A Course in Applied Mathematics for Teachers of Secondary Mathematics

1938 ◽  
Vol 31 (2) ◽  
pp. 51-62
Author(s):  
Cleon C. Richtmeyer
Keyword(s):  
Applied Mathematics ◽  
Secondary Mathematics ◽  
The Many

It has long been the feeling of the writer that the present curricula for teachers of secondary mathematics tend more to theory than to applications, and that a need exists for a course in which the many applications of mathematics could be considered. This feeling increased in intensity due to the following trends in teaching of secondary mathematics: (1) A shift in emphasis from disciplinary values to appreciation and application; and (2) The reorganization of secondary mathematics to include a general course for all students. These trends both imply a teacher with a broad background of knowledge of the application of mathematics.

scholarly journals Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data

2021 ◽  
Author(s):  
Randall Clark ◽  
Lawson Fuller ◽  
Jason Platt ◽  
Henry D. I. Abarbanel
Keyword(s):  
Nonlinear Dynamics ◽  
Biological Networks ◽  
Applied Mathematics ◽  
Voltage Response ◽  
Synaptic Connections ◽  
Neuron Models ◽  
Detailed Specification ◽  
Reduced Dimension ◽  
The Many ◽  
Voltage Dynamics

AbstractUsing methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case the reduced dimension data driven forecasting (DDF) models are shown to predict accurately for times after the training period.When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized.The DDF constructions are reduced dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model.As the DDF models use only voltage data and forecast only voltage data they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced dimension neuron models, say of the integrate-and-fire type, in developing and analyzing large networks of neurons.When one does have detailed HH model neurons for network components, a reduced dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

scholarly journals Address of the president, Sir Frederick Gowland Hopkins, O. M., at the anniversary meeting, November 30, 1935

1936 ◽  
Vol 119 (813) ◽  
pp. 88-113 ◽  
Keyword(s):  
Wave Equation ◽  
Applied Mathematics ◽  
Electromagnetic Theory ◽  
Mathematical Ability ◽  
Text Book ◽  
De Vries ◽  
The Many ◽  
The University

It is my traditional duty to remind you of the losses the Society has suffered in the death of eighteen members. Four of these, Theobald Smith, Hugo de Vries, Friedrich Went, and H. F. Osborn, were distinguished Foreign Members. Among the fourteen Fellows are two who were active members of the Council, Dr. H. H. Thomas and Sir John McLennan. By the death of Sir Horace Lamb, the Society has lost a Fellow who for more than forty years was one of the most prominent and successful among the many workers in applied mathematics in this country. He was fortunate in his generation; Maxwell had shown the importance of the wave equation in electromagnetic theory; the work of Stokes, Rayleigh, and Thomson had aroused fresh interest in problems in heat and hydrodynamics, in all of which it was of importance. Lamb realized this and utilized his mathematical ability in the development of some of its many consequences. His papers on hydrodynamics and elasticity added to our knowledge in a marked degree. And in addition he was a great teacher. His text-book on “ Hydrodynamics ,” the outcome of a course of lectures to undergraduates at Cambridge in 1875, is a model of what such a book should be, and the distinction of many of his pupils is clear evidence of the value of his work as a Professor at Manchester. To quote from a resolution of the Council and Senate, “He inspired all who knew him in the University with respect and esteem, and his many friends with warm affection.”

A Brief List of Mathematical Books Suitable for Libraries in High Schools and Normal Schools

1925 ◽  
Vol 18 (8) ◽  
pp. 477-489
Keyword(s):  
High Schools ◽  
Secondary Schools ◽  
Applied Mathematics ◽  
Foreign Languages ◽  
Ordinary Sense ◽  
Normal Schools ◽  
Teachers College ◽  
The Many

The following brief list is prepared to meet the many requests which come to Teachers College for information as to books for the use of teachers of mathematics or suitable for libraries in high schools and normal schools. An effort has been made to select a few books which will he helpful to students and teachers in such schools, but it must be understood that numerous other works are eminently worthy of having a place in such a list. No books in foreign languages have been included, but the department of mathematics of Teachers College will gladly give information relating to such books to any who may inquire. Except in the field of applied mathematics, no books have been included which are, in the ordinary sense of the term, textbooks for secondary schools. The prices given are subject to change, but are approximately correct.

Ocean Science

1974 ◽  
Vol 27 (1) ◽  
pp. 91-110 ◽  
Author(s):  
James Lighthill
Keyword(s):  
Applied Mathematics ◽  
Hundredth Anniversary ◽  
Ocean Science ◽  
University Of Cambridge ◽  
The Many ◽  
The University

In this paper the Lucasian Professor of Applied Mathematics in the University of Cambridge studies the role of ocean science in the service of mankind, and examines the interaction between the many disciplines which make up that science. The paper, which was written in May 1972 (and a version of which was published in the Bulletin of the Institute of Mathematics and its Applications for February 1973), was presented at a conference held in Greenwich on 12–14 September 1973 to celebrate the hundredth anniversary of the Royal Naval College. (Note: the National Institute of Oceanography referred to in the text is now known as the Institute of Oceanographic Sciences.)

scholarly journals Johannes Kepler and his making of the Rudolphine Tables

2021 ◽  
Vol 105 (564) ◽  
pp. 425-432
Author(s):  
Mark J. Cooker
Keyword(s):  
Applied Mathematics ◽  
Johannes Kepler ◽  
History Of ◽  
The Many

This Article is about the many complicated tasks that one mathematician had to carry out, and the barriers he had to overcome in order to publish one very important book in the history of applied mathematics.

