More on Productivity
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:
- 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.
- Instructions for using Obsidian, managing notes, reading lists, and useful plugins. This section demonstrates how I use Obsidian, my preferred knowledge management tool.
- 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:
- It had to be private, and nobody had to be able to read the entries.
- 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
Aldric Chen
3 years ago
Jack Dorsey's Meeting Best Practice was something I tried. It Performs Exceptionally Well in Consulting Engagements.
Yes, client meetings are difficult. Especially when I'm alone.
Clients must tell us their problems so we can help.
In-meeting challenges contribute nothing to our work. Consider this:
Clients are unprepared.
Clients are distracted.
Clients are confused.
Introducing Jack Dorsey's Google Doc approach
I endorse his approach to meetings.
Not Google Doc-related. Jack uses it for meetings.
This is what his meetings look like.
Prior to the meeting, the Chair creates the agenda, structure, and information using Google Doc.
Participants in the meeting would have 5-10 minutes to read the Google Doc.
They have 5-10 minutes to type their comments on the document.
In-depth discussion begins
There is elegance in simplicity. Here's how Jack's approach is fantastic.
Unprepared clients are given time to read.
During the meeting, they think and work on it.
They can see real-time remarks from others.
Discussion ensues.
Three months ago, I fell for this strategy. After trying it with a client, I got good results.
I conducted social control experiments in a few client workshops.
Context matters.
I am sure Jack Dorsey’s method works well in meetings. What about client workshops?
So, I tested Enterprise of the Future with a consulting client.
I sent multiple emails to client stakeholders describing the new approach.
No PowerPoints that day. I spent the night setting up the Google Doc with conversation topics, critical thinking questions, and a Before and After section.
The client was shocked. First, a Google Doc was projected. Second surprise was a verbal feedback.
“No pre-meeting materials?”
“Don’t worry. I know you are not reading it before our meeting, anyway.”
We laughed. The experiment started.
Observations throughout a 90-minute engagement workshop from beginning to end
For 10 minutes, the workshop was silent.
People read the Google Doc. For some, the silence was unnerving.
“Are you not going to present anything to us?”
I said everything's in Google Doc. I asked them to read, remark, and add relevant paragraphs.
As they unlocked their laptops, they were annoyed.
Ten client stakeholders are typing on the Google Doc. My laptop displays comment bubbles, red lines, new paragraphs, and strikethroughs.
The first 10 minutes were productive. Everyone has seen and contributed to the document.
I was silent.
The move to a classical workshop was smooth. I didn't stimulate dialogue. They did.
Stephanie asked Joe why a blended workforce hinders company productivity. She questioned his comments and additional paragraphs.
That is when a light bulb hit my head. Yes, you want to speak to the right person to resolve issues!
Not only that was discussed. Others discussed their remark bubbles with neighbors. Debate circles sprung up one after the other.
The best part? I asked everyone to add their post-discussion thoughts on a Google Doc.
After the workshop, I have:
An agreement-based working document
A post-discussion minutes that are prepared for publication
A record of the discussion points that were brought up, argued, and evaluated critically
It showed me how stakeholders viewed their Enterprise of the Future. It allowed me to align with them.
Finale Keynotes
Client meetings are a hit-or-miss. I know that.
Jack Dorsey's meeting strategy works for consulting. It promotes session alignment.
It relieves clients of preparation.
I get the necessary information to advance this consulting engagement.
It is brilliant.
Jon Brosio
3 years ago
Every time I use this 6-part email sequence, I almost always make four figures.
(And you can have it for free)
Master email to sell anything.
Most novice creators don't know how to begin.
Many use online templates. These are usually fluff-filled and niche-specific.
They're robotic and "salesy."
I've attended 3 courses, read 10 books, and sent 600,000 emails in the past five years.
Outcome?
This *proven* email sequence assures me a month's salary every time I send it.
What you will discover in this article is that:
A full 6-part email sales cycle
The essential elements you must incorporate
placeholders and text-filled images
(Applies to any niche)
This can be a product introduction, holiday, or welcome sequence. This works for email-saleable products.
Let's start
Email 1: Describe your issue
This email is crucial.
How to? We introduce a subscriber or prospect's problem. Later, we'll frame our offer as the solution.
