Choose.

DNA makes us distinct.

We act alike. Most people follow the same road, ignoring differences. We remain quiet about our uniqueness for fear of exclusion (family, social background, religion). We live a more or less imposed life.

Off the beaten path, we stand out from the others. We obey without realizing we're sewing a shroud. We're told to do as everyone else and spend 40 years dreaming of a golden retirement and regretting not living.

“One of the greatest regrets in life is being what others would want you to be, rather than being yourself.” - Shannon L. Alder

Others dare. Again, few are creative; most follow the example of those who establish a business for the sake of entrepreneurship. To live.

They pick a potential market and model their MVP on an existing solution. Most mimic others, alter a few things, appear to be original, and end up with bland products, adding to an already crowded market.

SaaS, PaaS, etc. followed suit. It's reduced pricing, profitability, and product lifespan.

As competitors become more aggressive, their profitability diminishes, making life horrible for them and their employees. They fail to innovate, cut costs, and close their company.

Few of them look happy and fulfilled.

How did they do it?

The answer is unsettlingly simple.

They are themselves.

• They start their company, propelled at first by a passion or maybe a calling.

• Then, at their own pace, they create it with the intention of resolving a dilemma.

• They assess what others are doing and consider how they might improve it.

• In contrast to them, they respond to it in their own way by adding a unique personal touch. Therefore, it is obvious.

Originals, like their DNA, can't be copied. Or if they are, they're poorly printed. Originals are unmatched. Artist-like. True collectors only buy Picasso paintings by the master, not forgeries, no matter how good.

Imaginative people are constantly ahead. Copycats fall behind unless they innovate. They watch their competition continuously. Their solution or product isn't sexy. They hope to cash in on their copied product by flooding the market.

They're mostly pirates. They're short-sighted, unlike creators.

Creators see further ahead and have no rivals. They use copiers to confirm a necessity. To maintain their individuality, creators avoid copying others. They find copying boring. It's boring. They oppose plagiarism.

It's thrilling and inspiring.

It will also make them more able to withstand their opponents' tension. Not to mention roadblocks. For creators, impediments are games.

Others fear it. They race against the clock and fear threats that could interrupt their momentum since they lack inventiveness and their product has a short life cycle.

Creators have time on their side. They're dedicated. Clearly. Passionate booksellers will have their own bookstore. Their passion shows in their book choices. Only the ones they love.

The copier wants to display as many as possible, including mediocre authors, and will cut costs. All this to dominate the market. They're digging their own grave.

The bookseller is just one example. I could give you tons of them.

Closing remarks

Entrepreneurs might follow others or be themselves. They risk exhaustion trying to predict what their followers will do.

It's true.

Life offers choices.

Being oneself or doing as others do, with the possibility of regretting not expressing our uniqueness and not having lived.

“Be yourself; everyone else is already taken”. Oscar Wilde

The choice is yours.

Y Combinators Winter 2022 Demo Day continues the trend of more startups engaging in accelerator Demo Days. Our team evaluated almost 400 projects in Y Combinator's ninth year.

After Winter 2021 Demo Day, we noticed a hurry pushing shorter rounds, inflated valuations, and larger batches.

Despite the batch size, this event's behavior showed a return to normalcy. Our observations show that investors evaluate and fund businesses more carefully. Unlike previous years, more YC businesses gave investors with data rooms and thorough pitch decks in addition to valuation data before Demo Day.

Demo Day pitches were virtual and fast-paced, limiting unplanned meetings. Investors had more time and information to do their due research before meeting founders. Our staff has more time to study diverse areas and engage with interesting entrepreneurs and founders.

This was one of the most regionally diversified YC cohorts to date. This year's Winter Demo Day startups showed some interesting tendencies.

Trends and Industries to Watch Before Demo Day

Demo day events at any accelerator show how investment competition is influencing startups. As startups swiftly become scale-ups and big success stories in fintech, e-commerce, healthcare, and other competitive industries, entrepreneurs and early-stage investors feel pressure to scale quickly and turn a notion into actual innovation.

Too much eagerness can lead founders to focus on market growth and team experience instead of solid concepts, technical expertise, and market validation. Last year, YC Winter Demo Day funding cycles ended too quickly and valuations were unrealistically high.

Scrum Ventures observed a longer funding cycle this year compared to last year's Demo Day. While that seems promising, many factors could be contributing to change, including:

• Market patterns are changing and the economy is becoming worse.

• the industries that investors are thinking about.

• Individual differences between each event batch and the particular businesses and entrepreneurs taking part

The Winter 2022 Batch's Trends

Each year, we also wish to examine trends among early-stage firms and YC event participants. More international startups than ever were anticipated to present at Demo Day.

Less than 50% of demo day startups were from the U.S. For the S21 batch, firms from outside the US were most likely in Latin America or Europe, however this year's batch saw a large surge in startups situated in Asia and Africa.

