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Pen Magnet

Pen Magnet

3 years ago

Why Google Staff Doesn't Work

More on Productivity

Mickey Mellen

Mickey Mellen

2 years ago

Shifting from Obsidian to Tana?

I relocated my notes database from Roam Research to Obsidian earlier this year expecting to stay there for a long. Obsidian is a terrific tool, and I explained my move in that post.

Moving everything to Tana faster than intended. Tana? Why?

Tana is just another note-taking app, but it does it differently. Three note-taking apps existed before Tana:

  1. simple note-taking programs like Apple Notes and Google Keep.

  2. Roam Research and Obsidian are two graph-style applications that assisted connect your notes.

  3. You can create effective tables and charts with data-focused tools like Notion and Airtable.

Tana is the first great software I've encountered that combines graph and data notes. Google Keep will certainly remain my rapid notes app of preference. This Shu Omi video gives a good overview:

Tana handles everything I did in Obsidian with books, people, and blog entries, plus more. I can find book quotes, log my workouts, and connect my thoughts more easily. It should make writing blog entries notes easier, so we'll see.

Tana is now invite-only, but if you're interested, visit their site and sign up. As Shu noted in the video above, the product hasn't been published yet but seems quite polished.

Whether I stay with Tana or not, I'm excited to see where these apps are going and how they can benefit us all.

David G Chen

David G Chen

3 years ago

If you want to earn money, stop writing for entertainment.

When you stop blogging for a few weeks, your views and profits plummet.

Because you're writing fascinating posts for others. Everyone's done ithat…

My medium stats for May-June

If I keep writing, the graph should maintain velocity, you could say. If I wrote more, it could rise.

However, entertaining pieces still tend to roller coaster and jump.

this type of writing is like a candle. They burn out and must be replaced. You must continuously light new ones to maintain the illumination.

When you quit writing, your income stops.

A substitute

Instead of producing amusing articles, try solving people's issues. You should answer their search questions.

Here's what happens when you answer their searches.

Website stats by pageviews per day

My website's Google analytics. As a dentist, I answer oral health questions.

This chart vs. Medium is pretty glaring, right?

As of yesterday, it was averaging 15k page views each day.

How much would you make on Medium with 15k daily views?

Evergreen materials

In SEO, this is called evergreen content.

Your content is like a lush, evergreen forest, and by green I mean Benjamins.

Photo by Alexander Mils on Unsplash

Do you have knowledge that you can leverage? Why not help your neighbors and the world?

Answer search inquiries and help others. You'll be well rewarded.

This is better than crafting candle-like content that fizzles out quickly.

Is beauty really ephemeral like how flowers bloom? Nah, I prefer watching forests grow instead (:

Leonardo Castorina

Leonardo Castorina

3 years ago

How to Use Obsidian to Boost Research Productivity

Tools for managing your PhD projects, reading lists, notes, and inspiration.

As a researcher, you have to know everything. But knowledge is useless if it cannot be accessed quickly. An easy-to-use method of archiving information makes taking notes effortless and enjoyable.
As a PhD student in Artificial Intelligence, I use Obsidian (https://obsidian.md) to manage my knowledge.

The article has three parts:

  1. What is a note, how to organize notes, tags, folders, and links? This section is tool-agnostic, so you can use most of these ideas with any note-taking app.
  2. Instructions for using Obsidian, managing notes, reading lists, and useful plugins. This section demonstrates how I use Obsidian, my preferred knowledge management tool.
  3. Workflows: How to use Zotero to take notes from papers, manage multiple projects' notes, create MOCs with Dataview, and more. This section explains how to use Obsidian to solve common scientific problems and manage/maintain your knowledge effectively.

This list is not perfect or complete, but it is my current solution to problems I've encountered during my PhD. Please leave additional comments or contact me if you have any feedback. I'll try to update this article.
Throughout the article, I'll refer to your digital library as your "Obsidian Vault" or "Zettelkasten".
Other useful resources are listed at the end of the article.

1. Philosophy: Taking and organizing notes

Carl Sagan: “To make an apple pie from scratch, you must first create the universe.”

