Algebraic varieties, affine and projective varieties, dimensions of varieties, singular points, divisors, differentials, intersections. Schemes, cohomology, curves and surfaces, varieties over the complex numbers.
Introduction to group theory. Isomorphism theorems. Permutation groups and Cayley’s theorem. Conjugacy classes. Lagrange’s theorem and the Sylow theorems. principle ideal domains. Polynomial ring.
Lebesgue measure and integration on the line. Convergence theorems. General measure and integration. Lp spaces. Decomposition of measures. Radon Nikodym theorem. Product measures and Fubini’s theorem.
This course introduces fundamental principles in teaching and learning for graduate students in the event that they choose a career in academia. In addition, this course acculturates students to the practices and culture of Sabanci University. Through a series of workshops, graduate students will learn about best practices and ethical considerations in teaching and learning, …