Of a Liberal Education in General

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Contents

Geometry cannot be superseded
31
Value of Geometry
32
Arithmetic to be learnt
33
Conic Sections 35 Mechanics and Hydrostatics
34
Newtons Principia
36
Astronomy
37
Optics 39 The Higher Mathematics are Progressive Studies SECT 5 Of Analytical Mathematics as an Educational Study
38
Meaning of Analysis 41 Merits of Analysis
41
Analysis compared with Geometry
42
Is not an exercise of the Reason
43
Does not exemplify the usual kind of reasoning
44
Does not depend on the matter reasoned
45
Exemplified in Proportion
46
In Trigonometry
47
In Conic Sections
48
In Statics 50 In Dynamics 51 In Astronomy
49
Analysis not valuable in Education 52 As the Mathematical element
52
Analysis evades difficulties 54 Standard Geometrical Demonstrations to be used 55 With Questions 56 And Problems
53
Geometry necessary as introductory to Analysis
57
Analysis ill understood disgusts students
58
Faculties which Analysis cultivates
59
Hence Analysis worthless as discipline
60
Latin long the language of literature 98 As an accomplishment
61
Is lost in Analysis
63
Hence the educational value is lost
64
Geometrical Mathematicians solve problems better
65
Recapitulation
66
Writing Latin verse
90
Writing Greek prose
92
And Greek verse
93
Of the Value of Permanent Studies
95
Objections urged against Permanent Studies 105 They do not narrow the mind
105
On account of their excellence
106
Though read with Commentators
107
Are such like the Aristotelian Commentators
108
The memory is to be used in cultivating the reason
109
Schoolboy ridicule of cramming
110
Common ridicule of technicalities
111
Rules to be learnt before reasons
112
Value of new methods of teaching
113
Old methods to be respected
114
Mathematics and Classics both necessary
115
Have been united generally
116
And usefully
118
CHAPTER II
120
sities
128
They occur in his Travels in America 129 Ascribed to me opinions opposite to what I have expressed
129
Pretending to seek my views
130
Our College system agrees with Mr Lyells Pro
131
He does not condemn our peculiarities 133 He condemns me for recommending respect
133
What will Mr Lyell do with unwilling students
134
Lectures will not secure attention
135
Hence Examinations instituted
136
Mr Lyells confusion about a critical spirit
137
Mode of teaching the Philosophy of Science
138
How do men learn to think for themselves?
139
Progressive Sciences may be introduced at Cam bridge
140
Is the College System new in our Universities?
141
It is as old as the Reformation
142
It is established by the Statutes
143
Is it desirable to have only a few College Tutors
144
Present faults of the College System
145
Mr Lyells remedies not effective
146
Examinations are means of teaching 148 May be separated from Lectures
148
But are then not a good Education
149
Examinations and Lectures must agree
150
College Examinations
151
Difference of Examinations and Lectures
152
Examinations will then govern all
153
And Private Tutors will be sought
154
Evil consequences of this
155
Incurred in mere Paper Examinations
156
And with changing Examiners
157
These evils to be avoided
158
A Standard course requisite
159
Case when the Lecturers are the Examiners
160
Cannot be general in the University
161
Advantages of Oral Examinations
162
Their alleged disadvantages 164 The time required for them is great
164
The Examiners must be accomplished
165
The Examinees must be prompt
166
Are Oral Examinations fit for School only
167
Oral Examinations with Diagrams
168
Disputations at Cambridge
169
Difficulty of reviving them
170
Examiners may propose difficulties
171
We must have Paper as well as Oral Examina tions
172
Paper Answers should be made public
173
Fairness of Paper Examinations
174
Permanent before Progressive Mathematical sub jects
185
And in Classics 187 Examination at beginning of residence
187
Prizes out of the common course
188
Those principles applicable to Cambridge
189
OF THE METHOD OF TEACHING IN CLASSICS AND MATHEMATICS
191
System in 1772 Moderators notices
192
Disputations
193
Compliments of Moderators
194
Examinations of Questionists
195
Subjects
196
Problems
197
Hours
198
Examination by Fathers of Colleges
200
Junior Optimes
201
Proctors Senior Optimes
202
Medallists
203
The Polloi
204
Advantages of the Disputations
205
Causes of Change
206
Annual Examination Syndicate of 1773
208
Graces of 1779 Arrangements of Classes
210
The Law better than the present practice
211
Grace of 1792 for the better attendance of Schools
212
Grace of 1808 A day added to the Examination
213
Books then current in the University
214
Introduction of Analysis
215
Inconvenient result
216
Tendency to innovate
217
Inconveniences felt
218
Grace of 1827 New Plan of Examination
219
Grace of 1828 The Polloi
220
Graces of 1831 1832 Further alterations
221
Graces of 1836 1837 Alterations for the Polloi
222
Grace of 1838 Alterations for the Honours 224 Grace of 1840 Syndicate reappointed
224
Tendency of the changes Classes abolished
225
Reason of this
226
Time extended for Examinees 228 And for Examiners
227
Time added to Questions from Books
229
Knowledge of Principles aimed
230
Want of Standard Books
231
Resulting evils
232
The Remedies 234 A Standard Course of Study
234
To be drawn up by a Board
235
Subjects not to be treated analytically Conic Sections
236
Mechanics Dr Woods
237
Dr Whewells Mechanics
238
Oscillations
239
Newtons Principia
16
110
25
Progressive Studies as well as Permanent Studies are necessary
56
First of Classical Teaching 120 Teaching at School
64
And Mathematical in particular
68
List of such subjects
69
But Analysis does not supersede Geometry
71
Division of Mathematical writings
72
Capital Works to be studied
73
List of them restricted
74
Original Investigations not to be required
75
To be admitted in practical problems
76
Systematic Treatises to be read
77
Elementary Treatises
78
Not to be rapidly changed
79
To be selected by authority
80
Not to supersede Geometry
81
English and Foreign Mathematics
82
The study of Newton not an evil
83
Chance of a school of English Mathematicians
84
We require Mathematics as an Education
85
Necessity of Latin as a Permanent Study 87 And of Greek
87
Latin and Greek as Progressive Studies
88
Progressive cannot supersede Permanent Studies
89
Latin more necessary than Greek
90
May translations supersede Latin and Greek
91
Do Translations perplex Examinations
92
Translations are valuable in Literature
93
Capital works in Classical Literature
94
Cannot be superseded by private teaching
95
Writing Latin to be practised
96
College Lectures
121
Their difference from Professorial Lectures
122
Previous knowledge required
123
Difference of students capacity
124
Size of Classes
125
Professorial Lectures necessary
126
Their advantages and disadvantages
127
The First Three Sections
131
Hydrostatics 243 Optics 244 Astronomy 245 Differential Calculus
132
Examinations vivā voce to be restored 247 The possibility of this 248 The character which they should have 249 They must be vigorous 250 Paper ...
137
Examination for Higher Honours 254 Answers to be published 255 Reason why Cambridge should improve Exami nations
139

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