Interesting Mathematics Books

Mathematical Beginnings

• Trigonometry, by I. Gelfand and A. Shen, 2001.
• Algebra, by I. Gelfand and A. Shen, 2003.
• Method of Coordinates, by I. M. Gelfand, A. A. Kirillov, E. G. Glagoleva, 1990.
• Functions and Graphs, by Gelfand, Glagoleva, and Shnol, 1990.
• Basic Mathematics by Serge Lang.
• Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, by Liping Ma, 1999.

Elementary Mathematics

• Yearning for the Impossible: The Surprising Truths of Mathematics by John Stillwell
• Numbers and Geometry, by John Stillwell, 1997.
• Mathematics and its History, 2nd ed, by John Stillwell, 2004.
• Mathematics: A Very Short Introduction, by Timothy Gowers, 2002.
• What Is Mathematics?: An Elementary Approach to Ideas and Methods, by Richard Courant and Herbert Robbins, Revised by Ian Stewart, 1996.
• A History of Pi, by Petr Beckman, 1976.
• Journey Through Genius by William Dunham.
• A Course of Pure Mathematics by G.H. Hardy

Advanced Mathematics

• Mathematics, Form and Function, by Saunders Mac Lane, 1986. (Unfortunately out of print.)
• Proofs and Refutations: The Logic of Mathematical Discovery, by Imre Lakatos, 1976.
• Proofs from the Book, by M. Aigner and G. Ziegler, 2002.
• Mathematical Omnibus by D. Fuchs and S. Tabachnikov
• Glimpses of Algebra and Geometry by G. Toth

The Future of Mathematics -- Reflections on the Past, Research for the Future
Particularly Important For Graduate Students

• Mathematics: Frontiers and Perspectives, 2000.
• Mathematics Unlimited: 2001 and Beyond, 2001.
• Visions in Mathematics - Towards 2000, Special Volume of Geometric and Functional Analysis, 1999.

Linear Algebra

• Linear Algebra and its Applications, by Gilbert Strang, 2005.
• Linear Algebra Done Right, by Sheldon Axler, 2004.