More on Entrepreneurship/Creators

Raad Ahmed
3 years ago
How We Just Raised $6M At An $80M Valuation From 100+ Investors Using A Link (Without Pitching)
Lawtrades nearly failed three years ago.
We couldn't raise Series A or enthusiasm from VCs.
We raised $6M (at a $80M valuation) from 100 customers and investors using a link and no pitching.
Step-by-step:
We refocused our business first.
Lawtrades raised $3.7M while Atrium raised $75M. By comparison, we seemed unimportant.
We had to close the company or try something new.
As I've written previously, a pivot saved us. Our initial focus on SMBs attracted many unprofitable customers. SMBs needed one-off legal services, meaning low fees and high turnover.
Tech startups were different. Their General Councels (GCs) needed near-daily support, resulting in higher fees and lower churn than SMBs.
We stopped unprofitable customers and focused on power users. To avoid dilution, we borrowed against receivables. We scaled our revenue 10x, from $70k/mo to $700k/mo.
Then, we reconsidered fundraising (and do it differently)
This time was different. Lawtrades was cash flow positive for most of last year, so we could dictate our own terms. VCs were still wary of legaltech after Atrium's shutdown (though they were thinking about the space).
We neither wanted to rely on VCs nor dilute more than 10% equity. So we didn't compete for in-person pitch meetings.
AngelList Roll-Up Vehicle (RUV). Up to 250 accredited investors can invest in a single RUV. First, we emailed customers the RUV. Why? Because I wanted to help the platform's users.
Imagine if Uber or Airbnb let all drivers or Superhosts invest in an RUV. Humans make the platform, theirs and ours. Giving people a chance to invest increases their loyalty.
We expanded after initial interest.
We created a Journey link, containing everything that would normally go in an investor pitch:
- Slides
- Trailer (from me)
- Testimonials
- Product demo
- Financials
We could also link to our AngelList RUV and send the pitch to an unlimited number of people. Instead of 1:1, we had 1:10,000 pitches-to-investors.
We posted Journey's link in RUV Alliance Discord. 600 accredited investors noticed it immediately. Within days, we raised $250,000 from customers-turned-investors.
Stonks, which live-streamed our pitch to thousands of viewers, was interested in our grassroots enthusiasm. We got $1.4M from people I've never met.
These updates on Pump generated more interest. Facebook, Uber, Netflix, and Robinhood executives all wanted to invest. Sahil Lavingia, who had rejected us, gave us $100k.
We closed the round with public support.
Without a single pitch meeting, we'd raised $2.3M. It was a result of natural enthusiasm: taking care of the people who made us who we are, letting them move first, and leveraging their enthusiasm with VCs, who were interested.
We used network effects to raise $3.7M from a founder-turned-VC, bringing the total to $6M at a $80M valuation (which, by the way, I set myself).
What flipping the fundraising script allowed us to do:
We started with private investors instead of 2–3 VCs to show VCs what we were worth. This gave Lawtrades the ability to:
- Without meetings, share our vision. Many people saw our Journey link. I ended up taking meetings with people who planned to contribute $50k+, but still, the ratio of views-to-meetings was outrageously good for us.
- Leverage ourselves. Instead of us selling ourselves to VCs, they did. Some people with large checks or late arrivals were turned away.
- Maintain voting power. No board seats were lost.
- Utilize viral network effects. People-powered.
- Preemptively halt churn by turning our users into owners. People are more loyal and respectful to things they own. Our users make us who we are — no matter how good our tech is, we need human beings to use it. They deserve to be owners.
I don't blame founders for being hesitant about this approach. Pump and RUVs are new and scary. But it won’t be that way for long. Our approach redistributed some of the power that normally lies entirely with VCs, putting it into our hands and our network’s hands.
This is the future — another way power is shifting from centralized to decentralized.

Micah Daigle
3 years ago
Facebook is going away. Here are two explanations for why it hasn't been replaced yet.
And tips for anyone trying.
We see the same story every few years.
BREAKING NEWS: [Platform X] launched a social network. With Facebook's reputation down, the new startup bets millions will switch.
Despite the excitement surrounding each new platform (Diaspora, Ello, Path, MeWe, Minds, Vero, etc.), no major exodus occurred.
Snapchat and TikTok attracted teens with fresh experiences (ephemeral messaging and rapid-fire videos). These features aren't Facebook, even if Facebook replicated them.
