Although there are at present many occupations that require a good deal of skill and training in advanced mathematics, mathematics itself is still often regarded as a curious profession demanding singular talents and a singular personality. My own character – apart from a certain tolerance of solitude, even a preference for it – has always seemed to me to be quite ordinary and although, as a ch...

Throughout his philosophical career, Carnap places the foundations of logic and mathematics at the center of his inquiries: he is concerned above all with the Kantian question "How is mathematics (both pure and applied) possible?" Although he changes his mind about many particular issues, Carnap never gives up his belief in the importance and centrality of this question—nor does he ever waver i...

<p>Realistic Mathematics Education (RME) is an instructional theory that has been implemented in many countries around the world to link mathematics real-world situations. The effectiveness of implementing RME education highly dependent on role teachers. This study was conducted with 64 high school teachers survey their understanding and perspectives status implementation teaching topics ...

We suggest that, similar to the many applications of chiral effective Lagrangian made recently to semileptonic decays of heavy hadrons involving Goldstone bosons, chiral symmetry can also be applied to many-body nonleptonic decays of heavy hadrons. As examples we establish the chiral effective Hamiltonian for some typical many-body nonleptonic decays of bottom hadrons. We discuss the lowest-ord...

the desire and drive for excellence in any endeavor in life requires an effort from the individual; in addition it requires a constellation of features around such individuals that help them to become successful. for surgeons, it is the operating room staff, the administrative and medical assistants and our residents and fellows. however, perhaps the most important contribution to a physician’s...

We consider some large systems of di erential equations that have been introduced as model many-body problems. These systems have solutions that oscillate on a wide range of time scales. We apply the formalism of optimal prediction to these systems, using conditional expectations of the equations of motion to construct e ective equations for the most slowly-varying quantities. We verify the acc...

Colorimetric data can be readily computed from measured spectral data, however, as illustrated by metameric pairs, the mapping from spectral data to colorimetric values is many-to-one and therefore typically not invertible. In this paper, we investigate inversions of the spectrum-to-colorimetry mapping when the input is constrained to a single color reproduction medium. Under this constraint, a...