30400 - MATHEMATICS AND STATISTICS - MODULE 1 (MATHEMATICS)

This course covers the fundamentals of Multi-Variable Calculus, Discrete Mathematics and Linear Algebra .

• Multi-Variable Calculus
• Riemann Integral.
• Discrete Mathematics.
• Basic Probability.
• Linear Algebra: Vector Spaces, Matrices, Determinant, Rank.

• Explain the theoretical foundations of mathematics: axioms, definitions, theorems, proofs.
• Explain in detail, through definitions, theorems and proofs, some selected topics of Real Analysis, Discrete Mathematics, and Linear Algebra
• Illustrate the structure of a mathematical reasoning through the description of the steps in a proof.

• Use selected basic computational techniques (partial derivatives, integrals, sequences, asymptotic notation, combinatorial calculus, determinants).

• Formulate definitions, theorems and their proofs as presented in the course.
• Use the theorems, definitions and techniques learnt in class to analyze the correctness of new statements.
• Perform corresponding calculations and solve problems posed in the form of exercises.

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

• Exercises: the course material includes a collection of exercises, some of them taken from past exam papers, that help students improve their performances.

• Students can take the exam in two ways:

   

  - through assignments and a short general exam taken only in the first exam session (Dec 2023). The final grade will come from assignments grade (50%) and the short general exam grade (50%)

  - through a unique general exam covering the entire program, worth 100% of the final grade.

   

• Assignments and general exams consist of open ended questions. All types of questions contribute to the assessment of the students' acquired knowledge. Questions are aimed at verifying the knowledge of specific facts and properties about mathematical objects in order to assess students' ability to correctly apply theorems and other mathematical statements in solving dedicated problems.

• Lecture notes prepared by the teachers, homework assignments and exercises, available online.