Fall 2024: Math 2270 Calculus III for science and mathematics
Fall 2024: Math 8300 Introduction to Algebraic Geometry (graduate course)
Syllabus Lecture notes:
08/19 Relation with field theory
08/23 Singular and non-singular points
08/28 Hilbert's Nullstellensatz
08/30 More on Zariski topology
09/13 Properties of regular maps
09/18 The local ring of a variety at a point
09/23 The tangent space (intrinsic definition)
09/30 The blow up of C^n at a point
10/02 The blow-up of a quasi-projective variety at a point
10/16 Linear systems of divisors
10/18 Linear systems of divisors - continued
10/21 The degree of a divisor on a curve
10/25 Bezout's Theorem - continued
10/28 The dimension of a divisor
10/30 The dimension of a divisor -continued
11/04 Regular differential 1-forms
11/06 Rational differential 1-forms
11/08 The canonical class
11/11 Exercises on differential forms
11/13 Canonical classes of curves in the projective plane
11/15 Statement of the Riemann-Roch Theorem
11/18 More on Riemann-Roch
11/20 Applications of Riemann-Roch
11/22 More problems on Riemann-Roch
11/25 On elliptic curves
Spring 2024: Math8800 Directed Reading for PhD students
Topics covered: Sheaf Cohomology (Hartshorne, Chapter III)
Fall 2023: MATH 3300 Applied Linear Algebra (section 45756)
Fall 2023: MATH 3300 Applied Linear Algebra (section 49943)
Fall 2023: MATH 8300 Toric Geometry and Cluster Varieties (graduate course)
Spring 2023: Math 2500 Accelerated calculus for engineers
You can download the textbook for free here
Fall 2022: Math 2250 Calculus I
You can download the textbook for free here