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Owolabi Judah

Owolabi Judah

3 years ago

How much did YouTube pay for 10 million views?

More on Entrepreneurship/Creators

Nick Nolan

Nick Nolan

3 years ago

In five years, starting a business won't be hip.

Photo by Daryan Shamkhali on Unsplash

People are slowly recognizing entrepreneurship's downside.

Growing up, entrepreneurship wasn't common. High school class of 2012 had no entrepreneurs.

Businesses were different.

They had staff and a lengthy history of achievement.

I never wanted a business. It felt unattainable. My friends didn't care.

Weird.

People desired degrees to attain good jobs at big companies.

When graduated high school:

  • 9 out of 10 people attend college

  • Earn minimum wage (7%) working in a restaurant or retail establishment

  • Or join the military (3%)

Later, entrepreneurship became a thing.

2014-ish

I was in the military and most of my high school friends were in college, so I didn't hear anything.

Entrepreneurship soared in 2015, according to Google Trends.

Screenshot from Google Trends

Then more individuals were interested. Entrepreneurship went from unusual to cool.

In 2015, it was easier than ever to build a website, run Facebook advertisements, and achieve organic social media reach.

There were several online business tools.

You didn't need to spend years or money figuring it out. Most entry barriers were gone.

Everyone wanted a side gig to escape the 95.

Small company applications have increased during the previous 10 years.

Screenshot from Oberlo

2011-2014 trend continues.

2015 adds 150,000 applications. 2016 adds 200,000. Plus 300,000 in 2017.

The graph makes it look little, but that's a considerable annual spike with no indications of stopping.

By 2021, new business apps had doubled.

Entrepreneurship will return to its early 2010s level.

I think we'll go backward in 5 years.

Entrepreneurship is half as popular as it was in 2015.

In the late 2020s and 30s, entrepreneurship will again be obscure.

Entrepreneurship's decade-long splendor is fading. People will cease escaping 9-5 and launch fewer companies.

That’s not a bad thing.

I think people have a rose-colored vision of entrepreneurship. It's fashionable. People feel that they're missing out if they're not entrepreneurial.

Reality is showing up.

People say on social media, "I knew starting a business would be hard, but not this hard."

More negative posts on entrepreneurship:

Screenshot from LinkedIn

Luke adds:

Is being an entrepreneur ‘healthy’? I don’t really think so. Many like Gary V, are not role models for a well-balanced life. Despite what feel-good LinkedIn tells you the odds are against you as an entrepreneur. You have to work your face off. It’s a tough but rewarding lifestyle. So maybe let’s stop glorifying it because it takes a lot of (bleepin) work to survive a pandemic, mental health battles, and a competitive market.

Entrepreneurship is no longer a pipe dream.

It’s hard.

I went full-time in March 2020. I was done by April 2021. I had a good-paying job with perks.

When that fell through (on my start date), I had to continue my entrepreneurial path. I needed money by May 1 to pay rent.

Entrepreneurship isn't as great as many think.

Entrepreneurship is a serious business.

If you have a 9-5, the grass isn't greener here. Most people aren't telling the whole story when they post on social media or quote successful entrepreneurs.

People prefer to communicate their victories than their defeats.

Is this a bad thing?

I don’t think so.

Over the previous decade, entrepreneurship went from impossible to the finest thing ever.

It peaked in 2020-21 and is returning to reality.

Startups aren't for everyone.

If you like your job, don't quit.

Entrepreneurship won't amaze people if you quit your job.

It's irrelevant.

You're doomed.

And you'll probably make less money.

If you hate your job, quit. Change jobs and bosses. Changing jobs could net you a greater pay or better perks.

When you go solo, your paycheck and perks vanish. Did I mention you'll fail, sleep less, and stress more?

Nobody will stop you from pursuing entrepreneurship. You'll face several challenges.

Possibly.

Entrepreneurship may be romanticized for years.

Based on what I see from entrepreneurs on social media and trends, entrepreneurship is challenging and few will succeed.

Andy Raskin

Andy Raskin

3 years ago

I've Never Seen a Sales Deck This Good

Photo by Olu Eletu

It’s Zuora’s, and it’s brilliant. Here’s why.

My friend Tim got a sales position at a Series-C software company that garnered $60 million from A-list investors. He's one of the best salespeople I know, yet he emailed me after starting to struggle.

Tim has a few modest clients. “Big companies ignore my pitch”. Tim said.

