I am planning to Masters of Science in Financial Engineering (FE).
I do not have math background at all. So I have resigned from my job and now doing mathematics.
I am unable to determine whether the expertise in the following list of topics is a prerequisite for FE (See below list). I generally consult https://quantnet.com/
for details. But i am not getting any clue for the below topics.
I am clear about the rest of the topics (At high level which are required) as a pre-requisite for FE.
When i say expertise, I mean an indepth subject knowledge. By mean knowledge i mean knowing/learning to the extent it is needed to complete another topic.
Kindly guide me.
01. Circle :
1.1 Equation of circle -standard form-centreand radius of a circle with a given linesegment as diameter & equation of circlethrough three non collinear points -parametric equations of a circle.
1.2 Position of a point in the plane of a circle -power of a point-definition of tangent-lengthof tangent
1.3 Position of a straight line in the plane of acircle-conditions for a line to be tangent -chord joining two points on a circle -equation of the tangent at a point on thecircle- point of contact-equation of normal.
1.4 Chord of contact - pole and polar-conjugatepoints and conjugate lines - equation ofchord with given middle point.
1.5 Relative position of two circles- circlestouching each other externally, internallycommon tangents -centers of similitude-equation of pair of tangents from an externalpoint.
02. System of circles:
2.1 Angle between two intersecting circles.
2.2 Radical axis of two circles- properties-Common chord and common tangent of two circles - radical centre.
2.3 Intersection of a line and a Circle.
3.1 Conic sections -Parabola- equation ofparabola in standard form-different formsof parabola- parametric equations.
3.2 Equations of tangent and normal at a pointon the parabola ( Cartesian and parametric)
4.1 Equation of ellipse in standard form-Parametric equations.
4.2 Equation of tangent and normal at a pointon the ellipse (Cartesian and parametric)-condition for a straight line to be a tangent.
5.1 Equation of hyperbola in standard form-Parametric equations.
5.2 Equations of tangent and normal at a pointon the hyperbola (Cartesian andparametric)- conditions for a straight line tobe a tangent- Asymptotes.
Definition of locus - Illustrations.
To find equations of locus - Problems connected to it.
Transformation of Axes :
Transformation of axes - Rules, Derivations and Illustrations.
Rotation of axes - Derivations - Illustrations.
The Straight Line :
Revision of fundamental results.
Straight line - Normal form - Illustrations.
Straight line - Symmetric form.
Straight line - Reduction into various forms.
Intersection of two Straight Lines.
Family of straight lines - Concurrent lines.
Condition for Concurrent lines.
Angle between two lines.
Length of perpendicular from a point to a Line.
Distance between two parallel lines.
Concurrent lines - properties related to a triangle
Pair of Straight lines:
Equations of pair of lines passing through origin, angle between a pair of lines.
Condition for perpendicular and coincident lines, bisectors of angles.
Pair of bisectors of angles.
Pair of lines - second degree general equation.
Conditions for parallel lines - distance between them, Point of intersection of pair of lines.
Homogenizing a second degree equation with a first degree equation in X and Y.
5 Three Dimensional Coordinates:
Section formulas - Centroid of a triangle and tetrahedron.
6 Direction Cosines and Direction Ratios :
7 Plane :
Cartesian equation of Plane - Simple Illustrations.