Reddit reviews Diane Arbus: An Aperture Monograph: Fortieth-Anniversary Edition

It's hard to do without knowing what ticks your eye. For example, Martin Parr & Ansel Adams do little for me, while I thoroughly enjoy Bresson's geometric intersections with life and wagnerian Salgado.

Having said that:

• Diane Arbus: An Aperture Monograph
  
  
  
• Daido Moriyama's Tokyo
  
  
• Henri Cartier Bresson - The Decisive Moment
  
  
• Salgado - Migrations
  
  
• Sally Mann - Deep South

I don't really think instruction books are worth it anymore. You can learn the basics much faster online for free. What the internet can't provide is a good printed book filled with classic photography. If she is going to Columbia (and perhaps hearing the great Rosalind Krauss), these classics are mandatory anyway.

One of the best books on photography ever written:
Barthes: Camera Lucida

A few classic photography books everyone with a faint interest in the medium will love:

Ansel Adams
Diane Arbus
Henri Cartier-Bresson
The Photographers Eye