERIA Pass: 5 points out of 10 (a minimum of 3.5 in the final exam is required). The deadline for resignation of the continuous assessment will be published during the course. In the “convocatoria extraordinaria” every student that does not attend the final exam will be graded “no presentado” Continuous assessment in the extraordinary examination: in case one student has failed the ordinary examination, having attended the final exam and participated in the continuous assessment, the mark to be considered as continuous assessment for that extraordinary examination will be the final mark obtained in the ordinary examination.
TIMETABLE Number of weeks 2–3 4
Topics Solving full rank linear equations. Operations with matrices and vectors Solving linear equations. Vector spaces and sub-spaces
1–2
Orthogonal proyections
1 -- 2
Determinants. Properties and applications
3
Eigenvalues, eigenvectors, diagonalization and definite matrices (symmetrical matrices). Recurrence relations.
Remaining time
Review lectures, quizzes, and other topics.
Quiz reviews
There will be two quiz reviews: the first around the middle of the term, the second at the end of the term.
The schedule of seminar will be published during the course.
RESOURCES BASIC BIBLIOGRAPHY Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714. (There is no Spanish version)
COMPLEMENTARY BIBLIOGRAPHY Poole, David. Linear Algebra: A Modern Introduction (2nd ed.), Brooks Cole, ISBN 9780534998455
OTHER RESOURCES Virtual Campus Websites
Faculty of Economics and Business Magazines and books of special interest to the subject Mathematical Software (GNU / Octave, Matlab, Python, Derive or similar)
