30407 - ADVANCED MATHEMATICS AND STATISTICS - MODULE 1 (APPLIED MATHEMATICS)

To feel comfortable in this course, students should be familiar with differential calculus and linear algebra.

This course covers advanced topics in Real Mathematical Analysis and Linear Algebra. Emphasis is given to the methodological approach, with focus on theorems, proofs, and reasoning.

• Linear Algebra: Vector Spaces over Fields, Bases, Subspaces, Linear Operators in Vector Spaces, Linear Codes.
• Fundamental ideas and theorems on Several Variables Differential Calculus (Continuity, Partial Derivatives, Differentiability).

• Explain in detail, through definitions, theorems and proofs, some selected topics of Linear Algebra and of Real Analysis, with their applications in Economics and Computer Science.
• Illustrate the structure of a mathematical reasoning through the description of the steps in a proof.

• Use selected basic computational techniques relevant to some selected topics.
• Formulate definitions, theorems and their proofs as presented in the course.
• Justify the correctness of new statements (that is, statements that are not part of the syllabus) using the theorems, definitions and techniques learnt in class.
• Argue about the truthfulness or fallacy of new statements, using the relevant tools in the more appropriate way.

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

Exercises: the course material includes a collection of exercises that help students improve their performances.

Partial tests and general exams consist of closed and open ended questions.

• Closed questions assess the students' ability to use the correct computational technique to solve simple problems. In addition they might chech the students' comprehension of definitions, theorems and the links between them.
• Open ended questions allow for the assessment of the students' ability to correctly state definitions, state and prove theorems and apply the knowledge to state and prove other statements. In addition, they provide a way to assess students' ability to argue about the truthfulness or fallacy of new (to the students) statements.
• Grading is relative to the class.
• The general exam is graded with respect to the partial relative grading scale.

Lecture notes and exercises, available online.