185 lines
7.7 KiB
Markdown
185 lines
7.7 KiB
Markdown
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# MA0301 - Spring 2021 - Diskret Matematikk
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Using styling files from [oysteikt/texmf](https://gitlab.stud.idi.ntnu.no/oysteikt/texmf)
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## Exercises
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| Num | Exercise PDF | Answer PDF | Solutions PDF |
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| --- | ------------------------- | ---------------- | ------------------------- |
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| 1 | [wiki.math.ntnu.no][ex1] | [ex1.pdf][as1] | [wiki.math.ntnu.no][so1] |
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| 2 | [wiki.math.ntnu.no][ex2] | [ex2.pdf][as2] | [wiki.math.ntnu.no][so2] |
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| 3 | [wiki.math.ntnu.no][ex3] | [ex3.pdf][as3] | [wiki.math.ntnu.no][so3] |
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| 4 | [wiki.math.ntnu.no][ex4] | [ex4.pdf][as4] | [wiki.math.ntnu.no][so4] |
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| 5 | [wiki.math.ntnu.no][ex5] | [ex5.pdf][as5] | [wiki.math.ntnu.no][so5] |
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| 6 | [wiki.math.ntnu.no][ex6] | [ex6.pdf][as6] | [wiki.math.ntnu.no][so6] |
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| 7 | [wiki.math.ntnu.no][ex7] | [ex7.pdf][as7] | [wiki.math.ntnu.no][so7] |
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| 8 | [wiki.math.ntnu.no][ex8] | [ex8.pdf][as8] | [wiki.math.ntnu.no][so8] |
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| 9 | [wiki.math.ntnu.no][ex9] | [ex9.pdf][as9] | [wiki.math.ntnu.no][so9] |
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| 10 | [wiki.math.ntnu.no][ex10] | [ex10.pdf][as10] | [wiki.math.ntnu.no][so10] |
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| 11 | [wiki.math.ntnu.no][ex11] | [ex11.pdf][as11] | [wiki.math.ntnu.no][so11] |
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| 12 | [wiki.math.ntnu.no][ex12] | [ex12.pdf][as12] | [wiki.math.ntnu.no][so12] |
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[ex1]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-1-2021-new.pdf "Exercise 1 Questions"
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[ex2]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-2-2021-new.pdf "Exercise 2 Questions"
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[ex3]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-3-2021.pdf "Exercise 3 Questions"
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[ex4]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-4-2021.pdf "Exercise 4 Questions"
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[ex5]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-5-2021.pdf "Exercise 5 Questions"
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[ex6]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-6-2021.pdf "Exercise 6 Questions"
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[ex7]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-7-2021.pdf "Exercise 7 Questions"
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[ex8]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-8-2021.pdf "Exercise 8 Questions"
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[ex9]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-9-2021.pdf "Exercise 9 Questions"
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[ex10]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-10-2021.pdf "Exercise 10 Questions"
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[ex11]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-11-2021.pdf "Exercise 11 Questions"
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[ex12]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-12-2021.pdf "Exercise 12 Questions"
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[as1]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise1.pdf "Exercise 1 Answers"
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[as2]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise2.pdf "Exercise 2 Answers"
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[as3]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise3.pdf "Exercise 3 Answers"
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[as4]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise4.pdf "Exercise 4 Answers"
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[as5]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise5.pdf "Exercise 5 Answers"
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[as6]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise6.pdf "Exercise 6 Answers"
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[as7]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise7.pdf "Exercise 7 Answers"
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[as8]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise8.pdf "Exercise 8 Answers"
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[as9]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise9.pdf "Exercise 9 Answers"
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[as10]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise10.pdf "Exercise 10 Answers"
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[as11]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise11.pdf "Exercise 11 Answers"
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[as12]: http://oysteikt.pages.stud.idi.ntnu.no/v21-ma0301/exercise12.pdf "Exercise 12 Answers"
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[so1]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-1-2021-solutions.pdf "Exercise 1 Solutions"
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[so2]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-2-2021-solutions.pdf "Exercise 2 Solutions"
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[so3]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-3-2021-solutions.pdf "Exercise 3 Solutions"
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[so4]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-4-2021-solutions.pdf "Exercise 4 Solutions"
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[so5]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-5-2021-solutions.pdf "Exercise 5 Solutions"
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[so6]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-6-2021-solutions.pdf "Exercise 6 Solutions"
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[so7]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-7-2021-solutions.pdf "Exercise 7 Solutions"
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[so8]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-8-2021-solutions.pdf "Exercise 8 Solutions"
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[so9]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-9-2021-solutions.pdf "Exercise 9 Solutions"
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[so10]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-10-2021-solutions.pdf "Exercise 10 Solutions"
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[so11]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-11-2021-solutions.pdf "Exercise 11 Solutions"
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[so12]: https://wiki.math.ntnu.no/_media/ma0301/2021v/set-12-2021-solutions.pdf "Exercise 12 Solutions"
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---
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## Automation
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---
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### VSCode snippets
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[See snippets for LaTeX](https://gitlab.stud.idi.ntnu.no/oysteikt/v21-ma0301/-/blob/master/exam_template/.vscode/latex.code-snippets)
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[See snippets for Makefile](https://gitlab.stud.idi.ntnu.no/oysteikt/v21-ma0301/-/blob/master/exam_template/.vscode/makefile.code-snippets)
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---
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### Chrome plugin
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#### Chapter 1. 2. 3. Boolean calculator
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Automates calculating boolean expression step by step by running the input through https://boolean-algebra.com/
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Outputs the resulting set of expressions to either propositional logic, boolean algebra or set operations.
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Converts output to LaTeX
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- [X] Finished
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**NOTE: there are some bugs when converting boolean algebra AND operations to PL/S**
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#### Chapter 4. Induction
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Automates proof by induction by running the input through https://wolframalpha.com/
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Converts output to LaTeX
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- [ ] Finished
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#### Chapter 6. Combinatorics
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Permutations / Combinations Calculator
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Computes permutations and combinations
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Outputs to LaTeX
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- [X] Finished
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---
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### Python framework
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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)
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#### Chapter 1. Truthtables (propositional logic)
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**Capabilities:**
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- [X] Calculate and render truthtable for propositional logic expressions
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#### Chapter 3. Sets
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**Capabilities:**
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- [ ] Calculate and output powersets
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#### Chapter 5. Relations
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**Capabilities:**
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Proofs:
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- [X] Check whether relation is reflexive
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- [X] Check whether relation is symmetric
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- [X] Check whether relation is antisymmetric
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- [X] Check whether relation is transitive
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- [X] Check whether relation is an equivalence relation
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- [X] Check whether relation is a partial order
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Graphs:
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- [X] Draw a hasse diagram from a partial order
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- [X] Draw an graph from any relation
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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**
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#### Chapter 6. Combinatorics
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**Capabilities:**
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- [X] Make an inclusion exclusion expression from list of conditions
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#### Chapter 7. Graph theory
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**Capabilities:**
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Inputs:
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- [X] Input a graph from a matrix
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- [X] Input a graph from a node/edge list
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- [X] Input a complete graph from a node number
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Outputs:
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- [X] Output a graph to a matrix
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- [X] Draw an undirected graph
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- [X] Draw a directed graph
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- [X] Find a minimal spanning tree with Kruskals algorithm
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#### Chapter 8. Finite state automata
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**Capabilities:**
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- [X] Draw a finite state machine
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- [ ] Output a finite state machine table
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- [ ] Calculate input based on a finite state machine
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#### Python
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**Capabilities:**
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- [X] Include a raw python program, and capture its output into a listing |