Facebook's core is simple: you publish items (typically text/images) and your friends (generally people you know IRL) can discuss them.
It's cool. Sometimes I don't want to, but sh*t. I like it.
Because, well, I like many folks I've met. I enjoy keeping in touch with them and their banter.
I dislike Facebook's corporation. I've been cautiously optimistic whenever a Facebook-killer surfaced.
None succeeded.
Why? Two causes, I think:
People couldn't switch quickly enough, which is reason #1
Your buddies make a social network social.
Facebook started in self-contained communities (college campuses) then grew outward. But a new platform can't.
If we're expected to leave Facebook, we want to know that most of our friends will too.
Most Facebook-killers had bottlenecks. You have to waitlist or jump through hoops (e.g. setting up a server).
Same outcome. Upload. Chirp.
After a week or two of silence, individuals returned to Facebook.
Reason #2: The fundamental experience was different.
Even when many of our friends joined in the first few weeks, it wasn't the same.
There were missing features or a different UX.
Want to reply with a meme? No photos in comments yet. (Trying!)
Want to tag a friend? Nope, sorry. 2019!
Want your friends to see your post? You must post to all your friends' servers. Good luck!
It's difficult to introduce a platform with 100% of the same features as one that's been there for 20 years, yet customers want a core experience.
If you can't, they'll depart.
The causes that led to the causes
Having worked on software teams for 14+ years, I'm not surprised by these challenges. They are a natural development of a few tech sector meta-problems:
Lean startup methodology
Silicon Valley worships lean startup. It's a way of developing software that involves testing a stripped-down version with a limited number of people before selecting what to build.
Billion people use Facebook's functions. They aren't tested. It must work right away*
*This may seem weird to software people, but it's how non-software works! You can't sell a car without wheels.
2. Creativity
Startup entrepreneurs build new things, not copies. I understand. Reinventing the wheel is boring.
We know what works. Different experiences raise adoption friction. Once millions have transferred, more features (and a friendlier UX) can be implemented.
3. Cost scaling
True. Building a product that can sustain hundreds of millions of users in weeks is expensive and complex.
Your lifeboats must have the same capacity as the ship you're evacuating. It's required.
4. Pure ideologies
People who work on Facebook-alternatives are (understandably) critical of Facebook.
They build an open-source, fully-distributed, data-portable, interface-customizable, offline-capable, censorship-proof platform.
Prioritizing these aims can prevent replicating the straightforward experience users expect. Github, not Facebook, is for techies only.
What about the business plan, though?
Facebook-killer attempts have followed three models.
Utilize VC funding to increase your user base, then monetize them later. (If you do this, you won't kill Facebook; instead, Facebook will become you.)
Users must pay to utilize it. (This causes a huge bottleneck and slows the required quick expansion, preventing it from seeming like a true social network.)
Make it a volunteer-run, open-source endeavor that is free. (This typically denotes that something is cumbersome, difficult to operate, and is only for techies.)
Wikipedia is a fourth way.
Wikipedia is one of the most popular websites and a charity. No ads. Donations support them.
A Facebook-killer managed by a good team may gather millions (from affluent contributors and the crowd) for their initial phase of development. Then it might sustain on regular donations, ethical transactions (e.g. fees on commerce, business sites, etc.), and government grants/subsidies (since it would essentially be a public utility).
When you're not aiming to make investors rich, it's remarkable how little money you need.
If you want to build a Facebook competitor, follow these tips:
Drop the lean startup philosophy. Wait until you have a finished product before launching. Build it, thoroughly test it for bugs, and then release it.
Delay innovating. Wait till millions of people have switched before introducing your great new features. Make it nearly identical for now.
Spend money climbing. Make sure that guests can arrive as soon as they are invited. Never keep them waiting. Make things easy for them.
Make it accessible to all. Even if doing so renders it less philosophically pure, it shouldn't require technical expertise to utilize.
Constitute a nonprofit. Additionally, develop community ownership structures. Profit maximization is not the only strategy for preserving valued assets.
Last thoughts
Nobody has killed Facebook, but Facebook is killing itself.
The startup is burying the newsfeed to become a TikTok clone. Meta itself seems to be ditching the platform for the metaverse.
I wish I was happy, but I'm not. I miss (understandably) removed friends' postings and remarks. It could be a ghost town in a few years. My dance moves aren't TikTok-worthy.
Who will lead? It's time to develop a social network for the people.