Before diving into Obsidian, let's establish a Personal Knowledge Management System and a Zettelkasten. You can skip to Section 2 if you already know these terms.
Niklas Luhmann, a prolific sociologist who wrote 400 papers and 70 books, inspired this section and much of Zettelkasten. Zettelkasten means “slip box” (or library in this article). His Zettlekasten had around 90000 physical notes, which can be found here.
There are now many tools available to help with this process. Obsidian's website has a good introduction section: https://publish.obsidian.md/hub/

Notes

We'll start with "What is a note?" Although it may seem trivial, the answer depends on the topic or your note-taking style. The idea is that a note is as “atomic” (i.e. You should read the note and get the idea right away.
The resolution of your notes depends on their detail. Deep Learning, for example, could be a general description of Neural Networks, with a few notes on the various architectures (eg. Recurrent Neural Networks, Convolutional Neural Networks etc..).
Limiting length and detail is a good rule of thumb. If you need more detail in a specific section of this note, break it up into smaller notes. Deep Learning now has three notes:

  • Deep Learning
  • Recurrent Neural Networks
    - Convolutional Neural Networks

Repeat this step as needed until you achieve the desired granularity. You might want to put these notes in a “Neural Networks” folder because they are all about the same thing. But there's a better way:

#Tags and [[Links]] over /Folders/

The main issue with folders is that they are not flexible and assume that all notes in the folder belong to a single category. This makes it difficult to make connections between topics.
Deep Learning has been used to predict protein structure (AlphaFold) and classify images (ImageNet). Imagine a folder structure like this:

- /Proteins/ 
     - Protein Folding
- /Deep Learning/
     - /Proteins/ 

Your notes about Protein Folding and Convolutional Neural Networks will be separate, and you won't be able to find them in the same folder.
This can be solved in several ways. The most common one is to use tags rather than folders. A note can be grouped with multiple topics this way. Obsidian tags can also be nested (have subtags).

You can also link two notes together. You can build your “Knowledge Graph” in Obsidian and other note-taking apps like Obsidian.


My Knowledge Graph. Green: Biology, Red: Machine Learning, Yellow: Autoencoders, Blue: Graphs, Brown: Tags.


My Knowledge Graph and the note “Backrpropagation” and its links.


Backpropagation note and all its links

Why use Folders?

Folders help organize your vault as it grows. The main suggestion is to have few folders that "weakly" collect groups of notes or better yet, notes from different sources.
Among my Zettelkasten folders are:


My Zettelkasten's 5 folders

They usually gather data from various sources:

MOC: Map of Contents for the Zettelkasten.
Projects: Contains one note for each side-project of my PhD where I log my progress and ideas. Notes are linked to these.
Bio and ML: These two are the main content of my Zettelkasten and could theoretically be combined.
Papers: All my scientific paper notes go here. A bibliography links the notes. Zotero .bib file
Books: I make a note for each book I read, which I then split into multiple notes.

Keeping images separate from other files can help keep your main folders clean.

I will elaborate on these in the Workflow Section.

My general recommendation is to use tags and links instead of folders.

Maps of Content (MOC) 

Making Tables of Contents is a good solution (MOCs).
These are notes that "signposts" your Zettelkasten library, directing you to the right type of notes. It can link to other notes based on common tags. This is usually done with a title, then your notes related to that title. As an example:

An example of a Machine Learning MOC generated with Dataview.

As shown above, my Machine Learning MOC begins with the basics. Then it's on to Variational Auto-Encoders. Not only does this save time, but it also saves scrolling through the tag search section.
So I keep MOCs at the top of my library so I can quickly find information and see my library. These MOCs are generated automatically using an Obsidian Plugin called Dataview (https://github.com/blacksmithgu/obsidian-dataview).
Ideally, MOCs could be expanded to include more information about the notes, their status, and what's left to do. In the absence of this, Dataview does a fantastic job at creating a good structure for your notes.
In the absence of this, Dataview does a fantastic job at creating a good structure for your notes.

2. Tools: Knowing Obsidian

Obsidian is my preferred tool because it is free, all notes are stored in Markdown format, and each panel can be dragged and dropped. You can get it here: https://obsidian.md/

Obsidian interface. 

Obsidian is highly customizable, so here is my preferred interface:


The theme is customized from https://github.com/colineckert/obsidian-things

Alternatively, each panel can be collapsed, moved, or removed as desired. To open a panel later, click on the vertical "..." (bottom left of the note panel).

My interface is organized as follows:

How my Obsidian Interface is organized.