YC Startup Directory

163 out of 399 startups were B2B software and services companies. Financial, healthcare, and consumer startups were common.

Our team doesn't plan to attend every pitch or speak with every startup's founders or team members. Let's look at cleantech, Web3, and health and wellness startup trends.

Our Opinions Following Conversations with 87 Startups at Demo Day

In the lead-up to Demo Day, we spoke with 87 of the 125 startups going. Compared to B2C enterprises, B2B startups had higher average valuations. A few outliers with high valuations pushed B2B and B2C means above the YC-wide mean and median.

Many of these startups develop business and technology solutions we've previously covered. We've seen API, EdTech, creative platforms, and cybersecurity remain strong and increase each year.

While these persistent tendencies influenced the startups Scrum Ventures looked at and the founders we interacted with on Demo Day, new trends required more research and preparation. Let's examine cleantech, Web3, and health and wellness startups.

Hardware and software that is green

Cleantech enterprises demand varying amounts of funding for hardware and software. Although the same overarching trend is fueling the growth of firms in this category, each subgroup has its own strategy and technique for investigation and identifying successful investments.

Many cleantech startups we spoke to during the YC event are focused on helping industrial operations decrease or recycle carbon emissions.

• Carbon Crusher: Creating carbon negative roads

• Phase Biolabs: Turning carbon emissions into carbon negative products and carbon neutral e-fuels

• Seabound: Capturing carbon dioxide emissions from ships

• Fleetzero: Creating electric cargo ships

• Impossible Mining: Sustainable seabed mining

• Beyond Aero: Creating zero-emission private aircraft

• Verdn: Helping businesses automatically embed environmental pledges for product and service offerings, boost customer engagement

• AeonCharge: Allowing electric vehicle (EV) drivers to more easily locate and pay for EV charging stations

• Phoenix Hydrogen: Offering a hydrogen marketplace and a connected hydrogen hub platform to connect supply and demand for hydrogen fuel and simplify hub planning and partner program expansion

• Aklimate: Allowing businesses to measure and reduce their supply chain’s environmental impact

• Pina Earth: Certifying and tracking the progress of businesses’ forestry projects

• AirMyne: Developing machines that can reverse emissions by removing carbon dioxide from the air

• Unravel Carbon: Software for enterprises to track and reduce their carbon emissions

Web3: NFTs, the metaverse, and cryptocurrency

Web3 technologies handle a wide range of business issues. This category includes companies employing blockchain technology to disrupt entertainment, finance, cybersecurity, and software development.

Many of these startups overlap with YC's FinTech trend. Despite this, B2C and B2B enterprises were evenly represented in Web3. We examined:

• Stablegains: Offering consistent interest on cash balance from the decentralized finance (DeFi) market

• LiquiFi: Simplifying token management with automated vesting contracts, tax reporting, and scheduling. For companies, investors, and finance & accounting

• NFTScoring: An NFT trading platform

• CypherD Wallet: A multichain wallet for crypto and NFTs with a non-custodial crypto debit card that instantly converts coins to USD

• Remi Labs: Allowing businesses to more easily create NFT collections that serve as access to products, memberships, events, and more

• Cashmere: A crypto wallet for Web3 startups to collaboratively manage funds

• Chaingrep: An API that makes blockchain data human-readable and tokens searchable

• Courtyard: A platform for securely storing physical assets and creating 3D representations as NFTs

• Arda: “Banking as a Service for DeFi,” an API that FinTech companies can use to embed DeFi products into their platforms

• earnJARVIS: A premium cryptocurrency management platform, allowing users to create long-term portfolios

• Mysterious: Creating community-specific experiences for Web3 Discords

• Winter: An embeddable widget that allows businesses to sell NFTs to users purchasing with a credit card or bank transaction

• SimpleHash: An API for NFT data that provides compatibility across blockchains, standardized metadata, accurate transaction info, and simple integration

• Lifecast: Tools that address motion sickness issues for 3D VR video

• Gym Class: Virtual reality (VR) multiplayer basketball video game

• WorldQL: An asset API that allows NFT creators to specify multiple in-game interpretations of their assets, increasing their value

• Bonsai Desk: A software development kit (SDK) for 3D analytics

• Campfire: Supporting virtual social experiences for remote teams

• Unai: A virtual headset and Visual World experience

• Vimmerse: Allowing creators to more easily create immersive 3D experiences

Fitness and health

Scrum Ventures encountered fewer health and wellness startup founders than Web3 and Cleantech. The types of challenges these organizations solve are still diverse. Several of these companies are part of a push toward customization in healthcare, an area of biotech set for growth for companies with strong portfolios and experienced leadership.

