ETHAN BLOCH   BARD COLLEGE

Books

  1. A First Course in Geometric Topology and Differential Geometry, Birkhäuser, Boston, 1996.
    2. A First Course in Geometric Topology and Differential Geometry, cover publisher's information
    Errata for "A First Course in Geometric Topology and Differential Geometry"
  2. Proofs and Fundamentals: A First Course in Abstract Mathematics, Birkhäuser, Boston, 2000.
    3. This book is now replaced by the second edition, listed below. All errors stated in the errata for the first edition (except for a few that were caught too late) have been corrected in the second edition, and many other changes have been made.
    Errata for "Proofs and Fundamentals, first edition"
  3. Proofs and Fundamentals: A First Course in Abstract Mathematics, second edition, Springer, New York, 2010.
    4. Proofs and Fundamentals, 2nd ed., cover Publisher's information
    Errata for "Proofs and Fundamentals," second edition"
    Proof of Zorn's Lemma
    You are the Professor
  4. The Real Numbers and Real Analysis, Springer, New York, 2011.
    5. The Real Numbers and Real Analysis, cover Publisher's information
    Errata for "The Real Numbers and Real Analysis"

 

Open Material

  1. Precalculus Review: Summary and Exercises for Students Taking Calculus, Version 1.1, September 2023.
    2. Precalculus Review, cover PDF

Papers

  1. (with R. Connelly and D. W. Henderson) The space of simplexwise linear homeomorphisms of a convex 2-disk, Topology 23 (1984), 161-175.  PDF

  2. Simplexwise linear near-embeddings of a 2-disk into R2, Trans. Amer. Math. Soc. 288 (1985), 701-722.  PDF

  3. Strictly convex simplexwise linear embeddings of a 2-disk, Trans. Amer. Math. Soc. 288 (1985), 723-737.  PDF

  4. Simplexwise linear near-embeddings of a 2-disk into R2, II, Topology Appl. (1987), 93-101.  PDF

  5. Simplexwise linear and piecewise linear near self-homeomorphisms of surfaces, Fund. Math. 132 (1989), 151-162.  PDF

  6. Complexes whose boundaries cannot be pushed around, Discrete Comput. Geom. 4 (1989), 365-374.

  7. A combinatorial Chern-Weil theorem for 2-plane bundles with even Euler characteristic, Israel J. Math. 67 (1989), 193-216.  PDF

  8. The angle defect for arbitrary polyhedra, Beiträge Algebra Geom. 39 (1998), 379-393.

  9. Critical points and the angle defect, Geom. Dedicata 109 (2004), 121-137.  PDF

  10. The angle defect for odd-dimensional simplicial manifolds, Discrete Comput. Geom. 35 (2006), 311-328.  PDF

  11. Mod 2 degree and a generalized no retraction theorem, Math. Nachr. 279 (2006), 490-494.  PDF

  12. A simple proof of a generalized no retraction theorem, Amer. Math. Monthly 116 (2009), 342-350.  PDF

  13. A characterization of the angle defect and the Euler characteristic in dimension 2, Discrete Comput. Geom. 43 (2010), 100-120.  PDF

  14. Polyhedral representation of discrete Morse functions, Discrete Math. 313 (2013), 1342-1348.  PDF

  15. Functions of finite simplicial complexes that are not locally determined, Australas. J. Combin. 65 (2016), 261-272.  PDF

  16. Strongly-Delaunay starshaped polygons, Beiträge Algebra Geom. 63 (2022), 477-493.  view-only PDF

  17. A Poincare-Hopf theorem for oriented triangulated surfaces via tiles, submitted  PDF

  18. Lattice diagrams of knots and diagrams of lattice stick knots (with M. Allardice), submitted for publication.  arXiv: 1803.03685

  19. An upper bound for the lattice edge number of knots and links with simple lattice diagrams, in preparation.

Ethan Bloch
Professor of Mathematics
Bard College

Office Hours: