MA0301/README.md

# MA0301 - Spring 2021 - Diskret Matematikk

Using styling files from [oysteikt/texmf](https://gitlab.stud.idi.ntnu.no/oysteikt/texmf)

## Exercises

| Num | Exercise PDF              | Answer PDF       | Solutions PDF             |
| --- | ------------------------- | ---------------- | ------------------------- |
| 1   | [wiki.math.ntnu.no][ex1]  | [ex1.pdf][as1]   | [wiki.math.ntnu.no][so1]  |
| 2   | [wiki.math.ntnu.no][ex2]  | [ex2.pdf][as2]   | [wiki.math.ntnu.no][so2]  |
| 3   | [wiki.math.ntnu.no][ex3]  | [ex3.pdf][as3]   | [wiki.math.ntnu.no][so3]  |
| 4   | [wiki.math.ntnu.no][ex4]  | [ex4.pdf][as4]   | [wiki.math.ntnu.no][so4]  |
| 5   | [wiki.math.ntnu.no][ex5]  | [ex5.pdf][as5]   | [wiki.math.ntnu.no][so5]  |
| 6   | [wiki.math.ntnu.no][ex6]  | [ex6.pdf][as6]   | [wiki.math.ntnu.no][so6]  |
| 7   | [wiki.math.ntnu.no][ex7]  | [ex7.pdf][as7]   | [wiki.math.ntnu.no][so7]  |
| 8   | [wiki.math.ntnu.no][ex8]  | [ex8.pdf][as8]   | [wiki.math.ntnu.no][so8]  |
| 9   | [wiki.math.ntnu.no][ex9]  | [ex9.pdf][as9]   | [wiki.math.ntnu.no][so9]  |
| 10  | [wiki.math.ntnu.no][ex10] | [ex10.pdf][as10] | [wiki.math.ntnu.no][so10] |
| 11  | [wiki.math.ntnu.no][ex11] | [ex11.pdf][as11] | [wiki.math.ntnu.no][so11] |
| 12  | [wiki.math.ntnu.no][ex12] | [ex12.pdf][as12] | [wiki.math.ntnu.no][so12] |

[ex1]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-1-2021-new.pdf "Exercise 1 Questions"
[ex2]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-2-2021-new.pdf "Exercise 2 Questions"
[ex3]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-3-2021.pdf "Exercise 3 Questions"
[ex4]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-4-2021.pdf "Exercise 4 Questions"
[ex5]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-5-2021.pdf "Exercise 5 Questions"
[ex6]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-6-2021.pdf "Exercise 6 Questions"
[ex7]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-7-2021.pdf "Exercise 7 Questions"
[ex8]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-8-2021.pdf "Exercise 8 Questions"
[ex9]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-9-2021.pdf "Exercise 9 Questions"
[ex10]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-10-2021.pdf "Exercise 10 Questions"
[ex11]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-11-2021.pdf "Exercise 11 Questions"
[ex12]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-12-2021.pdf "Exercise 12 Questions"

[as1]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise1.pdf "Exercise 1 Answers"
[as2]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise2.pdf "Exercise 2 Answers"
[as3]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise3.pdf "Exercise 3 Answers"
[as4]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise4.pdf "Exercise 4 Answers"
[as5]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise5.pdf "Exercise 5 Answers"
[as6]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise6.pdf "Exercise 6 Answers"
[as7]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise7.pdf "Exercise 7 Answers"
[as8]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise8.pdf "Exercise 8 Answers"
[as9]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise9.pdf "Exercise 9 Answers"
[as10]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise10.pdf "Exercise 10 Answers"
[as11]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise11.pdf "Exercise 11 Answers"
[as12]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise12.pdf "Exercise 12 Answers"

[so1]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-1-2021-solutions.pdf "Exercise 1 Solutions"
[so2]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-2-2021-solutions.pdf "Exercise 2 Solutions"
[so3]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-3-2021-solutions.pdf "Exercise 3 Solutions"
[so4]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-4-2021-solutions.pdf "Exercise 4 Solutions"
[so5]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-5-2021-solutions.pdf "Exercise 5 Solutions"
[so6]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-6-2021-solutions.pdf "Exercise 6 Solutions"
[so7]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-7-2021-solutions.pdf "Exercise 7 Solutions"
[so8]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-8-2021-solutions.pdf "Exercise 8 Solutions"
[so9]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-9-2021-solutions.pdf "Exercise 9 Solutions"
[so10]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-10-2021-solutions.pdf "Exercise 10 Solutions"
[so11]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-11-2021-solutions.pdf "Exercise 11 Solutions"
[so12]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-12-2021-solutions.pdf "Exercise 12 Solutions"

---

## Automation

---

### VSCode snippets

[See snippets for LaTeX](https://gitlab.stud.idi.ntnu.no/oysteikt/v21-ma0301/-/blob/master/exam_template/.vscode/latex.code-snippets)

[See snippets for Makefile](https://gitlab.stud.idi.ntnu.no/oysteikt/v21-ma0301/-/blob/master/exam_template/.vscode/makefile.code-snippets)

---

### Chrome plugin

#### Chapter 1. 2. 3. Boolean calculator

  Automates calculating boolean expression step by step by running the input through https://boolean-algebra.com/

  Outputs the resulting set of expressions to either propositional logic, boolean algebra or set operations.

  Converts output to LaTeX

 - [X] Finished

#### Chapter 4. Induction

  Automates proof by induction by running the input through https://wolframalpha.com/

  Converts output to LaTeX

 - [ ] Finished

#### Chapter 7. Combinatorics

  Permutations / Combinations Calculator

  Computes permutations and combinations

  Outputs to LaTeX

 - [X] Finished

---

### Python framework

See examples of what the engine for the exam template can do here: [exam_template_graphics.pdf](http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exam_template_graphics.pdf)

#### Chapter 1. Truthtables (propositional logic)

**Capabilities:**

 - [X] Calculate and render truthtable for propositional logic expressions

#### Chapter 3. Sets

**Capabilities:**

 - [ ] Calculate and output powersets

#### Chapter 5. Relations

**Capabilities:**

  Proofs:

 - [X] Check whether relation is reflexive
 - [X] Check whether relation is symmetric
 - [X] Check whether relation is antisymmetric
 - [X] Check whether relation is transitive
 - [X] Check whether relation is an equivalence relation
 - [X] Check whether relation is a partial order

  Graphs:

 - [X] Draw a hasse diagram from a partial order
 - [X] Draw an graph from any relation

 Note: Checking whether a relation has a property in this context means that it goes over every pair of related elements and looks for contradictions. **This program can not prove relation properties algebraically**

#### Chapter 7. Graph theory

**Capabilities:**

  Inputs:

 - [X] Input a graph from a matrix
 - [X] Input a graph from a node/edge list
 - [X] Input a complete graph from a node number

  Outputs:

 - [X] Output a graph to a matrix
 - [X] Draw an undirected graph
 - [X] Draw a directed graph
 - [ ] Find a minimal spanning tree with Kruskals algorithm

#### Chapter 8. Finite state automata

**Capabilities:**

 - [X] Draw a finite state machine
 - [ ] Output a finite state machine table
 - [ ] Calculate input based on a finite state machine