On January 1, "Public Domain Day," thousands of creative works immediately join the public domain. The original creator or copyright holder loses exclusive rights to reproduce, adapt, or publish the work, and anybody can use it. It happens with movies, poems, music, artworks, books (where creative rights endure 70 years beyond the author's death), and sometimes source code.

Public domain creative works open the door to new uses. 400,000 sound recordings from before 1923, including Winnie-the-Pooh, were released this year.  With most of A.A. Milne's 1926 Winnie-the-Pooh characters now available, we're seeing innovative interpretations Milne likely never planned. The ancient hyphenated version of the honey-loving bear is being adapted for a horror movie: "Winnie-the-Pooh: Blood and Honey"... with Pooh and Piglet as the baddies.

Counterintuitively, experimenting and recombination can occasionally increase IP value. Open source movements allow the public to build on (or fork and duplicate) existing technologies. Permissionless innovation helps Android, Linux, and other open source software projects compete. Crypto's success at attracting public development is also due to its support of open source and "remix culture," notably in NFT forums.

Production memes

NFT projects use several IP strategies to establish brands, communities, and content. Some preserve regular IP protections; others offer NFT owners the opportunity to innovate on connected IP; yet others have removed copyright and other IP safeguards.

By using the "Creative Commons Zero" (cc0) license, artists can intentionally select for "no rights reserved." This option permits anyone to benefit from derivative works without legal repercussions. There's still a lot of confusion between copyrights and NFTs, so nothing here should be considered legal, financial, tax, or investment advice. Check out this post for an overview of copyright vulnerabilities with NFTs and how authors can protect owners' rights. This article focuses on cc0.

Nouns, a 2021 project, popularized cc0 for NFTs. Others followed, including: A Common Place, Anonymice, Blitmap, Chain Runners, Cryptoadz, CryptoTeddies, Goblintown, Gradis, Loot, mfers, Mirakai, Shields, and Terrarium Club are cc0 projects.

Popular crypto artist XCOPY licensed their 1-of-1 NFT artwork "Right-click and Save As Guy" under cc0 in January, exactly one month after selling it. cc0 has spawned many derivatives.

"Right-click Save As Guy" by XCOPY (1)/derivative works (2)

XCOPY said Monday he would apply cc0 to "all his existing art." "We haven't seen a cc0 summer yet, but I think it's approaching," said the artist. - predicting a "DeFi summer" in 2020, when decentralized finance gained popularity.

Why do so many NFT authors choose "no rights"?

Promoting expansions of the original project to create a more lively and active community is one rationale. This makes sense in crypto, where many value open sharing and establishing community.

Creativity depends on cultural significance. NFTs may allow verifiable ownership of any digital asset, regardless of license, but cc0 jumpstarts "meme-ability" by actively, not passively, inviting derivative works. As new derivatives are made and shared, attention might flow back to the original, boosting its reputation. This may inspire new interpretations, leading in a flywheel effect where each derivative adds to the original's worth - similar to platform network effects, where platforms become more valuable as more users join them.

cc0 licence allows creators "seize production memes."

"SEASON 1 MEME CARD 2"

Physical items are also using cc0 NFT assets, thus it's not just a digital phenomenon. The Nouns Vision initiative turned the square-framed spectacles shown on each new NounsDAO NFT ("one per day, forever") into luxury sunglasses. Blitmap's pixel-art has been used on shoes, apparel, and caps. In traditional IP regimes, a single owner controls creation, licensing, and production.

The physical "blitcap" (3rd level) is a descendant of the trait in the cc0 Chain Runners collection (2nd), which uses the "logo" from cc0 Blitmap (1st)! The Logo is Blitmap token #84 and has been used as a trait in various collections. The "Dom Rose" is another popular token. These homages reference Blitmap's influence as a cc0 leader, as one of the earliest NFT projects to proclaim public domain intents. A new collection, Citizens of Tajigen, emerged last week with a Blitcap characteristic.

These derivatives can be a win-win for everyone, not just the original inventors, especially when using NFT assets to establish unique brands. As people learn about the derivative, they may become interested in the original. If you see someone wearing Nouns glasses on the street (or in a Super Bowl ad), you may desire a pair, but you may also be interested in buying an original NounsDAO NFT or related derivative.

