Sheldon Jay Axler (born 6 November 1949, Philadelphia) is an American mathematician, professor of mathematics and the Dean of the College of Science and Engineering at San Francisco State University. He has made contributions to mathematics education, publishing several mathematics textbooks.
He went to Palmetto High School at Miami, Florida (1967). He obtained his AB in mathematics with highest honors at Princeton University (1971) and his Ph.D. in mathematics, under professor Donald Sarason, from the University of California, Berkeley (1975, Dissertation: "Subalgebras of "). As a postdoc he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology.
Axler received the Lester R. Ford Award for expository writing in 1996 from the Mathematical Association of America. In the awarded paper, "Down With Determinants!", Axler shows "how linear algebra can be done better without determinants". In 2012 he became a fellow of the American Mathematical Society.
Axler's book Linear Algebra Done Right eschews the use of determinants, in favor of other methods.
- Linear Algebra Done Right, third edition, Undergraduate Texts in Mathematics, Springer, 2015 (twelfth printing, 2009).
- (with John E. McCarthy, and Donald Sarason) editors. Holomorphic Spaces, Cambridge University Press 1998.
- (with Paul Bourdon, and Wade Ramey) Harmonic Function Theory, second edition, Graduate Texts in Mathematics, Springer, 2001.
- Harmonic Function Theory software, a Mathematica package for symbolic manipulation of harmonic functions, version 7.00, released 1 January 2009 (previous versions released in 1992, 1993, 1994, 1996, 1999, 2000, 2001, 2002, 2003, and 2008).
- Precalculus: A Prelude to Calculus, Wiley, 2009 (third printing, 2010).
- (with Peter Rosenthal and Donald Sarason) editors. A Glimpse at Hilbert Space Operators, Birkhäuser, 2010.
- College Algebra, John Wiley & Sons 2011.
- Algebra & Trigonometry, John Wiley & Sons, January 2011.
- Axler, Sheldon (1995). "Down with determinants!". Amer. Math. Monthly. 102: 139–154. doi:10.2307/2975348.
- List of Fellows of the American Mathematical Society, retrieved 2012-11-03.