I've worked in a People role at seven early-stage firms for over 15 years (I enjoy chasing a dream!). Few of the seven achieved profitability, including unicorn status or acquisition.

Did early-stage startups share anything? Was there a difference between winners and losers? YES.

I support founders and entrepreneurs building financially sustainable enterprises with a compelling cause. This isn't something everyone would do. A company's success demands more than guts. Founders drive startup success.

Six Qualities of Successful Startups

Successful startup founders either innately grasped the correlation between strong team engagement and a well-executed business model, or they knew how to ask and listen to others (executive coaches, other company leaders, the team itself) to learn about it.

Successful startups:

1. Co-founders agreed and got along personally.

Multi-founder startups are common. When co-founders agree on strategic decisions and are buddies, there's less friction and politics at work.

As a co-founder, ask your team if you're aligned. They'll explain.

I've seen C-level leaders harbor personal resentments over disagreements. A co-departure founder's caused volatile leadership and work disruptions that the team struggled to manage during and after.

2. Team stayed.

Successful startups have low turnover. Nobody is leaving. There may be a termination for performance, but other team members will have observed the issues and agreed with the decision.

You don't want organizational turnover of 30%+, with leaders citing performance issues but the team not believing them. This breeds suspicion.

Something is wrong if many employees leave voluntarily or involuntarily. You may hear about lack of empowerment, support, or toxic leadership in exit interviews and from the existing team. Intellectual capital loss and resource instability harm success.

3. Team momentum.

A successful startup's team is excited about its progress. Consistently achieving goals and having trackable performance metrics. Some describe this period of productivity as magical, with great talents joining the team and the right people in the right places. Increasing momentum.

I've also seen short-sighted decisions where only some departments, like sales and engineering, had goals. Lack of a unified goals system created silos and miscommunication. Some employees felt apathetic because they didn't know how they contributed to team goals.

4. Employees advanced in their careers.

Even if you haven't created career pathing or professional development programs, early-stage employees will grow and move into next-level roles. If you hire more experienced talent and leaders, expect them to mentor existing team members. Growing companies need good performers.

New talent shouldn't replace and discard existing talent. This creates animosity and makes existing employees feel unappreciated for their early contributions to the company.

5. The company lived its values.

Culture and identity are built on lived values. A company's values affect hiring, performance management, rewards, and other processes. Identify, practice, and believe in company values. Starting with team values instead of management or consultants helps achieve this. When a company's words and actions match, it builds trust.

When company values are beautifully displayed on a wall but few employees understand them, the opposite is true. If an employee can't name the company values, they're useless.

6. Communication was clear.

When necessary information is shared with the team, they feel included, trusted, and like owners. Transparency means employees have the needed information to do their jobs. Disclosure builds trust. The founders answer employees' questions honestly.

Information accessibility decreases office politics. Without transparency, even basic information is guarded and many decisions are made in secret. I've seen founders who don't share financial, board meeting, or compensation and equity information. The founders' lack of trust in the team wasn't surprising, so it was reciprocated.

The Choices

Finally. All six of the above traits (leadership alignment, minimal turnover, momentum, professional advancement, values, and transparency) were high in the profitable startups I've worked at, including unicorn status or acquisition.

I've seen these as the most common and constant signals of startup success or failure.

These characteristics are the product of founders' choices. These decisions lead to increased team engagement and business execution.

Here's something to consider for startup employees and want-to-bes. 90% of startups fail, despite the allure of building something new and gaining ownership. With the emotional and time investment in startup formation, look for startups with these traits to reduce your risk.

Both you and the startup will thrive in these workplaces.

Unexpected Success

Shopify CEO and co-founder Tobias Lutke. Shopify is worth $48 billion.

World-renowned entrepreneur Tobi

Tobi never expected his first online snowboard business to become a multimillion-dollar software corporation.

Tobi founded Shopify to establish a 20-person company.

The publicly traded corporation employs over 10,000 people.

Here's Tobi Lutke's incredible story.

