Mathematics for Economics
A.Y. 2023/2024
Learning objectives
The aim of the course is to provide basic mathematical methods for solving a wide range of applications in economics.
Main topics of the course are: Linear Algebra, Functions of Several Variables and Optimization Problems.
Main topics of the course are: Linear Algebra, Functions of Several Variables and Optimization Problems.
Expected learning outcomes
Basic mathematical methods and tools required to read and understand contemporary literature and modelling in economics.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Linear Algebra: vector, vector operations, matrices, matrices operations. Linear systems: matrix representation. Rank of a matrix. Linear independency. Inverse of a matrix. Gaussian elimination method (linear system solution, determinant and inverse matrix computation). Symmetric matrices. Norm of a vector. Basis and dimension in R^n. Geometry of the 3D space.
Multivariable functions. Special case: graphs of functions of two variables. Level curves. Quadratic forms. Continuity and differentiability of multivariable functions. Partial derivatives, gradient and Hessian matrix. Two variable functions: tangent plane and gradient vector. Convex and concave functions. Optimization problems: first and second orderd conditions for unconstrained problems. Constrained optimization: equality constraints and method of the Lagrangian multipliers. Constrained optimization: inequality constraints and Karush-Khun-Tucker conditions. Linear programming (basic concepts).
Multivariable functions. Special case: graphs of functions of two variables. Level curves. Quadratic forms. Continuity and differentiability of multivariable functions. Partial derivatives, gradient and Hessian matrix. Two variable functions: tangent plane and gradient vector. Convex and concave functions. Optimization problems: first and second orderd conditions for unconstrained problems. Constrained optimization: equality constraints and method of the Lagrangian multipliers. Constrained optimization: inequality constraints and Karush-Khun-Tucker conditions. Linear programming (basic concepts).
Prerequisites for admission
Numerical sets. Intervals of the real line. Monomials, polynomials, power function with rational exponent, power function with negative exponent. Elementary functions: sine, cosine, exponential functions, logarithms, natural logarithms. Functions composition. Real functions and their properties. Plot of real functions. Limits of real functions. Continuity and differentiability. Derivatives of elementary functions. Maxima and minima of real functions. Solution of 2x2 and 3x3 linear systems. Geometry: circumference, ellipse, parabola, hyperbola.
Teaching methods
Lecture-style instruction, integrated with slides created by the teacher. Usage of multimedia (video) and advanced software for improving the learning experience. Use of theoretical and real--life examples to show how the topics addressed in class can be directly applied in an economic framework.
Teaching Resources
K. Sydsæter, P. Hammond with A. StrØm; Essential Mathematics for Economic Analysis; Pearson.
R. A. Adams, C. Essex; Calculus: a complete course; Pearson
M. P. Deisenroth, A. A. Faisal, C.S. Ong, Mathematics for Machine Learning
Teacher's notes.
R. A. Adams, C. Essex; Calculus: a complete course; Pearson
M. P. Deisenroth, A. A. Faisal, C.S. Ong, Mathematics for Machine Learning
Teacher's notes.
Assessment methods and Criteria
The exam consists of a written test.
The test consists of theoretical questions (both open and mutiple choice questions) aimed to verify the comprehension of the topics studied in class. The test includes also exercises devoted to check the ability of applying independently the methodologies studied in class. The duration of the test depends on the number and on the structure of the questions, but it will not exceed 3 hours.
Results will be communicated via personal e-mail and on the UNIMIA web portal.
The test consists of theoretical questions (both open and mutiple choice questions) aimed to verify the comprehension of the topics studied in class. The test includes also exercises devoted to check the ability of applying independently the methodologies studied in class. The duration of the test depends on the number and on the structure of the questions, but it will not exceed 3 hours.
Results will be communicated via personal e-mail and on the UNIMIA web portal.
MAT/06 - PROBABILITY AND STATISTICS - University credits: 6
Practicals: 16 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Benfenati Alessandro, Marta Alessio
Educational website(s)
Professor(s)