English Vs Math Essay, Research Paper
English Vs. Math
To most people English or Language Arts is a creative course and math is just a logical, you get it or you don t class. My purpose writing this paper is to change your mind. I believe that Math is just as, or more creative than English. I will demonstrate this through a couple of examples.
First, we must understand what is behind the creative aspect in English. Most people consider that English is the, creative, subject because of titles such as creative writing and creative thinking and in contrast there is no creative something in math. In English when we are, let s say, going to write a creative short story we use our imaginations and there are no limits. Now on the other hand in math when faced with a problem such as; if you have 300 meters of fence and have to enclose a rectangular field. What would be the dimensions of the field that would yield the largest area? When mathematicians go to solve one of these they have to be creative in their problem solving.
Perhaps, one of the best ways to demonstrate creativity in math is through an identity question. An identity question is where you have an equation and you try to manipulate each side individually without touching the other side and get them to be equal. We start off with something like sin squared theta over cos theta plus cos and the objective here is to prove that it is identical to sec theta. At first looks there is no connection but by using creative methods and hours of work eventually we figure out the way to do it.
First I would make everything over Cos.
SinX. + CosX. | Sec.
Then I would apply a law
Then a simple law
You can prove that it is creative because a computer can t solve this equation, (a computer thinks logically). Technically a computer could solve this equation but it could just tell you if they were equal and not to the same level of accuracy. A computer would input a value for. on both sides and if the answer is equal then the equation is equal. The problem with this is that when you get into trigonometry there could be a difference in the decilionth decimal place. A computer can t work with the abstract which is what is in my example. A computer may take 2 seconds or a million years to find an answer or it may give the wrong answer! The other point is that a computer can only perform things in a certain order it can t guess or have a feeling about a question, which brings in the creative aspect.
Another example happened during one of my Calculus classes that I believe to be the most abstract and creative of the maths. A fellow student and me figured out pie. We figured out that the integral from 0 to1 of the square root of x minus 1 is equal to half of pie. We had huge problems figuring out this equation but persistence eventually won out and we solved it. Later we found out that this was a University Calculus level question and we shouldn t have been able to solve it due to our lack of skills in this area. Creativity then can be the only culprit for our derivation of the solution.
Finally one of my strongest points is that on some of the more creative math units the more creative people usually the artsy type do a lot better than in the other units and by no means because these units are easier. Remember that I am not saying that English isn t creative, just that Math is more creative than anyone gives it credit for.
There are three complementary methods to set font attributes in LaTeX math mode: [fntguide] describes math alphabets and math versions. several extension packages provide alternative math styles (cf. Table 2 ).
Math alphabets are a counterpart to the mathematical alphanumeric symbols block in Unicode. Both are “to be used for mathematical variables where style variations are important semantically”. The font guide [fntguide] defines in section 3:
Some math fonts are selected explicitly by one-argument commands such as \mathsf
Math fonts [. ] have the same five attributes as text fonts: encoding, family, series, shape and size. However, there are no commands that allow the attributes to be individually changed. Instead, the conversion from math fonts to these five attributes is controlled by the math version .
The predefined math alphabets are:
\mathnormal is used by default for alphanumeric characters in math mode. It sets the letter shape according to character class and math style. (Table 1 shows the default letter shapes for common math styles).
The specifier “roman” is ambiguous: roman shape stands for upright. while roman type stands for serif (as opposed to sans serif).
Many packages define additional math alphabets (cf. Table 5 ).
In contrast to the similar named text commands, math alphabets are not orthogonal, e. g. the code $\mathit<\mathbf>$ sets the letter a in upright bold type.
The number of mathematical symbols exceeds the maximal number of characters in a TeX font file by an order of magnitude. 3 Grouping math fonts with common characteristics in math versions simplifies the setting of font attributes for mathematical expressions.
Math versions set up “math symbol fonts” for non-alphanumeric symbols and bind the math alphabet commands to fonts using default values for non-specified font attributes. TeX limits the number of (symbol + alphanumeric) fonts per math version to 16.
