Pre-requisite for Financial Engineering

Dear experts,
I am planning to pursue a Masters in Financial from one of the UK universities.
Given that the H1B (Work-visa) becoming tough to get I am not too inclined to apply to US universities.
My educational background
1.      High school-commerce (no mathematics)
2.      Bachelors - commerce (no mathematics)
3.      Chartered Account - (no mathematics)
4.      Costs and Works Accountig (no mathematics)
5.      CFA ( basic risk related maths
Experience: Telecom industry/Amex cards/Retail and commercial banks
Recent Profile: Prudential reporting to the regulators/capital and liquidity stress testing
Previous industry: Risk management consulting in Big 4 firm (EY, PWC, KPMG, Deloitte)
My daily routine: Study all the hours (24,7,365). I have tutors who come to my place and teach me the subjects. I have another 1.5 yrs I can give my complete attention to studies (does not include university time). Please do not see it as my arrogance. This is the level of effort and dedication I can /willing to put.
My goal now: Pursue Financial Engineering
Current status: Completed practicing High school mathematics except for Coordinate geometry and Vector algebra
Question1: are these topics required for financial engineering?
Topics: Please see file ‘High school Consolidated list of topics.doc’
Also completing c-language/starting c++-object oriented…
Once c,c++ are completed, then Python.

My next steps: trying to identify the topics required for high level mathematics:
Topics: Please see attached file BSc-Mathematics-Syllabus-01122015
Question: I request the experts to highlight the topics which are required or add a comment to highlight the topic required as a pre-requisite for FE.

Further, I am possessed/obsessed with the charismatic word ‘stochastic calculus’. This is my target or my fancy.
When I googled and read about the pre-requisites for this level of mathematics, I came across the following threads.
Pre-requisite for Stochastic calculus
one of the threads
•      learn real analysis level 101
•      learn basics of proofs and what is differentiability and integrability
•      master basic probability
•      combine your knowledge to learn stoch calc
•      you should be be very well versed with integration and differentiation - Advanced calculus level. Believe math for physicists should cover it.
•      university level math for engineers should be sufficient; but proofs well you can learn them
•      get a decent book on real analysis aimed at undergrads.

Kindly guide me. Thank you in advance for your valuable time and knowledge sharing.

Thank you
Who is Participating?
The links are good for stochastic calculus.
For FEit is impossible to get too much Statistics or Probability
ExcellearnerAuthor Commented:

Thank you.

I have completed the high-school level of Permutations and combinations, and Probability.

I intend to do it at Undergrad level (probability topic which includes calculus) soon.

Do you have any view on the topics under Coordinate geometry and Vector algebra-document: High school Consolidated

thank you
ExcellearnerAuthor Commented:
aburr/other experts,

I am taking your comment seriously.
Can you please suggest me a book each on Probability and statistics which serves to build my skills and maturity required for Financial Engineering.

Please help me.

Thank you
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