#set page(
  paper: "us-letter",
  header: align(center, text(17pt)[
    *Gravitational wave*
  ]),
  numbering: "1",
)

#set heading(numbering: "1.")

#outline(
  indent: 1em
)

#set text(
  font: "Times New Roman",
  size: 11pt
)

#set par(justify: true)

= Introduction

Almost every references I read on gravitational wave start with some tensor algebras and basica general relativity (GR). While I do not have problem with those presentations, I reckon that is not how I would teach myself. From a theorist perspective, learning about GW is like building a lego tower, you have to start with the foundation and work your way up. This is great for building a solid foundation(assuming you go over all the exercise), but I feel like I never know where I am going, especially when it is being taught in a multiple weeks or even semester class. 
To me, it is more important to have the entire blueprint of the course in front of me first. I need to know the map of navigating through different sections of the lecture and how they are related to one another before I know how to get there. I often tell myself or say in a lecture: "this is some detail we will revisit later". And this is exactly what I am going to write this lecture note. And the fun part of this way going through the material is you get to be the driver as well. To start with, just read this introduction and maybe the second chapter for some basic information, then you can decide which part of this lecture interested you most and dig in. I try to make this lecture as nonlinear as possible. We are not building a tower from the ground up, it is more like we are going into a theme park or a zoo, you should be able to pick whatever interested you the most and go wild. There will be some sections that are prerequesite for others, but I will note that down in each section such that you know how to navigate between them.

We are going to start with some observational properties about GW, such as what is the data we are looking at, how GW interact with detectors, and how are the features in the data related to the source properties. Then, we are going to take a tour of how do we extract information from a signal stream and relate that to properties of the source. We are then going to go through a bit more detail in how gravitational wave model are represented in the form of a waveform model. After that, we are jumping a bit into the guts of different kinds of GW detectors. At this point, you actually have most of the ingridients to start a summer research project.
Then we are going a bit more hardcore into different type of sources that might be interesting if you care about GW.


Now I fully understand my style of writing could be confusing to some people, and it is almost certainly less structured than other materials. I like to try new things does not mean the new things are inherently better. I encourage the readers to also read through some other more estabilish materials such as, especially when you need to quote or cite some establish facts.

= Observational properties of gravitational wave

= Solving parameter estimation problems

= Basic Waveform model

= Gravitational wave detectors

== Ground-based Interferometers
== Space-based Interferometers
== Pulsar timing array
== Cosmic microwave background inprints

= Source models
== Vanilla black holes
== Binary neutron stars

= Making of waveform models

= Finally General relativity and numerical relativity

= Beyond general relativity
== Lensing
== nonGR effect

= Population models
