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
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```