Elon Musk tweeted his admiration for the Shopify creator.

30-October-2019.

Musk praised Shopify founder Tobi Lutke on Twitter.

Happened:

Explore this programmer's journey.

What difficulties did Tobi experience as a young child?

Germany raised Tobi.

Tobi's parents realized he was smart but had trouble learning as a toddler.

Tobi was learning disabled.

Tobi struggled with school tests.

Tobi's learning impairments were undiagnosed.

Tobi struggled to read as a dyslexic.

Tobi also found school boring.

Germany's curriculum didn't inspire Tobi's curiosity.

“The curriculum in Germany was taught like here are all the solutions you might find useful later in life, spending very little time talking about the problem…If I don’t understand the problem I’m trying to solve, it’s very hard for me to learn about a solution to a problem.”

Studying computer programming

After tenth grade, Tobi decided school wasn't for him and joined a German apprenticeship program.

This curriculum taught Tobi software engineering.

He was an apprentice in a small Siemens subsidiary team.

Tobi worked with rebellious Siemens employees.

Team members impressed Tobi.

Tobi joined the team for this reason.

Tobi was pleased to get paid to write programming all day.

His life could not have been better.

Devoted to snowboarding

Tobi loved snowboarding.

He drove 5 hours to ski at his folks' house.

His friends traveled to the US to snowboard when he was older.

However, the cheap dollar conversion rate led them to Canada.

2000.

Tobi originally decided to snowboard instead than ski.

Snowboarding captivated him in Canada.

On the trip to Canada, Tobi encounters his wife.

Tobi meets his wife Fiona McKean on his first Canadian ski trip.

They maintained in touch after the trip.

Fiona moved to Germany after graduating.

Tobi was a startup coder.

Fiona found work in Germany.

Her work included editing, writing, and academics.

“We lived together for 10 months and then she told me that she need to go back for the master's program.”

With Fiona, Tobi immigrated to Canada.

Fiona invites Tobi.

Tobi agreed to move to Canada.

Programming helped Tobi move in with his girlfriend.

Tobi was an excellent programmer, therefore what he did in Germany could be done anywhere.

He worked remotely for his German employer in Canada.

Tobi struggled with remote work.

Due to poor communication.

No slack, so he used email.

Programmers had trouble emailing.

Tobi's startup was developing a browser.

After the dot-com crash, individuals left that startup.

It ended.

Tobi didn't intend to work for any major corporations.

Tobi left his startup.

He believed he had important skills for any huge corporation.

He refused to join a huge corporation.

Because of Siemens.

Tobi learned to write professional code and about himself while working at Siemens in Germany.

Siemens culture was odd.

Employees were distrustful.

Siemens' rigorous dress code implies that the corporation doesn't trust employees' attire.

It wasn't Tobi's place.

“There was so much bad with it that it just felt wrong…20-year-old Tobi would not have a career there.”

Focused only on snowboarding

Tobi lived in Ottawa with his girlfriend.

Canada is frigid in winter.

Ottawa's winters last.

Almost half a year.

Tobi wanted to do something worthwhile now.

So he snowboarded.

Tobi began snowboarding seriously.

He sought every snowboarding knowledge.

He researched the greatest snowboarding gear first.

He created big spreadsheets for snowboard-making technologies.

Tobi grew interested in selling snowboards while researching.

He intended to sell snowboards online.

He had no choice but to start his own company.

A small local company offered Tobi a job.

Interested.

He must sign papers to join the local company.

He needed a work permit when he signed the documents.

Tobi had no work permit.

He was allowed to stay in Canada while applying for permanent residency.

“I wasn’t illegal in the country, but my state didn’t give me a work permit. I talked to a lawyer and he told me it’s going to take a while until I get a permanent residency.”

Tobi's lawyer told him he cannot get a work visa without permanent residence.

His lawyer said something else intriguing.

Tobis lawyer advised him to start a business.

Tobi declined this local company's job offer because of this.

Tobi considered opening an internet store with his technical skills.

He sold snowboards online.

