Reading+Log+2


 * Comments  [[image:baby_jesus.gif]] **** WOW **
 * Reading log 2 **


 * I. Pre-reading: **

a. Read the title and answer:

What do you think the text will be about? I think that the text will be about classification of the study themes of math and their definition and description.

b. Do you know any branches of math? Mention some · Geometry · Analysis · Algebra · Probabilities ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Calculus

<span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Write a list of 5 words (minimum) that you think will be in the reading. ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Mathematic ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Themes ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Study ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Geometry ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Analysis ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Algebra ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Probabilities ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt;">Calculus <span style="font-family: 'Arial','sans-serif'; font-size: 8pt; line-height: 115%;">Image taken on Sept 06th, 2009 from: <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 8pt; line-height: 115%;">[] <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">

<span style="color: #14b000; font-family: 'Arial','sans-serif'; font-size: 13.5pt;">Good <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Once you finish, please click on the following link and finish answering the rest of the questions in this page. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">[|http://www.math.niu.edu/~rusin/known-math/index/tour_div.html] <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 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.
 * __<span style="color: #b72464; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Notice: __**<span style="color: #b72464; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> You have to read the text starting on "the branches of mathematics" and read all about:

<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 1. Read the text carefully and see how many words from your list are in the text. Mention them <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">I found the following word in the text which was jutted with <span style="color: #7030a0; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">green <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> in the same order in the text. ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Mathematic ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Algebra ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Geometry ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Analysis ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Calculus ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Probabilities ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Study ·<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b050; font-family: 'Arial','sans-serif'; font-size: 10pt;">Themes <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 10pt;">These are all the word from my list. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 2. Find 5 new math terms and define them <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> __ in your own words __. <span style="font-family: 'Times New Roman','serif'; font-size: 10pt; line-height: 115%;">•<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Foundation <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">: Is the branch of math that studies the language of math (logic and set of numbers). <span style="font-family: 'Times New Roman','serif'; font-size: 10pt; line-height: 115%;">•<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Analysis <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">: Is the study of functions, the real number line, and the ideas of continuity and limit. It is subdivided into five areas that we should name: Calculus and Real Analysis, Complex Analysis, Differential Equations, Theory of Functions, and Numerical Analysis and Optimization. <span style="font-family: 'Times New Roman','serif'; font-size: 10pt; line-height: 115%;">•<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Probability and statistic <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">: Is the branch that studies the validity of the measurements of the possibility to make something. <span style="font-family: 'Times New Roman','serif'; font-size: 10pt; line-height: 115%;">•<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">Complex Analysis <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">: is a sub area of a branch of math called analysis. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="font-family: 'Times New Roman','serif'; font-size: 10pt;">•<span style="font-family: 'Times New Roman'; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> <span style="color: #00b0f0; font-family: 'Times New Roman','serif'; font-size: 12pt;">The Mathematics Subject Classification (MSC) <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">: MSC is the system of classification that I used in the researches by the community of Scientifics. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #891fdb; font-family: 'Arial','sans-serif'; font-size: 10pt;"> **<span style="color: #14b000; font-family: 'Arial','sans-serif'; font-size: 13.5pt;">very good Cristina ** <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt;">3. Read the following sentences extracted from a reading about Branches of Mathematics and explain what the referents (in <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> **<span style="color: red; font-family: 'Arial','sans-serif'; font-size: 10pt;">red **<span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt;"> in the sentence) refer to. Be careful, in some items you can find more than one referent underlined: <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> a. Because algebra uses symbols rather than numbers, <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #f23518; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">it __**<span style="color: #f23518; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">can produce general rules that apply to all numbers. <span style="color: #ff33cc; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">‘It’ <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">refers to ‘using symbols rather than numbers’. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> b. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">Geometry was systematized by the ancient Greeks, especially Pythagoras and Euclid. It has been admired from ancient times onward for **__<span style="color: #e90c0c; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">its simplicity __**<span style="color: #e90c0c; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">and elegance. <span style="font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">This referent is about ‘geometry’. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">c. Astronomers built mechanical devices consisting of gears and fixed spheres <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #f21818; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">that __**<span style="color: #f21818; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">described the orbits of celestial bodies with astonishing accuracy. <span style="color: #ff33cc; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">‘That’ <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">refers to the ‘devices’ <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> d. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">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. <span style="color: #333333; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #e30d0d; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">These problems __**<span style="color: #e30d0d; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">include the determination of Newton’s three laws of motion and the theory of electromagnetism. <span style="color: #ff33cc; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">‘These problems’ <span style="font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">referent is about ‘problems that had been insoluble by the methods of arithmetic, algebra, and geometry’. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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 **__<span style="color: #ef1a1a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">it __**<span style="color: #ef1a1a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">is possible to conceive of infinities of different “sizes.” <span style="color: #ff33cc; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">‘It’ <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">is refers to ‘ conceiving of infinities of different “sizes”’. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> f. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">Multiplication can be shown to be repeated addition, and introducing division, <span style="color: #333333; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #d90d0d; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">its inverse __**<span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">, produces rational numbers. <span style="font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">That referent is about multiplication. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">g. <span style="color: blue; font-family: 'MS Reference Sans Serif','sans-serif'; font-size: 10pt; line-height: 115%;">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. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> The problem in developing <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #ea1a1a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">such models __**<span style="color: #ea1a1a; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">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 <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> **__<span style="color: #d30d0d; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">these equations __**<span style="color: #d30d0d; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">is very sensitive to changes in the initial conditions. <span style="color: #ff33cc; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">‘Such models’ <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">refers to global climate models. ‘These equations’ are the equations used in complex systems as earth’s atmosphere.
 * II. Reading: **
 * <span style="color: #14b000; font-family: 'Arial','sans-serif'; font-size: 13.5pt;">Correct **

