30448 - MATHEMATICS - MODULE 1 (THEORY AND METHODS)

This course covers the fundamentals of Real Mathematical Analysis and Linear Algebra. Emphasis is given to the methodological approach, with focus on reasoning.

• Real and Complex numbers. Euclidean Spaces.
• Functions
• Topology.
• Convergence of sequences and series.
• Continuity.
• Differentiability.
• Riemann integral.
• Vectors and two- and three-dimensional geometry.
• Linear algebra.

• Explain the basic facts about the relevant topics
• List the fundamental definitions and theorems.
• Describe the theoretical links among mathematical objects
• Explain in detail some selected topics
• Illustrate the structure of mathematical reasoning through examples

• Use selected basic computational techniques
• Use definitions, theorems and mathematical reasoning to prove simple statements.
• Argue about the correctness of statements using the theorems, definitions and techniques learned in class.

• Face-to-face lectures
• Exercises (exercises, database, software etc.)
• Individual assignments

• Face to Face lectures present the most important facts about the topics.
• Multiple Exercises sessions help students familiarize with the mathematical reasoning and some simple computational techniques
• Individual assignments offer the students the opportunity to test both their computational skills (through quizzes) and their reasoning skills (through open ended questions).

The exam can be taken in two ways:

• a single written test (100% of the final grade)
• 5 individual written assignments during the semester (66% of the final grade) + an end of semester written test (34% of the final grade)

All tests and assignments consist of multiple choice and open-ended questions.

Multiple choice questions test the student's knowledge and understanding the basic facts about the relevant topics, their ability to recognize the links among mathematical objects and to use basic computational techniques.
 

Open-ended questions test the student's ability to explain the key-concepts about fundamental topics, to use mathematical reasoning to prove simple statements and to argue about the correctness of other statements.

• S. CERREIA VIOGLIO, M. MARINUCCI, E. VIGNA, Principles of Mathematics for Economics.
• Lecture notes and exercises, available online.