Course description

Advanced Analysis involves the in-depth examination and interpretation of complex data, systems, or scenarios to uncover insights, trends, and solutions. It integrates tools like statistical models, machine learning, and domain-specific methodologies. This process is often used to inform decision-making, optimize performance, and predict outcomes. Applicable across industries, it combines technical expertise with critical thinking to address sophisticated challenges.

What will i learn?

• Understand the Euclidean distance function on Rn and appreciate its properties, and state and use the Triangle and Reverse Triangle Inequalities for the Euclidean distance function on Rn
• Explain the definition of continuity for functions from Rn to Rm and determine whether a given function from Rn to Rm is continuous
• Explain the geometric meaning of each of the metric space properties and be able to verify whether a given distance function is a metric
• Distinguish between open and closed balls in a metric space and be able to determine them for given metric spaces Define convergence for sequences in a metric space and determine whether a given sequence in a metric space converges