Blitmap Logo Hat (1), Chain Runners #780 ft. Hat (2), and Blitmap Original "Logo #87" (3)

Co-creating open source

NFTs' power comes from smart contract technology's intrinsic composability. Many smart contracts can be integrated or stacked to generate richer applications.

"Money Legos" describes how decentralized finance ("DeFi") smart contracts interconnect to generate new financial use cases. Yearn communicates with MakerDAO's stablecoin $DAI and exchange liquidity provider Curve by calling public smart contract methods. NFTs and their underlying smart contracts can operate as the base-layer framework for recombining and interconnecting culture and creativity.

cc0 gives an NFT's enthusiast community authority to develop new value layers whenever, wherever, and however they wish.

Multiple cc0 projects are playable characters in HyperLoot, a Loot Project knockoff.

Open source and Linux's rise are parallels. When the internet was young, Microsoft dominated the OS market with Windows. Linux (and its developer Linus Torvalds) championed a community-first mentality, freely available the source code without restrictions. This led to developers worldwide producing new software for Linux, from web servers to databases. As people (and organizations) created world-class open source software, Linux's value proposition grew, leading to explosive development and industry innovation. According to Truelist, Linux powers 96.3% of the top 1 million web servers and 85% of smartphones.

With cc0 licensing empowering NFT community builders, one might hope for long-term innovation. Combining cc0 with NFTs "turns an antagonistic game into a co-operative one," says NounsDAO cofounder punk4156. It's important on several levels. First, decentralized systems from open source to crypto are about trust and coordination, therefore facilitating cooperation is crucial. Second, the dynamics of this cooperation work well in the context of NFTs because giving people ownership over their digital assets allows them to internalize the results of co-creation through the value that accrues to their assets and contributions, which incentivizes them to participate in co-creation in the first place.

Licensed to create

If cc0 projects are open source "applications" or "platforms," then NFT artwork, metadata, and smart contracts provide the "user interface" and the underlying blockchain (e.g., Ethereum) is the "operating system." For these apps to attain Linux-like potential, more infrastructure services must be established and made available so people may take advantage of cc0's remixing capabilities.

These services are developing. Zora protocol and OpenSea's open source Seaport protocol enable open, permissionless NFT marketplaces. A pixel-art-rendering engine was just published on-chain to the Ethereum blockchain and integrated into OKPC and ICE64. Each application improves blockchain's "out-of-the-box" capabilities, leading to new apps created from the improved building blocks.

Web3 developer growth is at an all-time high, yet it's still a small fraction of active software developers globally. As additional developers enter the field, prospective NFT projects may find more creative and infrastructure Legos for cc0 and beyond.

Electric Capital Developer Report (2021), p. 122

Growth requires composability. Users can easily integrate digital assets developed on public standards and compatible infrastructure into other platforms. The Loot Project is one of the first to illustrate decentralized co-creation, worldbuilding, and more in NFTs. This example was low-fi or "incomplete" aesthetically, providing room for imagination and community co-creation.

Loot began with a series of Loot bag NFTs, each listing eight "adventure things" in white writing on a black backdrop (such as Loot Bag #5726's "Katana, Divine Robe, Great Helm, Wool Sash, Divine Slippers, Chain Gloves, Amulet, Gold Ring"). Dom Hofmann's free Loot bags served as a foundation for the community.

Several projects have begun metaphorical (lore) and practical (game development) world-building in a short time, with artists contributing many variations to the collective "Lootverse." They've produced games (Realms & The Crypt), characters (Genesis Project, Hyperloot, Loot Explorers), storytelling initiatives (Banners, OpenQuill), and even infrastructure (The Rift).

Why cc0 and composability? Because consumers own and control Loot bags, they may use them wherever they choose by connecting their crypto wallets. This allows users to participate in multiple derivative projects, such as  Genesis Adventurers, whose characters appear in many others — creating a decentralized franchise not owned by any one corporation.

Genesis Project's Genesis Adventurer (1) with HyperLoot (2) and Loot Explorer (3) versions

When to go cc0

There are several IP development strategies NFT projects can use. When it comes to cc0, it’s important to be realistic. The public domain won't make a project a runaway success just by implementing the license. cc0 works well for NFT initiatives that can develop a rich, enlarged ecosystem.