I love helping teams write the strategic story that drives sales, marketing, and fundraising. Tim and I had lunch at Amber India on Market Street to evaluate his deck.

After a feast, I asked Tim when prospects tune out.

He said, “several slides in”.

Intent on maximizing dining ROI, Tim went back to the buffet for seconds. When he returned, I pulled out my laptop and launched into a Powerpoint presentation.

“What’s this?” Tim asked.

“This,” I said, “is the greatest sales deck I have ever seen.”

Five Essentials of a Great Sales Narrative

I showed Tim a sales slide from IPO-bound Zuora, which sells a SaaS platform for subscription billing. Zuora supports recurring payments (e.g. enterprise software).

Ex-Zuora salesman gave me the deck, saying it helped him close his largest business. (I don't know anyone who works at Zuora.) After reading this, a few Zuora employees contacted me.)

Tim abandoned his naan in a pool of goat curry and took notes while we discussed the Zuora deck.

We remarked how well the deck led prospects through five elements:

(The ex-Zuora salesperson begged me not to release the Zuora deck publicly.) All of the images below originate from Zuora's website and SlideShare channel.)

#1. Name a Significant Change in the World

Don't start a sales presentation with mentioning your product, headquarters, investors, clients, or yourself.

Name the world shift that raises enormous stakes and urgency for your prospect.

Every Zuora sales deck begins with this slide:

Zuora coined the term subscription economy to describe a new market where purchasers prefer regular service payments over outright purchases. Zuora then shows a slide with the change's history.

Most pitch recommendation advises starting with the problem. When you claim a problem, you put prospects on the defensive. They may be unaware of or uncomfortable admitting the situation.

When you highlight a global trend, prospects open up about how it affects them, worries them, and where they see opportunity. You capture their interest. Robert McKee says:

…what attracts human attention is change. …if the temperature around you changes, if the phone rings — that gets your attention. The way in which a story begins is a starting event that creates a moment of change.

#2. Show There’ll Be Winners and Losers

Loss aversion affects all prospects. They avoid a loss by sticking with the status quo rather than risking a gain by changing.

To fight loss aversion, show how the change will create winners and losers. You must show both

  1. that if the prospect can adjust to the modification you mentioned, the outcome will probably be quite favorable; and

  2. That failing to do so is likely to have an unacceptable negative impact on the prospect's future

Zuora shows a mass extinction among Fortune 500 firms.

…and then showing how the “winners” have shifted from product ownership to subscription services. Those include upstarts…

…as well as rejuvenated incumbents:

To illustrate, Zuora asks:

Winners utilize Zuora's subscription service models.

#3. Tease the Promised Land

It's tempting to get into product or service details now. Resist that urge.

Prospects won't understand why product/service details are crucial if you introduce them too soon, therefore they'll tune out.

Instead, providing a teaser image of the happily-ever-after your product/service will assist the prospect reach.

Your Promised Land should be appealing and hard to achieve without support. Otherwise, why does your company exist?

Zuora shows this Promised Land slide after explaining that the subscription economy will have winners and losers.

Not your product or service, but a new future state.

(I asked my friend Tim to describe his Promised Land, and he answered, "You’ll have the most innovative platform for ____." Nope: the Promised Land isn't possessing your technology, but living with it.)

Your Promised Land helps prospects market your solution to coworkers after your sales meeting. Your coworkers will wonder what you do without you. Your prospects are more likely to provide a persuasive answer with a captivating Promised Land.

#4. Present Features as “Mystic Gifts” for Overcoming Difficulties on the Road to the Promised Land

Successful sales decks follow the same format as epic films and fairy tales. Obi Wan gives Luke a lightsaber to help him destroy the Empire. You're Gandalf, helping Frodo destroy the ring. Your prospect is Cinderella, and you're her fairy godmother.

Position your product or service's skills as mystical gifts to aid your main character (prospect) achieve the Promised Land.

Zuora's client record slide is shown above. Without context, even the most technical prospect would be bored.

Positioned in the context of shifting from an “old” to a “new world”, it's the foundation for a compelling conversation with prospects—technical and otherwise—about why traditional solutions can't reach the Promised Land.

#5. Show Proof That You Can Make the Story True.

In this sense, you're promising possibilities that if they follow you, they'll reach the Promised Land.

The journey to the Promised Land is by definition rocky, so prospects are right to be cautious. The final part of the pitch is proof that you can make the story come true.