“I was thinking of setting up an online store software because I figured that would exist and use it as a way to sell snowboards…make money while snowboarding and hopefully have a good life.”

What brought Tobi and his co-founder together, and how did he support Tobi?

Tobi lived with his girlfriend's parents.

In Ottawa, Tobi encounters Scott Lake.

Scott was Tobis girlfriend's family friend and worked for Tobi's future employer.

Scott and Tobi snowboarded.

Tobi pitched Scott his snowboard sales software idea.

Scott liked the idea.

They planned a business together.

“I was looking after the technology and Scott was dealing with the business side…It was Scott who ended up developing relationships with vendors and doing all the business set-up.”

Issues they ran into when attempting to launch their business online

Neither could afford a long-term lease.

That prompted their online business idea.

They would open a store.

Tobi anticipated opening an internet store in a week.

Tobi seeks open-source software.

Most existing software was pricey.

Tobi and Scott couldn't afford pricey software.

“In 2004, I was sitting in front of my computer absolutely stunned realising that we hadn’t figured out how to create software for online stores.”

They required software to:

• to upload snowboard images to the website.

• people to look up the types of snowboards that were offered on the website. There must be a search feature in the software.

• Online users transmit payments, and the merchant must receive them.

• notifying vendors of the recently received order.

No online selling software existed at the time.

Online credit card payments were difficult.

How did they advance the software while keeping expenses down?

Tobi and Scott needed money to start selling snowboards.

Tobi and Scott funded their firm with savings.

“We both put money into the company…I think the capital we had was around CAD 20,000(Canadian Dollars).”

Despite investing their savings.

They minimized costs.

They tried to conserve.

No office rental.

They worked in several coffee shops.

Tobi lived rent-free at his girlfriend's parents.

He installed software in coffee cafes.

How were the software issues handled?

Tobi found no online snowboard sales software.

Two choices remained:

1. Change your mind and try something else.

2. Use his programming expertise to produce something that will aid in the expansion of this company.

Tobi knew he was the sole programmer working on such a project from the start.

“I had this realisation that I’m going to be the only programmer who has ever worked on this, so I don’t have to choose something that lots of people know. I can choose just the best tool for the job…There is been this programming language called Ruby which I just absolutely loved ”

Ruby was open-source and only had Japanese documentation.

Latin is the source code.

Tobi used Ruby twice.

He assumed he could pick the tool this time.

Why not build with Ruby?

How did they find their first time operating a business?

Tobi writes applications in Ruby.

He wrote the initial software version in 2.5 months.

Tobi and Scott founded Snowdevil to sell snowboards.

Tobi coded for 16 hours a day.

His lifestyle was unhealthy.

He enjoyed pizza and coke.

“I would never recommend this to anyone, but at the time there was nothing more interesting to me in the world.”

Their initial purchase and encounter with it

Tobi worked in cafes then.

“I was working in a coffee shop at this time and I remember everything about that day…At some time, while I was writing the software, I had to type the email that the software would send to tell me about the order.”

Tobi recalls everything.

He checked the order on his laptop at the coffee shop.

Pennsylvanian ordered snowboard.

Tobi walked home and called Scott. Tobi told Scott their first order.

They loved the order.

How were people made aware about Snowdevil?

2004 was very different.

Tobi and Scott attempted simple website advertising.

Google AdWords was new.

Ad clicks cost 20 cents.

Online snowboard stores were scarce at the time.

Google ads propelled the snowdevil brand.

Snowdevil prospered.

They swiftly recouped their original investment in the snowboard business because to its high profit margin.

Tobi and Scott struggled with inventories.

“Snowboards had really good profit margins…Our biggest problem was keeping inventory and getting it back…We were out of stock all the time.”

Selling snowboards returned their investment and saved them money.

They did not appoint a business manager.

They accomplished everything alone.

Sales dipped in the spring, but something magical happened.

Spring sales plummeted.

They considered stocking different boards.

They naturally wanted to add boards and grow the business.

However, magic occurred.

Tobi coded and improved software while running Snowdevil.

