Coordinate geometry/vector algebra -Prerequsite for Financial engineering.

Dear experts,

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 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.

03. Parabola:
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)

04. Ellipse:
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.

05. Hyperbola:
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.

Locus :
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 :
Direction Cosines.
Direction Ratios.

7 Plane :
Cartesian equation of Plane - Simple Illustrations.

Thank you
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The topics listed above look like a partial syllabus for Analytic Geometry, which is a pre-Calculus course that many people would take in high school.  For a Masters in Financial Engineering, I expect you would also need several college level math courses: two terms of Calculus, Differential Equations, and Linear Algebra.  There should be some computer literacy requirement like a course in Python or R.  And some exposure to Matlab would certainly be helpful as well.

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ExcellearnerAuthor Commented:
D-glitch, thank you for your response.

I have covered calculus curriculum at high-school.

Your comment: 'For a Masters in Financial Engineering, I expect you would also need several college level math courses.'
So are you suggesting that I should have thorough knowledge or is it i should have understanding. Getting an understanding will not be time-demanding. Hence my anxiety.

So what is your view/opinion?

With to regard to your comment: 'also need several college level math courses'

I have listed the following in addition to stochastic calculus by Shreve

Differential Equations & Differential Equations : Problem Solving Sessions
Solid Geometry & Solid Geometry : Problem Solving Sessions

Abstract Algebra : Problem Solving Sessions
Real Analysis : Problem Solving Sessions

Vector Calculus : Problem Solving Sessions

Linear Algebra : Problem Solving Sessions

Integral Transforms ( i am not sure, so still figuring if this topic is required)
Numerical Analysis - I  ( i am not sure, so still figuring if this topic is required)
Number Theory - I  ( i am not sure, so still figuring if this topic is required)
I think you need to be very comfortable with Calculus, Differential Equations, Linear Algebra, and Numerical Analysis.
If Integral Transforms means Fourier and Laplace transforms, they are probably necessary as well.
I am not sure how relevant Solid Geometry and Real Analysis are to FE.
Number Theory would be helpful for Cryptography and Security issues, but probably not FE.

Familiarity (if not fluency) with the Tool du jour is very important as well, and I am guessing that it is Matlab for most practitioners.  If you can use Matlab for your study sessions you will be killing lots of birds.
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"I am unable to determine whether the expertise in the following list of topics is a prerequisite for FE (See below list)."

The topics you list are interesting but of secondary use to financial engineering. Others have listed some useful math topics. I would add as of primary concern
Statistics - you cannot have too much background in statistics
probability - in depth

These two topics are MUST
I have to agree with aburr.  Probability and Statistics are the basis of Risk Assessment.  This is stuff you really have to know, not just be familiar with.
ExcellearnerAuthor Commented:
Thank you both abhurr and d-glitch

I will comeback with a comprehensive list. I want to miss out on any valuable suggestion/input from you.

You both sound familiar with FE prerequsite and curriculum. Do you have any prior knowledge about this field?

Thank you
ExcellearnerAuthor Commented:
Abhur, you mention 'topics you list are interesting...'

If I am right, i think you are referring to the list of topics I have included, covering coordinate geometry and Vector algebra, in my original message/question.

I am happy if I do not need to read these thoroughly. This saves me time for other higher level mathematics.

Kindly confirm if I understood your message correctly.

Thank you
Operations Research should be added to the list. It includes simplex algorithm for linear programming.
Geometric pictures are shown in the Simplex and Linear Programming links.

It depends how far you want to go with FE. If you want to be a support programmer, possibly you can study enough to understand what the "rocket scientists/Quant Engineers" are talking about. Keep this thought in mind. Millions or billions of dollars are potentially involved in your yearly activities. The competition is therefore going to be highly competitive. Having a thorough understanding of the basics (to the point that you can write the books - maybe not every theorem proof) is essential before you get to the hard stuff.

The later generation of financial engineers were more likely to have PhDs in mathematics or physics and often started their careers in academics or non-financial fields.

Physics? Really?
...correlated Brownian motions...
We will consider an American style put option on the geometric average of the prices of n assets...

Jump to pages 411-412 where there are discussions of the existence of a finite dimensional invariant submanifold G ... and "the standard problem in differential geometry" and Hilbert spaces.

Now to get an idea of more complexity in this book, glance at every page between 337 and 412. This is very hard math/physics-like discipline in my opinion.

This is not something most of us are able to learn on our own. Instead to make your millions, I advise going to a top school. Here's one ORFE at Princeton U:

>> So are you suggesting that I should have thorough knowledge or is it i should have understanding. Getting an understanding will not be time-demanding. Hence my anxiety.
It is a good to make the distinction between knowing and understanding. When you know something, you can teach it to someone else. Understanding is OK for getting a feel for the difficulty of a topic and then referring back to the topic when you need it in your job. ORFE is just too complex to just try to understand it. You better know it one step at a time.

If you undertake this complex goal, realizing the competition is fierce, then take your time in the next years to know the basics and then the advanced material.

Notice this person's usage of the word "know". "understand" is not in his vocabulary.
ExcellearnerAuthor Commented:
abhurr and d-glitch,

I have apologise if my below statement has offended either of you in any way. My sincere apologies.

Do you have any prior knowledge about this field?

The reason I made this statement was I struggled to get  guidance from colleges/lecturers in India in this matter.

I have read several threads but I could not conclude with next steps.

I did commerce in my high school and college and I have no background in mathematics. I worked in pseudo risk management functions/stress testing of banks. My colleagues and I found I was good at maths. So I quit my job and pursuing mathematics.

My journey with EE for the last twelve years has been incredible. Hence, I thought I will post my question to the experts in this forum.

Apologies once again. My thinking was, I was happy to receive your guidance but certainly not to challenge either of you.

Thank you
I would make sure you have your specific goal in mind, and then find a graduate school's syllabus that corresponds to your goal, and then identify every prerequisite to get in. With the prerequisite tree, start learning at the leaves and know your way up.

The last time I did that for an engineering subject, I looked at the prerequisites and their prerequisites, and so on, until I realized that I would be starting a new endeavor at the college sophomore level; and it would take me 5 years while working to get to the basics to enter graduate school. Since I also have a family, I gave up on that goal.
>> I have no background in mathematics
Oh, I didn't know that. But with time, that can change.

I once tutored a 30 year old woman who wanted to go to med-school and wanted help in Chemistry. She understood the concepts very well, but couldn't do math. I had to start with 3rd grade math. We spent a lot of time getting up to algebra.

Two years later, she called to let me know that she got an A in Calculus on her own, but still not in Med school. Two years later, she got into an osteopathic medicine school and become a D.O.
ExcellearnerAuthor Commented:
Dear experts,

Thank you all for your responses/inputs.

Now it is time for me to act.

I have started this question with a specific purpose, and I am glad to see such energy/inputs from the experts.

In the interest of keeping it focused, I think i received the response to my question.

So I will shortly close this question, and I will post another question to give a broader picture and seek focused guidance.

In the meantime I am happy to see the responses from the others who have already put some effort.

Thank you
"Kindly confirm if I understood your message correctly."

you understood correctly
"Apologies once again"
you have absolutely no need to apologize to me.
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