**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Examples of counting problems in geometry:
Grassmanians and intersections.
Chasles problems on conics.
Fixed points of transformations.
Bezout's theorem and 9-point circles.
- How to “count properly”:
Transversal intersections.
Fundamental theorem of algebra and multiplicity.
- Grassmanians and Projective space:
Cell decompositions.
Schubert cells.
Schubert calculus.
- Moving and blowing-up:
Resultants and plane curve intersections.
Singular intersections by moving.
Singular intersections by blow-up.
- The Hilbert Polynomial:
Interpretation of coeffs of the Hilbert polynomial
- Intersection theory on Algebraic surfaces/4-manifolds.
Divisors and their intersections.
Neron-Severi group
Hodge Index theorem
- Introductory K-theory Lambda rings Chern classes for lambda rings Formal Grothendieck-Riemann-Roch theorem

- W. Fulton and R. Lazarsfeld, Interesection Theory, Memoirs of AMS.
- J. W. Milnor, Topology from a differentiable viewpoint Princeton Univ. Press (1965).
- J. W. Milnor and J. D. Stasheff, Characteristic Classes Princeton Univ. Press (1974).
- W. Fulton, Intersection theory 2nd ed. Springer (1998).
- M. F. Atiyah and I. G. McDonald, Commutative Algebra Oxford University Press (1978).
- A. Beauville, Complex Algebraic Surfaces I London Math. Society (1996).
- V. Srinivas, Algebraic K-Theory Birkhauser (2008).