At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians.
A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
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The public school system in 1915 enrolled approximately 82,000children of all ages, of whom about half were boys and half girls.They are taught in 98 elementary schools and 10 high schools. Theelementary course comprises eight grades. At the beginning of theschool year 1915-16 two junior high schools were opened for pupils ofthe seventh and eighth grades. It is to be expected that this planwill soon be extended throughout the city, so that the enrollment inelementary schools will be made up of pupils of the first six gradesonly. The distribution by grade is given in Table 3. The kindergartengrades and the special ungraded classes are omitted.
About 77 per cent of the children are enrolled in the grades below theseventh, about 13 per cent in the seventh and eighth grades, a littleover six per cent in the first two years of the high school, and lessthan three and one-half per cent in the third and fourth.
This distribution includes all pupils, from the beginners in the firstgrade to the older boys in the seventh and eighth grades. It iscertain, however, that differentiated instruction for vocationalpurposes is not possible or advisable for the younger children.According to the commonly accepted view among educators, vocationaltraining should not be undertaken before the age of 12 years, and manybelieve that this is too early. In an elementary school of 1,000pupils there would be about 80 boys 12 years old and over. Applyingto this number the ratios given in the previous table we obtain thefollowing:
A comparison of the course with that for corresponding grades of theelementary schools shows some marked differences. Less time is devotedto English in the junior high school and considerably more toarithmetic, geography, and history. Mechanical drawing, not taught inthe elementary schools except incidentally in the manual trainingclasses, is given an hour each week. All boys receive one hour ofmanual training a week against slightly less than one and one-halfhours in the seventh and eighth elementary grades, but they may electan additional two and one-half hours a week in this subject, togetherwith applied arithmetic during the first year, or with bookkeepingduring the second. Girls may elect an additional two and one-halfhours a week of domestic science, with bookkeeping. The manualtraining for boys comprises woodwork and bookbinding.
In the opinion of the Survey Staff a general industrial course shouldcover instruction in at least the following five subjects: Industrialmathematics, mechanical drawing, industrial science, shop work, andthe study of economic and working conditions in wage earning pursuits.These may be offered as independent electives or they may be requiredof all pupils who elect the industrial course. The details oforganization must, of course, be worked out by trial and experiment.They will probably vary in different schools and from year to year.
It is difficult to determine the exact function of the manual trainingshop work in cabinet making and bookbinding which figures in thecurriculum at present. That the work was not planned with vocationaltraining in mind seems clear from the action of the school board inadding bookbinding to the course about the middle of the year. Thebookbinding trade is one of the smallest in the city, and there islittle probability that more than one boy among the total numberenrolled in both junior high schools will enter it after leavingschool.
Two years ago the Ohio State legislature extended the compulsoryattendance period from 14 to 15 for boys and from 14 to 16 for girls.The result has been to force into the first years of the high schoolcourse a considerable number of pupils who have no intention of takingthe complete four year course, and who will leave as soon as theyreach the end of the compulsory period. That these pupils are probablynot getting all that they might out of the time they attend highschool is no argument against the present compulsory attendance agelimit, which should be raised rather than lowered.
The two technical high schools, the East Technical and West Technical,occupy an important place among the secondary schools of the city. Atthe present time the two schools enroll nearly two-fifths of the boysattending high school. The course comprises four years' work. In theEast Technical the shopwork includes joinery and wood-turning duringthe first year, and pattern making and foundry work during the secondyear. In the West Technical the first year course includes patternmaking and either forging or sheet metal work; and that of the secondyear, forging, pipe-fitting, brazing, riveting, and cabinet making.During the remaining two years of the course the student may elect aparticular trade, devoting about 10 hours a week to practice in theshop during the last half of the third year, and from 11 to 15 hoursduring the fourth year.
The proportion of pupils who graduate is small and the mortalityduring the first two years is very heavy. This is due in part to thefact that the type of pupil who leaves school early is more likely toelect a technical course than an academic course. About 25 per cent ofeach entering class drops out after attending one year, and 25 percent of the remainder by the end of the second year. By the time thethird year is reached the classes are greatly depleted and thesurvivors as a rule are of the more intelligent and prosperous type.Only a small proportion of them expect to enter skilled manualoccupations. Table 9 shows the distribution of the third and fourthyear students among the different trade courses during the firstsemester of 1915-16.
That relatively few of these students will ultimately becomejourneymen workmen is shown by the records of the boys graduated inthe past. The principal of the East Technical High School recentlysent a questionnaire to all the students graduated up to 1915, askingfor information as to their present occupations and their earningsduring the first four years after graduation. Of those who replied,over 60 per cent either were attending college, or employed asdraftsmen or chemists. About 28 per cent were employed in the skilledtrades. The distribution in detail is shown in Table 10.
The output of the schools falls into two main divisions: those wholeave at the end of the second year or earlier, and those whograduate. The records show that most of the pupils who reach the thirdyear complete the course, but nearly half drop out during the firstand second years. The benefit they obtain from these two years'attendance is problematical. The course was designed on the basis offour years' attendance, and the work of the first two years is to aconsiderable degree a preparation for that of the last two.
A trade school of this kind would relieve the first and second yearclasses of many pupils that the technical high schools do not want andcannot adequately provide for. The minimum entering age should be notless than 14, and no requirement other than age should be imposed.This would draw part of the over-age pupils from the grades and takefrom the junior high school a certain number of boys who could profitby the greater amount of time given to shop work in the trade school.
The apprentice school conducted by the Y.M.C.A. represents anothertype of apprentice training. The instruction is given during the day.The apprentices are sent to the school by various firms in the cityunder an arrangement whereby the boys attend four and one-half hourseach week during regular shop time. In February, 1916, the enrollmentconsisted of 46 apprentices, practically all from the metal trades.The employers pay the tuition fee, which amounts to $20 a year. Thecourse requires four years' work of 40 weeks each, a total of 720hours. It comprises instruction in shop mathematics, drawing, English,physics, and industrial hygiene. No shop equipment is used. Fifteenboys were graduated from the course this year.
It is the opinion of the Survey Staff that the only practicablesolution of this problem lies in the day continuation school, backedby a compulsory law which will bring every boy and girl at work underthe age of 18 into school for a certain number of hours per week. Onlythrough a comprehensive plan that will reach large numbers of youngworkers can the difficulties inherent in the administration of smallclasses be overcome. The night schools have never been successful inholding boys long enough to make more than a beginning intrade-extension training. It is certain that growing boys should notbe expected to add two hours of study to their nine or 10 hours ofunaccustomed labor in the shop. Both individual and communityinterests demand that this problem be taken up in such a way as toobviate the sharp cleavage between the boy's school life and hisworking life. From every point of view it is unwise to permit him tolose all contact with the educational agencies of the city during hisfirst years at work. 2ff7e9595c
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