< under which your project can be released (even if nothing will be publicly released). This license will have to be chosen in one of these lists: [OpenSource.org/licenses](http://opensource.org/licenses/alphabetical), or [GNU.org/licenses](https://www.gnu.org/licenses/license-list.html). I recommend one of these: [the MIT license](http://mit-license.org/), [the GNU GPLv3 license](https://gnu.org/licenses/gpl.html), [the BSD license](http://opensource.org/licenses/BSD-2-Clause), or [the WFTPL license](http://www.wtfpl.net/).
- one file named `README.md` or `README` explaining **in a few lines** what is the project about,
- one file named `INSTALL` explaining *briefly* how to use the project. You have to list the modules/packages required by your program (if you used any), and any special manipulations required to use and test your program(s),
- one *optional* file name `TODO`, that can contain a list of point that still need to be worked on. Can be used to assess how advanced the team was on their subject. And if they tried some extra method but have not been able to complete the job, this document will state what would be required to conclude the extra ideas.
- one file named `SectionSSS__TeamYYY__Project1_CS101_2015.pdf` (in the **PDF format**, not Word `.doc.` or `.docx`) containing a **report of their work process**. More details about that report document are below,
- and finally, a list of Python programs (as many as you want, at least one), that solve the problem(s) we gave you.
---
### About the report
We need to specify a little bit what this report should contain.
The goal of such document is for you to be trained on technical communication, oriented on these three points:
- state what was your task(s), what approaches you considered and tried to complete,
- optionally, the report can contain remarks of any kind about the project (was it interesting? can we improve it for next year?)
#### Outline ?
The suggested outline is the following:
1. introduction (one paragraph), about the general domain and subject, the task, and the solution that you implemented,
2. first part giving details about the task(s), what model did you chose, what convention did you follow. The mathematical and scientific notations has to be explained here. Reference books and website can be given here (or at the end of the report),
3. details about your Python programs, which one does what, and how. You also have to specify how to use each program (if it is a command line program, is there arguments to give to the script? if not, is there something to change inside the program?). You also have to clearly say what external modules you used. If you program requires any external module that is not included in Anaconda, you need to include a link to the official webpage from where that module(s) can be downloaded (freely).
#### Tool to write your report ?
The suggested way to write this report is either:
- the more common solution: to use [Microsoft Word](https://simple.wikipedia.org/wiki/Microsoft_Word) or any word processing software, and to convert to document to PDF before sending it,
- or to start using $\\LaTeX{}$, the [standard for technical and scientific documents](https://simple.wikipedia.org/wiki/LaTeX). An excellent tool your team could use is the free website [ShareLaTeX.com](https://www.sharelatex.com/register), that can allow your team to collaboratively write your report.
---
## Style to follow for your programs:
### Conventions
Your team has to follow the [Python typing conventions](https://www.python.org/dev/peps/pep-0008/), as we do in lectures, labs and exams from January.
Your programs will be automatically read by the [pylint](http://www.pylint.org/) software, than you can [download freely](http://docs.pylint.org/installation.html#note-for-windows-users) and [use easily within Spyder](https://pythonhosted.org/spyder/pylint.html) (on Windows, type `conda install pylint` or `pip install pylint` on a DOS console, *when being connected to Internet*).
A too important number of syntax or style warnings or errors in one of your Python program might reduce your final mark for the project.
### `@author` in the doctstring of each program
As Spyder is doing it automatically, we ask you to include a line like this one in each of the docstring (the big string between triple quotes `"""`) in the beginning of each Python program:
@author: Team 1 Section A3
---
## CS101 Project
### When ?
> In March/April, 4 weeks.
### Ideas (4 to 8, 6 will be good)
#### Some project ideas:
##### Numerical integration (1D, 2D and more)
Implementing Riemann's rectangle method, basic Monte-Carlo method, and then triangle method, the Simson method etc.
Monte-Carlo method can be used to compute integral in 2D (surface) and 3D (volume) and more (cf. Vijay's mail).
**Bonus:** graphical representation of the methods (plotting the rectangles, the triangles etc under the curve).
##### Constraints optmization
A program to automatically produce the future time tables?
Cf. Abhijit's mail.
##### Matrix operations
- Matrix (as list of lists) operations: sum, subtraction, multiplications, integer power (two approaches, basic one in $O(n^4)$ or optimized one $M^{(2n)} = (M^n)^2$ and $M^{(2n+1)} = M(M^n)^2$ in $O(n^3 \log(n))$). Then the Gram-Schmidt process (can be used to compute the rank), the Gauss elimination method applied to computing the inverse ($M^{-1}$ when defined) and the determinant.
Bonus can be to implement this with OOP: Matrices as a class, with proper overloading of Python's operations (`+`, `-`, `\*`, `\*\*`, `/`, etc), by wrapping the functions inside special method `\_\_add\_\_`, `\_\_pow\_\_` etc.
The goal is to be able to use matrices as any Python numbers: `M1 + (M2 - M3)**4` for instance.
##### 1D optimization and differentiation (with plotting)
- Finding the zero of a *nice* function with different approaches (dichotomy/binary search, Newton's method, method of the secant, etc). **Bonus:** graphical representation. Application to computing a square root of any number, and a $n^{\\text{th}}$ root.
- Numerical derivation (1D) and gradient (2D, 3D) ? **Bonus:** graphical representation
##### 2D optimization and differentiation (with plotting)
Introduction to convex optimization in 2 dimension: [gradient descent](https://en.wikipedia.org/wiki/Gradient_descent) and more advanced methods.
Numerically compute a gradient, and implement the basic gradient descent method.
Extra work can be to implement better methods (conjugated gradient descent, optimal steps gradient descent) etc.
**Bonus:** graphical representation, in 2D it is possible to show the gradient descent (one picture). Like [this example](https://en.wikipedia.org/wiki/File:Gradient_descent.svg).
##### DE and DE systems.
Solving and plotting solutions to Differential Equations, and DE systems, with basic methods (Euler method, or the matrix one) or the good module.
- TODO: include suggestions from Vijay.
- FIXME which one? SymPy?
##### About cryptography
About prime numbers ? Computing prime numbers, many approaches (efficiency is important), and some applications to cryptography.
Simple implementation of a Cesar cypher protocol and hacking the Cesar cypher, and maybe a basic RSA protocol (with small keys) ?
> More ideas from MA101, PH101, EE101, MA102 CB101, EE102 ?
Or from the huge list of problems from [projecteuler.net](https://projecteuler.net/archives) (by selecting only easy and short ones -- but not too easy!).
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