Greetings if you're working on it. I'm not a company founder, but I like to help hard-working folks.

Tim Denning
2 years ago
One of the biggest publishers in the world offered me a book deal, but I don't feel deserving of it.
My ego is so huge it won't fit through the door.
I don't know how I feel about it. I should be excited. Many of you have this exact dream to publish a book with a well-known book publisher and get a juicy advance.
Let me dissect how I'm thinking about it to help you.
How it happened
An email comes in. A generic "can we put a backlink on your website and get a freebie" email.
Almost deleted it.
Then I noticed the logo. It seemed shady. I found the URL. Check. I searched the employee's LinkedIn. Legit. I avoided middlemen. Check.
Mixed feelings. LinkedIn hasn't valued my writing for years. I'm just a guy in an unironed t-shirt whose content they sell advertising against.
They get big dollars. I get $0 and a few likes, plus some email subscribers.
Still, I felt adrenaline for hours.
I texted a few friends to see how they felt. I wrapped them.
Messages like "No shocker. You're entertaining online." I didn't like praises, so I blushed.
The thrill faded after hours. Who knows?
Most authors desire this chance.
"You entitled piece of crap, Denning!"
You may think so. Okay. My job is to stand on the internet and get bananas thrown at me.
I approached writing backwards. More important than a book deal was a social media audience converted to an email list.
Romantic authors think backward. They hope a fantastic book will land them a deal and an audience.
Rarely occurs. So I never pursued it. It's like permission-seeking or the lottery.
Not being a professional writer, I've never written a good book. I post online for fun and to express my opinions.
Writing is therapeutic. I overcome mental illness and rebuilt my life this way. Without blogging, I'd be dead.
I've always dreamed of staying alive and doing something I love, not getting a book contract. Writing is my passion. I'm a winner without a book deal.
Why I was given a book deal
You may assume I received a book contract because of my views or follows. Nope.
They gave me a deal because they like my writing style. I've heard this for eight years.
Several authors agree. One asked me to improve their writer's voice.
Takeaway: highlight your writer's voice.
What if they discover I'm writing incompetently?
An edited book is published. It's edited.
I need to master writing mechanics, thus this concerns me. I need help with commas and sentence construction.
I must learn verb, noun, and adjective. Seriously.
Writing a book may reveal my imposter status to a famous publisher. Imagine the email
"It happened again. He doesn't even know how to spell. He thinks 'less' is the correct word, not 'fewer.' Are you sure we should publish his book?"
Fears stink.
I'm capable of blogging. Even listicles. So what?
Writing for a major publisher feels advanced.
I only blog. I'm good at listicles. Digital media executives have criticized me for this.
It is allegedly clickbait.
Or it is following trends.
Alternately, growth hacking.
Never. I learned copywriting to improve my writing.
Apple, Amazon, and Tesla utilize copywriting to woo customers. Whoever thinks otherwise is the wisest person in the room.
Old-schoolers loathe copywriters.
Their novels sell nothing.
They assume their elitist version of writing is better and that the TikTok generation will invest time in random writing with no subheadings and massive walls of text they can't read on their phones.
I'm terrified of book proposals.
My friend's book proposal suggestion was contradictory and made no sense.
They told him to compose another genre. This book got three Amazon reviews. Is that a good model?
The process disappointed him. I've heard other book proposal horror stories. Tim Ferriss' book "The 4-Hour Workweek" was criticized.
Because he has thick skin, his book came out. He wouldn't be known without that.
I hate book proposals.
An ongoing commitment
Writing a book is time-consuming.
I appreciate time most. I want to focus on my daughter for the next few years. I can't recreate her childhood because of a book.
No idea how parents balance kids' goals.
My silly face in a bookstore. Really?
Genuine thought.
I don't want my face in bookstores. I fear fame. I prefer anonymity.
I want to purchase a property in a bad Australian area, then piss off and play drums. Is bookselling worth it?
Are there even bookstores anymore?
(Except for Ryan Holiday's legendary Painted Porch Bookshop in Texas.)
What's most important about books
Many were duped.
Tweets and TikTok hopscotch vids are their future. Short-form content creates devoted audiences that buy newsletter subscriptions.
Books=depth.
Depth wins (if you can get people to buy your book). Creating a book will strengthen my reader relationships.
It's cheaper than my classes, so more people can benefit from my life lessons.
A deeper justification for writing a book
Mind wandered.