Many of the most successful cc0 projects have introduced flexible intellectual property. The Nouns brand is as obvious for a beer ad as for real glasses; Loot bags are simple primitives that make sense in all adventure settings; and the Goblintown visual style looks good on dwarfs, zombies, and cranky owls as it does on Val Kilmer.

The ideal cc0 NFT project gives builders the opportunity to add value:

• vertically, by stacking new content and features directly on top of the original cc0 assets (for instance, as with games built on the Loot ecosystem, among others), and

• horizontally, by introducing distinct but related intellectual property that helps propagate the original cc0 project’s brand (as with various Goblintown derivatives, among others).

These actions can assist cc0 NFT business models. Because cc0 NFT projects receive royalties from secondary sales, third-party extensions and derivatives can boost demand for the original assets.

Using cc0 license lowers friction that could hinder brand-reinforcing extensions or lead to them bypassing the original. Robbie Broome recently argued (in the context of his cc0 project A Common Place) that giving away his IP to cc0 avoids bad rehashes down the line. If UrbanOutfitters wanted to put my design on a tee, they could use the actual work instead of hiring a designer. CC0 can turn competition into cooperation.

Community agreement about core assets' value and contribution can help cc0 projects. Cohesion and engagement are key. Using the above examples: Developers can design adventure games around whatever themes and item concepts they desire, but many choose Loot bags because of the Lootverse's community togetherness. Flipmap shared half of its money with the original Blitmap artists in acknowledgment of that project's core role in the community. This can build a healthy culture within a cc0 project ecosystem. Commentator NiftyPins said it was smart to acknowledge the people that constructed their universe. Many OG Blitmap artists have popped into the Flipmap discord to share information.

cc0 isn't a one-size-fits-all answer; NFTs formed around well-established brands may prefer more restrictive licenses to preserve their intellectual property and reinforce exclusivity. cc0 has some superficial similarities to permitting NFT owners to market the IP connected with their NFTs (à la Bored Ape Yacht Club), but there is a significant difference: cc0 holders can't exclude others from utilizing the same IP. This can make it tougher for holders to develop commercial brands on cc0 assets or offer specific rights to partners. Holders can still introduce enlarged intellectual property (such as backstories or derivatives) that they control.

Blockchain technologies and the crypto ethos are decentralized and open-source. This makes it logical for crypto initiatives to build around cc0 content models, which build on the work of the Creative Commons foundation and numerous open source pioneers.

NFT creators that choose cc0 must select how involved they want to be in building the ecosystem. Some cc0 project leaders, like Chain Runners' developers, have kept building on top of the initial cc0 assets, creating an environment derivative projects can plug into. Dom Hofmann stood back from Loot, letting the community lead. (Dom is also working on additional cc0 NFT projects for the company he formed to build Blitmap.) Other authors have chosen out totally, like sartoshi, who announced his exit from the cc0 project he founded, mfers, and from the NFT area by publishing a final edition suitably named "end of sartoshi" and then deactivating his Twitter account. A multi-signature wallet of seven mfers controls the project's smart contract. 

cc0 licensing allows a robust community to co-create in ways that benefit all members, regardless of original creators' continuous commitment. We foresee more organized infrastructure and design patterns as NFT matures. Like open source software, value capture frameworks may see innovation. (We could imagine a variant of the "Sleepycat license," which requires commercial software to pay licensing fees when embedding open source components.) As creators progress the space, we expect them to build unique rights and licensing strategies. cc0 allows NFT producers to bootstrap ideas that may take off.

VeeFriends is one NFT project I'm sure will last.

I believe in blockchain technology and JPEGs, aka NFTs. NFTs aren't JPEGs. It's not as it seems.

Gary Vaynerchuk is leading the pack with his new NFT project VeeFriends, I wrote a year ago. I was spot-on. It's the most innovative project I've seen.

Since its minting in May 2021, it has given its holders enormous value, most notably the first edition of VeeCon, a multi-day superconference featuring iconic and emerging leaders in NFTs and Popular Culture. First-of-its-kind NFT-ticketed Web3 conference to build friendships, share ideas, and learn together.

VeeFriends holders got free VeeCon NFT tickets. Attendees heard iconic keynote speeches, innovative talks, panels, and Q&A sessions.

It was a unique conference that most of us, including me, are looking forward to in 2023. The lineup was epic, and it allowed many to network in new ways. Really memorable learning. Here are a couple of gratitude posts from the attendees.

