Wikipedia talk:School and university projects/Discrete and numerical mathematics/Learning plan/Academic year 2016-2017

Important: First comments come from Epistemowikia, although, to prevent confusion, the corresponding page has been whitened there, but you can see its history here. --Jmleonrojas (talk) 09:06, 26 September 2017 (UTC)

Final grade

After having seen how it has been run at other universities, I think that one student's collaboration with the project could be graded up to 45 % of their final grade. So, this one should consist of:

1. Individual work (IW):
1. for having done a minimum of 4 major contributions, at least one per each header topic, up to 30 % of the grade (that is to say, if they would make exactly one major contribution per topic, it would correspond to 7,5 % of the grade per topic);
2. for having substantially contributed to that an article be quality marked by the English Wikipedia community, up to 7,5 % more;
2. Collaborative work (CW) within a team of 6 people:
1. for having done a minimum of 4 major contributions, at least one per each header topic, up to 30 % of the grade (that is to say, if they would make exactly one major contribution per topic, it would correspond to 5 % of the grade per topic, earned by each one of the members of the team (although these members could redistribute the total percentage gained as a team according to its own self-evaluation as a team);
2. for having achieved that their contribution as a team has been quality marked by the English Wikipedia community, up to 7,5 % more (1,25 % per each member or the inner self-redistribution they could make);
3. for having work as a team, 1,25 % more for each member (or the inner self-redistribution they could make).
3. Final exam (FE), up to 55 %.

Thus, the final grade would consist of:

${\begin{aligned}IW+CW+FE&=IW+CW+\left(\leqslant 5,5\right)\\&=IW+\left({\overline {0,5}}+{\overline {0,125}}+{\overline {0,125}}\right)+\left(\leqslant 5,5\right)\\&=\left(\left(\leqslant 3\right)+\left(\leqslant 0,75\right)\right)+\left({\overline {0,5}}+{\overline {0,125}}+{\overline {0,125}}\right)+\left(\leqslant 5,5\right)\\&\leqslant 10\end{aligned}}$

with ${\overline {\mathit {n}}}$ expressing the 'fuzziness' of the number ${\mathit {n}}$, due to the possible inner self-redistribution of some marks.

--Jmleonrojas (talk) 14:52 12 feb 2017 (UTC)

After reviewing the proposal, nothing remains except to modify it. On the one side, to limit the mark of the final exam, would be unfair precisely with those students who would have worked in the project. On the other side, the opinion of the Wikipedia community is not a normal term of the sum and it should be an added summand to the final grade, although, since we do not limit the mark of the final exam, all of them are added summands.

All in all, if a student collaborates in the project, individually and within a team:

(the abbreviations mean: FE = Final Exam, IW = Individual Work, CW = Collaborative Work)

${\begin{aligned}FE+IW+CW&=\left(\leqslant 10\right)+IW+CW\\&=\left(\leqslant 10\right)+\left(\left(\leqslant 3\right)+\left(\leqslant 0,75\right)\right)+CW\\&=\left(\leqslant 10\right)+\left(\left(\leqslant 3\right)+\left(\leqslant 0,75\right)\right)+\left({\overline {0,5}}+{\overline {0,125}}+{\overline {0,125}}\right)\end{aligned}}$

in other words, if they gain, say, 3 points because of their collaboration, it would be sufficient that they obtain 7 points on the final exam to earn a 10 as the final grade.

Similarly, if a student decided to limit themselves to individual collaboration:

$\left\{{\begin{aligned}CW&=0\\FE+IW&=\left(\leqslant 10\right)+IW\\&=\left(\leqslant 10\right)+\left(\left(\leqslant 3\right)+\left(\leqslant 0,75\right)\right)\end{aligned}}\right.$

Likewise, if they decided to limit themselves to collaboration within a team:

$\left\{{\begin{aligned}IW&=0\\FE+CW&=\left(\leqslant 10\right)+CW\\&=\left(\leqslant 10\right)+\left({\overline {0,5}}+{\overline {0,125}}+{\overline {0,125}}\right)\end{aligned}}\right.$

Finally, if they decided not to collaborate with the project:

$\left\{{\begin{aligned}IW&=0\\CW&=0\\FE&\leqslant 10\end{aligned}}\right.$

--Jmleonrojas (talk) 19:05 13 feb 2017 (UTC)

Logic problems

(There is a talk on the talk page of the corresponding learning plan in Spanish).