If I write this book, my daughter will follow it. "Look what you can do, love, when you ignore critics."
That's my favorite.
I'll be her best leader and teacher. If her dad can accomplish this, she can too.
My kid can read my book when I'm gone to remember her loving father.
Last paragraph made me cry.
The positive
This book thing might make me sound like Karen.
The upside is... Building in public, like I have with online writing, attracts the right people.
Proof-of-work over proposals, beautiful words, or huge aspirations. If you want a book deal, try writing online instead of the old manner.
Next steps
No idea.
I'm a rural Aussie. Writing a book in the big city is intimidating. Will I do it? Lots to think about. Right now, some level of reflection and gratitude feels most appropriate.
Sometimes when you don't feel worthy, it gives you the greatest lessons. That's how I feel about getting offered this book deal.
Perhaps you can relate.
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JEFF JOHN ROBERTS
3 years ago
What just happened in cryptocurrency? A plain-English Q&A about Binance's FTX takedown.
Crypto people have witnessed things. They've seen big hacks, mind-boggling swindles, and amazing successes. They've never seen a day like Tuesday, when the world's largest crypto exchange murdered its closest competition.
Here's a primer on Binance and FTX's lunacy and why it matters if you're new to crypto.
What happened?
CZ, a shrewd Chinese-Canadian billionaire, runs Binance. FTX, a newcomer, has challenged Binance in recent years. SBF (Sam Bankman-Fried)—a young American with wild hair—founded FTX (initials are a thing in crypto).
Last weekend, CZ complained about SBF's lobbying and then exploited Binance's market power to attack his competition.
How did CZ do that?
CZ invested in SBF's new cryptocurrency exchange when they were friends. CZ sold his investment in FTX for FTT when he no longer wanted it. FTX clients utilize those tokens to get trade discounts, although they are less liquid than Bitcoin.
SBF made a mistake by providing CZ just too many FTT tokens, giving him control over FTX. It's like Pepsi handing Coca-Cola a lot of stock it could sell at any time. CZ got upset with SBF and flooded the market with FTT tokens.
SBF owns a trading fund with many FTT tokens, therefore this was catastrophic. SBF sought to defend FTT's worth by selling other assets to buy up the FTT tokens flooding the market, but it didn't succeed, and as FTT's value plummeted, his liabilities exceeded his assets. By Tuesday, his companies were insolvent, so he sold them to his competition.
Crazy. How could CZ do that?
CZ likely did this to crush a rising competition. It was also personal. In recent months, regulators have been tough toward the crypto business, and Binance and FTX have been trying to stay on their good side. CZ believed SBF was poisoning U.S. authorities by saying CZ was linked to China, so CZ took retribution.
“We supported previously, but we won't pretend to make love after divorce. We're neutral. But we won't assist people that push against other industry players behind their backs," CZ stated in a tragic tweet on Sunday. He crushed his rival's company two days later.
So does Binance now own FTX?
No. Not yet. CZ has only stated that Binance signed a "letter of intent" to acquire FTX. CZ and SBF say Binance will protect FTX consumers' funds.
Who’s to blame?
You could blame CZ for using his control over FTX to destroy it. SBF is also being criticized for not disclosing the full overlap between FTX and his trading company, which controlled plenty of FTT. If he had been upfront, someone might have warned FTX about this vulnerability earlier, preventing this mess.
Others have alleged that SBF utilized customer monies to patch flaws in his enterprises' balance accounts. That happened to multiple crypto startups that collapsed this spring, which is unfortunate. These are allegations, not proof.
Why does this matter? Isn't this common in crypto?
Crypto is notorious for shady executives and pranks. FTX is the second-largest crypto business, and SBF was largely considered as the industry's golden boy who would help it get on authorities' good side. Thus far.
Does this affect cryptocurrency prices?
Short-term, it's bad. Prices fell on suspicions that FTX was in peril, then rallied when Binance rescued it, only to fall again later on Tuesday.
These occurrences have hurt FTT and SBF's Solana token. It appears like a huge token selloff is affecting the rest of the market. Bitcoin fell 10% and Ethereum 15%, which is bad but not catastrophic for the two largest coins by market cap.

Greg Satell
2 years ago
Focus: The Deadly Strategic Idea You've Never Heard Of (But Definitely Need To Know!
Steve Jobs' initial mission at Apple in 1997 was to destroy. He killed the Newton PDA and Macintosh clones. Apple stopped trying to please everyone under Jobs.