Folders/Search:
This is where I keep all relevant folders. I usually use the MOC note to navigate, but sometimes I use the search button to find a note.

Tags:
I use nested tags and look into each one to find specific notes to link.

cMenu:
Easy-to-use menu plugin cMenu (https://github.com/chetachiezikeuzor/cMenu-Plugin)

Global Graph:
The global graph shows all your notes (linked and unlinked). Linked notes will appear closer together. Zoom in to read each note's title. It's a bit overwhelming at first, but as your library grows, you get used to the positions and start thinking of new connections between notes.

Local Graph:
Your current note will be shown in relation to other linked notes in your library. When needed, you can quickly jump to another link and back to the current note.

Links:
Finally, an outline panel and the plugin Obsidian Power Search (https://github.com/aviral-batra/obsidian-power-search) allow me to search my vault by highlighting text.

Start using the tool and worry about panel positioning later. I encourage you to find the best use-case for your library.

Plugins

An additional benefit of using Obsidian is the large plugin library. I use several (Calendar, Citations, Dataview, Templater, Admonition):
Obsidian Calendar Plugin: https://github.com/liamcain
It organizes your notes on a calendar. This is ideal for meeting notes or keeping a journal.

Calendar addon from hans/obsidian-citation-plugin
Obsidian Citation Plugin: https://github.com/hans/
Allows you to cite papers from a.bib file. You can also customize your notes (eg. Title, Authors, Abstract etc..)

Plugin citation from hans/obsidian-citation-plugin
Obsidian Dataview: https://github.com/blacksmithgu/
A powerful plugin that allows you to query your library as a database and generate content automatically. See the MOC section for an example.
Allows you to create notes with specific templates like dates, tags, and headings.

Templater. Obsidian Admonition: https://github.com/valentine195/obsidian-admonition
Blocks allow you to organize your notes.

Plugin warning. Obsidian Admonition (valentine195)
There are many more, but this list should get you started.

3. Workflows: Cool stuff

Here are a few of my workflows for using obsidian for scientific research. This is a list of resources I've found useful for my use-cases. I'll outline and describe them briefly so you can skim them quickly.
3.1 Using Templates to Structure Notes
3.2 Free Note Syncing (Laptop, Phone, Tablet)
3.3 Zotero/Mendeley/JabRef -> Obsidian — Managing Reading Lists
3.4 Projects and Lab Books
3.5 Private Encrypted Diary

3.1 Using Templates to Structure Notes

Plugins: Templater and Dataview (optional).
To take effective notes, you must first make adding new notes as easy as possible. Templates can save you time and give your notes a consistent structure. As an example:


An example of a note using a template.

### [[YOUR MOC]]
# Note Title of your note
**Tags**:: 
**Links**::

The top line links to your knowledge base's Map of Content (MOC) (see previous sections). After the title, I add tags (and a link between the note and the tag) and links to related notes.
To quickly identify all notes that need to be expanded, I add the tag “#todo”. In the “TODO:” section, I list the tasks within the note.
The rest are notes on the topic.
Templater can help you create these templates. For new books, I use the following template:

### [[Books MOC]]
# Title
**Author**:: 
**Date::
**Tags:: 
**Links::


A book template example.

Using a simple query, I can hook Dataview to it.

dataview  
table author as Author, date as “Date Finished”, tags as “Tags”, grade as “Grade”  
from “4. Books”  
SORT grade DESCENDING


using Dataview to query templates.

3.2 Free Note Syncing (Laptop, Phone, Tablet)

No plugins used.

One of my favorite features of Obsidian is the library's self-contained and portable format. Your folder contains everything (plugins included).

Ordinary folders and documents are available as well. There is also a “.obsidian” folder. This contains all your plugins and settings, so you can use it on other devices.
So you can use Google Drive, iCloud, or Dropbox for free as long as you sync your folder (note: your folder should be in your Cloud Folder).

For my iOS and macOS work, I prefer iCloud. You can also use the paid service Obsidian Sync.
3.3 Obsidian — Managing Reading Lists and Notes in Zotero/Mendeley/JabRef
Plugins: Quotes (required).

3.3 Zotero/Mendeley/JabRef -> Obsidian — Taking Notes and Managing Reading Lists of Scientific Papers

My preferred reference manager is Zotero, but this workflow should work with any reference manager that produces a .bib file. This file is exported to my cloud folder so I can access it from any platform.

