Summer of Math Exposition

Why is this "Fundamental" to arithmetic?

An animated video about the fundamental theorem of arithmetic and uniqueness of prime factorisation (UPF). The video starts off by giving examples of why UPF is non-trivial and then proceeds to show why it is truly fundamental again using examples. Afterwards a proof of UPF is provided from first principles.

Analytics

7.1 Overall score*
45 Votes
20 Comments
Rank 5

Comments

Having taken an algebra course last year I found it easy to follow the beginning, but I think it was too much jargon for a layman. I did like the presence examples and connections to concepts taught in secondary school though.

5

The introduction and the topic at hand were easy and approachable; based on concepts that many are acquainted with in school. What I admired a lot about this submission is how, as the video continues to delve deeper into the subject, the creator helps the audience follow along easily; for example with the vocabulary section of the video. Only later on, when it came to the actual proof of uniqueness, the creator easily lost the audience with the definitions of integers a, b, a', b', p and k, which was a shame. (Grammatical mistake at 14:38 with "uniqueness" being spelt as "uniquness".)

7.4

I had watched your video a few weeks ago and enjoyed it. Clear explanation and nice visualizations. Also liked examples used in the video.

6.9

Good Job.

7.3

Very well presented in-depth overview of the FTA. A Summary at the end would have made it even better, I think. Found the 1st section of the video particularly thought-provoking. I doubt that I could maintain a viewer's interest for a 20 minute discussion on Number Theory, so it is to the author's great credit that they were able to do so.

6.2

Just I think a video with sponsor is not the best for this challenge

7

I felt like this was well done. Would have rather not seen the brilliant ad in this however.

7.2

I like the video a lot, because It helps the viewer to grasp the relevance off the Fundamental Theorem of Arithmetic. The section I like the most is the one about the non-triviality of the Theorem, I find It very clever.

6.8

This is an excellent video. I have had similar appreciation for the FTA myself but didn't think about all these details. Nice work!

8

This is a really nice video with great graphics. The pacing is good and I was able to follow everything pretty easily, though the latter parts became more difficult to understand, even though I'm not a mathematician. I must say, though, that I strongly object to having a commercial in the middle, particularly for a video that's entered into a contest. But the video itself is of very high quality.

8

This video is a little long and the topic isn’t very interesting.itjust wasn’t the video forme.

4

I genuinely enjoyed the motivation for this video. Really well done My guess is that this was due to the nature of the competition, but I did feel as though there was quite a bit of info within a single long-form video. At moments, this made lose track about the overarching theme of the video. As the channel grows, it will be nice to be able to reference other videos that you've developed.

5.4

I stopped watching at the sponsorship message. I'm here to watch maths, not advertising. If it's just a 'please subscribe' popup then I moan about it but don't mark down the score. Similar here. Even if it's a skippable plug, that's not the point.

5.4

Goal Orientation: 7/10 Novelty: 2/10 Thought-Provoking: 8/10 Comprehensibility: 7/10 Technological: 6/10 Overall Average: 6/10

6.4

I had already seen this video and I am subscribed to the channel. The quality is very good (although the video is a bit too long). The subject is interesting but not entirely new

7

well done and forcing to remember the fondamentals, but not bringing new concept or idea

6.6

Really well explained a hard topic in a way that requires very little prior knowledge. Around the time when Z[√-5] was introduced however it got a bit boring cause I had to think to much ¯\_(ツ)_/¯

7.1

Ah it's been a while UFDs (Unique Factorisation Domain)s. This was a solid video on the fundamental theorem of arithmetic for the integers. It's great that one considered when 'factorisations' say of rational numbers may or may not be considered simplified. I've always ever proved the FTA by using Euclid's Algorithm / Bezout coefficients first to obtain Euclid's Lemma, as the last section of the video flashes up. It was nice to see in this video a direct proof of Euclid's Lemma. Perhaps in future it would be nice to delve further into some ring theory, Euclidean Domains => PIDs => UFDs, and eg discuss irreducibility of Gaussian integers. The example of (1 + sqrt(-5)) * (1 - sqrt(-5)) is some really motivating and teasing material!

7.2

great video.....hope you will answer my(@rudrarakeshkumargohil) small doubts in the comments !

8.3

Very clear. I really liked the development of the zeta function. Nice examples and proofs.

7.3