# Course: ENGSCI 213

Although I wrote this late - as in the exam is already over - still I want to write down outlines of all my courses.

So here is the contents of the course ENGSCI 213, "Mathematical Modelling 2 SE" (i.e. "for software engineering").

linear algebra Gaussian Elimination row operations / pivot position pivot column pivot variable free variable row reduced echolon form elementary matrix permutation matrix trivial solution linear combination span linear independence invertible matrix properties LU factorization partial pivoting * rook pivoting * full pivoting transformations linear transformation onto one-to-one translation & homogeneous subspace column space of a matrix null space of a matrix basis coordinate vector (of a point/vector) relative to a basis dimension (of a subspace) rank (of a matrix) invertible matrices determinant ~ of triangular matrices ~ and row operations * the proportional change of the "area" of the "unit cube" eigenvalue (an) eigenvector (corresponding to an eigenvalue) diagnolizable matrices the Power Method the Inverse Power Method affine combination affine span standard homogeneous form affinely dependent barycentric coordinates iterative methods for linear systems of equations Jacobi Method (simultaneous corrections) matrix form Gauss-Seidel Method (sequential corrections) matrix form convergence considerations Frobenius Norm data analysis using R mean, standard deviation, variance centre, spread, (!!) skewness confidence interval standard error !! hypothesis testing (general) null hypothesis / alternative hypothesis "test statistic" "p-value" (testing normality) normal quantile-quantile plot Shapiro-Wilk Test its hypothesis Central Limit Theorum (just interpreting it) transforming the data by taking logarithm intention on normality intention on equal variance t-test assumptions & hypotheses "one-sample t-test" two-sample t-tests variance-equality considerations "Welch Two Sample t-test" Levene Test its hypothesis interpreting R output One-way analysis of variance assumptions & hypotheses why it works (intending to understand the "ANOVA Table") degrees of freedom Tukey Intervals vs. Bonferroni Correction Probability Probability Frequentist View vs. Subjectivist View Sample Space Event (Null Event) (n) Mutually Exclusive Events Partition partitioning a sample space partitioning an event Probability Distribution Discrete ~ Partition Theorum Bayes' Theorum (up to the "extended form") Statistical Independence mutually independent Discrete Probability Distributions Probability Mass Function Binomial D Bernoulli Trial Poisson D ~ Poission Process Expected Value linear combination Variance linear combination Continuous Probability Distributions Probability Function (density) Distribution Function (cumulative) properties Uniform Distribution properties / parameters Exponential Distribution 'memoryless' property (e.g. `P(X>=30|X>=20)==P(X>=10)`) relationship with Poisson Distribution Normal Distribution ~ nature, perhaps from Central Limit Theorum Markov Processes Stochaistic Process state sample space state space finite ~ stationary ~ period horizon finite ~ infinite ~ Markov Property Markov Process / Markov Chain transition probability "one step transition probabilities" transition matrices `P[t]` (for period t) "n step transition probabilites" stationary ~ "value", `v[i,t]`, of being in state i during period t. "total expected value for starting in state `i` over `t` periods", `V[i,t]` Limiting Distribution Stopping Problem