My Zotero library is tagged as follows:

My reference manager's tags

For readings, I usually search for the tags “!!!” and “To-Read” and select a paper. Annotate the paper next (either on PDF using GoodNotes or on physical paper).
Then I make a paper page using a template in the Citations plugin settings:


An example of my citations template.

Create a new note, open the command list with CMD/CTRL + P, and find the Citations “Insert literature note content in the current pane” to see this lovely view.


Citation generated by the article https://doi.org/10.1101/2022.01.24.22269144

You can then convert your notes to digital. I found that transcribing helped me retain information better.

3.4 Projects and Lab Books

Plugins: Tweaker (required).
PhD students offering advice on thesis writing are common (read as regret). I started asking them what they would have done differently or earlier.

“Deep stuff Leo,” one person said. So my main issue is basic organization, losing track of my tasks and the reasons for them.
As a result, I'd go on other experiments that didn't make sense, and have to reverse engineer my logic for thesis writing. - PhD student now wise Postdoc

Time management requires planning. Keeping track of multiple projects and lab books is difficult during a PhD. How I deal with it:

  • One folder for all my projects
  • One file for each project
    I use a template to create each project
### [[Projects MOC]]  
# <% tp.file.title %>  
**Tags**::  
**Links**::  
**URL**::  
**Project Description**::## Notes:  
### <% tp.file.last_modified_date(“dddd Do MMMM YYYY”) %>  
#### Done:  
#### TODO:  
#### Notes

You can insert a template into a new note with CMD + P and looking for the Templater option.

I then keep adding new days with another template:

### <% tp.file.last_modified_date("dddd Do MMMM YYYY") %>  
#### Done:  
#### TODO:  
#### Notes:

This way you can keep adding days to your project and update with reasonings and things you still have to do and have done. An example below:


Example of project note with timestamped notes.

3.5 Private Encrypted Diary

This is one of my favorite Obsidian uses.
Mini Diary's interface has long frustrated me. After the author archived the project, I looked for a replacement. I had two demands:

  1. It had to be private, and nobody had to be able to read the entries.
  2. Cloud syncing was required for editing on multiple devices.

Then I learned about encrypting the Obsidian folder. Then decrypt and open the folder with Obsidian. Sync the folder as usual.
Use CryptoMator (https://cryptomator.org/). Create an encrypted folder in Cryptomator for your Obsidian vault, set a password, and let it do the rest.
If you need a step-by-step video guide, here it is:

Conclusion

So, I hope this was helpful!
In the first section of the article, we discussed notes and note-taking techniques. We discussed when to use tags and links over folders and when to break up larger notes.
Then we learned about Obsidian, its interface, and some useful plugins like Citations for citing papers and Templater for creating note templates.
Finally, we discussed workflows and how to use Zotero to take notes from scientific papers, as well as managing Lab Books and Private Encrypted Diaries.
Thanks for reading and commenting :)

Read original post here

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Jake Prins

Jake Prins

3 years ago

What are NFTs 2.0 and what issues are they meant to address?

New standards help NFTs reach their full potential.

NFTs 2.0

NFTs lack interoperability and functionality. They have great potential but are mostly speculative. To maximize NFTs, we need flexible smart contracts.

Current requirements are too restrictive.

Most NFTs are based on ERC-721, which makes exchanging them easy. CryptoKitties, a popular online game, used the 2017 standard to demonstrate NFTs' potential.

This simple standard includes a base URI and incremental IDs for tokens. Add the tokenID to the base URI to get the token's metadata.

This let creators collect NFTs. Many NFT projects store metadata on IPFS, a distributed storage network, but others use Google Drive. NFT buyers often don't realize that if the creators delete or move the files, their NFT is just a pointer.

This isn't the standard's biggest issue. There's no way to validate NFT projects.

Creators are one of the most important aspects of art, but nothing is stored on-chain.

ERC-721 contracts only have a name and symbol.

Most of the data on OpenSea's collection pages isn't from the NFT's smart contract. It was added through a platform input field, so it's in the marketplace's database. Other websites may have different NFT information.

In five years, your NFT will be just a name, symbol, and ID.

Your NFT doesn't mention its creators. Although the smart contract has a public key, it doesn't reveal who created it.

The NFT's creators and their reputation are crucial to its value. Think digital fashion and big brands working with well-known designers when more professionals use NFTs. Don't you want them in your NFT?

