Math Keyboard layout for QWERTY keyboards on Windows

The Math Keyboard layout supports all characters defined in the international mathematics standard ISO 80000-2 and a small collection of other characters. Most associations are intuitive, based on either the shape of the character (for example, AltGr A produces ∀) or the initial letter of its name (for example, AltGr I produces ∆, increment). For some char­ac­ters, key combinations are needed; for example, ` R produces the right arrow →. The layout can be used on any QWERTY keyboard, but it works best on a US keyboard.

The layout delivered as a zipped file. Unzip it and run the setup.exe file; the installation may take a minute or so. Consult Windows Help for information on assigning shortcuts to keyboard layouts, so that you can switch between layouts with keyboard commands.

(Math keyboard layout in AltGr state)
Meanings of keys in the AltGr state.

Character repertoire

For the main set of characters supported by the layout, see Mathematical symbols in ISO 80000-2 – a test page.

The use of these characters is described in detail in the e-book Writing Mathematical Expressions.

Some additional characters are included, due to their common use or due to a natural assigment to a key. In particular, all superscript and subscript digits can be typed using the normal keys 0 1 2… together with AltGr (“right alt”) for superscripts and Shift AltGr for subscripts.

US keyboard as reference

This description of the layout uses the common US keyboard as a frame of reference. You can use it on any QWERTY keyboard, but you need to take differences in account when interpreting the instructions. For example, a reference to the grave (backtick) key ` means the key in the upper left corner of the keyboard. In non-US keyboards, the key may well have other engravings than the US keyboard, which has the grave (`) and the tilde (~) there.

The layout is somewhat more difficult to use on non-US keyboards, because you need to remember some differences. For example, the key that produces the minus sign (−) is the one on the right of the 0, with the hyphen engraved on it on US keyboards, so we denote it by - but it has for example the plus sign (+) in some other keyboards. In that case, the user needs to remember that the plus key produces the minus sign. If this is too awkward, consider creating a variant of this layout, adapted to the physical keyboard you use.

(US keyboard, with all states of keys shown)
Common US keyboard. The Alt key on the right of the space bar is used as AltGr key when using the Math keyboard layout.

Key principles

Notes

The Math Keyboard layout was implemented using the Microsoft Keyboard Layout Creator (MSKLC) on (32-bit) Windows 7.

The layout contains only a two Greek letters: π as AltGr Shift D and δ as AltGr P. Greek letters can be conveniently typed using the standard Greek keyboard layout in Windows. If you use it on a QWERTY keyboard, the A key produces α, the B key produces β, etc., with just a few non-obvious assignments: θ ≘ U, η ≘ H, ξ ≘ J, χ ≘ J, ω ≘ V.