The most convincing proof is a success story about how you assisted someone comparable to the prospect. Zuora's sales people use a deck of customer success stories, but this one gets the essence.

I particularly appreciate this one from an NCR exec (a Zuora customer), which relates more strongly to Zuora's Promised Land:

Not enough successful customers? Product demos are the next best evidence, but features should always be presented in the context of helping a prospect achieve the Promised Land.

The best sales narrative is one that is told by everyone.

Success rarely comes from a fantastic deck alone. To be effective, salespeople need an organization-wide story about change, Promised Land, and Magic Gifts.

Zuora exemplifies this. If you hear a Zuora executive, including CEO Tien Tzuo, talk, you'll likely hear about the subscription economy and its winners and losers. This is the theme of the company's marketing communications, campaigns, and vision statement.

According to the ex-Zuora salesperson, company-wide story alignment made him successful.

The Zuora marketing folks ran campaigns and branding around this shift to the subscription economy, and [CEO] Tien [Tzuo] talked it up all the time. All of that was like air cover for my in-person sales ground attack. By the time I arrived, prospects were already convinced they had to act. It was the closest thing I’ve ever experienced to sales nirvana.

The largest deal ever

Tim contacted me three weeks after our lunch to tell me that prospects at large organizations were responding well to his new deck, which we modeled on Zuora's framework. First, prospects revealed their obstacles more quickly. The new pitch engages CFOs and other top gatekeepers better, he said.

A week later, Tim emailed that he'd signed his company's biggest agreement.

Next week, we’re headed back to Amber India to celebrate.

DC Palter

DC Palter

2 years ago

How Will You Generate $100 Million in Revenue? The Startup Business Plan

A top-down company plan facilitates decision-making and impresses investors.

Photo by Andy Hermawan on Unsplash

A startup business plan starts with the product, the target customers, how to reach them, and how to grow the business.

Bottom-up is terrific unless venture investors fund it.

If it can prove how it can exceed $100M in sales, investors will invest. If not, the business may be wonderful, but it's not venture capital-investable.

As a rule, venture investors only fund firms that expect to reach $100M within 5 years.

Investors get nothing until an acquisition or IPO. To make up for 90% of failed investments and still generate 20% annual returns, portfolio successes must exit with a 25x return. A $20M-valued company must be acquired for $500M or more.

This requires $100M in sales (or being on a nearly vertical trajectory to get there). The company has 5 years to attain that milestone and create the requisite ROI.

This motivates venture investors (venture funds and angel investors) to hunt for $100M firms within 5 years. When you pitch investors, you outline how you'll achieve that aim.

I'm wary of pitches after seeing a million hockey sticks predicting $5M to $100M in year 5 that never materialized. Doubtful.

Startups fail because they don't have enough clients, not because they don't produce a great product. That jump from $5M to $100M never happens. The company reaches $5M or $10M, growing at 10% or 20% per year.  That's great, but not enough for a $500 million deal.

Once it becomes clear the company won’t reach orbit, investors write it off as a loss. When a corporation runs out of money, it's shut down or sold in a fire sale. The company can survive if expenses are trimmed to match revenues, but investors lose everything.

When I hear a pitch, I'm not looking for bright income projections but a viable plan to achieve them. Answer these questions in your pitch.

  • Is the market size sufficient to generate $100 million in revenue?

  • Will the initial beachhead market serve as a springboard to the larger market or as quicksand that hinders progress?

  • What marketing plan will bring in $100 million in revenue? Is the market diffuse and will cost millions of dollars in advertising, or is it one, focused market that can be tackled with a team of salespeople?

  • Will the business be able to bridge the gap from a small but fervent set of early adopters to a larger user base and avoid lock-in with their current solution?

  • Will the team be able to manage a $100 million company with hundreds of people, or will hypergrowth force the organization to collapse into chaos?

  • Once the company starts stealing market share from the industry giants, how will it deter copycats?

The requirement to reach $100M may be onerous, but it provides a context for difficult decisions: What should the product be? Where should we concentrate? who should we hire? Every strategic choice must consider how to reach $100M in 5 years.

Focusing on $100M streamlines investor pitches. Instead of explaining everything, focus on how you'll attain $100M.

As an investor, I know I'll lose my money if the startup doesn't reach this milestone, so the revenue prediction is the first thing I look at in a pitch deck.