<span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">4. Design a mind map <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> __ showing the branches of math, defining and giving examples of each one of them. __



<span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">5. What branch of mathematics interests you the most <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> __ and why __ ? <span style="color: #19c3ff; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">I like all branches of math; however I feel great interest for probability and statistic because I think that to know the things about the lived reality and to be able to predict future reactions with mathematical ideas is very attractive and exciting. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> 6. Think about two branches of mathematics, now compare and contrast them in terms of what they study. <span style="color: #3a7dce; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Algebra and geometry are two branches of math <span style="color: #548dd4; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">. <span style="color: #7030a0; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="color: #92d050; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Each one is concerned with a different area of math. Algebra study <span style="color: #92d050; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">symmetry, patterns, discrete sets, and the rules for manipulating arithmetic operations while, geometry study shapes and sets, and the properties of them. <span style="color: #ff4f96; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> <span style="color: #3a7dce; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">However they can not be totally different since both study sets and geometry as algebra has a formal concept of symmetry, <span style="color: #548dd4; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> <span style="color: #92d050; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">but geometry uses it for work with shapes. <span style="color: blue; font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;"> <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">One first step in dividing the mathematics literature is to decide which books and articles intend to //reveal the structure of mathematics itself//, and those which intend to //apply mathematics to closely allied areas//. This division between mathematics and its applications is of course vague. Indeed, we'll see that the two groups cut across each other on the MathMap. The first group divides roughly into just a few broad overlapping areas: <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Of course, the division of the subject areas into these broad headings is a little fuzzy: combinatorics is only weakly associated to the rest of "algebra"; Lie groups are arguably a part of analysis or topology instead of algebra, differential geometry is in practice closer to analysis than geometry, and so on.  The second broad part of the mathematics literature includes those areas which could be considered either independent disciplines or central parts of mathematics, as well as those areas which clearly use mathematics but involve non-mathematical ideas too. It is important to note that the collection of files at this site covers only the //mathematical// aspects of these subjects; we provide only cursory links to observational and experimental data, mathematically routine applications, computer paradigms, and so on. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Finally note that every branch of mathematics has its own history, collections of important works -- reference, research, biographical, or expository -- and in many cases a suite of important algorithms. The MSC classification allows these topics to be included within each major heading at a secondary level. However, these themes are sometimes best woven together into areas of study which are not so much research into mathematics as research into the enterprise of mathematics -- <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|"epi-mathematics"] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">, perhaps. The Mathematics Subject Classification (MSC) scheme breaks down these general areas into 63 numbered subject classifications with widely varying characteristics. (This is the classification system used by the research mathematical societies.) We adhere to the polite fiction that these areas are more distinct than the subfields of some of the larger areas; more detail is available in the pages for the various areas. Continue the tour by clicking on any of the major branches of mathematics described above. You might want to **begin with a tour of** [|**foundations**]<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">In a word, "no". It's false to assume that mathematics consists of discrete subfields, it's false to assume that there is an objective way to gather those subfields into main divisions, and it's false to assume that there is an accurate two-dimensional positioning of the parts. For example, a division into "Pure" and "Applied" Mathematics is traditional, but the boundaries are unclear and cross-fertilization is common. Within the first part it is also traditional to identify Algebra, Geometry, and Analysis as the three largest areas, but again this division is somewhat artificial as we have noted. Yet the picture we have described above //is// consistent with the images painted in other sources. Some other systems for classifying mathematics are presented for browsing in the set of <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|subject headings] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> used at this site. Each system is different and yet it is generally possible to match parts of one classification scheme with parts of another. The National Science Foundation, for example, organizes its mathematics programs into <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">a division which clearly maintains the same larger areas we have indicated, though it gathers the smaller ones somewhat differently. To get another perspective, consider the division into branches of mathematics taken from <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|The Concise Columbia Electronic Encyclopedia, Third Edition] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> or <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Wikipedia] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">. For another comparison, here are lists of divisions of comparable length used by the American Mathematical Society to track the employment of new Ph.D.'s. The "Field of Thesis" record uses the following divisions in 1998 and 1999 (shown here with number of new Ph.D.'s in the US in each field that year); here the fields are sorted to mimic the divisions used above: <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">So we must accept that different tour guides would partition the landscape in different ways; yet it seems clear that there are some commonly-recognized divisions within the discipline.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 24pt; line-height: 115%;">The Divisions of Mathematics **