VeeFriends Series 2

This article explains VeeFriends if you're still confused.

GaryVee's hand-drawn doodles have evolved into wonderful characters. The characters' poses and backgrounds bring the VeeFriends IP to life.

Yes, this is the second edition of VeeFriends, and at current prices, it's one of the best NFT opportunities in years. If you have the funds and risk appetite to invest in NFTs, VeeFriends Series 2 is worth every penny. Even if you can't invest, learn from their journey.

1. Art Is the Start

Many critics say VeeFriends artwork is below average and not by GaryVee. Art is often the key to future success.

Let's look at one of the first Mickey Mouse drawings. No one would have guessed that this would become one of the most beloved animated short film characters. In Walt Before Mickey, Walt Disney's original mouse Mortimer was less refined.

First came a mouse...

These sketches evolved into Steamboat Willie, Disney's first animated short film.

Fred Moore redesigned the character artwork into what we saw in cartoons as kids. Mickey Mouse's history is here.

Looking at how different cartoon characters have evolved and gained popularity over decades, I believe Series 2 characters like Self-Aware Hare, Kind Kudu, and Patient Pig can do the same.

GaryVee captures this journey on the blockchain and lets early supporters become part of history. Time will tell if it rivals Disney, Pokemon, or Star Wars. Gary has been vocal about this vision.

2. VeeFriends is Intellectual Property for the Coming Generations

Most of us grew up watching cartoons, playing with toys, cards, and video games. Our interactions with fictional characters and the stories we hear shape us.

GaryVee is slowly curating an experience for the next generation with animated videos, card games, merchandise, toys, and more.

VeeFriends UNO, a collaboration with Mattel Creations, features 17 VeeFriends characters.

VeeFriends and Zerocool recently released Trading Cards featuring all 268 Series 1 characters and 15 new ones. Another way to build VeeFriends' collectibles brand.

At Veecon, all the characters were collectible toys. Something will soon emerge.

Kids and adults alike enjoy the YouTube channel's animated shorts and VeeFriends Tunes. Here's a song by the holder's Optimistic Otter-loving daughter.

This VeeFriends story is only the beginning. I'm looking forward to animated short film series, coloring books, streetwear, candy, toys, physical collectibles, and other forms of VeeFriends IP.

3. Veefriends will always provide utilities

Smart contracts can be updated at any time and authenticated on a ledger.

VeeFriends Series 2 gives no promise of any utility whatsoever. GaryVee released no project roadmap. In the first few months after launch, many owners of specific characters or scenes received utilities.

Every benefit or perk you receive helps promote the VeeFriends brand.

Recent partnerships are listed below.

• MaryRuth's Multivitamin Gummies

• Productive Puffin holders from VeeFriends x Primitive

• Pickleball Scene & Clown Holders Only

Pickleball & Competitive Clown Exclusive experience, anteater multivitamin gummies, and Puffin x Primitive merch

Considering the price of NFTs, it may not seem like much. It's just the beginning; you never know what the future holds. No other NFT project offers such diverse, ongoing benefits.

4. Garyvee's team is ready

Gary Vaynerchuk's team and record are undisputed. He's a serial entrepreneur and the Chairman & CEO of VaynerX, which includes VaynerMedia, VaynerCommerce, One37pm, and The Sasha Group.

Gary founded VaynerSports, Resy, and Empathy Wines. He's a Candy Digital Board Member, VCR Group Co-Founder, ArtOfficial Co-Founder, and VeeFriends Creator & CEO. Gary was recently named one of Fortune's Top 50 NFT Influencers.

Gary Vayenerchuk aka GaryVee

Gary documents his daily life as a CEO on social media, which has 34 million followers and 272 million monthly views. GaryVee Audio Experience is a top podcast. He's a five-time New York Times best-seller and sought-after speaker.

Gary can observe consumer behavior to predict trends. He understood these trends early and pioneered them.

• 1997 — Realized e-potential commerce's and started winelibrary.com. In five years, he grew his father's wine business from $3M to $60M.

• 2006 — Realized content marketing's potential and started Wine Library on YouTube. TV

• 2009 — Estimated social media's potential (Web2) and invested in Facebook, Twitter, and Tumblr.