The predefined math versions are normal and bold with the defaults:
Packages can define additional math versions, e. g. the wrisym package defines a mono math version. A sans math version example is available from a comp.text.tex post
Math versions are intended for mathematical content in a special context, e. g. a bold section heading. Setting a math version resembles the individual selection of text font attributes (bold, sans-serif, monospaced).
Math versions can only be changed outside of math mode. The commands \boldsymbol (amsmath ) and \bm (bm ) behave like “in-line math versions”. they typeset their argument using the fonts of the bold math version but can be used inside math mode.
Example: four ways to set the letter a in a bold sans-serif font:
Unicode provides about 2500 math characters. Font files used by 8-bit TeX engines can hold up to 256 characters. The standard math fonts adhere to the original limit of 128 characters.
A math style is a document-level feature that determines the default letter shape in math mode (i. e. the shape attribute of letters in the \mathnormal math alphabet ).
Default letter shapes for common math styles
Unicode math alphabets contain Latin and Greek letters. With LaTeX, this is simplest achieved with a font that contains all required letters in one file.
There is only one established LaTeX font encoding that contains Latin and Greek letters, the OML font encoding. The standard Greek font encoding T7 is just a “reserved name” and the de-facto standard Greek text font encoding LGR has no Latin letters. Unfortunately, OML support is limited to a few (mostly italic) fonts.
The LaTeX font encodings guide [encguide] names the OML encoding TeX math italic and defines:
The OML encoding contains italic Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols.
The reference to italic shape is odd:
No other font encoding is specific to the font shape.
The different font selection and the semantic of font features in math do not interfere with the font encoding. Both, \DeclareSymbolFont and \DeclareMathAlphabet require a shape argument. Thus it is possible to set up OML encoded math alphabets in roman
This seems to be more a remnant of pre-NFSS times than a necessary restriction – there is only one OML encoded font in Knuth's Computer Modern fonts: Computer Modern Math Italic (cmmi).
Drop the italic from the definition. Optionally add an explanation:
The OML encoding contains Latin and Greek letters for use in mathematical formulas (typically used for variables) together with some symbols. It first appeared in the Computer Modern Math Italic (cmmi) font.
The name TeX math italic can be interpreted as “the encoding of Computer Modern Math Italic ” rather than “an encoding for math italic” fonts.
A less confusing name would be TeX math letters or Original/Old Math Letters. The latter would also explain the acronym OML.
Unfortunately, support for the OML encoding is missing for many font families even if the text font defines Greek letters. Supported font families can be found searching for oml*.fd files and grepping for DeclareFont.*OML in *.sty files.
Table 3 lists the findings for a selection of TeXLive 2009 + some additionally installed font packages.
If there is an alias (substitution) from the text font to a math-variant, only the text font is listed.
Many text fonts define substitutions also for upright shape, however mapping to an italic variant of the OML encoded font. These are not listed as supporting m/n or bx/n here.
Font families supporting the OML encoding
This section compares math font selection in LaTeX and Unicode. It suggests a set of 14 math alphabets that covers all Unicode mathematical alphanumeric symbols and discusses compatibility issues between math typesetting with traditional (8-bit) TeX engines versus the unicode-math package for Unicode-enabled TeX engines (XeTeX, LuaTeX).
Chapter 2 Mathematical Character Repertoire of [tr25] lists 14 Mathematical Alphabets in Table 2.1. These mathematical alphabets are a superset of the predefined math alphabets in the LaTeX core.
Unicode assignes code points to most letters of the mathematical alphabets in the mathematical alphanumeric symbols Unicode block. The plain (upright, serifed) letters have been unified with the existing characters in the Basic Latin and Greek blocks.
Table 4 maps the 14 Unicode mathematical alphabets to LaTeX commands according to the naming scheme below. Table 5 lists the status of LaTeX support for the mathematical alphanumeric symbols. Full support is provided by the unicode-math package .
Mapping Unicode mathematical alphanumeric symbols to LaTeX math alphabets matching their Unicode names.
no small Greek, full Greek with possible with OML encoded fonts ( omlmath*.sty auxiliary styles or OMLmath* options to isomath ).
Some italic math fonts (e. g. cmr, cmbr) have old-style numbers in place of italic digits. As there are no math italic digits in Unicode, this is no problem when mapping Unicode symbols to math alphabets.