Sample exam questions and some answers

Here you have some examples of possible exam questions:

Sample exam questions and some answers

Each question is designed to be resolved within a maximum of 30 minutes. As I have written them on Wikipedia, they contain hypertext. However, you should do them without checking the solutions. The exam will be a closed book exam.

Red links conrrespond to articles not yet created. Let me encourage you to work on them; if you are joined to the university project 'Discrete and numerical mathematics', then you could build a contribution by working in any of them, even a major one, and if you are not a participant, please do not forget the minihackathons.

Cordial greetings.

--Jmleonrojas (talk) 08:11 6 abr 2017 (UTC)

Bibliography (theory and proposed and solved exercises) and two examples of exam

Hello:

I would briefly like to remind you that on the learning plan page:

Wikipedia:School and university projects/Discrete and numerical mathematics/Learning plan

there are direct links to the highlighted parts dealt with in class, any of them including bibliography (theory and proposed and solved exercises). For example, in the case of number theory:

Wikipedia:School and university projects/Discrete and numerical mathematics/Learning plan#Number theory

including a page on Epistemowikia in which your fellow students of past courses have worked in them (in Spanish, for the time being, albeit any help is always welcome):

propuestos sobre números naturales y enteros y algunas soluciones Ejercicios propuestos sobre números naturales y enteros y algunas soluciones

In addition, you can find two examples of exam (only for the midterm, for the time being: themes 1 and 2), the one that we solved in the whole class and another and some solutions:

Wikipedia:School and university projects/Discrete and numerical mathematics/Learning plan#Sample exam questions and some answers

For example, you can check the solution to the question about finding out the digits x,y such that 12xy567 be divisible by 33, now not discovering a divisibility rule by 33 (as we did in class) but using divisibility rules by 3 and by 11.

As I asked in my earlier message, let me encourage you to continue working, creating and collaborating on Wikipedia, together you could create and collaborate on writing articles about the major topics of the course, as well as on the Wikipedia project, in case you are joined to it. For example, you could build in Mediawiki format the resolution to the previous question and provide it as an example in an article. You can also review the exercises on the Epistemowikia page and perhaps take advantage of some that may serve as an example in a Wikipedia article. For those who do not participate in the project, I remind you that something similar could be done through the proposal of a minihackathon.

Cordial greetings. --Jmleonrojas (talk) 17:43 24 apr 2017 (UTC)

About the solution of the third question of the second sample exam

Hello:

You are asking me for the solution of the third question of the second sample exam (about RSA).

I would remind you that:

RSA (cryptosystem)

is a minihackathon, a recommended practice (albeit optional, you already know me). Mind you, I also recommend that you work on them in collaboration with each other, as a team.

Anyway, if the current wording of the Wikipedia article, RSA (cryptosystem) does not convince you, why do not you help to 'clarify' it? I know you have little time but why you do not do it? Starting with your class notes, why you do not draw up, in a clear way, both the method and an example, either the one given out in class or the above third question?

We all would appreciate it very much, for sure.

Cordial greetings.

--Jmleonrojas (talk) 18:42 2 may 2017 (UTC)

On Friday 28 May lab/seminar meeting

Hello:

On Friday 28 May lab/seminar meeting, we introduced a new hackathon, this time about permutation generation methods.

Here you can find a basic scheme, that I encourage you to continue and complete:

Permutation generation methods

There you can read the wording of the recommended specific practice in that meeting, about generating the next permutation in lexicographic order.

You also find there a link to the 1977 Robert Sedgewick's classic review.

Sedgewick proved that, in those days, Heap's algorithm was the most effective algorithm to generate permutations by machine computing:

Heap's algorithm

We also spoke about Steinhaus-Johnson-Trotter's algorithm:

Steinhaus-Johnson-Trotter algorithm

and we pointed out that it was known already to 17th century by those people in charge of swinging the tuned bells in the major churches:

Change ringing

And please feel free to create new pages on Wikipedia and to contribute to those ones already created, at your discretion.

Cordial greetings.