Label the:
Problem
Why it still hasn't been fixed
Resulting implications for the customer
This puts our new subscriber in solve mode and queues our offer:
Email 2: Amplify the consequences
We're still causing problems.
We've created the problem, but now we must employ emotion and storytelling to make it real. We also want to forecast life if nothing changes.
Let's feel:
What occurs if it is not resolved?
Why is it crucial to fix it immediately?
Tell a tale of a person who was in their position. To emphasize the effects, use a true account of another person (or of yourself):
Email 3: Share a transformation story
Selling stories.
Whether in an email, landing page, article, or video. Humanize stories. They give information meaning.
This is where "issue" becomes "solution."
Let's reveal:
A tale of success
A new existence and result
tools and tactics employed
Start by transforming yourself.
Email 4: Prove with testimonials
No one buys what you say.
Emotionally stirred people buy and act. They believe in the product. They feel that if they buy, it will work.
Social proof shows prospects that your solution will help them.
Add:
Earlier and Later
Testimonials
Reviews
Proof this deal works:
Email 5: Reveal your offer
It's showtime.
This is it. Until now, describing the offer and offering links to a landing page have been sparse in the email pictures.
We've been tense. Gaining steam. Building suspense. Email 5 reveals all.
In this email:
a description of the deal
A word about a promise
recapitulation of the transformation
and make a reference to the urgency Everything should be spelled out clearly:
Email no. 6: Instill urgency
When there are stakes, humans act.
Creating and marketing with haste raises the stakes. Urgency makes a prospect act because they'll miss out or gain immensely.
Urgency converts. Use:
short time
Screening
Scarcity
Urgency and conversions. Limited-time offers are easy.
TL;DR
Use this proven 6-part email sequence (that turns subscribers into profit):
Introduce a problem
Amplify it with emotions
Share transformation story
Prove it works with testimonials
Value-stack and present your offer
Drive urgency and entice the purchase
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Emma Jade
3 years ago
6 hacks to create content faster
Content gurus' top time-saving hacks.
I'm a content strategist, writer, and graphic designer. Time is more valuable than money.
Money is always available. Even if you're poor. Ways exist.
Time is passing, and one day we'll run out.
Sorry to be morbid.
In today's digital age, you need to optimize how you create content for your organization. Here are six content creation hacks.
1. Use templates
Use templates to streamline your work whether generating video, images, or documents.
Setup can take hours. Using a free resource like Canva, you can create templates for any type of material.
This will save you hours each month.
2. Make a content calendar
You post without a plan? A content calendar solves 50% of these problems.
You can prepare, organize, and plan your material ahead of time so you're not scrambling when you remember, "Shit, it's Mother's Day!"
3. Content Batching
Batching content means creating a lot in one session. This is helpful for video content that requires a lot of setup time.
Batching monthly content saves hours. Time is a valuable resource.
When working on one type of task, it's easy to get into a flow state. This saves time.
4. Write Caption
On social media, we generally choose the image first and then the caption. Writing captions first sometimes work better, though.
Writing the captions first can allow you more creative flexibility and be easier if you're not excellent with language.
Say you want to tell your followers something interesting.
Writing a caption first is easier than choosing an image and then writing a caption to match.
Not everything works. You may have already-created content that needs captioning. When you don't know what to share, think of a concept, write the description, and then produce a video or graphic.
Cats can be skinned in several ways..
5. Repurpose
Reuse content when possible. You don't always require new stuff. In fact, you’re pretty stupid if you do #SorryNotSorry.
Repurpose old content. All those blog entries, videos, and unfinished content on your desk or hard drive.
This blog post can be turned into a social media infographic. Canva's motion graphic function can animate it. I can record a YouTube video regarding this issue for a podcast. I can make a post on each point in this blog post and turn it into an eBook or paid course.
And it doesn’t stop there.
My point is, to think outside the box and really dig deep into ways you can leverage the content you’ve already created.
6. Schedule Them
If you're still manually posting content, get help. When you batch your content, schedule it ahead of time.
Some scheduling apps are free or cheap. No excuses.
Don't publish and ghost.
Scheduling saves time by preventing you from doing it manually. But if you never engage with your audience, the algorithm won't reward your material.
Be online and engage your audience.
Content Machine
Use these six content creation hacks. They help you succeed and save time.
Owolabi Judah
3 years ago
How much did YouTube pay for 10 million views?
