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Fix a few minor typos

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Alexander Zeilmann
2021-12-20 21:02:50 +01:00
parent e05191f1c3
commit c0c50b4e2d
9 changed files with 89 additions and 89 deletions
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104
data/blog/deriving-ols-estimator.mdx
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@ -9,12 +9,12 @@ summary: 'How to derive the OLS Estimator with matrix notation and a tour of mat
# Introduction
Parsing and display of math equations is included in this blog template. Parsing of math is enabled by `remark-math` and `rehype-katex`.
KaTeX and its associated font is included in `_document.js` so feel free to use it in any pages.
KaTeX and its associated font is included in `_document.js` so feel free to use it on any page.
^[For the full list of supported TeX functions, check out the [KaTeX documentation](https://katex.org/docs/supported.html)]
Inline math symbols can be included by enclosing the term between the `$` symbol.
Math code blocks is denoted by `$$`.
Math code blocks are denoted by `$$`.
The dollar signal displays without issue since only text without space and between two `$` signs are considered as math symbols.[^2]
@ -30,23 +30,23 @@ The vector of outcome variables $\mathbf{Y}$ is a $n \times 1$ matrix,
```tex
\mathbf{Y} = \left[\begin{array}
{c}
y_1 \\
. \\
. \\
. \\
y_n
{c}
y_1 \\
. \\
. \\
. \\
y_n
\end{array}\right]
```
$$
\mathbf{Y} = \left[\begin{array}
{c}
y_1 \\
. \\
. \\
. \\
y_n
{c}
y_1 \\
. \\
. \\
. \\
y_n
\end{array}\right]
$$
@ -54,45 +54,45 @@ The matrix of regressors $\mathbf{X}$ is a $n \times k$ matrix (or each row is a
```latex
\mathbf{X} = \left[\begin{array}
{ccccc}
x_{11} & . & . & . & x_{1k} \\
. & . & . & . & . \\
. & . & . & . & . \\
. & . & . & . & . \\
x_{n1} & . & . & . & x_{nn}
{ccccc}
x_{11} & . & . & . & x_{1k} \\
. & . & . & . & . \\
. & . & . & . & . \\
. & . & . & . & . \\
x_{n1} & . & . & . & x_{nn}
\end{array}\right] =
\left[\begin{array}
{c}
\mathbf{x}'_1 \\
. \\
. \\
. \\
\mathbf{x}'_n
{c}
\mathbf{x}'_1 \\
. \\
. \\
. \\
\mathbf{x}'_n
\end{array}\right]
```
$$
\mathbf{X} = \left[\begin{array}
{ccccc}
x_{11} & . & . & . & x_{1k} \\
. & . & . & . & . \\
. & . & . & . & . \\
. & . & . & . & . \\
x_{n1} & . & . & . & x_{nn}
{ccccc}
x_{11} & . & . & . & x_{1k} \\
. & . & . & . & . \\
. & . & . & . & . \\
. & . & . & . & . \\
x_{n1} & . & . & . & x_{nn}
\end{array}\right] =
\left[\begin{array}
{c}
\mathbf{x}'_1 \\
. \\
. \\
. \\
\mathbf{x}'_n
{c}
\mathbf{x}'_1 \\
. \\
. \\
. \\
\mathbf{x}'_n
\end{array}\right]
$$
The vector of error terms $\mathbf{U}$ is also a $n \times 1$ matrix.
At times it might be easier to use vector notation. For consistency I will use the bold small x to denote a vector and capital letters to denote a matrix. Single observations are denoted by the subscript.
At times it might be easier to use vector notation. For consistency, I will use the bold small x to denote a vector and capital letters to denote a matrix. Single observations are denoted by the subscript.