Concluding remarks

1984 ◽  
Vol 313 (1524) ◽  
pp. 185-186
Keyword(s):  
Solar System ◽  
Geomagnetic Field ◽  
General Circulation ◽  
Applied Mathematics ◽  
The Core ◽  
Atmospheric General Circulation ◽  
200Th Anniversary ◽  
The Many ◽  
Academy Of Sciences ◽  
Solid Bodies

This Discussion Meeting was the first to review the many very interesting aspects of the rotation of bodies in the Solar System. During this session, the 200th anniversary of the death occurred of one of the greatest of all mathematicians, L. Euler, who, among other contributors to both pure and applied mathematics, established the laws of the rotation of solid bodies. Euler was born at Basle on 15 April 1707 and died at St Petersburg (Leningrad) on 18 September 1783. He worked as an Associate of the Academy of Sciences at St Petersburg on the invitation of Catherine the Great, with a period in Berlin as a Member of the Academy of Sciences on the invitation of Frederick the Great. Virtually all the papers given at this Discussion Meeting illustrate the fundamental principles he first enunciated. Studies of the variations of the Earth’s rotation, the discovery of which is a most interesting chapter of astronomy, have become a most important clue for understanding the motions in the Earth’s core responsible for generating the geomagnetic field and its secular variation, and now the shorter term variations accurately determined from modern techniques seem likely to similarly contribute to understanding the atmospheric general circulation. The rotation rate of Mars determined by astronomers from surface markings has been followed for over a century, but shows no such variations, partly because the methods so far available are not very accurate and partly because the core of Mars cannot be large.

scholarly journals Address of the President, Sir Frederick Gowland Hopkins, at the anniversary meeting, November 30, 1935

1936 ◽  
Vol 153 (879) ◽  
pp. 247-272
Keyword(s):  
Wave Equation ◽  
Applied Mathematics ◽  
Electromagnetic Theory ◽  
Mathematical Ability ◽  
Text Book ◽  
De Vries ◽  
The Many ◽  
The University

It is my traditional duty to remind you of the losses the society has suffered in the death of eighteen members. pour of these, Theobald Smith, Hugo de Vries, Friedrich Went, and H. F. Osborn, were distinguished Foreign Members. Among the fourteen Fellows are two who were active members of.the Council, Dr. H. H. Thomas and Sir John McLennan. By the death of Sir Horace Lamb, the Society has 1ost a Fellow who for more than forty years was one of the most prominent and successful among the many workers in applied mathematics in this country. He was fortunate in his generation; Maxwell had shown the importance of the wave equation in electromagnetic theory; the work of Stokes, Rayleigh. and Thomson had aroused fresh interest in problems in heat and hydrodynamics, in all of which it was of importance, Lamb realized this and utilized his mathematical ability in the development of some of its many consequences. His papers on hydrodynamics and elasticity added to our knowledge in a marked degree. And in addition he was a great teacher. His text-book on " Hydrodynamics ," the outcome of a course of lectures to undergraduates at (Cambridge in 1875, is a model of what such a book should be, and the distinction of many of his pupils is clear evidence of the value of his work as a professor at Manchester. To quote from a resolution of the (Council and Senate, "He inspired all who knew him in the University with respect and esteem, and his many friends with warm affection."

Identifying suboptimalities with factorial model comparison

2018 ◽  
Vol 41 ◽  
Author(s):  
Wei Ji Ma
Keyword(s):  
Experimental Design ◽  
Model Comparison ◽  
Process Models ◽  
Multiple Forms ◽  
Factorial Experimental Design ◽  
Factorial Model ◽  
Multiple Components ◽  
The Many

AbstractGiven the many types of suboptimality in perception, I ask how one should test for multiple forms of suboptimality at the same time – or, more generally, how one should compare process models that can differ in any or all of the multiple components. In analogy to factorial experimental design, I advocate for factorial model comparison.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

The many faces of obligation

2020 ◽  
Vol 43 ◽  
Author(s):  
Michael Tomasello
Keyword(s):  
Third Party ◽  
The Many ◽  
Sense Of Obligation

Abstract My response to the commentaries focuses on four issues: (1) the diversity both within and between cultures of the many different faces of obligation; (2) the possible evolutionary roots of the sense of obligation, including possible sources that I did not consider; (3) the possible ontogenetic roots of the sense of obligation, including especially children's understanding of groups from a third-party perspective (rather than through participation, as in my account); and (4) the relation between philosophical accounts of normative phenomena in general – which are pitched as not totally empirical – and empirical accounts such as my own. I have tried to distinguish comments that argue for extensions of the theory from those that represent genuine disagreement.

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