By Bermudez T., Bonilla A., Peris A.

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This text discusses a few tools of describing and touching on mathematical items and of continually and unambiguously signaling the logical constitution of mathematical arguments.

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It should perhaps be started by organizing it around some structure like the MAA, AMATYC, or SIAM local sections where this may well be feasible. The excellent experiences that students obtain from such structured interactive competitions is usually highly beneficial to them and our profession. © 1999 by Chapman & Hall/CRC It seems to be one of the good side effects of concerns for more modeling in the mathematics curriculum. 8 Other Benefits of Modeling The introduction of modeling courses and other alternative formats, such as math clinics, for providing meaningful training in modern applied mathematics can provide a host of benefits that extend far beyond the students themselves.

Mathematical Programming. One can argue that linear programming (LP) is just as important (as an applied or pure subject) as is linear algebra. Polyhedra and cones are hardly less basic things than vector spaces. Yet it was the great success of LP in applications that brought it such widespread attention. LP was also the obvious tool for solving a great variety of different sorts of problems. It thus became a very popular topic in many (less open-ended) modeling courses. Even then, it took several decades before many mathematics departments took it seriously.

And, on the other hand, Samuel Johnson in “The Adventurer, No. 126” (1754): Though learning may be conferred by solitude, its application must be attained by general converse . . he that never compares his notions with those of others . . very seldom discovers the objections which may be raised against his opinions . . he is only fondling an error . . Whether learning is done in an individual or collaborative setting, motivation of some sort is a crucial prerequisite. It is frequently asserted that we learn from experience.

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C-supercyclic versus R^(+)-supercyclic operators by Bermudez T., Bonilla A., Peris A.


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