 * <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Foundations] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> considers questions in logic or set theory -- the very language of mathematics.
 * <span style="color: #00b050; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Algebra] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> is principally concerned with symmetry, patterns, discrete sets, and the rules for manipulating arithmetic operations; one might think of this as the outgrowth of arithmetic and algebra classes in primary and secondary school.
 * <span style="color: #00b050; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Geometry] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> is concerned with shapes and sets, and the properties of them which are preserved under various kinds of motions. Naturally this is related to elementary geometry and analytic geometry.
 * <span style="color: #00b050; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Analysis] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> studies functions, the real number line, and the ideas of continuity and limit; this is perhaps the natural successor to courses in graphing, trigonometry, and calculus . (This is a very large area; we subdivide it later into five areas which we may label Calculus and Real Analysis, Complex Analysis, Differential Equations, Theory of Functions, and Numerical Analysis and Optimization.)
 * <span style="color: #00b050; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Probability] <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[| and Statistics] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">, for example, has a dual nature -- mathematical and experimental. This classification scheme focuses on the former -- the study of the validity of the measurements one might make.
 * <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|Computational sciences] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> have obviously flourished in the last half-century, and consider algorithms and information handling. Here we are concerned with what might be computed, not with compilers, architectures, and so on.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Significant mathematics must be developed to formulate ideas in the <span style="color: blue; font-family: 'Times New Roman','serif'; font-size: 12pt;">[|physical sciences] <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">, engineering, and other branches of science. Again it is the theoretical underpinnings which concern us here rather than the experiment or tangible construction.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 18pt;">But is this division "real"? **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Algebra and Number Theory
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Topology and Foundations
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Geometric Analysis
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Analysis
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Statistics and Probability
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Computational Mathematics
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Applied Mathematics
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">1998
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Logic/Discrete Math/Combinatorics/Computer Science (109)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Algebra and Number Theory (160)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Geometry and Topology (143)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Differential, Integral, and Difference Equations (98)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Real or Complex Analysis (39)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Functional Analysis (41)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Harmonic Analysis and Topological Groups (44)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Numerical Analysis, Approximations (61)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Probability and Statistics (291)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Applied Mathematics (122)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Linear, Nonlinear Optimization and Control (27)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Other/Unknown (23) || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">1999
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Logic/Discrete Math/Combinatorics/Computer Science (90)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Algebra and Number Theory (169)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Geometry and Topology (132)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Differential, Integral, and Difference Equations (98)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Real, Complex, Functional, and Harmonic Analysis (105)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Numerical Analysis, Approximations (79)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Probability (51)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Statistics (269)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Applied Mathematics (100)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Linear, Nonlinear Optimization and Control (23)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Mathematics Education (14)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Other/Unknown (3) ||