Mathematical Tapas: Volume 2 (From Undergraduate to Graduate Level)

This textbook presents a collection of interesting and sometimes original exercises for motivated students in mathematics. Written in the same spirit as Volume 1, this second volume of Mathematical Tapas includes carefully selected problems at the intersection between undergraduate and graduate level. Hints, answers and (sometimes) comments are presented alongside the 222 “tapas” as well as 8 conjectures or open problems. Topics covered include metric, normed, Banach, inner-product and Hilbert spaces; differential calculus; integration; matrices; convexity; and optimization or variational problems. Suitable for advanced undergraduate and graduate students in mathematics, this book aims to sharpen the reader’s mathematical problem solving abilities.