Flapan did her undergraduate studies at Hamilton College (New York), graduating in 1977, and went on to graduate studies at the University of Wisconsin–Madison, earning a Ph.D. in 1983 under the supervision of Daniel McMillan. After postdoctoral studies at Rice University and the University of California, Santa Barbara she joined the Pomona faculty in 1986.
Flapan's research is in low-dimensional topology and knot theory. She has published numerous papers, as well as worked on three books.  She is the author of the book When Topology Meets Chemistry: A Topological Look at Molecular Chirality (Cambridge University Press and Mathematical Association of America, 2000). In 2009, Flapan edited the book Applications of Knot Theory along with Dorothy Buck.  With James Pommersheim and Tim Marks she also wrote the book Number Theory: A Lively Introduction with Proofs, Applications, and Stories (John Wiley & Sons, 2010).
In 2011, Flapan was one of three winners of the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics, from the Mathematical Association of America. In 2012 she became a fellow of the American Mathematical Society, and in the same year as part of the bicentennial of Hamilton College was honored with a Hamilton Alumni Achievement Medal.
- Faculty listing, Pomona Mathematics Dept., retrieved 2013-01-22.
- Curriculum vitae, retrieved 2013-01-22.
- Award citation, January 2011 Prizes and Awards, MAA, retrieved 2013-01-22.
- Erica Flapan at the Mathematics Genealogy Project
- , AMS Bookstore, retrieved 2014-07-18.
- Halmo award recipients, MAA, retrieved 2013-01-22.
- List of Fellows of the American Mathematical Society, retrieved 2013-01-21.
- Hamilton Alumni Achievement Medals, Hamilton College, retrieved 2013-01-22.