Ali's $1,054,053.74 YouTube Adsense haul.
YouTuber, entrepreneur, and former doctor Ali Abdaal. He began filming productivity and financial videos in 2017. Ali Abdaal has 3 million YouTube subscribers and has crossed $1 million in AdSense revenue. Crazy, no?
Ali will share the revenue of his top 5 youtube videos, things he's learned that you can apply to your side hustle, and how many views it takes to make a livelihood off youtube.
First, "The Long Game."
All good things take time to bear fruit. Compounding improves everything. Long-term work yields better returns. Ali made his first dollar after nine months and 85 videos.
Second, "One piece of content can transform your life, but you never know which one."
Had he abandoned YouTube at 84 videos without making any money, he wouldn't have filmed the 85th video that altered everything.
Third Lesson: Your Industry Choice Can Multiply.
The industry or niche you target as a business owner or side hustler can have a major impact on how much money you make.
Here are the top 5 videos.
1) 9.8m views: $191,258.16 for 9 passive income ideas
Ali made 2 points.
We should consider YouTube videos digital assets. They're investments, which make us money. His investments are yielding passive income.
Investing extra time and effort in your films can pay off.
2) How to Invest for Beginners — 5.2m Views: $87,200.08.
This video did poorly in the first several weeks after it was published; it was his tenth poorest performer. Don't worry about things you can't control. This applies to life, not just YouTube videos.
He stated we constantly have anxieties, fears, and concerns about things outside our control, but if we can find that line, life is easier and more pleasurable.
3) How to Build a Website in 2022— 866.3k views: $42,132.72.
The RPM was $48.86 per thousand views, making it his highest-earning video. Squarespace, Wix, and other website builders are trying to put ads on it and competing against one other, so ad rates go up.
Because it was beyond his niche, Ali almost didn't make the video. He made the video because he wanted to help at least one person.
4) How I take notes on my iPad in medical school — 5.9m views: $24,479.80
85th video. It's the video that affected Ali's YouTube channel and his life the most. The video's success wasn't certain.
5) How I Type Fast 156 Words Per Minute — 8.2M views: $25,143.17
Ali didn't know this video would perform well; he made it because he can type fast and has been practicing for 10 years. So he made a video with his best advice.
How many views to different wealth levels?
It depends on geography, niche, and other monetization sources. To keep things simple, he would solely utilize AdSense.
How many views to generate money?
To generate money on Youtube, you need 1,000 subscribers and 4,000 hours of view time. How much work do you need to make pocket money?
Ali's first 1,000 subscribers took 52 videos and 6 months. The typical channel with 1,000 subscribers contains 152 videos, according to Tubebuddy. It's time-consuming.
After monetizing, you'll need 15,000 views/month to make $5-$10/day.
How many views to go part-time?
Say you make $35,000/year at your day job. If you work 5 days/week, you make $7,000/year each day. If you want to drop down from 5 days to 4 days/week, you need to make an extra $7,000/year from YouTube, or $600/month.
What's the quit-your-job budget?
Silicon Valley Girl is in a highly successful niche targeting tech-focused folks in the west. When her channel had 500k views/month, she made roughly $3,000/month or $47,000/year, enough to quit your work.
Marina has another 1.5m subscriber channel in Russia, which has a lower rpm because fewer corporations advertise there than in the west. 2.3 million views/month is $4,000/month or $50,000/year, enough to quit your employment.
Marina is an intriguing example because she has three YouTube channels with the same skills, but one is 16x more profitable due to the niche she chose.
In Ali's case, he made 100+ videos when his channel was producing enough money to quit his job, roughly $4,000/month.
How many views make you rich?
Depending on how you define rich. Ali felt prosperous with over $100,000/year and 3–5m views/month.
Conclusion
YouTubers and artists don't treat their work like a company, which is a mistake. Businesses have been attempting to figure this out for decades, if not centuries.
We can learn from the business world how to monetize YouTube, Instagram, and Tiktok and make them into sustainable enterprises where we can hire people and delegate tasks.
Bonus
Watch Ali's video explaining all this:
This post is a summary. Read the full article here
Shalitha Suranga
3 years ago
The Top 5 Mathematical Concepts Every Programmer Needs to Know
Using math to write efficient code in any language
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.
Inbuilt max and min functions can minimize verbose if statements.
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.
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):
Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.
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.