Math 4 introduction - What is Mathematics for?

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  • 1. What isMathematics for?
  • 2. Kevin is two years older than his wife Angela. In 15 years, the sum of their ages will be one more than thrice Kevin’s age now. What are their present ages?A bank teller has some P50 bills and some P200 bills. The teller has five more P200 bills than P50 bills. The total value of the money is P7250. Find the number of P50 bills.A gardener has 26 kg of a mixture of a fertilizer and weed killer. If one kilo of the mixture is replaced by weed killer the result is a mixture that is 5% weed killer. What percent of the original mixture was weed killer? A ladder is to be constructed with 16 rungs whose lengths decrease uniformly from 20 inches at the base to 16 inches at the top. Find the total length of material needed for the rungs. The angle of elevation from the ground to the top of a cliff is 320 at point A. Point B is exactly 100 feet nearer the cliff, and the angle of elevation from that point is 420. Find the height of the cliff.
  • 3. Our future lawyers, clergy, andstatesmen are expected at the University to learn a good deal aboutcurves, and angles, and numberand proportions; not because thesesubjects have the smallest relationto the needs of their lives, butbecause in the very act of learn­ing them they are likely to acquirethat habit of steadfast and accuratethinking, which is indispensible inall the pursuits of life.• JD Fitch, 1906
  • 4. Mathematics and natural philosophy are so peculiarly engaging anddelightful as would induce every­one to wish an acquaintance withthem. Besides this, the facultiesof the mind, like the membersof a body, are strengthened andimproved by exercise. Mathematical reasoning and deductions are,therefore, a fine preparation forinvestigating the abstruse speculations of the law.• Thomas Jefferson
  • 5. Mathematics is the study whichforms the foundation of the course[at West Point]. This is necessary,both to impart to the mind thatcombined strength and versatility,the peculiar vigor and rapidity ofcomparison necessary for militaryaction, and to pave the way forprogress in the higher militarySciences.• Congressional Committee on Military Affairs, 1834
  • 6. Give 100 loaves to five men sothat the shares are in arithmeticprogression and the sum of thetwo smallest is 1/7 of the threegreatest.- a problem found in the RhindPapyrus, Egyptian textbook ofmathematics c. 1650 BC
  • 7. Simplify: 1 1 1 1 2  2 2 − 2 x y x y − 1 1 1 1 2 − 2 2  2 x y x y   8   2 2 x y x− y x y   −2 x− y x y y 2 x 2
  • 8. What mathematics education is for is not for jobs. It is to teach the race to reason. It does not, heaven knows, always succeed, but it is the bestmethod that we have. It is not the only road to the goal, but there is none better. Furthermore, it is worth teaching.­ Underwood Dudley, American Mathematics Society