This course is the continuation of a year-long Algebra and Analysis module for second-year mathematics undergraduates. I was appointed as an examiner for the weekly oral examinations, where I had to prepare three different exercise sheets for each session. Volunteer students were required to solve one theoretical question (including a proof) and one or two exercises, based on a pre-announced program aligned

Syllabus

• Review of linear algebra fundamentals
• Linear forms and duality
• Euclidean spaces
• Endomorphisms of Euclidean spaces
• Isometries in dimensions 2 and 3
• Bilinear and quadratic forms
• Series of functions
• Power series
• Functions of several variables
• Parameter-dependent integrals
• Double integrals