THE COURSE OF MATHEMATICAL 

 STUDIES*. 



THE seventh query f, so far as it relates to the limits beyond 

 which it is not expedient that the undergraduate course of ma- 

 thematics should extend, seems naturally to form a part of a 

 more general question, namely, how the whole time given to the 

 study of mathematics may "be most advantageously employed. 

 In order to discuss this more general question, it is necessary to 

 consider on what grounds the study of mathematics is made to 

 form part of our system of education. 



I. The grounds are two-fold : mathematics 1 are studied as 

 ancillary to natural philosophy and as a means of training and 

 developing the mind. In the latter point of view they are 

 chiefly valuable, because they deal with necessary and not con- 

 tingent truth J. Of every necessarily true proposition which the 



Cambridge University Commission, 1852. Evidence on Mathematical Studies 

 and Examinations, p. wi. 



1* The seventh query is : Would you be disposed to recommend the limitation 

 of some of the subjects included in the present range of the examinations, for 

 instance to omit such propositions and applications of the Calculus of Variations, 

 of the theories of Definite and Elliptic Integrals, of the Planetary and Lunar 

 theories, of the theories of Heat, Electricity, and Magnetism, of the undulatory 

 theory of Light, as require for their treatment a very refined and laborious analysis ? 

 Might such higher mode of treating these subjects be advantageously reserved for 

 examination for special prizes at periods subsequent to the Degree of B. A. ? Would 

 not the concentration of the attention of Students upon a smaller number of sub- 

 jects, and those restricted within narrower limits, tend to increase the accuracy 

 and raise the character of their knowledge, and to bring their instruction more 

 completely within the grasp of the public and recognized teaching of the Univer- 

 sity? 



This applies to mixed as well as to pure mathematics ; the necessity of the 

 conclusion being, however, in the latter absolute, and in the former hypothetical, 



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