The Nature of Mathematics
Mathematics relies on both logic and creativity, and it is pursued
both for a variety of practical purposes and for its basic interest.
The essence of mathematics lies in its beauty and its intellectual
challenge. This essay is divided into three sections, which are
patterns and relationships, mathematics, science and technology and
mathematical inquiry.
Firstly, Mathematics is the science of patterns and relationships. As
a theoretical order, mathematics explores the possible relationships
among abstractions without concern for whether those abstractions have
counterparts in the real world. The abstractions can be anything from
strings of numbers to geometric figures to sets of equations. In
deriving, for instance, an expression for the change in the surface
area of any regular solid as its volume approaches zero,
mathematicians have no interest in any correspondence between
geometric solids and physical objects in the real world.
A central line of investigation in theoretical mathematics is
identifying in each field of study a small set of basic ideas and
rules from which all other interesting ideas and rules in that field
can be logically deduced. Mathematicians are particularly pleased when
previously unrelated parts of mathematics are found to be derivable
from one another, or from some more general theory. Part of the sense
of beauty that many people have perceived in mathematics lies not in
finding the greatest richness or complexity but on the contrary, in
finding the greatest economy and simplicity of representation and
proof. As mathematics has progressed, more and more relationships have
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... middle of paper ...
... that fit those rules, which includes inventing additional rules and
finding new connections between old rules.
In conclusion, the nature of mathematics is very unique and as we have
seen in can we applied everywhere in world. For example how do our
street light work with mathematical instructions? Our daily life is
full of mathematics, which also has many connections to nature.
Abstractions from nature are one the important element in mathematics.
Mathematics is a universal subject that has connections to many
different areas including nature.
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1. http://users.powernet.co.uk/bearsoft/Maths.html
2. http://weblife.bangor.ac.uk/cyfrif/eng/resources/spirals.htm
3. http://www.project2061.org/tools/benchol/ch2/ch2.htm
4. http://www.headmap.org/unlearn/alfred/1.htm
One example of a “nontraditional” mathematical moment the article gives is of a child in the sandbox, “Louis, that bucket holds a lot of sand. How many plastic cupfuls do you think it will take to fill it to the top?” Asking that question all of the sudden turns a plastic cup, a plastic bucket and sand into math manipulatives. Teachers often get hung up on the concept of manipulatives, but really a manipulative is simply “a small item that someone can use to sort, categorize, count, measure, match, and make patterns”, and in the case of the sand Louis is using both the concept of volume as well as counting. Other examples of materials you could are, stones, sticks,
Math is everywhere when most people first think of math or the word “Algebra,” they don’t get too excited. Many people say “Math sucks” or , “When are we ever going to use it in our lives.” The fact is math will be used in our lives quite frequently. For example, if we go watch a softball game all it is, is one giant math problem. Softball math can be used in many
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
The story I chose for this analysis is “Why, you reckon?” by Langston Hughes. IN this analysis I will be focusing on how the great depression in Harlem had effect on the story, how racism played a part, and how or if the characters were justifyied in their actions. During this time period the intense racial divide combined with the economic harships that plagued the U.S. during the 1923’s makes for an interesting story that makes you think if the charaters were really justified.
Robert, A. Wayne and Dale E. Varberg. Faces of Mathematics. New York: Harper & Row Publishers, Inc., 1978.
John Von Neumann was a very famous mathematician/ scientist whose work influenced theories and formulas we still use in the 21st century. He worked with many other influential mathematicians and scientists. His work influenced game theory, the quantum theory, automata theory, and defense planning. Von Neumann was a hard worker and was always working on new and old projects from when he began his career until the day he died.
The famous song “Let the Mystery Be,” written and performed by Iris Dement in 1992, is centered on Iris’s personal philosophy on the question of religion and life’s origins. The song begins with the chorus, which is repeated two times throughout track. The first half of the chorus states that people are always concerned with the question of how life began and what happens after we die. Then in the second half, Iris ties the theme of the song together by maintaining that since no one knows the exact answer to these questions, she’ll just “let the mystery be.” The first verse of the tune considers popular perspectives on the questions mentioned in the chorus. She begins each idea with, “some say…” and then summarizes its ideology. Some of the
Observation: Teacher goes over to student struggling with math worksheet. Brings over abacus and sits next to him. Begins to demonstrate. “Now how many do we take away?” child is the one to show the math on abacus. “Now how many are left?” prompts child to count the rings in order to figure out problem. Slides first number over, gets student to take away the right number. Then counts the remaining to get the right answer.
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
Mathematics is part of our everyday life. Things you would not expect to involve math
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
...re encompassing way, it becomes very clear that everything that we do or encounter in life can be in some way associated with math. Whether it be writing a paper, debating a controversial topic, playing Temple Run, buying Christmas presents, checking final grades on PeopleSoft, packing to go home, or cutting paper snowflakes to decorate the house, many of our daily activities encompass math. What has surprised me the most is that I do not feel that I have been seeking out these relationships between math and other areas of my life, rather the connections just seem more visible to me now that I have a greater appreciation and understanding for the subject. Math is necessary. Math is powerful. Math is important. Math is influential. Math is surprising. Math is found in unexpected places. Math is found in my worldview. Math is everywhere. Math is Beautiful.