Advanced ABC's of mathematics

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Can you name the advanced ABC's of mathematics?

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1st letter/# wordsTermHint
A (1)Element of an ordered pair plotted on the horizontal axis.
A (2)Describes a series that converges when all terms are replaced by their absolute values.
A (2)The highest point over the entire domain of a function or relation.
A (2)Field of mathematics concerned with study of algebraic structures e.g. groups, rings and fields.
A (2)Number, sum of its positive factors, excluding itself, is greater than the given number.
A (1)The first derivative of the velocity equation; the second derivative of the position function.
A (1)Matrix formed by taking the transpose of the cofactor matrix of a given original matrix.
A (2)Transformation involving any combination of translations, reflections, stretches, shrinks, or rotations.
A (2)The cardinality of the natural numbers.
A (1)Ringlike section formed by concentric circles.
A (1)Sphere: 2 points directly opposite each other.
A (3)Method for approximating value of a function near a known value; uses tangent line at the known value of the function to approximate the function's graph.
A (2)Coordinate plane to graph complex numbers.
A (5)The angle describing the direction of a complex number on the complex plane.
B (2)Experiment in which a single action, e.g. flipping a coin, is repeated; Possible results are classified as 'success' or 'failure'.
1st letter/# wordsTermHint
B (1)A cycloid hanging downwards.
C (1)A heart-shaped graph.
C (1)Curve naturally formed by a slack rope hanging between 2 fixed points; NOT a parabola, though resembles one; e.g. graph of the hyperbolic cosine function.
C (2)Method to find volume of solid for which cross-sections by parallel planes have equal areas.
C (2)A step function of x which is the least integer greater than or equal to x.
C (1)Center of mass of a figure of uniform density.
C (1)A line segment, ray, or line that extends from a vertex of a triangle to the opposite side.
C (2)Study of complex natural systems which obey rules but give an impression of randomness.
C (1)cos θ + isin θ; or equivalently e.
C (1)Surface generated by a straight line, the generator, passing through a fixed point, the vertex, moving along a fixed curve, the directrix.
C (2)Point on a curve at which the derivative of a function is either 0 or does not exist.
C (1)A sharp point on a curve.
C (1)The path traced by a point on a wheel as the wheel rolls, without slipping, along a flat surface.
C (1)Surface generated by a straight line intersecting and moving along a closed plane curve, the directrix, while remaining parallel to a fixed straight line that is not on or parallel to the plane of the directrix.

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