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

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

This course covers advanced topics in Linear Algebra. Emphasis is given to mathematical reasoning.

Vector Spaces, Linear Mappings, Structure of Vector Spaces, Bases, Matrices, Eigenvalues and Eigenvectors, Matrix Decompositions. 

• Explain the basic facts about the relevant topics 

• Describe the theoretical links among mathematical objects 

• Explain in detail some selected topics of Linear Algebra. 

• 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) 

• some 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 open-ended questions. 

All questions test the student's knowledge and understanding of the basic facts about the relevant topics, their ability to recognize the links among mathematical objects and to use basic computational techniques. Moreover, the questions test the student's ability to use mathematical reasoning to prove simple statements and to argue about the correctness of other statements. 

Lecture notes and exercises, available online.