• 2014: Ethereum and Bitcoin investments

• 2021 — Believed in NFTs and Web3 enough to launch VeeFriends

GaryVee isn't all of VeeFriends. Andy Krainak, Dave DeRosa, Adam Ripps, Tyler Dowdle, and others work tirelessly to make VeeFriends a success.

GaryVee has said he'll let other businesses fail but not VeeFriends. We're just beginning his 40-year vision.

I have more confidence than ever in a company with a strong foundation and team.

5. Humans die, but characters live forever

What if GaryVee dies or can't work?

A writer's books can immortalize them. As long as their books exist, their words are immortal. Socrates, Hemingway, Aristotle, Twain, Fitzgerald, and others have become immortal.

Everyone knows Vincent Van Gogh's The Starry Night.

We all love reading and watching Peter Parker, Thor, or Jessica Jones. Their behavior inspires us. Stan Lee's message and stories live on despite his death.

GaryVee represents VeeFriends. Creating characters to communicate ensures that the message reaches even those who don't listen.

Gary wants his values and messages to be omnipresent in 268 characters. Messengers die, but their messages live on.

Gary envisions VeeFriends creating timeless stories and experiences. Ten years from now, maybe every kid will sing Patient Pig.

6. I love the intent.

Gary planned to create Workplace Warriors three years ago when he began designing Patient Panda, Accountable Ant, and Empathy elephant. The project stalled. When NFTs came along, he knew.

Gary wanted to create characters with traits he values, such as accountability, empathy, patience, kindness, and self-awareness. He wants future generations to find these traits cool. He hopes one or more of his characters will become pop culture icons.

These emotional skills aren't taught in schools or colleges, but they're crucial for business and life success. I love that someone is teaching this at scale.

In the end, intent matters.

Humans Are Collectors

Buy and collect things to communicate. Since the 1700s. Medieval people formed communities around hidden metals and stones. Many people still collect stamps and coins, and luxury and fashion are multi-trillion dollar industries. We're collectors.

The early 2020s NFTs will be remembered in the future. VeeFriends will define a cultural and technological shift in this era. VeeFriends Series 1 is the original hand-drawn art, but it's expensive. VeeFriends Series 2 is a once-in-a-lifetime opportunity at $1,000.

If you are new to NFTs, check out How to Buy a Non Fungible Token (NFT) For Beginners

This is a non-commercial article. Not financial or legal advice. Information isn't always accurate. Before making important financial decisions, consult a pro or do your own research.

This post is a summary. Read the full article here

Here is the ugly stuff, read this if you have a founder in your life or are trying to become one. Your call.

#1 You'll try to talk yourself to sleep, but it won't always work.

As founders, we're all driven. Good and bad, you're restless. Success requires resistance and discipline. Your startup will be on your mind 24/7, and not everyone will have the patience to listen to your worries, ideas, and coffee runs. You become more self-sufficient than ever before.

#2 No one will understand what you're going through unless they've been a founder.

Some of my closest friends don't understand the work that goes into starting a business, and we can't blame them.

#3 You'll feel alienated.

Your problems aren't common; calling your bestie won't help. You must search hard for the right resources. It alienates you from conversations you no longer relate to. (No 4th of July, no long weekends!)

#4 Since you're your "own boss," people assume you have lots of free time.

Do you agree? I was on a webinar with lots of new entrepreneurs, and one woman said, "I started my own business so I could have more time for myself." This may be true for some lucky people, and you can be flexible with your schedule. If you want your business to succeed, you'll probably be its slave for a while.

#5 No time for illness or family emergencies.

Both last month. Oh, no! Physically and emotionally withdrawing at the worst times will give you perspective. I learned this the hard way because I was too stubborn to postpone an important interview. I thought if I rested all day and only took one call, I'd be fine. Nope. I had a fever and my mind wasn't as sharp, so my performance and audience interaction suffered. Nope. Better to delay than miss out.

Oh, and setting a "OoO" makes you cringe.

#6 Good luck with your mental health, perfectionists.

When building a startup, it's difficult to accept that there won't be enough time to do everything. You can't make them all, not perfectly. You must learn to accept things that are done but not perfect.

#7 As a founder, you'll make mistakes, but you'll want to make them quickly so you can learn.

Hard lessons are learned quicker. You'll need to pivot and try new things often; some won't work, and it's best to discover them sooner rather than later.

