Lecture 3: Abstract Quasiminimality

Generic stability, regularity, and quasiminimality

We study (and sometimes introduce) the notions generic stability, regularity, homogeneous pregeometries, quasiminimality, and their mutual relations, in arbitrary first order theories. We prove that “infinite-dimensional homogeneous pregeometries” coincide with generically stable strongly regular types (p(x), x = x). We prove that in a theory without the strict order property, regular types are...

Lectures on Integer Matrices

Introduction 2 Lecture 1. Hermite and Smith normal forms 3 Lecture 2. Integral similarity and the Latimer-MacDuffee-Taussky theorem 8 Lecture 3. Ideal class numbers, integral matrices nonderogatory modulo every prime and maximal orders of number fields 12 Lecture 4. Factorizations of integer matrices as products of elementary matrices, involutions etc 20 Lecture 5. Additive commutators. Solving...

CS 617 Object Oriented Systems Lecture 3 Object Abstractions, Encapsulation, Abstract Data Types 3:30-5:00pm Thu, Jan 10

Comparison of Lecture and Group Discussion Methods on Learning Anatomical Sciences: A Study in PhD students

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Lecture Notes on the Diperna-lions Theory in Abstract Measure Spaces

Contents 1. Introduction 1 2. Reminders on the Cauchy-Lipschitz theory 4 3. Nonsmooth vector fields in Euclidean spaces 4 4. Abstract setup 7 5. Derivations and their regularity 10 6. Eulerian side 11 6.1. Existence of solutions to the continuity equation 11 6.2. Uniqueness of solutions to the continuity equation 14 7. Lagrangian side 16 7.1. ODE's associated to derivations and Regular Lagrangi...