Would paintings be as valuable if their artists were unknown? Would you believe it's real?

Buying directly from an on-chain artist would reduce scams. Current standards don't allow this data.

Most creator profiles live on centralized marketplaces and could disappear. Current platforms have outpaced underlying standards. The industry's standards are lagging.

For NFTs to grow beyond pointers to a monkey picture file, we may need to use new Web3-based standards.

Introducing NFTs 2.0

Fabian Vogelsteller, creator of ERC-20, developed new web3 standards. He proposed LSP7 Digital Asset and LSP8 Identifiable Digital Asset, also called NFT 2.0.

NFT and token metadata inputs are extendable. Changes to on-chain metadata inputs allow NFTs to evolve. Instead of public keys, the contract can have Universal Profile addresses attached. These profiles show creators' faces and reputations. NFTs can notify asset receivers, automating smart contracts.

LSP7 and LSP8 use ERC725Y. Using a generic data key-value store gives contracts much-needed features:

  • The asset can be customized and made to stand out more by allowing for unlimited data attachment.

  • Recognizing changes to the metadata

  • using a hash reference for metadata rather than a URL reference

This base will allow more metadata customization and upgradeability. These guidelines are:

  • Genuine and Verifiable Now, the creation of an NFT by a specific Universal Profile can be confirmed by smart contracts.

  • Dynamic NFTs can update Flexible & Updatable Metadata, allowing certain things to evolve over time.

  • Protected metadata Now, secure metadata that is readable by smart contracts can be added indefinitely.

  • Better NFTS prevent the locking of NFTs by only being sent to Universal Profiles or a smart contract that can interact with them.

Summary

NFTS standards lack standardization and powering features, limiting the industry.

ERC-721 is the most popular NFT standard, but it only represents incremental tokenIDs without metadata or asset representation. No standard sender-receiver interaction or security measures ensure safe asset transfers.

NFT 2.0 refers to the new LSP7-DigitalAsset and LSP8-IdentifiableDigitalAsset standards.

They have new standards for flexible metadata, secure transfers, asset representation, and interactive transfer.

With NFTs 2.0 and Universal Profiles, creators could build on-chain reputations.

NFTs 2.0 could bring the industry's needed innovation if it wants to move beyond trading profile pictures for speculation.

Alex Mathers

Alex Mathers

3 years ago   Draft

12 practices of the zenith individuals I know

Follow Alex’s Instagram for his drawings and bonus ideas.

Calmness is a vital life skill.

It aids communication. It boosts creativity and performance.

I've studied calm people's habits for years. Commonalities:

Have learned to laugh at themselves.

Those who have something to protect can’t help but make it a very serious business, which drains the energy out of the room.

They are fixated on positive pursuits like making cool things, building a strong physique, and having fun with others rather than on depressing influences like the news and gossip.

Every day, spend at least 20 minutes moving, whether it's walking, yoga, or lifting weights.

Discover ways to take pleasure in life's challenges.

Since perspective is malleable, they change their view.

Set your own needs first.

Stressed people neglect themselves and wonder why they struggle.

Prioritize self-care.

Don't ruin your life to please others.

Make something.

Calm people create more than react.

They love creating beautiful things—paintings, children, relationships, and projects.

Hold your breath, please.

If you're stressed or angry, you may be surprised how much time you spend holding your breath and tightening your belly.

Release, breathe, and relax to find calm.

Stopped rushing.

Rushing is disadvantageous.

Calm people handle life better.

Are attuned to their personal dietary needs.

They avoid junk food and eat foods that keep them healthy, happy, and calm.

Don’t take anything personally.

Stressed people control everything.

Self-conscious.

Calm people put others and their work first.

Keep their surroundings neat.

Maintaining an uplifting and clutter-free environment daily calms the mind.

Minimise negative people.

Calm people are ruthless with their boundaries and avoid negative and drama-prone people.

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

A mathematical expression/formula in the Linux codebase, a screenshot by the author

Inbuilt max and min functions can minimize verbose if statements.

Reducing a verbose nested-if with the min function in Neutralinojs, a screenshot by the author

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

GetWindowRect outputs an LPRECT geometric object, a screenshot by the author

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

The Git codebase defines a function with logarithmic time complexity, a screenshot by the author

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

A utility function that uses ceil, a screenshot by the author

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.