Afterward, there were few highly targeted moves. First, the pink iMac. Modest success. The iPod, iPhone, and iPad made Apple the world's most valuable firm. Each maneuver changed the company's center of gravity and won.
That's the idea behind Schwerpunkt, a German military term meaning "focus." Jobs didn't need to win everywhere, just where it mattered, so he focused Apple's resources on a few key goods. Finding your Schwerpunkt is more important than charts and analysis for excellent strategy.
Comparison of Relative Strength and Relative Weakness
The iPod, Apple's first major hit after Jobs' return, didn't damage Microsoft and the PC, but instead focused Apple's emphasis on a fledgling, fragmented market that generated "sucky" products. Apple couldn't have taken on the computer titans at this stage, yet it beat them.
The move into music players used Apple's particular capabilities, especially its ability to build simple, easy-to-use interfaces. Jobs' charisma and stature, along his understanding of intellectual property rights from Pixar, helped him build up iTunes store, which was a quagmire at the time.
In Good Strategy | Bad Strategy, management researcher Richard Rumelt argues that good strategy uses relative strength to counter relative weakness. To discover your main point, determine your abilities and where to effectively use them.
Steve Jobs did that at Apple. Microsoft and Dell, who controlled the computer sector at the time, couldn't enter the music player business. Both sought to produce iPod competitors but failed. Apple's iPod was nobody else's focus.
Finding The Center of Attention
In a military engagement, leaders decide where to focus their efforts by assessing commanders intent, the situation on the ground, the topography, and the enemy's posture on that terrain. Officers spend their careers learning about schwerpunkt.
Business executives must assess internal strengths including personnel, technology, and information, market context, competitive environment, and external partner ecosystems. Steve Jobs was a master at analyzing forces when he returned to Apple.
He believed Apple could integrate technology and design for the iPod and that the digital music player industry sucked. By analyzing competitors' products, he was convinced he could produce a smash by putting 1000 tunes in my pocket.
The only difficulty was there wasn't the necessary technology. External ecosystems were needed. On a trip to Japan to meet with suppliers, a Toshiba engineer claimed the company had produced a tiny memory drive approximately the size of a silver dollar.
Jobs knew the memory drive was his focus. He wrote a $10 million cheque and acquired exclusive technical rights. For a time, none of his competitors would be able to recreate his iPod with the 1000 songs in my pocket.
How to Enter the OODA Loop
John Boyd invented the OODA loop as a pilot to better his own decision-making. First OBSERVE your surroundings, then ORIENT that information using previous knowledge and experiences. Then you DECIDE and ACT, which changes the circumstance you must observe, orient, decide, and act on.
Steve Jobs used the OODA loop to decide to give Toshiba $10 million for a technology it had no use for. He compared the new information with earlier observations about the digital music market.
Then something much more interesting happened. The iPod was an instant hit, changing competition. Other computer businesses that competed in laptops, desktops, and servers created digital music players. Microsoft's Zune came out in 2006, Dell's Digital Jukebox in 2004. Both flopped.
By then, Apple was poised to unveil the iPhone, which would cause its competitors to Observe, Orient, Decide, and Act. Boyd named this OODA Loop infiltration. They couldn't gain the initiative by constantly reacting to Apple.
Microsoft and Dell were titans back then, but it's hard to recall. Apple went from near bankruptcy to crushing its competition via Schwerpunkt.
Rather than a destination, it is a journey
Trying to win everywhere is a strategic blunder. Win significant fights, not trivial skirmishes. Identifying a focal point to direct resources and efforts is the essence of Schwerpunkt.
When Steve Jobs returned to Apple, PC firms were competing, but he focused on digital music players, and the iPod made Apple a player. He launched the iPhone when his competitors were still reacting. When Steve Jobs said, "One more thing," at the end of a product presentation, he had a new focus.
Schwerpunkt isn't static; it's dynamic. Jobs' ability to observe, refocus, and modify the competitive backdrop allowed Apple to innovate consistently. His strategy was tailored to Apple's capabilities, customers, and ecosystem. Microsoft or Dell, better suited for the enterprise sector, couldn't succeed with a comparable approach.
There is no optimal strategy, only ones suited to a given environment, when relative strength might be used against relative weakness. Discovering the center of gravity where you can break through is more of a journey than a destination; it will become evident after you reach.

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.