## Least Squares
@ -107,7 +107,7 @@ $$y_i = \mathbf{x}'_i \beta + u_i$$
4. $Var(\mathbf{U}|\mathbf{X}) = \sigma^2 I_n$ (Homoskedascity)
**Aim**:
Find $\beta$ that minimises sum of squared errors:
Find $\beta$ that minimises the sum of squared errors:
$$
Q = \sum_{i=1}^{n}{u_i^2} = \sum_{i=1}^{n}{(y_i - \mathbf{x}'_i\beta)^2} = (Y-X\beta)'(Y-X\beta)
@ -120,22 +120,22 @@ Take matrix derivative w.r.t $\beta$:
```tex
\begin{aligned}
\min Q & = \min_{\beta} \mathbf{Y}'\mathbf{Y} - 2\beta'\mathbf{X}'\mathbf{Y} +
\beta'\mathbf{X}'\mathbf{X}\beta \\
& = \min_{\beta} - 2\beta'\mathbf{X}'\mathbf{Y} + \beta'\mathbf{X}'\mathbf{X}\beta \\
\text{[FOC]}~~~0 & = - 2\mathbf{X}'\mathbf{Y} + 2\mathbf{X}'\mathbf{X}\hat{\beta} \\
\hat{\beta} & = (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{Y} \\
& = (\sum^{n} \mathbf{x}_i \mathbf{x}'_i)^{-1} \sum^{n} \mathbf{x}_i y_i
\min Q & = \min_{\beta} \mathbf{Y}'\mathbf{Y} - 2\beta'\mathbf{X}'\mathbf{Y} +
\beta'\mathbf{X}'\mathbf{X}\beta \\
& = \min_{\beta} - 2\beta'\mathbf{X}'\mathbf{Y} + \beta'\mathbf{X}'\mathbf{X}\beta \\
\text{[FOC]}~~~0 & = - 2\mathbf{X}'\mathbf{Y} + 2\mathbf{X}'\mathbf{X}\hat{\beta} \\
\hat{\beta} & = (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{Y} \\
& = (\sum^{n} \mathbf{x}_i \mathbf{x}'_i)^{-1} \sum^{n} \mathbf{x}_i y_i
\end{aligned}
```
$$
\begin{aligned}
\min Q & = \min_{\beta} \mathbf{Y}'\mathbf{Y} - 2\beta'\mathbf{X}'\mathbf{Y} +
\beta'\mathbf{X}'\mathbf{X}\beta \\
& = \min_{\beta} - 2\beta'\mathbf{X}'\mathbf{Y} + \beta'\mathbf{X}'\mathbf{X}\beta \\
\text{[FOC]}~~~0 & = - 2\mathbf{X}'\mathbf{Y} + 2\mathbf{X}'\mathbf{X}\hat{\beta} \\
\hat{\beta} & = (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{Y} \\
& = (\sum^{n} \mathbf{x}_i \mathbf{x}'_i)^{-1} \sum^{n} \mathbf{x}_i y_i
\min Q & = \min_{\beta} \mathbf{Y}'\mathbf{Y} - 2\beta'\mathbf{X}'\mathbf{Y} +
\beta'\mathbf{X}'\mathbf{X}\beta \\
& = \min_{\beta} - 2\beta'\mathbf{X}'\mathbf{Y} + \beta'\mathbf{X}'\mathbf{X}\beta \\
\text{[FOC]}~~~0 & = - 2\mathbf{X}'\mathbf{Y} + 2\mathbf{X}'\mathbf{X}\hat{\beta} \\
\hat{\beta} & = (\mathbf{X}'\mathbf{X})^{-1}\mathbf{X}'\mathbf{Y} \\
& = (\sum^{n} \mathbf{x}_i \mathbf{x}'_i)^{-1} \sum^{n} \mathbf{x}_i y_i
\end{aligned}
$$

4
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@ -3,14 +3,14 @@ title: 'Markdown Guide'
date: '2019-10-11'
tags: ['github', 'guide']
draft: false
summary: 'Markdown cheatsheet for all your blogging needs - headers, lists, images, tables and more! An illustrated guide based on Github Flavored Markdown.'
summary: 'Markdown cheatsheet for all your blogging needs - headers, lists, images, tables and more! An illustrated guide based on GitHub Flavored Markdown.'
---
# Introduction
Markdown and Mdx parsing is supported via `unified`, and other remark and rehype packages. `next-mdx-remote` allows us to parse `.mdx` and `.md` files in a more flexible manner without touching webpack.
Github flavored markdown is used. `mdx-prism` provides syntax highlighting capabilities for code blocks. Here's a demo of how everything looks.
GitHub flavored markdown is used. `mdx-prism` provides syntax highlighting capabilities for code blocks. Here's a demo of how everything looks.