Table of key assignments

Unicode name (identifier) Glyph ShortcutNumber
ALMOST EQUAL TO ` ` U+2248
APPROXIMATELY EQUAL TO AltGr` U+2245
ASTERISK OPERATOR Shift2 U+2217
ASYMPTOTICALLY EQUAL TO AltGr` U+2243
BLACK-LETTER CAPITAL Z AltGrZ U+2128
CIRCLED TIMES AltGrShiftX U+2297
COLON EQUALS AltGr: U+2254
COMPLEMENT AltGrC U+2201
CONTOUR INTEGRAL` C U+222E
CORRESPONDS TO ` 6 U+2259
DEGREE SIGN ¹ AltGrO U+00B0
DIVIDES AltGr\ U+2223
DOT OPERATOR ` X U+22C5
DOUBLE INTEGRAL` J U+222C
DOUBLE-STRUCK CAPITAL C AltGrShiftC U+2102
DOUBLE-STRUCK CAPITAL N AltGrShiftN U+2115
DOUBLE-STRUCK CAPITAL P AltGrShiftP U+2119
DOUBLE-STRUCK CAPITAL Q AltGrShiftQ U+211A
DOUBLE-STRUCK CAPITAL R AltGrShiftR U+211D
DOUBLE-STRUCK CAPITAL Z AltGrShiftZ U+2124
DOWNWARDS ARROW ` D U+2193
ELEMENT OF AltGrE U+2208
EMPTY SET AltGr/ O U+2205
EQUAL TO BY DEFINITION AltGrShift; U+225D
FINITE PART INTEGRAL AltGrF U+2A0D
FOR ALL AltGrA U+2200
GREATER-THAN OR EQUAL TO AltGr. U+2265
GREATER-THAN SIGN > Shift. U+003E
GREEK SMALL LETTER DELTAδ AltGrShiftD U+03B4
GREEK SMALL LETTER PIπ AltGrP U+03C0
HAIR SPACE AltGrShift       U+200A
HORIZONTAL ELLIPSIS AltGr' U+2026
IDENTICAL TO AltGrQ U+2261
INCREMENT AltGrI U+2206
INFINITY AltGrShiftI U+221E
INTEGRAL U+222B
INTERSECTION AltGrY U+2229
LEFT CEILINGAltGrShift[ U+2308
LEFT FLOORAltGr[ U+230A
LEFT RIGHT ARROW ` B U+2194
LEFT RIGHT DOUBLE ARROW ` ShiftB U+21D4
LEFTWARDS ARROW ` L U+2190
LEFTWARDS DOUBLE ARROW ` ShiftL U+21D0
LESS-THAN OR EQUAL TO AltGr, U+2264
LESS-THAN SIGN < Shift, U+003C
LOGICAL AND Shift7 U+2227
LOGICAL OR AltGrV U+2228
MATHEMATICAL LEFT ANGLE BRACKET` [ U+27E8
MATHEMATICAL RIGHT ANGLE BRACKET` ] U+27E9
MINUS SIGN-U+2212
MINUS-PLUS SIGN` = U+2213
MUCH GREATER-THAN AltGrShift, U+226B
MUCH LESS-THAN AltGrShift. U+226A
MICRO SIGN µ AltGrM U+00B5
MIDLINE HORIZONTAL ELLIPSIS AltGrShift' U+22EF
MULTIPLICATION SIGN × AltGrX U+00D7
NABLA AltGrN U+2207
N-ARY INTERSECTION AltGrShiftY U+22C2
N-ARY PRODUCT ` P U+220F
N-ARY SUMMATION AltGrS U+2211
N-ARY UNION AltGrShiftU U+22C3
NO-BREAK SPACE   AltGr       U+000A
NOT AN ELEMENT OF ` ShiftE U+2209
NOT EQUAL TO Shift3 U+2260
NOT SIGN ¬ ` N U+00AC
PARALLEL TO AltGrShift\ U+2225
PARTIAL DIFFERENTIALAltGrD
PER MILLE SIGN ` 5 U+2030
PERPENDICULAR TO ` Shift\ U+27C2
PLUS SIGNB; Shift= U+002B
PLUS-MINUS SIGN± ` - U+00B1
PRIME ߰'U+2032
PROPORTIONAL TO ` ShiftP U+221D
RIGHT CEILINGAltGrShift] U+2309
RIGHT FLOORAltGr] U+230B
RIGHTWARDS ARROW ` R U+2192
RIGHTWARDS ARROW FROM BAR ` M U+21A6
RIGHTWARDS DOUBLE ARROW ` ShiftR U+21D2
RING OPERATORAltGrShiftO U+2218
SCRIPT CAPITAL F AltGrShiftF U+2131
SCRIPT CAPITAL L AltGrShiftL U+2112
SET MINUS \ U+2216
SPHERICAL ANGLE ` A U+2222
SQUARE ROOTAltGrR U+221A
SUBSET OF ` , U+2282
SUBSET OF OR EQUAL TO ` Shift. U+2286
SUBSCRIPT EIGHT AltGrShift8 U+2088
SUBSCRIPT FIVE AltGrShift5 U+2085
SUBSCRIPT FOUR AltGrShift4 U+2084
SUBSCRIPT MINUS AltGrShift+ U+208B
SUBSCRIPT PLUS AltGrShift= U+208A
SUBSCRIPT NINE AltGrShift9 U+2089
SUBSCRIPT ONE AltGrShift1 U+2081
SUBSCRIPT SIX AltGrShift6 U+2086
SUBSCRIPT SEVEN AltGrShift7 U+2087
SUBSCRIPT THREE AltGrShift3 U+2083
SUBSCRIPT TWO AltGrShift2 U+2083
SUBSCRIPT ZERO AltGrShift0 U+2080
SUPERSCRIPT EIGHT AltGr8 U+2078
SUPERSCRIPT FIVE AltGr5 U+2075
SUPERSCRIPT FOUR AltGr4 U+2074
SUPERSCRIPT MINUS AltGr- U+207B
SUPERSCRIPT NINE AltGr9 U+2079
SUPERSCRIPT ONE ¹ AltGr1 U+00B9
SUPERSCRIPT PLUS AltGr= U+207A
SUPERSCRIPT SIX AltGr6 U+2076
SUPERSCRIPT SEVEN AltGr7 U+2077
SUPERSCRIPT THREE ³ AltGr3 U+00B3
SUPERSCRIPT TWO ² AltGr2 U+00B2
SUPERSCRIPT ZERO AltGr0 U+2070
SUPERSET OF ` , U+2283
SUPERSET OF OR EQUAL TO ` Shift, U+2287
SURFACE INTEGRAL` S U+222F
THERE EXISTS AltGrShiftE U+2203
THIN SPACE Shift       U+2009
TILDE OPERATOR Shift` U+223C
UNION AltGrU U+222A
UPWARDS ARROW ` U U+2191
UPWARDS DOUBLE ARROW ` ShiftU U+21D1
VERTICAL LINE | Shift\ U+007C
WHITE SQUARE AltGrW U+25A1