Reaching the $100M goal needs to be the first thing the entrepreneur thinks about when putting together the business plan, the central story of the pitch, and the criteria for every important decision the company makes.

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Matthew Royse

Matthew Royse

3 years ago

5 Tips for Concise Writing

Here's how to be clear.

I have only made this letter longer because I have not had the time to make it shorter.” — French mathematician, physicist, inventor, philosopher, and writer Blaise Pascal

Concise.

People want this. We tend to repeat ourselves and use unnecessary words.

Being vague frustrates readers. It focuses their limited attention span on figuring out what you're saying rather than your message.

Edit carefully.

Examine every word you put on paper. You’ll find a surprising number that don’t serve any purpose.” — American writer, editor, literary critic, and teacher William Zinsser

How do you write succinctly?

Here are three ways to polish your writing.

1. Delete

Your readers will appreciate it if you delete unnecessary words. If a word or phrase is essential, keep it. Don't force it.

Many readers dislike bloated sentences. Ask yourself if cutting a word or phrase will change the meaning or dilute your message.

For example, you could say, “It’s absolutely essential that I attend this meeting today, so I know the final outcome.” It’s better to say, “It’s critical I attend the meeting today, so I know the results.”

Key takeaway

Delete actually, completely, just, full, kind of, really, and totally. Keep the necessary words, cut the rest.

2. Just Do It

Don't tell readers your plans. Your readers don't need to know your plans. Who are you?

Don't say, "I want to highlight our marketing's problems." Our marketing issues are A, B, and C. This cuts 5–7 words per sentence.

Keep your reader's attention on the essentials, not the fluff. What are you doing? You won't lose readers because you get to the point quickly and don't build up.

Key takeaway

Delete words that don't add to your message. Do something, don't tell readers you will.

3. Cut Overlap

You probably repeat yourself unintentionally. You may add redundant sentences when brainstorming. Read aloud to detect overlap.

Remove repetition from your writing. It's important to edit our writing and thinking to avoid repetition.

Key Takeaway

If you're repeating yourself, combine sentences to avoid overlap.

4. Simplify

Write as you would to family or friends. Communicate clearly. Don't use jargon. These words confuse readers.

Readers want specifics, not jargon. Write simply. Done.

Most adults read at 8th-grade level. Jargon and buzzwords make speech fluffy. This confuses readers who want simple language.

Key takeaway

Ensure all audiences can understand you. USA Today's 5th-grade reading level is intentional. They want everyone to understand.

5. Active voice

Subjects perform actions in active voice. When you write in passive voice, the subject receives the action.

For example, “the board of directors decided to vote on the topic” is an active voice, while “a decision to vote on the topic was made by the board of directors” is a passive voice.

Key takeaway

Active voice clarifies sentences. Active voice is simple and concise.

Bringing It All Together

Five tips help you write clearly. Delete, just do it, cut overlap, use simple language, and write in an active voice.

Clear writing is effective. It's okay to occasionally use unnecessary words or phrases. Realizing it is key. Check your writing.

Adding words costs.

Write more concisely. People will appreciate it and read your future articles, emails, and messages. Spending extra time will increase trust and influence.

Not that the story need be long, but it will take a long while to make it short.” — Naturalist, essayist, poet, and philosopher Henry David Thoreau

Nick Babich

Nick Babich

2 years ago

Is ChatGPT Capable of Generating a Complete Mobile App?

Image generated using midjourney

TL;DR: It'll be harder than you think.

Mobile app development is a complicated product design sector. You require broad expertise to create a mobile app. You must write Swift or Java code and consider mobile interactions.

When ChatGPT was released, many were amazed by its capabilities and wondered if it could replace designers and developers. This article will use ChatGPT to answer a specific query.

Can ChatGPT build an entire iOS app?

This post will use ChatGPT to construct an iOS meditation app. Video of the article is available.

App concepts for meditation

After deciding on an app, think about the user experience. What should the app offer?

Let's ask ChatGPT for the answer.

Asking ChatGPT to describe a concept of a mediation app.

ChatGPT described a solid meditation app with various exercises. Use this list to plan product design. Our first product iteration will have few features. A simple, one-screen software will let users set the timeframe and play music during meditation.

Structure of information

Information architecture underpins product design. Our app's navigation mechanism should be founded on strong information architecture, so we need to identify our mobile's screens first.

ChatGPT can define our future app's information architecture since we already know it.

