I m studying a BSc econ degree and I am only allowed to take one outside option in my second and third year, which needs to be a mathematical modules, considering that I want to pursue a master degree of mathematical finance. I have already taken calculas linear algebra and stats in year 1.
I am now struggling in choosing my outside option for my second year. I can choose between calculas & linear algebra (these 2 are considered as 1 course), statistics, or analysis? Which one of these are the most important?
The followings are the course content:
For Calculas & Linear Alegbra:
i will be learning how integrals may be calculated, or transformed by a variety of manipulations, and how they may be applied to the solution of differential equations. This aim is achieved by studying such topics as: Limiting processes. Riemann integral, Multiple integration, Improper integrals, Manipulation of integrals, Laplace transforms, the Riemann-Stieltjes integral (permitting application of the Laplace transform to discrete and continuous probability distributions) is studied in some detail, depending on the time constraints............Vector spaces and dimension. Linear transformations, kernel and image. Real inner products, orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. An application to popular dynamics. Singular values, and the singular values decomposition matrix. Direct sums, orthogonal projections, least square proximations, Fourier series. Right and left inverses and generalized inverses.
For stats:
Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. Joint distributions and joint moments. Marginal and conditional densities. Independence, covariance and correlation. Sums of random variables and compounding. Multinomial and bivariate normal distributions. Law of large numbers and central limit theorem. Poisson processes, Functions of random variables. Sampling distributions. Criteria of estimation: consistency, unbiasedness, efficiency, minimum variance. Sufficiency. Maximum likelihood estimation. Confidence intervals. Tests of simple hypotheses. Likelihood ratio tests. Wald tests, score tests.
For analysis,
Logic, integers, sets and functions, prime numbers, relations, real and complex numbers, greatest common divisor and modular arithmetic, infimum and supremum, sequences, limits, continuity, groups and vector spaces.
Plz help me to decide which one I should take, ( i m only allowed to choose one)