The following markdown cheatsheet is adapted from: https://guides.github.com/features/mastering-markdown/

2
data/blog/guide-to-using-images-in-nextjs.mdx
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@ -66,7 +66,7 @@ _Note_: If you try to save the image, it is in webp format, if your browser supp
# Limitations
- Due to the reliance of `next/image`, unless you are using an external image CDN like Cloudinary or Imgix, it is practically required to use Vercel for hosting. This is because the component acts like a serverless function that calls a highly optimized image CDN.
- Due to the reliance on `next/image`, unless you are using an external image CDN like Cloudinary or Imgix, it is practically required to use Vercel for hosting. This is because the component acts like a serverless function that calls a highly optimized image CDN.
If you do not want to be tied to Vercel, you can remove `imgToJsx` in `remarkPlugins` in `lib/mdx.js`. This would avoid substituting the default `img` tag.

16
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@ -15,13 +15,13 @@ authors: ['default', 'sparrowhawk']
[![Deploy with Vercel](https://vercel.com/button)](https://vercel.com/new/git/external?repository-url=https://github.com/timlrx/tailwind-nextjs-starter-blog)
This is a [Next.js](https://nextjs.org/), [Tailwind CSS](https://tailwindcss.com/) blogging starter template. Probably the most feature rich nextjs markdown blogging template out there. Comes out of the box configured with the latest technologies to make technical writing a breeze. Easily configurable and customizable. Perfect as a replacement to existing Jekyll and Hugo individual blogs.
This is a [Next.js](https://nextjs.org/), [Tailwind CSS](https://tailwindcss.com/) blogging starter template. Probably the most feature-rich Next.js markdown blogging template out there. Comes out of the box configured with the latest technologies to make technical writing a breeze. Easily configurable and customizable. Perfect as a replacement to existing Jekyll and Hugo individual blogs.
Check out the documentation below to get started.
Facing issues? Check the [FAQ page](https://github.com/timlrx/tailwind-nextjs-starter-blog/wiki) and do a search on past issues. Feel free to open a new issue if none has been posted previously.
Feature request? Check the past discussions to see if it has been brough up previously. Otherwise, feel free to start a new discussion thread. All ideas are welcomed!
Feature request? Check the past discussions to see if it has been brought up previously. Otherwise, feel free to start a new discussion thread. All ideas are welcomed!
## Examples
@ -51,7 +51,7 @@ I wanted it to be nearly as feature-rich as popular blogging templates like [bea
- [MDX - write JSX in markdown documents!](https://mdxjs.com/)
- Server-side syntax highlighting with line numbers and line highlighting via [rehype-prism-plus](https://github.com/timlrx/rehype-prism-plus)
- Math display supported via [KaTeX](https://katex.org/)
- Citation and biliography support via [rehype-citation](https://github.com/timlrx/rehype-citation)
- Citation and bibliography support via [rehype-citation](https://github.com/timlrx/rehype-citation)
- Automatic image optimization via [next/image](https://nextjs.org/docs/basic-features/image-optimization)
- Flexible data retrieval with [mdx-bundler](https://github.com/kentcdodds/mdx-bundler)
- Support for tags - each unique tag will be its own page
@ -103,7 +103,7 @@ You can start editing the page by modifying `pages/index.js`. The page auto-upda
`data/authors/default.md` - default author information (required). Additional authors can be added as files in `data/authors`.
`data/projectsData.js` - data used to generate styled card in projects page.
`data/projectsData.js` - data used to generate styled card on the projects page.
`data/headerNavLinks.js` - navigation links.
@ -117,7 +117,7 @@ You can start editing the page by modifying `pages/index.js`. The page auto-upda
`css/prism.css` - controls the styles associated with the code blocks. Feel free to customize it and use your preferred prismjs theme e.g. [prism themes](https://github.com/PrismJS/prism-themes).
`components/social-icons` - to add other icons, simply copy an svg file from [Simple Icons](https://simpleicons.org/) and map them in `index.js`. Other icons uses [heroicons](https://heroicons.com/).
`components/social-icons` - to add other icons, simply copy an svg file from [Simple Icons](https://simpleicons.org/) and map them in `index.js`. Other icons use [heroicons](https://heroicons.com/).
