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I am a math enthusiast. I am now feeling strong interest in bitcoin technology and key research areas. I would like to know what mathematics sub areas are required for bitcoin technology. I am more interested to the application side of bitcoin. For example corporate governance.

denim
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    I don't see what corporate governance has to do with a currency. – Pieter Wuille Dec 10 '21 at 21:00
  • I mean actually the decentralized autonomous organization (DAO) – denim Dec 12 '21 at 20:18
  • You may have better luck on https://ethereum.stackexchange.com; there are no DAOs on Bitcoin. – Pieter Wuille Dec 12 '21 at 20:29
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    SHA-256, RIPEMD-160, ECDSA, SECP256K1, PBKDF2, HMAC-SHA512, BASE58, Blockchain, Proof of Work, Linked List, Hash Table, and Hash Set are some keywords you can research. – Brandon Dec 15 '21 at 06:20
  • @Brandon. Thanks ! You mean that data structures and cryptography are the main focus? – denim Dec 16 '21 at 17:21
  • @denim, yes, after you are comfortable with the primitives you can move on to layer 2 solutions such as the Lighting Network which will require you to know about Payment Channels, Watch Towers, Onion Routing, and Pickhardt Payments. You will also want to know how BIP32 and BIP39 are used to grow a wallet from a seed. Schnorr and SegWit are also very important concepts to understand. An easy way to get a tour of every topic mentioned is to just watch Andreas Antonopoulos videos. But you will have to work out some math problems too. – Brandon Dec 19 '21 at 05:03
  • @Brandon, I see some of the videos of Antonopoulos about bitcoin. However i find most of the lectures are on abstract talks without deep technical details. Therefore i am looking to find some resources for the understanding of Bitcoin technologies ( e.g data structures, networks, payments etc. ) from the computer science engineering point of view. Could you please suggest some of the resources such as lecture notes and textbooks for this purpose? Thanks in advance ! – denim Feb 05 '22 at 11:50
  • @denim, "Mastering Bitcoin" and "Mastering the Lighting Network" Andreas Antonopoulos is likely what you are after. The are both open source and free on github. https://www.youtube.com/c/RenePickhardt is another great resource if you want to listen to lectures by a Bitcoin developer. Another good way to find lectures is to filter a YouTube search by videos longer than 20 minutes. Reading old posts from https://bitcointalk.org/ should get you the rest of the way. You need to know game theory, computer science, and crypto primitives for it all to make sense. – Brandon Feb 07 '22 at 08:19
  • @Brandon, Thanks again ! I understand as you mention that cryptography and Game theory are essentials. In computer science do you mean Computer networks and operating systems along with Data structures and algorithms? – denim Feb 07 '22 at 15:18
  • Well computer science is the study of algorithms and data structures. Bitcoin requires a network to operate, not necessarily the Internet, but some mechanism of transferring data between nodes, otherwise its centralized. If you are talking about data transfer you could read about blockstream satellites, SSL, TCP/IP, onion routing, bit torrent protocol, and BTC over HAM radio. Alternatively, the byzantine generals problem, feedback loops (markov chains applied to game theory), network effects (such as the electrical grid, internet, email, or cell phone service) deal with graph theory networks. – Brandon Feb 08 '22 at 01:44

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