Preface 1 Preliminaries: Galois theory, algebraic number theory 2 Lecture 1. CFT of Q: classical (Mo. 19/7/10, 9:40–10:40) 4 Lecture 2. CFT of Q: via adeles (Mo. 19/7/10, 11:00–12:00) 6 Lecture 3. Local CFT, local-global compatibility (Tu. 20/7/10, 9:40–10:40) 8 Lecture 4. Global CFT, l-adic characters (Tu. 20/7/10, 11:00–12:00) 10 Appendix A. More on GLC for GL1: algebraic Hecke characters 12 ...

Definition 1. An algebra (A,⊕,∗ , 0) with a binary operation ⊕ : A×A → A and with a unary operation ∗ : A → A and a constant 0, is said to be an MV -algebra iff satisfies the following conditions for all a, b, c ∈ A: (1) (A,⊕, 0) is a commutative monoid; (2) x⊕ 0∗ = 0∗ for every x ∈ A; (3) (x∗)∗ = x for every x ∈ A; (4) (x∗ ⊕ y)∗ ⊕ y = (x⊕ y∗)∗ ⊕ x for every x, y ∈ A. ¿From (4), setting y = 0∗,...

1 Jacquelyn F. Sullivan, Integrated Teaching and Learning Program and Laboratory, College of Engineering and Applied Science, University of Colorado at Boulder, 522 UCB, Boulder, CO 80309-0522, [email protected]. 2 Derek Reamon, Department of Mechanical Engineering, College of Engineering and Applied Science, University of Colorado at Boulder, 427 UCB, Boulder, CO 80309-0427, Dere...

During the summer of 2011, twenty-four high school students participated in an intense, three-week computer science course at the University of Virginia. The course met for twentyone three-hour sessions, thus encompassing more contact time than a standard college-level course. The course was structured in an “Inform, Experience, Implement” active-learning format: students were exposed to the hi...

Westminster College runs a math, science, and computing summer camp for middle school girls called AWE+SUM. Core to the camp is a set of workshops that allow for creative hands-on experiments and exploration. One of the most popular workshops is called “Programming with Alice” where we introduce the girls to programming concepts through Carnegie Mellon University’s Alice software. This paper de...

1. The hyperreals 3 1.1. Basic facts about the ordered real field 3 1.2. The nonstandard extension 4 1.3. Arithmetic in the hyperreals 5 1.4. The structure of N∗ 7 1.5. More practice with transfer 8 1.6. Problems 9 2. Logical formalisms for nonstandard extensions 10 2.1. Approach 1: The compactness theorem 11 2.2. Approach 2: The ultrapower construction 12 2.3. Problems 16 3. Sequences and seri...

The problem I would like to address focus on the role of communication within scientific communities. More specifically I intend to examine at what extent some parallelism can be observed between the construction of scientific representations and their subsequent transformation in social representations. I will try to examine the continuity as well as the discontinuity between science and commo...

Optical microcavity biosensors are emerging as one of the most sensitive microsystem biodetection technology that does not require amplification or labeling of the analyte. I will give an overview of the exciting possibilities provided by this highly sensitive technique for molecular diagnostics, nanoparticle detection and -manipulation. I will then talk about the prospects of boosting sensitiv...