`components/MDXComponents.js` - pass your own JSX code or React component by specifying it over here. You can then call them directly in the `.mdx` or `.md` file. By default, a custom link and image component is passed.
@ -172,14 +172,14 @@ Follow the interactive prompt to generate a post with pre-filled front matter.
**Vercel**
The easiest way to deploy the template is to use the [Vercel Platform](https://vercel.com) from the creators of Next.js. Check out the [Next.js deployment documentation](https://nextjs.org/docs/deployment) for more details.
**Netlify / Github Pages / Firebase etc.**
As the template uses `next/image` for image optimization, additional configurations has to be made to deploy on other popular static hosting websites like [Netlify](https://www.netlify.com/) or [Github Pages](https://pages.github.com/). An alternative image optimization provider such as Imgix, Cloudinary or Akamai has to be used. Alternatively, replace the `next/image` component with a standard `<img>` tag. See [`next/image` documentation](https://nextjs.org/docs/basic-features/image-optimization) for more details.
**Netlify / GitHub Pages / Firebase etc.**
As the template uses `next/image` for image optimization, additional configurations have to be made to deploy on other popular static hosting websites like [Netlify](https://www.netlify.com/) or [GitHub Pages](https://pages.github.com/). An alternative image optimization provider such as Imgix, Cloudinary or Akamai has to be used. Alternatively, replace the `next/image` component with a standard `<img>` tag. See [`next/image` documentation](https://nextjs.org/docs/basic-features/image-optimization) for more details.
The API routes used in the newsletter component cannot be used in a static site export. You will need to use a form API endpoint provider and substitute the route in the newsletter component accordingly. Other hosting platforms such as Netlify also offer alternative solutions - please refer to their docs for more information.
## Support
Using the template? Support this effort by giving a star on Github, sharing your own blog and giving a shoutout on Twitter or be a project [sponsor](https://github.com/sponsors/timlrx).
Using the template? Support this effort by giving a star on GitHub, sharing your own blog and giving a shoutout on Twitter or be a project [sponsor](https://github.com/sponsors/timlrx).
## Licence

6
data/blog/nested-route/introducing-multi-part-posts-with-nested-routing.md
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@ -18,13 +18,13 @@ We use Next.js catch all routes to handle the routing and path creations.
## Use Cases
Here's some reasons to use nested routes
Here are some reasons to use nested routes
- More logical content organisation (blogs will still be displayed based on the created date)
- Multi-part posts
- Different sub-routes for each author
- Internationalization (though it would be recommended to use [Next.js built in i8n routing](https://nextjs.org/docs/advanced-features/i18n-routing))
- Internationalization (though it would be recommended to use [Next.js built-in i8n routing](https://nextjs.org/docs/advanced-features/i18n-routing))
## Note
- The previous/next post links at bottom of the template is currently sorted by date. One could explore modifying the template to refer the reader to the previous/next post in the series, rather than by date.
- The previous/next post links at bottom of the template are currently sorted by date. One could explore modifying the template to refer the reader to the previous/next post in the series, rather than by date.

26
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@ -70,7 +70,7 @@ The default configuration resolves all components relative to the `components` d
**Note**:
Components which require external image loaders also require additional esbuild configuration.
Components which are dependent on global application state on lifecycle like the Nextjs `Link` component would also not work with this setup as each mdx file is built indepedently.
Components which are dependent on global application state on lifecycle like the Nextjs `Link` component would also not work with this setup as each mdx file is built independently.
For such cases, it is better to use component substitution.
## Table of contents component
@ -166,13 +166,13 @@ export const MDXLayoutRenderer = ({ layout, mdxSource, ...rest }) => {
}
```
Use the `MDXLayoutRenderer` component in a page where you want to accept a layout name to map to the desired layout.
Use the `MDXLayoutRenderer` component on a page where you want to accept a layout name to map to the desired layout.
You need to pass the layout name from the layout folder (it has to be an exact match).
## Analytics
The template now supports [plausible](https://plausible.io/), [simple analytics](https://simpleanalytics.com/) and google analytics.
Configure `siteMetadata.js` with the settings that correpond with the desired analytics provider.
Configure `siteMetadata.js` with the settings that correspond with the desired analytics provider.
