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ISSN 2562-2862 (online)

 

Category: JNMA Template

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JNMA template

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Rules:

For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$

Examples:

 

$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$

 

$$(\frac{\sqrt x}{y^3})$$

 

$$\left(\frac{\sqrt x}{y^3}\right)$$

 

$$\lim_{x\to 0}$$

 

 

Hints:

  1. To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose “Show Math As > TeX Commands”. (When you do this, the ‘$’ will not display. Make sure you add these. See the next point.)
  2. For inline formulas, enclose the formula in $...$. For displayed formulas, use $$...$$.
    These render differently. For example, type
    $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
    to show $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$ (which is inline mode) or type
    $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
    to show

    i=0ni2=(n2+n)(2n+1)6

    i=0ni2=(n2+n)(2n+1)6

    (which is display mode).

  3. For Greek letters, use \alpha\beta, …, \omega: $\alpha, \beta, … \omega$. For uppercase, use \Gamma\Delta, …, \Omega: $\Gamma, \Delta, …, \Omega$.
  4. For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$, \log_2 x: $\log_2 x$.
  5. Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {}. If you do 10^10, you will get a surprise: $10^10$. But 10^{10} gives what you probably wanted: $10^{10}$. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$. Observe the difference between x_i^2 $x_i^2$ and x_{i^2} $x_{i^2}$.
  6. Parentheses Ordinary symbols ()[] make parentheses and brackets $(2+3)[4+4]$. Use \{and \} for curly braces $\{\}$.

    These do not scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: (xy3)

    (xy3)

    . Using \left(\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is (xy3)

    (xy3)

    .

    \left and\right apply to all the following sorts of parentheses: ( and ) (x)

    (x)

    [ and ] [x]

    [x]

    \{ and \} {x}

    {x}

    | |x|

    |x|

    \vert |x|

    |x|

    \Vert x

    x

    \langle and \rangle x

    x

    \lceiland \rceil x

    x

    , and \lfloor and \rfloor x

    x

    \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .\left.\frac12\right\rbrace is 12}

    12}

    .

    If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives (((((x)))))

    (((((x)))))

    .

  7. Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n n1
    1n

    . Don’t forget {} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is i=0i2

    i=0i2

    . Similarly, \prod 

    \int 

    \bigcup 

    \bigcap 

    \iint 

    \iiint 

    \idotsint 

    .

  8. Fractions There are three ways to make these\frac ab applies to the next two groups, and produces ab
    ab

    ; for more complicated numerators and denominators use {}\frac{a+1}{b+1} is a+1b+1

    a+1b+1

    . If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is a+1b+1

    a+1b+1

    . Using \cfrac{a}{b}command is useful for continued fractions ab

    ab

    , more details for which are given in this sub-article.

  9. Fonts
    • Use \mathbb or \Bbb for “blackboard bold”: 
      CHNQRZ

      .

    • Use \mathbf for boldface: ABCDEFGHIJKLMNOPQRSTUVWXYZ
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

      abcdefghijklmnopqrstuvwxyz

      abcdefghijklmnopqrstuvwxyz

      .

    • Use \mathit for italics: ABCDEFGHIJKLMNOPQRSTUVWXYZ
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

       abcdefghijklmnopqrstuvwxyz

      abcdefghijklmnopqrstuvwxyz

      .

    • Use \pmb for boldfaced italics: ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
      ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

       abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz

      abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz

      .

    • Use \mathtt for “typewriter” font: 𝙰𝙱𝙲𝙳𝙴𝙵𝙶𝙷𝙸𝙹𝙺𝙻𝙼𝙽𝙾𝙿𝚀𝚁𝚂𝚃𝚄𝚅𝚆𝚇𝚈𝚉
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

       𝚊𝚋𝚌𝚍𝚎𝚏𝚐𝚑𝚒𝚓𝚔𝚕𝚖𝚗𝚘𝚙𝚚𝚛𝚜𝚝𝚞𝚟𝚠𝚡𝚢𝚣

      abcdefghijklmnopqrstuvwxyz

      .

    • Use \mathrm for roman font: ABCDEFGHIJKLMNOPQRSTUVWXYZ
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

      abcdefghijklmnopqrstuvwxyz

      abcdefghijklmnopqrstuvwxyz

      .

    • Use \mathsf for sans-serif font: 𝖠𝖡𝖢𝖣𝖤𝖥𝖦𝖧𝖨𝖩𝖪𝖫𝖬𝖭𝖮𝖯𝖰𝖱𝖲𝖳𝖴𝖵𝖶𝖷𝖸𝖹
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

      𝖺𝖻𝖼𝖽𝖾𝖿𝗀𝗁𝗂𝗃𝗄𝗅𝗆𝗇𝗈𝗉𝗊𝗋𝗌𝗍𝗎𝗏𝗐𝗑𝗒𝗓

      abcdefghijklmnopqrstuvwxyz

      .

    • Use \mathcal for “calligraphic” letters: 
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

    • Use \mathscr for script letters: 𝒜𝒞𝒟𝒢𝒥𝒦𝒩𝒪𝒫𝒬𝒮𝒯𝒰𝒱𝒲𝒳𝒴𝒵
      ABCDEFGHIJKLMNOPQRSTUVWXYZ

    • Use \mathfrak for “Fraktur” (old German style) letters: 𝔄𝔅𝔇𝔈𝔉𝔊𝔍𝔎𝔏𝔐𝔑𝔒𝔓𝔔𝔖𝔗𝔘𝔙𝔚𝔛𝔜𝔞𝔟𝔠𝔡𝔢𝔣𝔤𝔥𝔦𝔧𝔨𝔩𝔪𝔫𝔬𝔭𝔮𝔯𝔰𝔱𝔲𝔳𝔴𝔵𝔶𝔷
      ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz

      .

  10. Radical signs Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} x3‾‾√
    x3

    \sqrt[3]{\frac xy} xy‾‾√3

    xy3

    . For complicated expressions, consider using {...}^{1/2}instead.

  11. Some special functions such as “lim”, “sin”, “max”, “ln”, and so on are normally set in roman font instead of italic font. Use \lim\sin, etc. to make these: \sin x sinx
    sinx

    , not sin x sinx

    sinx

    . Use subscripts to attach a notation to \lim\lim_{x\to 0}

    limx0

    limx0

  12. There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:
    • \lt \gt \le \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq <>
      <>

      . You can use \not to put a slash through almost anything: \not\lt 

       but it often looks bad.

    • \times \div \pm \mp ×÷±
      ×÷±

      \cdot is a centered dot: xy

      xy

    • \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing 

    • {n+1 \choose 2k} or \binom{n+1}{2k} (n+12k)
      (n+12k)

    • \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto 

    • \land \lor \lnot \forall \exists \top \bot \vdash \vDash ¬
      ¬

    • \star \ast \oplus \circ \bullet 

    • \approx \sim \simeq \cong \equiv \prec \lhd \therefore 

    • \infty \aleph_0 0
      0

       \nabla \partial 

       \Im \Re 

    • For modular equivalence, use \pmod like this: a\equiv b\pmod n ab(modn)
      ab(modn)

      .

    • \ldots is the dots in a1,a2,,an
      a1,a2,,an

       \cdots is the dots in a1+a2++an

      a1+a2++an

    • Some Greek letters have variant forms: \epsilon \varepsilon ϵε
      ϵε

      \phi \varphi ϕφ

      ϕφ

      , and others. Script lowercase l is \ell 

      .