diff --git a/_config.yml b/_config.yml index 203825c0ac3de425e171ab657e6bdb8ee1cfd0e0..e378081f52d48050f1cd478148c1fef2784b1b0b 100644 --- a/_config.yml +++ b/_config.yml @@ -1,18 +1,20 @@ collections: - authors: + psets: + output: true + notes: output: true defaults: - scope: path: "" - type: "authors" + type: "psets" values: - layout: "author" + layout: "pset" - scope: path: "" - type: "posts" + type: "notes" values: - layout: "post" + layout: "note" - scope: path: "" values: diff --git a/_data/navigation.yml b/_data/navigation.yml index cb67c7c63c4338c8bfd2b4737d2293c7860c1b82..268b387831a349f3b9b53883d0129077c03a6a84 100644 --- a/_data/navigation.yml +++ b/_data/navigation.yml @@ -2,3 +2,5 @@ link: / - name: Problem Sets link: /psets.html +- name: Notes + link: /notes.html diff --git a/_layouts/post.html b/_layouts/note.html similarity index 59% rename from _layouts/post.html rename to _layouts/note.html index 0fab084a8253662d25f792b5d18519514ca52cee..b07fd4ac3472f1889a64cae10a9f198d20bcb985 100644 --- a/_layouts/post.html +++ b/_layouts/note.html @@ -3,8 +3,4 @@ layout: default --- <h1>{{ page.title }}</h1> -<p> - {{ page.date | date_to_string }} -</p> - {{ content }} diff --git a/_layouts/pset.html b/_layouts/pset.html new file mode 100644 index 0000000000000000000000000000000000000000..b07fd4ac3472f1889a64cae10a9f198d20bcb985 --- /dev/null +++ b/_layouts/pset.html @@ -0,0 +1,6 @@ +--- +layout: default +--- +<h1>{{ page.title }}</h1> + +{{ content }} diff --git a/_posts/2019-02-15-ch2-notes.md b/_notes/fourier_transform.md similarity index 97% rename from _posts/2019-02-15-ch2-notes.md rename to _notes/fourier_transform.md index 0015a639bb264c6905449de68da096b7e992ca95..693676ed05c87ac3deda8cefa0630ab606600dc4 100644 --- a/_posts/2019-02-15-ch2-notes.md +++ b/_notes/fourier_transform.md @@ -1,10 +1,9 @@ --- -title: Chapter 2 Notes +title: Fourier Transforms --- -This page contains some proofs that I needed to review to make sense of the material in chapter 2. - -It's based on my prior knowledge and some helpful websites: +To really make sense of chapter 2 I needed to review the properties of Fourier Transforms. These +notes are based on my prior knowledge and some helpful websites: - [Properties of Fourier Transform](http://fourier.eng.hmc.edu/e101/lectures/handout3/node2.html) - [symmetry.pdf](https://www.cs.unm.edu/~williams/cs530/symmetry.pdf) diff --git a/_posts/2019-02-14-pset1.md b/_psets/1.md similarity index 100% rename from _posts/2019-02-14-pset1.md rename to _psets/1.md diff --git a/_posts/2019-02-14-pset2.md b/_psets/2.md similarity index 94% rename from _posts/2019-02-14-pset2.md rename to _psets/2.md index 94c286d8cbb22998601cfb0bf6ac23b9b92083f9..26710fbf9286e071e82a71f6d48a49664445595f 100644 --- a/_posts/2019-02-14-pset2.md +++ b/_psets/2.md @@ -95,13 +95,14 @@ visible light? Note: in the previous problem I used $$\lambda$$ as the expected number of events of a Poisson process. Here I'll use $$N$$ to avoid confusion with wavelength. -We have already found that $$\sigma = \sqrt{N}$$. For large $$N$$, the Poisson -distribution is very close to the normal distribution. So about two thirds of the probability mass -lies between $$N - \sigma$$ and $$N + \sigma$$. Thus if $$\sigma \leq 0.01 N$$, in -any given second it's more likely than not that the number of photons emitted is within one percent -of the true mean. Thus we'd need $$\sqrt{N} \leq 0.01 N$$, i.e. $$N \geq 10^4$$. -To have the same probability that the number of observed photons is within $$10^{-6} N$$ of -the true value, we need $$N \geq 10^{12}$$. +Since the photons are generated independently and with a constant average rate, it's reasonable to +model their creation as a Poisson process. We have already found that $$\sigma = \sqrt{N}$$. For +large $$N$$, the Poisson distribution is very close to the normal distribution. So about two thirds +of the probability mass lies between $$N - \sigma$$ and $$N + \sigma$$. Thus if $$\sigma \leq 0.01 +N$$, in any given second it's more likely than not that the number of photons emitted is within one +percent of the true mean. Thus we'd need $$\sqrt{N} \leq 0.01 N$$, i.e. $$N \geq 10^4$$. To have the +same probability that the number of observed photons is within $$10^{-6} N$$ of the true value, we +need $$N \geq 10^{12}$$. The wavelength of visible light is about $$\num{500e-9} \si{m}$$, so the energy of each photon will be diff --git a/notes.html b/notes.html new file mode 100644 index 0000000000000000000000000000000000000000..ff57d2ebd4bc33ef9fc032bc1c24a32d2afd6410 --- /dev/null +++ b/notes.html @@ -0,0 +1,12 @@ +--- +title: Notes +--- +<h1>Notes</h1> + +<ul> + {% for note in site.notes %} + <li> + <h2><a href="{{ note.url | real_relative_url }}">{{ note.title }}</a></h2> + </li> + {% endfor %} +</ul> diff --git a/psets.html b/psets.html index 15284eae3e9a20138b083f940e756cf4c3c5a934..1efc5d6ebcbb054db8dbf2c66b0448886400cb8e 100644 --- a/psets.html +++ b/psets.html @@ -4,10 +4,9 @@ title: Problem Sets <h1>Problem Sets</h1> <ul> - {% for post in site.posts %} + {% for pset in site.psets %} <li> - <h2><a href="{{ post.url | real_relative_url }}">{{ post.title }}</a></h2> - <p>{{ post.excerpt }}</p> + <h2><a href="{{ pset.url | real_relative_url }}">{{ pset.title }}</a></h2> </li> {% endfor %} </ul>