Asking ChatGPT, “what is a good structure for a mediation app for iOS?”

ChatGPT uses the more complicated product's structure. When adding features to future versions of our product, keep this information picture in mind.

Color palette

Meditation apps need colors. We want to employ relaxing colors in a meditation app because colors affect how we perceive items. ChatGPT can suggest product colors.

Asking ChatGPT to provide a color palette with hex colors that will contain brand color, as well as primary and secondary colors.

See the hues in person:

Listing colors provided by the ChatGPT

Neutral colors dominate the color scheme. Playing with color opacity makes this scheme useful.

Changing the opacity of the brand color in Figma.

Ambiance music

Meditation involves music. Well-chosen music calms the user.

Let ChatGPT make music for us.

Aksing ChatGPT to write music.

ChatGPT can only generate text. It directs us to Spotify or YouTube to look for such stuff and makes precise recommendations.

Fonts

Fonts can impress app users. Round fonts are easier on the eyes and make a meditation app look friendlier.

ChatGPT can suggest app typefaces. I compare two font pairs when making a product. I'll ask ChatGPT for two font pairs.

Ask ChatGPT to provide two font pairs for a meditation app.

See the hues in person:

Two font pairs generated by ChatGPT.

Despite ChatGPT's convincing font pairing arguments, the output is unattractive. The initial combo (Open Sans + Playfair Display) doesn't seem to work well for a mediation app.

Content

Meditation requires the script. Find the correct words and read them calmly and soothingly to help listeners relax and focus on each region of their body to enhance the exercise's effect.

ChatGPT's offerings:

Asking ChatGPT to write a meditation script.

ChatGPT outputs code. My prompt's word script may cause it.

Timer

After fonts, colors, and content, construct functional pieces. Timer is our first functional piece. The meditation will be timed.

Let ChatGPT write Swift timer code (since were building an iOS app, we need to do it using Swift language).

Aksing ChatGPT to write a code for a timer.

ChatGPT supplied a timer class, initializer, and usage guidelines.

Sample for timer initializer and recommendations on how to use it provided by ChatGPT.

Apple Xcode requires a playground to test this code. Xcode will report issues after we paste the code to the playground.

XCode shows error messages when use use a code generated by ChatGPT.

Fixing them is simple. Just change Timer to another class name (Xcode shows errors because it thinks that we access the properties of the class we’ve created rather than the system class Timer; it happens because both classes have the same name Timer). I titled our class Timero and implemented the project. After this quick patch, ChatGPT's code works.

Successful project build in Xcode using a modified version of a code provided by the ChatGPT.

Can ChatGPT produce a complete app?

Since ChatGPT can help us construct app components, we may question if it can write a full app in one go.

Question ChatGPT:

Asking ChatGPT to write a meditation app for iOS.

ChatGPT supplied basic code and instructions. It's unclear if ChatGPT purposely limits output or if my prompt wasn't good enough, but the tool cannot produce an entire app from a single prompt.

However, we can contact ChatGPT for thorough Swift app construction instructions.

Asking ChatGPT about instructions for building SwiftUI app.

We can ask ChatGPT for step-by-step instructions now that we know what to do. Request a basic app layout from ChatGPT.

Ask ChatGPT to generate a layout for the iOS app.

Copying this code to an Xcode project generates a functioning layout.

A layout built by XCode using the code provided by ChatGPT.

Takeaways

  • ChatGPT may provide step-by-step instructions on how to develop an app for a specific system, and individual steps can be utilized as prompts to ChatGPT. ChatGPT cannot generate the source code for the full program in one go.

  • The output that ChatGPT produces needs to be examined by a human. The majority of the time, you will need to polish or adjust ChatGPT's output, whether you develop a color scheme or a layout for the iOS app.

  • ChatGPT is unable to produce media material. Although ChatGPT cannot be used to produce images or sounds, it can assist you build prompts for programs like midjourney or Dalle-2 so that they can provide the appropriate images for you.

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

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

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

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

Expressions in mathematics and built-in mathematical functions

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

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

Linux utilizes clear math expressions.

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

Inbuilt max and min functions can minimize verbose if statements.

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

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

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

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

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

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

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

Logarithms and Geometry Understanding

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

GetWindowRect is a Windows GUI SDK geometric object.

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

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

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

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

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

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

Employing Mathematical Data Structures

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

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

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

Recognizing Applications of Recursion

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

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

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

Conclusion

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

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