Users of UTF-8 enabled TeX engines (XeTeX, LuaTeX) can typeset mathematics with the experimental unicode-math package by Will Robertson. It provides a LaTeX interface to OpenType fonts with math support, e. g. Asana Math. Cambria Math, New Euler or XITS. with commands to access the complete mathematics character repertoire of the Unicode Standard
The three math font selection methods also work with unicode-math (with some modifications):
math alphabets map to a range of the mathematical alphanumeric symbols block in the current font (or a substitution defined with the range math font option).
With unicode-math, \mathbf. \mathsf. and \mathbfsf behave similar to “in-line math versions”. they consider the math style for upright vs. italic shape. Compatibility can be achieved via the options bold-style=upright and sans-style=upright. However, then also literal Mathematical Alphanumeric Characters like MATHEMATICAL BOLD ITALIC CAPITAL A are typeset upright.
In \mathbfsf and \mathbfsfit the order of the sf and bf selectors deviates from the order in the Unicode names, so that, e. g. the Unicode character MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL A is selected by the non-mnemonic \mathbfsfit .
A similar "confusion" of the order can be seen in XML Entity Definitions for Characters that lists the following alphabets for Mathematical Alphanumeric Characters:
XML Entity Definitions for Characters
Italic or Slanted
Bold Italic or Slanted
Double Struck (Open Face, Blackboard Bold)
Script (or Calligraphic)
Slanted Sans Serif
Slanted Bold Sans Serif
SANS-SERIF BOLD ITALIC
math versions are not directly supported but easy to emulate.
As Unicode fonts can hold all math symbols in a single font file, a single \setmathfont[<font features>]<<font name>> can replace the \mathversion<<mathversion>> command if a complete OpenType math font in the desired version is available.
However, complete OpenType math fonts are rare. Therefore unicode-math supports using multiple fonts with the range option. This way one can emulate, e. g. the bold math version via:
It would be nice if unicode-math could provide a \newmathversion command similar to the \newfontfamily in fontspec for such setups.
For alphanumerical characters, the \mathbf. \mathsf. and \mathsfbf behave like “in-line math versions” .
math styles are supported with the math-style package option that accepts the values TeX. ISO. french. upright. and literal .
lists differences between math symbol commands in «traditional» LaTeX and the unicode-math package.
Frank Mittelbach, Robin Fairbairns, Werner Lemberg, LaTeX3 Project Team, LaTeX font encodings. http://mirror.ctan.org/macros/latex/doc/encguide.pdf .
Barbara Beeton, Asmus Freytag, Murray Sargent III, Unicode Support for Mathematics. Unicode Technical Report #25: http://www.unicode.org/reports/tr25/ .
Barbara Beeton: Unicode and math, a combination whose time has come – Finally. TUGBoat, 21#3, 2000: http://www.tug.org/TUGboat/Articles/tb21-3/tb68beet.pdf .
The short answer is you need to buy a new font. Out of the box, Office 2010 and 2013 have only Cambria with all of the math characters that are needed for the Equation Editor. You can verify this is also your circumstance by clicking expand link at the bottom right of the TOOLS box in the EQUATION EDITOR > DESIGN tab (see the screen shot to the right)
After some considerable effort, I have still not found a compatible font so I have posted this with Microsoft Partner Support and after some back and forth, this is what they said:
…Cambria Math is the only supported font that can be used in Equation Editor in Word 2013 for the time being. Anyway, the DEFAULT FONT is a drop down box and it will have alternates after some improvements are made by the developing team.
A slightly longer answer is the work around of forcing your equation to “NORMAL TEXT” (see the screen shot to the right). The tells Word that you you are not writing math, just normal text which will then allow you to change the font at will. The risk here is that you will lose characters because they don’t exist in your new font (say Arial).
There is a way, but it requires to manually modify the registry.
Download one of the following fonts and install them:
Open the registry with “regedit.exe” and change the following values:
BE SUPER CAREFUL.
“Latin Modern Math”=dword:00000001
Finally, do the steps shown on this webpage. There will be more than a single option.
