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An essay on the history of mathematics
History of mathematicians
An essay on the history of mathematics
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Understanding Mathematics
This paper is an attempt to explain the structure of the process of understanding mathematical objects such as notions, definitions, theorems, or mathematical theories. Understanding is an indirect process of cognition which consists in grasping the sense of what is to be understood, showing itself in the ability to apply what is understood in other circumstances and situations. Thus understanding should be treated functionally: as acquiring sense. We can distinguish three basic planes on which the process of understanding mathematics takes place. The first is the plane of understanding the meaning of notions and terms existing in mathematical considerations. A mathematician must have the knowledge of what the given symbols mean and what the corresponding notions denote. On the second plane, understanding concerns the structure of the object of understanding wherein it is the sense of the sequences of the applied notions and terms that is important. The third plane-understanding the 'role' of the object of understanding-consists in fixing the sense of the object of understanding in the context of a greater entity, i.e., it is an investigation of the background of the problem. Additionally, understanding mathematics, to be sufficiently comprehensive, should take into account (apart from the theoretical planes) at least three other connected considerations-historical, methodological and philosophical-as ignoring them results in a superficial and incomplete understanding of mathematics.
In an outstanding book by P. J. Davis and R. Hersh, The Mathematical Experience, there is a small chapter devoted to the crisis of understanding mathematics. Alas, this fragment focuses only on the presentation of the d...
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...an't learn mathematics without its thorough understanding. My postulate is that, in the process of teaching mathematics, we should take into account both the history and philosophy (with methodology) of mathematics, since neglecting them makes the understanding of mathematics superficial and incomplete.
Bibliography
1. Philip J. Davis & Reuben Hersh, The Mathematical Experience, Birkhäuser Boston, 1981.
2. Izydora Dąmbska, W sprawie pojęcia rozumienia, in: Ruch Filozoficzny 4, 1958.
3. John R.Searle, Minds, Brains and Programs, in: Behavioral and Brain Sciences 3, Cambridge University Press 1980, p.417-424.
4. Danuta Gierulanka, Zagadnienie swoistości poznania matematycznego, Warszawa 1962.
5. Roger Penrose, The Emperor's New Mind, Oxsford University Press 1989.
6. Andrzej Lubomirski, O uogólnieniu w matematyce, Wrocław 1983.
When one is young they must learn from their parents how to behave. A child's parents impose society's unspoken rules in hope that one day their child will inuitivly decerne wrong from right and make decisions based on their own judgment. These moral and ethical decisions will affect one for their entire life. In Mark Twains, Adventures of Huckleberry Finn, Huck is faced with the decision of choosing to regard all he has been taught to save a friend, or listen and obey the morals that he has been raised with. In making his decision he is able to look at the situation maturely and grow to understand the moral imbalances society has. Hucks' decisions show his integrity and strength as a person to choose what his heart tells him to do, over his head.
Huntington’s disease is of great concern because it is a genetic disease that affects many people worldwide. Huntington’s is described by Wider and Luthi-Carter (2006) as the most prevalent inherited neurodegenerative disorder in humans, affecting between two to eight per 100,000 inhabitants of Western countries. Huntington’s also has a slow onset with an average age of onset around 40 (Wider & Luthi-Carter, 2006). Wider and Luthi-Carter (2006) note the cause of this disease to be a mutation in the huntingtin gene, which can be characterized by distinct symptoms. Chorea, from the Greek “to dance”, is the main distinguishing feature of this mutation and is described by Wider and Luthi-Carter (2006) as rapid involuntary movements that manifest as eyelid elevation, head bobbing, facial grimacing, and jerking of the limbs. Chorea is also noticeable in the way one walks, making an individual move in a zigzag pattern and appear to be thrown off balance by involuntary movements (Wider & Luthi-Carter, 2006). The disease duration is between ten and thirty years and is often first noticed in the early stages by symptoms including attention disorders, personality changes, and alterations in motor control (Wider & Luthi-Carter, 2006).
Kaplan, Justin. "Born to Trouble: One Hundred Years of Huckleberry Finn." Mark Twain Adventures of Huckleberry Finn: A Case Study in Critical Controversy. Eds. Gerald Graff and James Phelan. Boston: St. Martin's, 1995. 348-359.