```js
analytics: {
@ -241,7 +241,7 @@ comment: {
Information on authors is now split from `siteMetadata.js` and stored in its own `data/authors` folder as a markdown file. Minimally, you will need to have a `default.md` file with authorship information. You can create additional files as required and the file name will be used as the reference to the author.
Here's how an author markdown file might looks like:
Here's how an author markdown file might look like:
```md:default.md
---
@ -268,7 +268,7 @@ This is rendered in the `AuthorLayout` template.
### Multiple authors in blog post
The frontmatter of a blog post accepts an optional `authors` arrray field. If no field is specified, it is assumed that the default author is used. Simply pass in an array of authors to render multiple authors associated with post.
The frontmatter of a blog post accepts an optional `authors` array field. If no field is specified, it is assumed that the default author is used. Simply pass in an array of authors to render multiple authors associated with a post.
For example, the following frontmatter will display the authors given by `data/authors/default.md` and `data/authors/sparrowhawk.md`
@ -280,16 +280,16 @@ summary: 'My first post'
authors: ['default', 'sparrowhawk']
```
A demo of a multiple author post is shown in [Introducing Tailwind Nextjs Starter Blog post](/blog/introducing-tailwind-nextjs-starter-blog).
A demo of a multiple authors post is shown in [Introducing Tailwind Nextjs Starter Blog post](/blog/introducing-tailwind-nextjs-starter-blog).
## Copy button for code blocks
Hover over a code block and you will notice a Github inspired copy button! You can modify `./components/Pre.js` to further customise it.
Hover over a code block and you will notice a GitHub-inspired copy button! You can modify `./components/Pre.js` to further customise it.
The component is passed to `MDXComponents` and modifies all `<pre>` blocks.
## Line highlighting and line numbers
Line highlighting and line numbers is now supported out of the box thanks to the new [rehype-prism-plus plugin](https://github.com/timlrx/rehype-prism-plus)
Line highlighting and line numbers are now supported out of the box thanks to the new [rehype-prism-plus plugin](https://github.com/timlrx/rehype-prism-plus)
The following javascript code block:
@ -344,13 +344,13 @@ To modify the styles, change the following class selectors in the `prism.css` fi
## Newletter component (v1.1.3)
Introduced in v1.1.3, the newsletter component gives you a easy way to build an audience. It integrates with the following providers:
Introduced in v1.1.3, the newsletter component gives you an easy way to build an audience. It integrates with the following providers:
- [Mailchimp](https://mailchimp.com/)
- [Buttondown](https://buttondown.email/)
- [Convertkit](https://convertkit.com/)
To use it, specify the provider which you are using in the config file and add the necessary environmental variables to the `.env` file.
To use it, specify the provider which you are using in the config file and add the necessary environment variables to the `.env` file.
For more information on the required variables, check out `.env.sample.`
Two components are exported, a default `NewsletterForm` and a `BlogNewsletterForm` component, which is also passed in as an MDX component
@ -403,11 +403,11 @@ See [rehype-citation readme](https://github.com/timlrx/rehype-citation) for more
There are significant portions of the code that has been changed from v0 to v1 including support for layouts and a new mdx engine.
There's also no real reason to change if the previous one serves your needs and it might be easier to copy
the component changes you are interested to your existing blog rather than migrating everything over.
the component changes you are interested in to your existing blog rather than migrating everything over.
Nonetheless, if you want to do so and have not changed much of the template, you could clone the new version and copy over the blog post over to the new template.
Another alternative would be to pull the latest tempate version with the following code:
Another alternative would be to pull the latest template version with the following code:
```bash
git remote add template git@github.com:timlrx/tailwind-nextjs-starter-blog.git
@ -417,7 +417,7 @@ rm -rf node_modules
You can see an example of such a migration in this [commit](https://github.com/timlrx/timlrx.com/commit/bba1c185384fd6d5cdaac15abf802fdcff027286) for my personal blog.
v1 also uses `feed.xml` rather than `index.xml`, to avoid some build issues with vercel. If you are migrating you should add a redirect to `next.config.js` like so:
v1 also uses `feed.xml` rather than `index.xml`, to avoid some build issues with Vercel. If you are migrating you should add a redirect to `next.config.js` like so:
```
async redirects() {