He modified software constantly. He wanted speedier software.

He experimented to make the software more resilient.

Tobi received emails requesting the Snowdevil license.

They intended to create something similar.

“I didn’t stop programming, I was just like Ok now let me try things, let me make it faster and try different approaches…Increasingly I got people sending me emails and asking me If I would like to licence snowdevil to them. People wanted to start something similar.”

Software or skateboards, your choice

Scott and Tobi had to choose a hobby in 2005.

They might sell alternative boards or use software.

The software was a no-brainer from demand.

Daniel Weinand is invited to join Tobi's business.

Tobis German best friend is Daniel.

Tobi and Scott chose to use the software.

Tobi and Scott kept the software service.

Tobi called Daniel to invite him to Canada to collaborate.

Scott and Tobi had quit snowboarding until then.

How was Shopify launched, and whence did the name come from?

The three chose Shopify.

Named from two words.

First:

• Shop

Final part:

• Simplify

Shopify

Shopify's crew has always had one goal:

• creating software that would make it simple and easy for people to launch online storefronts.

Launched Shopify after raising money for the first time.

Shopify began fundraising in 2005.

First, they borrowed from family and friends.

They needed roughly $200k to run the company efficiently.

$200k was a lot then.

When questioned why they require so much money. Tobi told them to trust him with their goals. The team raised seed money from family and friends.

Shopify.com has a landing page. A demo of their goal was on the landing page.

In 2006, Shopify had about 4,000 emails.

Shopify rented an Ottawa office.

“We sent a blast of emails…Some people signed up just to try it out, which was exciting.”

How things developed after Scott left the company

Shopify co-founder Scott Lake left in 2008.

Scott was CEO.

“He(Scott) realized at some point that where the software industry was going, most of the people who were the CEOs were actually the highly technical person on the founding team.”

Scott leaving the company worried Tobi.

Tobis worried about finding a new CEO.

To Tobi:

A great VC will have the network to identify the perfect CEO for your firm.

Tobi started visiting Silicon Valley to meet with venture capitalists to recruit a CEO.

Initially visiting Silicon Valley

Tobi came to Silicon Valley to start a 20-person company.

This company creates eCommerce store software.

Tobi never wanted a big corporation. He desired a fulfilling existence.

“I stayed in a hostel in the Bay Area. I had one roommate who was also a computer programmer. I bought a bicycle on Craiglist. I was there for a week, but ended up staying two and a half weeks.”

Tobi arrived unprepared.

When venture capitalists asked him business questions.

He answered few queries.

Tobi didn't comprehend VC meetings' terminology.

He wrote the terms down and looked them up.

Some were fascinated after he couldn't answer all these queries.

“I ended up getting the kind of term sheets people dream about…All the offers were conditional on moving our company to Silicon Valley.”

Canada received Tobi.

He wanted to consult his team before deciding. Shopify had five employees at the time.

2008.

A global recession greeted Tobi in Canada. The recession hurt the market.

His term sheets were useless.

The economic downturn in the world provided Shopify with a fantastic opportunity.

The global recession caused significant job losses.

Fired employees had several ideas.

They wanted online stores.

Entrepreneurship was desired. They wanted to quit work.

People took risks and tried new things during the global slump.

Shopify subscribers skyrocketed during the recession.

“In 2009, the company reached neutral cash flow for the first time…We were in a position to think about long-term investments, such as infrastructure projects.”

Then, Tobi Lutke became CEO.

How did Tobi perform as the company's CEO?

“I wasn’t good. My team was very patient with me, but I had a lot to learn…It’s a very subtle job.”

2009–2010.

Tobi limited the company's potential.

He deliberately restrained company growth.

Tobi had one costly problem:

• Whether Shopify is a venture or a lifestyle business.

The company's annual revenue approached $1 million.

Tobi battled with the firm and himself despite good revenue.

His wife was supportive, but the responsibility was crushing him.

“It’s a crushing responsibility…People had families and kids…I just couldn’t believe what was going on…My father-in-law gave me money to cover the payroll and it was his life-saving.”

