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Host: Could you tell me a little about the beginnings of your entering the field of mathematicsMathematician: I started very, very young. I am self-taught, in fact. I have a high school degree, from the Bronx High School of Science. I don’t have a college degree. I only have an honorary doctorate.Host: Can you tell me about your time at high schoolMathematician: Yeah. In 1956 when the Russians put Sputnik in orbit, the United States got terrified, so they started having special programs for gifted children to study science. I benefited from all of this. I went to a special NY high school for science called the Bronx High School of Science; there was a wonderful science and math library there. I was very fortunate that I was there at the right time, at a time when the United States was trying to make new scientists. I took university level courses in high school and they were wonderful courses because they were done by some of the best people in their fields. They were really new. They were not following the old curriculum, the old subjects. In every way they were very up-to-date and modem presentations of mathematics, physics, chemistry and biology. I didn’t have to waste time with a course which was really out of date.And I also went to a program at Columbia University for bright high school students. These were professors at Columbia University teaching, Saturday morning, bright students from high school. That was wonderful. One of the things they did which were maybe even better than the course itself was that they let me use the Columbia University libraries. I was allowed to look at the books. I was reading immense quantifies of books on my own. I was an unbearable child; my mind was ablaze with mathematics and scientific ideas.Host: It was early that your interest and study of mathematics started. Was there a hook or something that triggered itMathematician: Well, I swallowed up many books. I looked for books that I could study on my own, books that emphasized the fundamental ideas. One of these books was A Mathematician’s Apology by G. H. Hardy that I mentioned before.Host: You read that very earlyMathematician: I read it very, very early. It is a delightful book. The normal textbooks require that you study one by one a vast series of textbooks. I looked for books that enable you to just parachute or jump into a subject without having to do fifteen courses first.Host: Well, as you have been working on it so long, what is your view about science Is mathematics discovered or is it inventedMathematician: As far as I am concerned, there are two kinds of science: One kind of science is when you already have an exciting field and you need to progress in that field. The most exciting thing for me is when you create a completely new field.Is mathematics discovered or is it invented When I was young, I thought things were black or white but as I grow older I understand that everything is complicated and different viewpoints are also correct. So, some days of die week I think mathematics is invented, other days of die week I think it is discovered. I mean, both viewpoints have validity and they illuminate the same subject from different angles.Host: Thank you for your time. 7he mathematician felt very lucky to learn some courses on new and modem scientific fields.
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Host: Could you tell me a little about the beginnings of your entering the field of mathematicsMathematician: I started very, very young. I am self-taught, in fact. I have a high school degree, from the Bronx High School of Science. I don’t have a college degree. I only have an honorary doctorate.Host: Can you tell me about your time at high schoolMathematician: Yeah. In 1956 when the Russians put Sputnik in orbit, the United States got terrified, so they started having special programs for gifted children to study science. I benefited from all of this. I went to a special NY high school for science called the Bronx High School of Science; there was a wonderful science and math library there. I was very fortunate that I was there at the right time, at a time when the United States was trying to make new scientists. I took university level courses in high school and they were wonderful courses because they were done by some of the best people in their fields. They were really new. They were not following the old curriculum, the old subjects. In every way they were very up-to-date and modem presentations of mathematics, physics, chemistry and biology. I didn’t have to waste time with a course which was really out of date.And I also went to a program at Columbia University for bright high school students. These were professors at Columbia University teaching, Saturday morning, bright students from high school. That was wonderful. One of the things they did which were maybe even better than the course itself was that they let me use the Columbia University libraries. I was allowed to look at the books. I was reading immense quantifies of books on my own. I was an unbearable child; my mind was ablaze with mathematics and scientific ideas.Host: It was early that your interest and study of mathematics started. Was there a hook or something that triggered itMathematician: Well, I swallowed up many books. I looked for books that I could study on my own, books that emphasized the fundamental ideas. One of these books was A Mathematician’s Apology by G. H. Hardy that I mentioned before.Host: You read that very earlyMathematician: I read it very, very early. It is a delightful book. The normal textbooks require that you study one by one a vast series of textbooks. I looked for books that enable you to just parachute or jump into a subject without having to do fifteen courses first.Host: Well, as you have been working on it so long, what is your view about science Is mathematics discovered or is it inventedMathematician: As far as I am concerned, there are two kinds of science: One kind of science is when you already have an exciting field and you need to progress in that field. The most exciting thing for me is when you create a completely new field.Is mathematics discovered or is it invented When I was young, I thought things were black or white but as I grow older I understand that everything is complicated and different viewpoints are also correct. So, some days of die week I think mathematics is invented, other days of die week I think it is discovered. I mean, both viewpoints have validity and they illuminate the same subject from different angles.Host: Thank you for your time. The mathematician would like to study one by one a vast series of textbooks.
