exercise-sheet-0.Rmd

---
title: "Exercise sheet 0: Math"
---

---------------------------------

# Exercise 1 - Recursions


### 1a)

Given the recursive Formulation, fill in the array underneath:

$$
a_{n} = a_{n-1} + d, \quad \forall n : 0 < n < x
$$

```{r, echo=FALSE}
htmltools::includeHTML("html/linearRecursion.html")
```




### 1b)

Given the recursive formulation, fill in the missing cell underneath:


:::: {#explaining .message-box }

::: {#note-exp .note-header}
```{r, include=knitr::is_html_output(), echo=FALSE,}
knitr::include_graphics("figures/infoicon.svg")
```
**Note**
:::
::: {#note-exp .note-body}


During the course of Bioinformatics we will use $i$ as the row and $j$ as the
column index

:::

::::


$$
D_{i, j} = max (D_{i-1. j-1} + 2, D_{i-1, j} + 3, D_{i, j-1} + 1)\ , \quad \forall i, j : i  \ge  j > 1
$$
```{r, echo=FALSE}
htmltools::includeHTML("html/matrixMax.html")
```

```{r, echo=FALSE}
htmltools::tags$script(src = "assets/js/recursions.js", type= "text/javascript")
```