seeking advice/evaluation on my plans for the next two years (courseworks, internships, etc)

(sorry for the duplicate!)
Background:
1. pure math major in US news #2, gpa: 3.72~3.76
2. CS courses taken: Data Structures in Java, Introduction to Computer Science and Programming Java, analysis of algorithm, discrete mathematics
3. math courses taken:
Linear algebra/calculus sequence/ODE, Measure Theoretic Probability Theory (grad course), Elliptic Partial Differential Equation (grad course), Complex Geometry I, II (grad course), Algebraic Topology, Topology, Analytical Number Theory, Differential Manifolds, Honors Complex Variables, Mathematical Quantum Mechanics, Modern Algebra I,II, Modern AnalysisI, II, Partial Differential Equation (undergrad level)
4. Statistics course taken: Bayesian inference, combinatorial probability theory
5. No research experience at all, only tutoring/mentoring experience in math (my resume is essentially empty)

plans in this summer
1. self-teach: linear regression/stats inference/optimization/time series
2. learn programming languages, mainly on C++ and python/build some side project to include in my resume/search for internship as data analyst/software engineer (I know it's already late, though)
3. read some books on quant

Future plans in my masters program starting September(18~21 months)
1. try to get in some research
2. Courses that I will take in my first year (maybe I'm underestimating the workload? but I want to take as many as possible from the below list)
Monte Carlo Simulation
Brownian motion and stochastic calculus
nonlinear optimization
machine learning
matrix algebra
applied linear algebra
numerical methods for stochastic differential equations
advanced computing for finance
financial statistics: time series, forecasting, mean reversion, and high frequency
3. I will try to do dissertation on machine learning in my second year (or at least related to statistics)
4. I won't have any time for interview prep, so I will mainly try to land an internship on software engineer/data science in my first summer (although I will apply for quant internship to "test the water") I will do Interview prep while I do summer internship, aiming to get a full time offer in my second year

Miscellaneous
1. I'm an international student and the masters program is in applied math

Any thoughts??
 
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