Host: Could you tell me a little about the beginnings of your entering the field of mathematicsMathematician: I started very, very young. I am self-taught, in fact. I have a high school degree, from the Bronx High School of Science. I don’t have a college degree. I only have an honorary doctorate.Host: Can you tell me about your time at high schoolMathematician: Yeah. In 1956 when the Russians put Sputnik in orbit, the United States got terrified, so they started having special programs for gifted children to study science. I benefited from all of this. I went to a special NY high school for science called the Bronx High School of Science; there was a wonderful science and math library there. I was very fortunate that I was there at the right time, at a time when the United States was trying to make new scientists. I took university level courses in high school and they were wonderful courses because they were done by some of the best people in their fields. They were really new. They were not following the old curriculum, the old subjects. In every way they were very up-to-date and modem presentations of mathematics, physics, chemistry and biology. I didn’t have to waste time with a course which was really out of date.And I also went to a program at Columbia University for bright high school students. These were professors at Columbia University teaching, Saturday morning, bright students from high school. That was wonderful. One of the things they did which were maybe even better than the course itself was that they let me use the Columbia University libraries. I was allowed to look at the books. I was reading immense quantifies of books on my own. I was an unbearable child; my mind was ablaze with mathematics and scientific ideas.Host: It was early that your interest and study of mathematics started. Was there a hook or something that triggered itMathematician: Well, I swallowed up many books. I looked for books that I could study on my own, books that emphasized the fundamental ideas. One of these books was A Mathematician’s Apology by G. H. Hardy that I mentioned before.Host: You read that very earlyMathematician: I read it very, very early. It is a delightful book. The normal textbooks require that you study one by one a vast series of textbooks. I looked for books that enable you to just parachute or jump into a subject without having to do fifteen courses first.Host: Well, as you have been working on it so long, what is your view about science Is mathematics discovered or is it inventedMathematician: As far as I am concerned, there are two kinds of science: One kind of science is when you already have an exciting field and you need to progress in that field. The most exciting thing for me is when you create a completely new field.Is mathematics discovered or is it invented When I was young, I thought things were black or white but as I grow older I understand that everything is complicated and different viewpoints are also correct. So, some days of die week I think mathematics is invented, other days of die week I think it is discovered. I mean, both viewpoints have validity and they illuminate the same subject from different angles.Host: Thank you for your time. The mathematician studied science in Bronx High School of Science.
No people doubt the fundamental importance of mothers in childrearing, but what do fathers do Much of what they contribute is simply being the second adult in the home. Bringing up children is demanding, stressful and exhausting. Two adults can support and make up for each other’s deficiencies and build on each other’s strength.As we all know, fathers also bring an array of’ unique qualities. Some are familiar: protector and role model. Teenage boys without fathers are notoriously prone to trouble. The pathway to adulthood for daughters is somewhat easier, but they must still learn from their fathers, in ways they cannot from their mothers, such as how to relate to men. They learn from their fathers about heterosexual trust, intimacy and difference. They learn to appreciate their own femininity from the one male who is most special in their lives. Most important, through loving and being loved by their fathers, they learn that they are love-worthy.Current research gives much deeper—and more surprising insight into the father’s role in childrearing. One significantly overlooked dimension of fathering is play. From their children’s birth through adolescence, fathers tend to emphasize game more than caretaking. The father’s style of play is likely to be both physically stimulating and exciting. With older children it involves more teamwork, requiring competitive testing of physical and mental skills. It frequently resembles a teaching relationship: come on, let me show you how. Mothers play more at the child’s level. They seem willing to let the child directly play.Kids, at least in the early years, seem to prefer to play with daddy. In one study of two and half years old who were given a choice, more than two-thirds chose to play with their fathers.The way fathers’ play has effects on everything from the management of emotions to intelligence and academic achievement. It is of particular importance in promoting self-control. According to one expert, "children who roughhouse with their fathers quickly learn that biting, kicking and other forms of physical violence are not acceptable." They learn when to "shut it down".At play and in other realms, fathers tend to lay stress on competition, challenge, initiative, risktaking and independence. Mothers, as caretakers, stress emotional security and personal safety. On the playground fathers often try to get the child to swing ever higher, while mothers are cautious, worrying about an accident.We know, too, that fathers’ involvement seems to be linked to enhanced verbal and problem solving skills and higher academic achievement. Several studies found that along with paternal strictness, the amount of time fathers spent reading with them was a strong predictor of their daughters’ verbal ability.For sons the results have been equally striking. Studies uncovered a strong relationship between fathers’ involvement and the mathematical abilities of their sons. Other studies found a relationship between paternal nurturing and boys’ verbal intelligence. The writer’s main point in writing this article is ().
Dried foodCenturies ago, man discovered that removing moisture from food helps to preserve it, and that tile easiest way to do this is to expose the food to sun and wind. In this way the North American indians produce pemmican (dried meat ground into powder and made into cakes), the Scandinavians make stockfish and the Arabs dried dates and ’apricot leather. ’All foods contain water—cabbage and other leaf vegetables contain as much as 93% water, potatoes and other root vegetables 80%, lean meat 75% and fish anything from 80% to 60% depending on how fatty it is. If this water is removed, the activity of the bacteria which cause food to go bad is checked.Fruit is sun-dried in Asia Minor, Greece, Spain and other Mediterranean countries, anti also in California, South Africa anti Australia. The methods used vary, but in general, the fruit is spread out on trays in drying yards in the hot sun. In order to percent darkening, pears, peaches and apricots are exposed to the fumes of burning sulphur before drying. Plums, for making prunes, and certain varieties of grapes for making raisins and currants, are dipped in an alkaline solution in order to crack the skins of the fruit slightly and remove their wax coating, so increasing the rate of drying.Nowadays most foods are dried mechanically. The conventional method of such dehydration is to put food in chambers through which hot air is blown at temperatures of about 110℃ at entry to about 43℃ at exit. This is the usual method for drying such things as vegetables, minced meat, and fish.Liquids such as milk coffee, tea, soups and eggs may be dried by pouring them over a heated horizontal steel cylinder or by spraying them into a chamber through which a current of hot air passes. In the first case, the dried material is scraped off the roller as a thin film which is then broken up into small, though still relatively coarse flakes. In the second process it falls to the bottom of the chamber as a fine powder. Where recognizable pieces of meat and vegetables are required, as in soup, the ingredients are dried separately and then mixed.Dried foods take up less room and weigh less than the same packed in cans or frozen, and they do not need to be stored in special conditions. For these reasons they are invaluable to climbers, explorers and soldiers in battle, who have little storage space. They are also popular with housewives because it takes so little time to cook them. Usually it is just a case of replacing the dried-out moisture with boiling water. We can infer from the last paragraph that ().
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