KinderCalculus/Glossary

arithmetic

• top - numerator
• bottom - denominator
• top heavy - improper fraction
• bottom heavy - proper fraction, may be unreduced
• cops - mnemonic for Covering Prime String, which is the Least Common Denominator

algebra

• layers - order of operation, the parse tree of an expression
• evert - generalized factorization or distribution applicable to a(b+c) = ab + ac, (f+g)' = f' + g', etc. switch inner and outer operators.
• nevadab - initialism for "combining like terms". "nev" = neighboring verb criteria, "ab" = alike base criteria, ad = add depth
• peers - operands that are both commutative and associative. Commutivity is symmetry of a verb, and associativity is symmetry of a verb chain, eg. (ab)c = a(bc).
• blead - the base-leaf-depth relationship of binary operators
• left & right divide - the inverse-exponential operators root & log

• noun - operands
• verbs - operators
• adjective - the negative (-) and reciprocal (1/*) noun modifiers
• shape - (verb) to assign a shape to a term. Shaping is useful for substitutions.

• invisible - implicit verbs & layers such as parentheses or multiplication in xy. the exponential operator is also invisible
• neighboring verbs - the relationship between a seed verb (+ & *) and its iterative counterpart (* & ^)
• forward verbs: +, *, ^ (exponential)
• reverse verbs: -, /, o--, --o
• forq: the forward-reverse-sequence identity, eg. (a*b)/c = a/c * b/c, log(a^b) = blog(a), or root(a^b) = root(a)*root(b)
• seed & repeater verbs: in the context of self-plus and self-times, the primitive operation is called the seed verb and the resulting operation from the repetition is the repeater verb. For instance, in 3x = x + x + x, the seed verb is "+" and the repeater verb is times. Likewise, x^3 = x * x * x has the seed verb "*" and repeater verb as "^".
• self-ish verbs: repeater verb
• center: of a verb is the group-theoretic Identity element, either 0 or 1, for verbs + or - respectively

• blunderwear - the algebraic pitfall where an inner layer is peeled off before an outer layer, or a layer is put onto an expression inside of the outer most layer
• snowflake - the pictorial representation of exponentiation, logarithms, and roots

• colo: slightly generalized factorization. This is an abbreviation for "common-leftover", emphasizing those the "common" part that is extracted and the remaining parts that are leftover in a factorization, eg. xy + xz has x as the common factor, and y & z as the leftovers. generalizing a bit, (y^x)*(z^x) = (yz)^x. colo & spread are opposites.
• spread: to distribute, as in x( y + z ) = xy + xz. spread & colo are opposites.
• sprolo: spread-colo identities, aka factoring & distributive identities. eg. a(b+c) = ab + ac, and many more.
• common leaves: common factors in reducing a fraction. The leaves stem from the factor tree.
• nudify: to solve for a variable, leaving it bare and naked. Used for comedic value and may be dismissed by conservative minded parents.
• fit: to satisfy an equation by substituting in values. For instance, x = 2 fits the equation x + 2 = 4

trigonometry

• tick - coordinate
• grid - coordinate system
• round ticks - polar coordinates
• circle grid - polar coordinate system
• square ticks - cartesian coordinates
• square grid - cartesian coordinate system
• bionic number - complex number

calculus

• mirrors = the diametric opposites in the product rule. In the integration-by-parts formula, the product g'f has the conjugate f'g. I use conjugate in this way, not to be confused with the complex conjugate of a+bi as a-bi. If you prefer another term altogether, "mirror" or "reflection" are good alternatives.
• forever big, forever small - infinity & infinitessimal respectively
• leak = the speed identity (cf)' = c(f'), where c is a constant.
• line = (verb) to assign a solid or dashed line to a shape to indicate speeded-function vs. a plain-function. This term is useful for exercises in integration by substitution or by parts.
• nudge = change in input or output. For example, x2-x1 is an input nudge, where f(x2)-f(x1) is the output nudge.
• nudge ratio = input nudge / output nudge
• segment = the interval of integration in a definite integral.
• sliver = a skinny rectangle in a Riemann sum
• speed = derivative
• steepness = the graphical interpretation of derivative as the slope of the tangent
• studr = (pronounced "studder") portmanteau that abbreviates the non-standard calculus definition of speed as the STandard of the nUDge Ratio. This is a mnemonic to help students remember the definition.
• sweep = Riemann Sum, also anti-derivative as appropriate
• tess = infinitesimal, forever small
• graphing terms:
  • cutting x-axis = in graphing, extreme points & inflection points divides the x-axis into regions of positive/negative y' & y"
  • dump water = concave down
  • falling = decreasing function in graphing
  • flat point = solutions of the equation y'(x)=0. we don't have a term for solutions of y"(x)=0. "Inflection" does not reflect all of the solutions
  • hold water = concave up
  • rising = increasing function in graphing
  • trap = solving for x in the equation y'(x)=0 or y"(x)=0