Singular Point (Algebraic Curve)
A singular point of an Algebraic Curve is a point where the curve has ``nasty'' behavior such as a Cusp or apoint of self-intersection (when the underlying field 
is taken as the Reals). More formally, apoint 
on a curve 
is singular if the 
and 
Partial Derivatives of 
are both zero at the point . (If the field is not the Reals or ComplexNumbers, then the Partial Derivative is computed formally using the usual rules of Calculus.)
Consider the following two examples. For the curve
the Cusp at (0, 0) is a singular point. For the curve
is a nonsingular point and this curve is nonsingular.See also Algebraic Curve, Cusp- Bordism Group
- Borel-Cantelli Lemma
- Borel Determinacy Theorem
- Borel Measure
- Borel Probability Measure
- Borel Set
- Borel's Expansion
- Borel Sigma Algebra
- Borel Space
- Borromean Rings
- Borrow
- Borsuk's Conjecture
- Borwein Conjectures
- Bouligand Dimension
- Bound
- Boundary
- Boundary Conditions
- Boundary Map
- Boundary Point
- Boundary Set
- Boundary Value Problem
- Bounded
- Bounded Variation
- Bound Variable
- Bourget Function