User:AnnaKoniuhova
My name is Anna Koniuhova and I am from Russia. I am in my first year of university studying commerce. UBC is a beautiful place and I hope to enjoy my next four years here.
As an elective I am taking philosophy and one of the people we study is Rene Descartes, thus I will describe the research I have found on him being a philosopher as well as a mathematician.
Rene Descartes was born on March 31, 1596, in a small town in Touraine called La Haye, which was later renamed La Haye-Descartes. At the age of ten he attended school in College Henry IV at La Fleche. In 1614 he left La Fleche to study civil and canon law at Poitiers and by 1616 he received the baccalaureate and licentiate degrees in law. In 1618, he joined the army of Prince Maurice of Nassau as an unpaid volunteer, but apparently he never saw combat. He saw the military as a means to view the world. During a tour of duty in Germany, events of lifelong importance happened to Descartes. In November 1619 he was sitting in a poele, a small stove-heated room, meditating on the disunity and uncertainty of his knowledge. He marveled at mathematics, a science in which he found certainty, necessity, and precision. How could he find a basis for all knowledge so that it might have the same unity and certainty as mathematics? Descartes saw the method to be pursued for putting all the sciences, all knowledge, on a firm footing. This method made clear both how new knowledge was to be achieved and how all-previous knowledge could be certain and unified. In addition to this method, the mathematics he proved was analytic geometry, which is a way of displaying graphs. A good resource is: http://www.jimloy.com/geometry/analytic.htm
In his own words more about his ideas:
I thought the following four [rules] would be enough, provided that I made a firm and constant resolution not to fail even once in the observance of them. The first was never to accept anything as true if I had not evident knowledge of its being so; that is, carefully to avoid precipitancy and prejudice, and to embrace in my judgment only what presented itself to my mind so clearly and distinctly that I had no occasion to doubt it. The second, to divide each problem I examined into as many parts as was feasible, and as was requisite for its better solution. The third, to direct my thoughts in an orderly way; beginning with the simplest objects, those most apt to be known, and ascending little by little, in steps as it were, to the knowledge of the most complex; and establishing an order in thought even when the objects had no natural priority one to another. And the last, to make throughout such complete enumerations and such general surveys that I might be sure of leaving nothing out. These long chains of perfectly simple and easy reasoning’s by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.
Discours de la Méthode. 1637.
Sources for biography: Rene Descartes- Meditations on First Philosophy Third Edition translated by Donald A. Cress from latin
Homework 12:
In the field of commerce, mathematics is used as much as any other volatile necessity needed in order to live. The air we breathe, the food we eat, and the numbers we use in commerce all relate as the major three factors necessary to complete a Bachelor of Business at UBC. In relation to courses I am currently taking, the relevance is undoubtedly present, therefore I may describe how in connection to my life, mathematics is everywhere from my micro/macro economics courses to my accounting courses and surprisingly enough it even relates to the business presentation course. Through the futile analysis of the role of mathematics in these three subjects I will begin to outline how the majority of my life is spent in the presence of mathematics, or likewise mathematics spends a lot of time in my presence.
To begin with, economics is based on the study of behavioral patterns of consumption on an individual level and national level. Learning about the principles of relevant costs, the pitfalls of ignoring opportunity costs and the sunk costs, and the risk of using average instead of marginal costs and benefits has an obvious connection between the calculus we go over in class daily. The analysis itself however, when given a graph of a demand curve has the ability to sway the attention from the numbers to the reasons why a person would decide to purchase one product over another. However, most of these decisions are actually based on as mentioned before the opportunity costs of choosing one thing over another. For instance, whilst it may seem that when I decide what to wear in the morning, the use of economics let alone mathematics is not taken into consideration in spite of that, the decisions I make are directly correlated to mathematics in general. If I choose to put on a pair of heels to a class I have a half an hour away, the opportunity cost I have therefore is probably being 5-10 minutes late to class and missing the first clicker question. Quantitatively, I can take that 5-10 minutes and divide it by the tuition fees I pay for that class and in dollar terms determine how much I have wasted in order to enjoy a longer walk to class. Without mathematics, such a calculation would seem impossible, as if the decision to wear heals or sneakers is completely irrelevant to the daily choices I may make.
Moreover, in accounting, the use of simple mathematics such as addition and subtraction seems to be the basis of the class itself. Creating balance sheets wherein one side of sheet is equal to the other has the remarkable correlation to writing out simple equations such as 2+2=4. The mind itself when doing accounting works in a way that quantifies things rather to categories, sections or in general to make rational decisions between whether the paycheck for next months rent is a debit or credit and shown as cash or whatever else it may be. Similarly to how a computer works our brains are set to look at 3 pieces of information insert them below.
The only place where the presence of mathematics could begin to be doubted is in the class for business presentation skills. Nonetheless, at closer analysis I learned that the structure of speech itself should be correlated to the rule 3, the time I take to say my part is vital in an audiences understanding, and the ability to relate from the beginning of a speech to the end, is as similar as getting a question and answer in any equation and relating the two together before finishing the problem. If our minds in fact are structured such that the information we process is nothing less than codes and rhythms of speech habits that rather make us pay more attention or less, the concept of speaking and communicating is all in theory mathematics. The amount of words used per sentence to make a point. The punctuation in those sentences, making sure that two periods at the end doesn’t occur just as two equal signs would not satisfy an equation.
Mathematics is undoubtedly in my field of study and in my life, whether it’s a good thing or bad thing to be surrounded by numbers all day long is a whole different question.
10. Suppose one-half of all people are chocolate eaters and one-half of all people are women. (i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.
(i) It does not follow that ¼ of all of the people are women chocolate eaters because the facts above state that ½ of the total people are women, it does not mean that they all eat chocolate. (ii) Similarly, it does not follow that ½ of men are chocolate eaters. Being a man or woman is independent of preference for chocolate.
11. A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?
This is not possible because the facts are inconsistent such that the situation doesn’t make sense with the question.
12. A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation.
If for instance the Bronx train arrives at 10:00, 10:10, 10:20, and the Brooklyn train arrives at 9:59, 10:09, 10:19 then he would take preference over the Brooklyn train and never visit because it arrives earlier.
13. If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?
If you consider the time between chimes then you know it takes 45/4 seconds to strike 10:00.
14. One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?
(i) There are six ways that two of the four babies can be correctly tagged. (ii) There are no ways that ¾ of the four babies can be correctly tagged and 1 incorrectly.
15. Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?
Alex is correct, you should not accept his bet because naturally the amount of red cards is 50/50 to the amount of black cards in the deck.