# 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 ![Boolean Calculator](.gitlab/graphics/chrome-extension/booleanalgebra.png) 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 **NOTE: there are some bugs when converting boolean algebra AND operations to PL/S** #### Chapter 4. Induction Automates proof by induction by running the input through https://wolframalpha.com/ Converts output to LaTeX - [ ] Finished #### Chapter 7. Combinatorics ![Permutation/Combination Calculator](.gitlab/graphics/chrome-extension/permscombs.png) 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