Reading+Log+2

Reading log 2
Read the following text and answer:

I. Pre-reading: a. Read the title and answer:

What do you think the text will be about? I think that in the text will treat all branches of mathematics, that is to say, all those elements that are derived from the general theme that is the mathematical.

Do you know any branches of math? Mention some 1. Algebra 2. Calculus 3. Analysis 4. Geometry 5. Statistics 6. Arithmetic 7. Probability 8. Trigonometry

c. Write a list of 5 words (minimum) that you think will be in the reading. 1. Branches 2. Mathematics 3. Trigonometric functions 4. Sine 5. Cosine 6. Tangent 4. Triangles 5. Angles 6. Limit 7. Theorys 8. Theorems 9. Numbers 10. Operations

Once you finish, please click on the following link and finish answering the rest of the questions in this page. [] __**Notice:**__ You have to read the text starting on "the branches of mathematics" and read all about: A. Arithmetic, B. Algebra, C. Geometry, D. Trigonometry, E. Calculus, F. Probability and statistics, G. Set theory and logic, H. Number theory, I. System analysis, and J. Chaos theory.

II. Reading:

1. Read the text carefully and see how many words from your list are in the text. Mention them The ten words in my list are in the text but in differents points.

2. Find 5 new math terms and define them __in your own words__. a. Cryptography is the ability to communicate through secret codes and ciphers use secret key to transform a text for it to be read by a single recipient. b. Foundations studying the branches of mathematics such as logic and set theory. c. Computational sciences are the sciences that study the algorithms and management of information concerning the computation. d. Lie groups are not as one might think from the algebra, but rather, in theory, are from the analysis or the topology and in practice, from the analysis of geometry. e. Analysis is the branch that studies in general terms graphs, trigonometry and calculus; of these three sub-branches came the study of functions, limits of functions, continuity of functions, etc.

3. Read the following sentences extracted from the reading and explain what thereferents (underlined in the sentence) refer to. Be careful, in some items you can find more than one referent underlined:

a. Because algebra uses symbols rather than numbers, __**it**__ can produce general rules that apply to all numbers. __**It**__ refers to Algebra. 

b. Geometry was systematized by the ancient Greeks, especially Pythagoras and Euclid. It has been admired from ancient times onward for __**its simplicity**__ and elegance. **__Its simplicity__** refers to Geometry.

c. Astronomers built mechanical devices consisting of gears and fixed spheres __**that**__ described the orbits of celestial bodies with astonishing accuracy. **__That__** refers to gears and fixed spheres.

d. The development of calculus in the 17th century made possible the solution of many problems that had been insoluble by the methods of arithmetic, algebra, and geometry. __**These problems**__ include the determination of Newton’s three laws of motion and the theory of electromagnetism. **__These problems__** refers to many problems that had been insoluble by the methods of arithmetic, algebra, and geometry.

e. He extended the intuitive concept of a set to include the possibility of sets containing an infinite number of objects, and he showed that __**it**__ is possible to conceive of infinities of different “sizes.”
 * __It__ **refers to conceive of infinities of different “sizes.”

f. Multiplication can be shown to be repeated addition, and introducing division, **__ its inverse __**, produces rational numbers. **__Its inverse__** refers to multiplication´s

g. Global climate modeling is an area of mathematical research that seeks to develop models for predicting the weather, given accurate data from weather satellites orbiting Earth. The problem in developing __**such models**__ arises not from lack of data but from the difficulty of modeling such a complex system (Earth’s atmosphere) with a small number of equations. In such models even a thousand equations may be considered small. The solution of **__these equations__** is very sensitive to changes in the initial conditions. **__Such models__** refers to models for predicting the weather. **__These equations__** refers to equations used to model the Earth´s atmosphere.

4. Design a mind map __showing the branches of math, defining and giving examples of each one of them__.

5. What branch of mathematics interests you the most __and why__ ? Algebra is a branch of mathematics that most interests me and catches my attention, because very simply explains the basic things we learn along the primary and prep school, which apply without knowing where they come.

6. Think about two branches of mathematics, now compare and contrast them in terms of what they study. Algebra and geometry are both branches of mathematics, but differ in that the first study symmetry, discrete sets, patterns and standards for the handling of arithmetic operations, while the second, geometric shapes and figures studied.

NOTA: Algunas de las respuestas estan basadas en el link anterior.