--Jmleonrojas (talk) 15:54 7 may 2017 (UTC)

More examples of exam (2nd part)

Hello:

Here you have more examples of exam questions, about what we have seen so far, with solutions:

Sample exam questions and some answers

Wether if you participate in the project 'Discrete and numerical mathematics' on Wikipedia or not, please let me again encourage you to continue working, creating and collaborating in the writing of articles around the core subjects of the course. For example, we might think about how could we include these examples of exam questions as examples in Wikipedia articles. We can also devote some effort to propose minihackathons, from which future definite contributions may likely arise.

Cordial greetings. --Jmleonrojas (talk) 17:16 7 may 2017 (UTC)

About the final exam

(You can read the complete talk, in Spanish, on the talk page of the corresponding learning plan in Spanish).

Hello:

The examples of exam (self-assessment mock exams), designed following the development of the course and to be done in two hours, have created this academic year, an apparent division into eight parts: logic [1], cardinality [2], number theory [3], cryptography [4(1)] and numerical analysis [4(2)], combinatorial theory [5 and 6], recurrent relations [7], graphs [8]. Half of them correspond to themes 1 and 2 and the other half to themes 3 and 4. We could then consider a 4-hour final exam consisting of two halves (two sessions) of two hours and four questions each one, with a break in the middle.

If we want to reduce to two hours the final exam lasting, we could choose — the day of the exam and by tossing a coin — 4 questions out of the 8, one for every two consecutive ones. Thus, some examples of distributions of questions in the exam would be {1, 3, 6, 8} and {2, 3, 5, 7} but either {2, 3, 4(1), 6} or {1, 4(2), 7, 8} not.

What do you think?

Cordial greetings.

--Jmleonrojas (talk) 09:54 9 may 2017 (UTC)

[...]

[...]

Maybe, randomly choosing 4 out of the 8 questions would be a more balanced and fairer situation.

Cordial greetings.

--Jmleonrojas (talk) 12:38 12 may 2017 (UTC).

[...]

Hello:

Maybe what you propose lacks randomness. Perhaps a random distribution of the 8 questions "into" the two 4-question exams were to be made.

In view of the foregoing, what would you say about the following reflection and proposal?

With so little time remaining for graphs, if it really remains, it makes no sense we see it as a separate chapter. So there might not be any question about them. On the other side, after reviewing the contents and taking into account the time spent and as it is the final exam, it has to agree with the published course program, so the 25 percent of the questions must match those studied in lab/seminars ("fixed" part of the final exam), thus the apparent division should be the following:

• [1]: Logic.
• [2]: Cardinality (including sets, relations, functions).
• [3 and 4]: Number theory.
• [5 and 6]: Combinatorial theory.
• [7 and 8]: Recurrent relations (including population dynamics and perhaps also graphs).
• [L/S] (25 %): Semantic tableaux, cryptography (RSA), numerical methods (Newton’s divided-difference interpolating polynomials), algebraic structures (L/S of 15 and 19 May).

So let us think about the final exam. I come to the exam with a list of 8 + 1 questions (the ninth one is the fixed question, "compulsory", which everyone must try to solve, corresponding to [L/S] [25 percent]). Then, we randomly choose 4 out of the 8 other questions. Finally, each one of you personally choose 3 questions (the other 75 percent) out of those already randomly chosen 4.

Cordial greetings.

--Jmleonrojas (talk) 07:14 13 may 2017 (UTC)

Project Euler

Hello:

I would like to share with you the Project Euler's website.

You can register on the site to solve a vast amount of math-related problems. They're made to be solved with some programming aid, in whichever programming language you prefer (some people even uses assembly to solve them), but some problems don't need it.

Greetings,

--Imhernand (talk) 08:56 12 may 2017 (UTC)

Hello:

Many, many thanks. It is a great site. For sure we'll make the most of it.

Cordial greetings.

--Jmleonrojas (talk) 09:53 12 may 2017 (UTC).

Introduction to graphs

Hello:

As usual, I would like to share with you a little new entry that I've added to my personal blog about graphs, which is available through the following link: https://lonamiwebs.github.io/blog/graphs/index.en.html.

It's a little introduction which merely shows what we had time for in the class, which sadly isn't much, because it's very interesting. The page also has an interactive example on which you can design your own graphs with the connections that you want.

Greetings,

--Imhernand (talk) 11:10 2 jun 2017 (UTC)