Mark Twain’s Adventures of Huckleberry Finn is considered the great American Novel with its unorthodox writing style and controversial topics. In the selected passage, Huck struggles with his self-sense of morality. This paper will analyze a passage from Adventures of huckleberry Finn and will touch on the basic function of the passage, the connection between the passage from the rest of the book, and the interaction between form and content.
For this paper, I will be considering the intersection between women in the United States of America and Mexico, in regard to the status of drug treatment in each country, and the roles that it plays in these women’s lives through a feministic perspective. Further, I will be discussing how gender is in direct juxtaposition to the outcomes of drug treatments in both countries, in regard to the base of the models used to treat. Another key issue in regard to the status of treatment is the notion of the Other, with special consideration to women. Whereby in this sense, I am defining the Other, as implying a double standard set of stigma to the female, not only as the “gendered” other, but further, into the Other as seen as a drug abuser/addict, which plays an important role in treatment as well, and especially when considering further role obligations that are attachments to women’s live, such as having and/or caring for children. Finally, it is imperative to consider these issues under a veil of feminism, for women are not equal in either country, and there is a need to understand some of the social constrictors that are unique to women, before we can expect there to be meaningful drug treatment outcomes.
Passer, M., Smith, R., Holt, N., Bremner, A., Sutherland, E., & Vliek, M. (2009). Psychology; Science of Mind and Behaviour. (European Edition). New York.
Huntington's disease affects three main areas of function: motor (physical), mood (emotional), and cognition (psychological). Motor function disturbances can fall into too much movement and too little movement. Chorea, involuntary dance-like movements, can affect any part of the body. It looks like restlessness, wrigg...
Huntington’s disease is named after George Huntington. This disease genetically is an inherited disorder that damages the mind and nervous system. This may affect actions of the body for example like movement, the ability to reason, awareness, and thinking and judgment. It can also affect their behavior. The word genetic is that the disorder is delivered on by each generation of offspring by special codes called genes(Patient.Co.Uk, 2011). Genes are relocated from a parent to offspring and is held to decide some characteristics of the children (Patient.Co.Uk, 2011).
Huntington’s Disease is a brain disorder affecting movement, cognition, and emotions (Schoenstadt). It is a genetic disorder generally affecting people in their middle 30s and 40s (Sheth). Worldwide, Huntington’s disease (affects between 3-7 per 100,000 people of European ancestry (Schoenstadt). In the United States alone, 1 in every 30,000 people has Huntington’s disease (Genetic Learning Center). Huntington’s Disease is a multi-faceted disease, with a complex inheritance pattern and a wide range of symptoms. There is also much research being done in the field of Huntington’s disease, because as of 2012, this disease is untreatable. THESIS.
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
Gross, R (2010). Psychology: The science of mind and behaviour. 6th ed. London: Hodder Education. p188.
Coon, D., & Mittterer, J. ( 2013). Introduction to psychology gateways to mind and behavior . (13th ed.). California: Wadsworth, Cengage Learning.
Wigner, Eugene P. 1960. The Unreasonable Effectiveness of Mathematics. Communications on Pure and Applied Mathematics 13: 1-14.
A novel structured on the theme of morality, the Adventures of Huckleberry Finn by Mark Twain focuses on Huck Finn’s multifaceted growing up process. Huck, through his escapades and misfortunes is obliged to endure the agonizing process from childhood to adulthood where he attains self-knowledge and discovers his own identity. Throughout the journey down the Mississippi River, Jim, Ms. Watson’s runaway slave, accompanies Huck, and is later joined by two con men. It is during this journey that a great moral crisis in Huck’s life occurs where he must make a painful decision as to whether he is going to give Jim up to the slave hunters or notify Ms. Watson about Jim’s whereabouts and assist him to remain a free man. This is the turning point in his character where through deep introspection, he learned to think and reason morally for himself. He comes to his own conclusions, unaffected by the accepted, and often hypocritical, perceptions of Southern culture. Huck also deciphers the truth in the face of lies held by the antagonistic society with its evil nature.
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.