Improving Maths & Econ profile for quant masters.

Dear Quantnet members, I'd be very grateful if you could share your opinion on what is the best way to proceed for me. (Apologies for a long text).

I'm currently finishing my undergraduate Maths & Economics degree from Russia's number 1 university in finance and social sciences.

My objective, though, is to become a front office quant developer. I'm therefore going to apply to a number of universities from the top of the Quantnet ranking + two or three UK programs (e.g. Oxford Mathematical and Computational Finance).

I do feel, though, that my knowledge of mathematics and programming is not sufficient for me to be competitive as an applicant and later as a job candidate.

My maths background is as follows:
Abstract Mathematics: Group Theory, Rings and Fields, Analysis and Elements of Topology, Modules and Vector Spaces, Elements of Mathematical Logic, Introduction to Lie Groups
Calculus: Limits, The Riemann Integral, Improper Integrals (convergence/divergence, dominated convergence), Double and Triple Integrals, Ordinary Differential Equations, Laplace Transforms (solving ODEs with Laplace Transforms; Beta and Gamma functions)
Linear Algebra: Diagonalisation, Jordan Normal Form and Differential Equations, Inner Products and Orthogonality, Orthogonal Diagonalisation and its Applications, Direct Sums and Projections, Generalised Inverses, Complex Matrices and Vector Spaces
Optimisation Theory: Multi-dimensional Calculus, Constrained and Unconstrained Optimisation, Differential and Difference Equations, Optimisation Under Inequality Constraints, Kuhn-Tucker Theorem, Elements of Convex Analysis, Finite & Infinite Horizon Dynamic Programming
Financial Mathematics: Derivatives Valuation using one-period models, multi-period models, continuous-time models. Black Scholes Model, Perpetual Options.

I have not been taught partial differential equations (this seems to be a prerequisite for some of the more technical programs such as Oxford, for example).
I have no formal training / online certificates in programming (apart from a half-year course in VBA). I'm quite proficient in Stata and have a limited experience of working in MATLAB.

To fill the gaps, I have two options:
  1. A one-year option is to go through Baruch MFE's online courses in C++/Python/VBA and self-study the essential disciplines such as PDE (if it's indeed essential).
  2. A two-year option is to enroll at a Master's level Data Analysis in Applied Science program delivered by Google's local competitor, Yandex: (syllabus: Reviews say that it is a hard-core program taught by a number of big names both from academia and industry. People also say that instead of merely teaching how to code, Yandex developed the course from first principles of mathematics/CS so that their alumni become proper data scientists and not just people with coding skills. Advantage: it's free for successful applicants. Disadvantages: takes more time => increased opportunity cost + alumni say the curriculum is really tough and painful + I would still have to fill my math gaps via self-study. So not sure about this option.
So given my objectives and background, as well as the syllabus of the 2-year program, which of the two options is optimal? Any input would be highly appreciated!

If that's relevant, I'm about to start an 18-month internship at a bulge bracket bank in Moscow. I will have the opportunity to work at both its fixed income and equities departments, but these guys only do traditional trading and brokerage, not a lot of quant-related stuff.