Description
Book SynopsisBased on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.
Table of ContentsThe Cauchy-Schwarz inequality Projections in $\mathbb{R}^3$--The elephant makes an appearance Projections in four dmensions Projections and cubes Incidences and matrices Basics of grids over finite fields Besicovitch-Kakeya conjecture in two dimensions A gentle entry into higher dimensions Some basic counting, probability and a few twists A more involved taste of probability Oscillatory integrals and fun that lies beyond Integer points and a crash course on Fourier analysis Return of the Fourier transform It is time to say goodbye Bibliography.
