How to Solve nonlinear system by newton method?

I have a year to take any course I want at my university.  Which of these course will best prepare me for graduate study in machine learning or analytics?

• Background: I have one year (3 quarters at my school) to take any course I want.  My long term goal is to be able to apply machine learning techniques effectively to business problems/ work in startups.  My knowledge at the time of embarking on this quest will be: Knowledge of data structures, 6 months exp programming, multivariate calculus. I've been using as a template for my study path. Unfortunately, I've found too many courses that seem seem extremely relevant.  But, I have no idea what I should really be preparing for.  Please help me trim this list to a manageable size.  I think at most I can take five of any of these courses in a single quarter.  More than likely 4 will be the feasible limit.  If you can tell me the top 4 most important courses from each subset, and then a fifth, that would be ideal.  Thanks so much in advance. Q1 Programming Languages   - Syntactic definition of programming languages. Introduction to programming language features including variables, data types, data abstraction, scoping, parameter disciplines, exception handling. Comparative study of several high-level programming languages. Computational Statistics   - This class is an introduction to statistical and, more generally       scientific, computing. The goal is for you to learn to think about and  express statistical and data analysis tasks computationally. One of the primary focuses (focii) in this class is working with data. Manipulating data into the right form in order to do analysis and create graphical displays is an extremely important and significant element of practical   statistics and indeed scientific activity.  Extensive use of R. Numerical Analysis A   - Error analysis, approximation, interpolation, numerical differentiation and integration. Programming in language such as Pascal, Fortran, or BASIC required. Linear Algebra Advanced Calculus   - Introduction to the rigorous treatment of abstract mathematical analysis. Proofs in mathematics, induction, sets, cardinality; real number system, theory of convergence of sequences. Intro to Databases Q2 Programming Languages B   -  Continuation of programming language principles. Further study of programming language paradigms such as functional and logic; additional programming language paradigms such as concurrent (parallel), dataflow, and constraint; key implementation issues for those paradigms; and programming languages semantics. Parallel Programming Parallel Programming   - Techniques for software development using the shared-memory and message-passing paradigms, on parallel architectures and networks of workstations. Locks, barriers and other techniques for synchronization. Applied Linear Algebra To understand the importance of linear algebra through applications To learn how the linear equations and eigenvalue problems appear in the practical applications To gain an insight of numerical solutions of linear equations and computation of eigenvalues and eigenvectors To learn how to solve linear equations and eigenvalue problems through Matlab-based projects Numerical Analysis B   - Solution of nonlinear equations and nonlinear systems. Minimization of functions of several variables. Simultaneous linear equations. Eigenvalue problems. Linear programming. Programming in language such as Pascal, Fortran, or BASIC required. Probability Theory   - Probability space; discrete probability, combinatorial analysis; independence, conditional probability; random variables, discrete and continuous distributions, probability mass function, joint and marginal density functions; expectation, moments, variance, Chebyshev inequality; sums of random variables, random walk, large number law, central limit theorem. Multivariate Data Analysis   - Multivariate normal distribution; Mahalanobis distance; sampling distributions of the mean vector and covariance matrix; Hotelling’s T2; simultaneous inference; one-way MANOVA; discriminant analysis; principal components; canonical correlation; factor analysis. Intensive use of computer analyses and real data sets. Game Theory Combinatorics   - Combinatorial methods using basic graph theory, counting methods, generating functions, and recurrence relations. Databases B Q3 Algorithms Artificial Intelligence Compilers Optimization - Linear programming, simplex method. Basic properties of unconstrained nonlinear problems, descent methods, conjugate direction method. Constrained minimization. Programming language required. Stochastic Processes  - Generating functions, branching processes, characteristic function; Markov chains; convergence of random variables, law of iterated logarithm; random processes, Brownian motion, stationary processes, renewal processes, queueing theory, martingales.

• Answer:

  In my opinion the three classes you cannot pass up are Numerical Analysis, Linear Algebra and Advanced Calculus.  Unfortunately those are all three in one quarter.  The programming classes are hit and miss depending on your university. Applied Linear Algebra could be awesome so could algorithms and optimization.  I would probably plug the optimization class because too few Data Scientists have education in this.