#8 Pyramid schemes abound.

I didn't realize how bad it was until I started a company. You must spy and constantly research. As a founder, you'll receive many emails from people claiming to "support" you. Be wary and keep your eyes open. When it's too good to be true. Some "companies" will try to get you to pay for "competitions" to "pitch at events." Don't do it.

#9 Keep your competitor research to a minimum.

Actually, competition is good. It means there's a market for those solutions. However, this can be mentally exhausting too. Learn about their geography and updates, but that's it.

#10 You'll feel guilty taking vacation.

I don't know what to say, but I no longer enjoy watching TV, and that's okay. Pay attention to things that enrich you, bring you joy, and have fun. It boosts creativity.

Being a startup founder may be one of the hardest professional challenges you face, but it's also a great learning experience. Your passion will take you places you never imagined and open doors to opportunities you wouldn't have otherwise. You'll meet amazing people. No regrets, no complaints. It's a roller coaster, but the good days are great.

Miss anything? Comment below

Prioritize big-ticket purchases

I've made several spending blunders. I get sick thinking about how much money I spent.

My financial mental model was poor back then.

Stoicism and mindfulness keep me from attaching to those feelings. It still hurts.

Until four or five years ago, I bought a new winter jacket every year.

Ten years ago, I spent twice as much. Now that I have a fantastic, warm winter parka, I don't even consider acquiring another one. No more spending. I'm not looking for jackets either.

Saving time and money by spending well is my thinking paradigm.

The philosophy is expressed in most languages. Cheap is expensive in the Netherlands. This applies beyond shopping.

In this essay, I will offer three examples of how this mental paradigm transformed my financial life.

Publishing books

In 2015, I presented and positioned my first book poorly.

I called the book Huge Life Success and made a funny Canva cover in 30 minutes. This:

That looks nothing like my present books. No logo or style. The book felt amateurish.

The book started bothering me a few weeks after publication. The advice was good, but it didn't appear professional. I studied the book business extensively.

I created a style for all my designs. Branding. Win Your Inner Wars was reissued a year later.

Title, cover, and description changed. Rearranging the chapters improved readability.

Seven years later, the book sells hundreds of copies a month. That taught me a lot.

Rushing to finish a project is enticing. Send it and move forward.

Avoid rushing everything. Relax. Develop your projects. Perform well. Perform the job well.

My first novel was underfunded and underworked. A bad book arrived. I then invested time and money in writing the greatest book I could.

That book still sells.

Traveling

I hate travel. Airports, flights, trains, and lines irritate me.

But, I enjoy traveling to beautiful areas.

I do it strangely. I make up travel rules. I never go to airports in summer. I hate being near airports on holidays. Unworthy.

No vacation packages for me. Those airline packages with a flight, shuttle, and hotel. I've had enough.

I try to avoid crowds and popular spots. July Paris? Nuts and bolts, please. Christmas in NYC? No, please keep me sane.

I fly business class behind. I accept upgrades upon check-in. I prefer driving. I drove from the Netherlands to southern Spain.

Thankfully, no lines. What if travel costs more? Thus? I enjoy it from the start. I start traveling then.

I rarely travel since I'm so difficult. One great excursion beats several average ones.

Personal effectiveness

New apps, tools, and strategies intrigue most productivity professionals.

No.

I researched years ago. I spent years investigating productivity in university.

I bought books, courses, applications, and tools. It was expensive and time-consuming.

Im finished. Productivity no longer costs me time or money. OK. I worked on it once and now follow my strategy.

I avoid new programs and systems. My stuff works. Why change winners?

Spending wisely saves time and money.

Spending wisely means spending once. Many people ignore productivity. It's understudied. No classes.

Some assume reading a few articles or a book is enough. Productivity is personal. You need a personal system.

Time invested is one-time. You can trust your system for life once you find it.

Concentrate on the expensive choices.

Life's short. Saving money quickly is enticing.

Spend less on groceries today. True. That won't fix your finances.

Adopt a lifestyle that makes you affluent over time. Consider major choices.

Are they causing long-term poverty? Are you richer?

Leasing cars comes to mind. The automobile costs a fortune today. The premium could accomplish a million nice things.

Focusing on important decisions makes life easier. Consider your future. You want to improve next year.

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.