New MS Word User 02-19-16
It is possible. Edit the equation first using the default font which is Cambria Math. Then type in a character selecting “normal text”. Now change the font of that character. Then cut and paste it over the Cambria Math character. It works!
In Word 7 or Word 10 use the Word 3 equations editor instead. Click insert and then object. Choose microsoft 3 and you are on your way.
How come the newer versions have less features than the older ones. Only with Microsoft!
I suppose time marches on and some features are dropped. I just confirmed that under SP1 for Office 2013 the same limitation of not being able to change the font still exists.
I agree – but it’s very annoying when changes are regressive, not progressive.
You may look up for some font such as XTIS Math font, or Asana Math font. These fonts can be used with microsoft equation. 🙂
Try searching for Asana Math.Categories Recent “How To’s”
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You can use a subset TeX markup in any matplotlib text string by placing it inside a pair of dollar signs ($).
Note that you do not need to have TeX installed, since matplotlib ships its own TeX expression parser, layout engine and fonts. The layout engine is a fairly direct adaptation of the layout algorithms in Donald Knuth’s TeX, so the quality is quite good (matplotlib also provides a usetex option for those who do want to call out to TeX to generate their text (see Text rendering With LaTeX ).
Any text element can use math text. You should use raw strings (precede the quotes with an 'r' ), and surround the math text with dollar signs ($), as in TeX. Regular text and mathtext can be interleaved within the same string. Mathtext can use DejaVu Sans (default), DejaVu Serif, the Computer Modern fonts (from (La)TeX), STIX fonts (with are designed to blend well with Times), or a Unicode font that you provide. The mathtext font can be selected with the customization variable mathtext.fontset (see Customizing matplotlib )
On “narrow” builds of Python, if you use the STIX fonts you should also set ps.fonttype and pdf.fonttype to 3 (the default), not 42. Otherwise some characters will not be visible .
Here is a simple example:
produces “alpha > beta”.
Mathtext should be placed between a pair of dollar signs ($). To make it easy to display monetary values, e.g. “$100.00”, if a single dollar sign is present in the entire string, it will be displayed verbatim as a dollar sign. This is a small change from regular TeX, where the dollar sign in non-math text would have to be escaped (‘\$’).
While the syntax inside the pair of dollar signs ($) aims to be TeX-like, the text outside does not. In particular, characters such as:
have special meaning outside of math mode in TeX. Therefore, these characters will behave differently depending on the rcParam text.usetex flag. See the usetex tutorial for more information.Subscripts and superscripts¶
To make subscripts and superscripts, use the '_' and '^' symbols:
There are also three global “font sets” to choose from, which are selected using the mathtext.fontset parameter in matplotlibrc .
cm. Computer Modern (TeX)
stix. STIX (designed to blend well with Times)
stixsans. STIX sans-serif
Additionally, you can use \mathdefault<. > or its alias \mathregular<. > to use the font used for regular text outside of mathtext. There are a number of limitations to this approach, most notably that far fewer symbols will be available, but it can be useful to make math expressions blend well with other text in the plot.Custom fonts¶
mathtext also provides a way to use custom fonts for math. This method is fairly tricky to use, and should be considered an experimental feature for patient users only. By setting the rcParam mathtext.fontset to custom. you can then set the following parameters, which control which font file to use for a particular set of math characters.
Each parameter should be set to a fontconfig font descriptor (as defined in the yet-to-be-written font chapter).
The fonts used should have a Unicode mapping in order to find any non-Latin characters, such as Greek. If you want to use a math symbol that is not contained in your custom fonts, you can set the rcParam mathtext.fallback_to_cm to True which will cause the mathtext system to use characters from the default Computer Modern fonts whenever a particular character can not be found in the custom font.
Note that the math glyphs specified in Unicode have evolved over time, and many fonts may not have glyphs in the correct place for mathtext.
An accent command may precede any symbol to add an accent above it. There are long and short forms for some of them.
\ddot a or \"a
In addition, there are two special accents that automatically adjust to the width of the symbols below:
Care should be taken when putting accents on lower-case i’s and j’s. Note that in the following \imath is used to avoid the extra dot over the i:
You can also use a large number of the TeX symbols, as in \infty. \leftarrow. \sum. \int .