Lecture 9 — December 1 , 2014

Math 140a: Foundations of Real Analysis I

1. Ordered Sets, Ordered Fields, and Completeness 1 1.1. Lecture 1: January 5, 2016 1 1.2. Lecture 2: January 7, 2016 4 1.3. Lecture 3: January 11, 2016 7 1.4. Lecture 4: January 14, 2014 9 2. Sequences and Limits 13 2.1. Lecture 5: January 19, 2016 13 2.2. Lecture 6: January 21, 2016 15 2.3. Lecture 7: January 26, 2016 18 2.4. Lecture 8: January 28, 2016 21 3. Extensions of R: the Extended Rea...

Generalized Synchronization Trees

[1] J. Ferlez, R. Cleaveland, and S. Marcus. Generalized synchronization trees. In FOSSACS 2014, volume 8412 of Lecture Notes in Computer Science, pages 304–319, Grenoble, France, 2014. Springer-Verlag. [2] Robin Milner. A Calculus of Communicating Systems. Number 92 in Lecture Notes in Computer Science. Springer-Verlag, 1980. [3] Edward Dean Tate Jr, Jessy W. Grizzle, and Huei Peng. Shortest p...

Lecture 9: Néron models

Lecture 9 — 3 March, 2014: ``9. Graph Isomorphism and the Lasserre Hierarchy.''

http://www.csc.kth.se/~lauria/sos14/ Let G and H be two graphs, we say that two graphs are isomorphic, denoted as G ≅ H, if there is a bijection π ∶ V(G) → V(H), such that {u, v} ∈ E(G) if and only if {π(u), π(v)} ∈ E(H). In this lecture, we discuss a recent paper by O’Donnell, Wright, Wu and Zhou 1 which proved the 1 R. O’Donnell, J. Wright, C. Wu, and Y. Zhou. Hardness of Robust Graph Isomorp...

Math 55a Lecture Notes

3 September 9, 2014 9 3.1 Direct products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Commutative diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Sub-things . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Let’s play Guess the BS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 Kernels . . . . . . . . ....