Throughout this trip, everyone supported Tobi.

They believed it.

$7 million in donations received

Tobi couldn't decide if this was a lifestyle or a business.

Shopify struggled with marketing then.

Later, Tobi tried 5 marketing methods.

He told himself that if any marketing method greatly increased their growth, he would call it a venture, otherwise a lifestyle.

The Shopify crew brainstormed and voted on marketing concepts.

Tested.

“Every single idea worked…We did Adwords, published a book on the concept, sponsored a podcast and all the ones we tracked worked.”

To Silicon Valley once more

Shopify marketing concepts worked once.

Tobi returned to Silicon Valley to pitch investors.

He raised $7 million, valuing Shopify at $25 million.

All investors had board seats.

“I find it very helpful…I always had a fantastic relationship with everyone who’s invested in my company…I told them straight that I am not going to pretend I know things, I want you to help me.”

Tobi developed skills via running Shopify.

Shopify had 20 employees.

Leaving his wife's parents' home

Tobi left his wife's parents in 2014.

Tobi had a child.

Shopify has 80,000 customers and 300 staff in 2013.

Public offering in 2015

Shopify investors went public in 2015.

Shopify powers 4.1 million e-Commerce sites.

Shopify stores are 65% US-based.

It is currently valued at $48 billion.

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.

Kim Kardashian created Skky Partners. Consumer products, internet & e-commerce, consumer media, hospitality, and luxury are company targets.

Some call this another Kardashian publicity gimmick.

This maneuver is brilliance upon closer inspection. Why?

1) Kim has amassed a sizable social media fan base:

Over 320 million Instagram and 70 million Twitter users follow Kim Kardashian.

Kim Kardashian's Instagram account ranks 8th. Three Kardashians in top 10 is ridiculous.

This gives her access to consumer data. She knows what people are discussing. Investment firms need this data.

Quality, not quantity, of her followers matters. Studies suggest that her following are more engaged than Selena Gomez and Beyonce's.

Kim's followers are worth roughly $500 million to her brand, according to a research. They trust her and buy what she recommends.

2) She has a special aptitude for identifying trends.

Kim Kardashian can sense trends.

She's always ahead of fashion and beauty trends. She's always trying new things, too. She doesn't mind making mistakes when trying anything new. Her desire to experiment makes her a good business prospector.

Kim has also created a lifestyle brand that followers love. Kim is an entrepreneur, mom, and role model, not just a reality TV star or model. She's established a brand around her appearance, so people want to buy her things.

Her fragrance collection has sold over $100 million since its 2009 introduction, and her Sears apparel line did over $200 million in its first year.

SKIMS is her latest $3.2bn brand. She can establish multibillion-dollar firms with her enormous distribution platform.

Early founders would kill for Kim Kardashian's network.

Making great products is hard, but distribution is more difficult. — David Sacks, All-in-Podcast

3) She can delegate the financial choices to Jay Sammons, one of the greatest in the industry.

Jay Sammons is well-suited to develop Kim Kardashian's new private equity fund.

Sammons has 16 years of consumer investing experience at Carlyle. This will help Kardashian invest in consumer-facing enterprises.

Sammons has invested in Supreme and Beats Electronics, both of which have grown significantly. Sammons' track record and competence make him the obvious choice.

Kim Kardashian and Jay Sammons have joined forces to create a new business endeavor. The agreement will increase Kardashian's commercial empire. Sammons can leverage one of the world's most famous celebrities.

“Together we hope to leverage our complementary expertise to build the next generation consumer and media private equity firm” — Kim Kardashian

Kim Kardashian is a successful businesswoman. She developed an empire by leveraging social media to connect with fans. By developing a global lifestyle brand, she has sold things and experiences that have made her one of the world's richest celebrities.

She's a shrewd entrepreneur who knows how to maximize on herself and her image.

Imagine how much interest Kim K will bring to private equity and venture capital.

I'm curious about the company's growth.

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.