Here are several startups we considered:

• Syrona Health: Personalized healthcare for women in the workplace

• Anja Health: Personalized umbilical cord blood banking and stem cell preservation

• Alfie: A weight loss program focused on men’s health that coordinates medical care, coaching, and “community-based competition” to help users lose an average of 15% body weight

• Ankr Health: An artificial intelligence (AI)-enabled telehealth platform that provides personalized side effect education for cancer patients and data collection for their care teams

• Koko — A personalized sleep program to improve at-home sleep analysis and training

• Condition-specific telehealth platforms and programs:

• Reviving Mind: Chronic care management covered by insurance and supporting holistic, community-oriented health care

• Equipt Health: At-home delivery of prescription medical equipment to help manage chronic conditions like obstructive sleep apnea

• LunaJoy: Holistic women’s healthcare management for mental health therapy, counseling, and medication

12 Startups from YC's Winter 2022 Demo Day to Watch

Bobidi: 10x faster AI model improvement

Artificial intelligence (AI) models have become a significant tool for firms to improve how well and rapidly they process data. Bobidi helps AI-reliant firms evaluate their models, boosting data insights in less time and reducing data analysis expenditures. The business has created a gamified community that offers a bug bounty for AI, incentivizing community members to test and find weaknesses in clients' AI models.

Magna: DeFi investment management and token vesting

Magna delivers rapid, secure token vesting so consumers may turn DeFi investments into primitives. Carta for Web3 allows enterprises to effortlessly distribute tokens to staff or investors. The Magna team hopes to allow corporations use locked tokens as collateral for loans, facilitate secondary liquidity so investors can sell shares on a public exchange, and power additional DeFi applications.

Perl Street: Funding for infrastructure

This Fintech firm intends to help hardware entrepreneurs get financing by [democratizing] structured finance, unleashing billions for sustainable infrastructure and next-generation hardware solutions. This network has helped hardware entrepreneurs achieve more than $140 million in finance, helping companies working on energy storage devices, EVs, and creating power infrastructure.

CypherD: Multichain cryptocurrency wallet

CypherD seeks to provide a multichain crypto wallet so general customers can explore Web3 products without knowledge hurdles. The startup's beta app lets consumers access crypto from EVM blockchains. The founders have crypto, financial, and startup experience.

Unravel Carbon: Enterprise carbon tracking and offsetting

Unravel Carbon's AI-powered decarbonization technology tracks companies' carbon emissions. Singapore-based startup focuses on Asia. The software can use any company's financial data to trace the supply chain and calculate carbon tracking, which is used to make regulatory disclosures and suggest carbon offsets.

LunaJoy: Precision mental health for women

LunaJoy helped women obtain mental health support throughout life. The platform combines data science to create a tailored experience, allowing women to access psychotherapy, medication management, genetic testing, and health coaching.

Posh: Automated EV battery recycling

Posh attempts to solve one of the EV industry's largest logistical difficulties. Millions of EV batteries will need to be decommissioned in the next decade, and their precious metals and residual capacity will go unused for some time. Posh offers automated, scalable lithium battery disassembly, making EV battery recycling more viable.

Unai: VR headset with 5x higher resolution

Unai stands apart from metaverse companies. Its VR headgear has five times the resolution of existing options and emphasizes human expression and interaction in a remote world. Maxim Perumal's method of latency reduction powers current VR headsets.

Palitronica: Physical infrastructure cybersecurity

Palitronica blends cutting-edge hardware and software to produce networked electronic systems that support crucial physical and supply chain infrastructure. The startup's objective is to build solutions that defend national security and key infrastructure from cybersecurity threats.

Reality Defender: Deepfake detection

Reality Defender alerts firms to bogus users and changed audio, video, and image files. Reality Deference's API and web app score material in real time to prevent fraud, improve content moderation, and detect deception.

Micro Meat: Infrastructure for the manufacture of cell-cultured meat

MicroMeat promotes sustainable meat production. The company has created technologies to scale up bioreactor-grown meat muscle tissue from animal cells. Their goal is to scale up cultured meat manufacturing so cultivated meat products can be brought to market feasibly and swiftly, boosting worldwide meat consumption.

Fleetzero: Electric cargo ships

This startup's battery technology will make cargo ships more sustainable and profitable. Fleetzero's electric cargo ships have five times larger profit margins than fossil fuel ships. Fleetzeros' founder has marine engineering, ship operations, and enterprise sales and business experience.

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.

Too much NFT, Discord, and shitposting.

How do you choose?

How do you recruit more members to join your NFT project?

In 2021, a successful NFT project required:

• Monkey/ape artwork

• Twitter and Discord bot-filled

• Roadmap overpromise

• Goal was quick cash.

2022 and the years after will change that.

These are 6 Rules for a Strong NFT Community in 2022:

THINK LONG TERM

This relates to roadmap planning. Hype and dumb luck may drive NFT projects (ahem, goblins) but rarely will your project soar.

Instead, consider sustainability.

Plan your roadmap based on your team's abilities.

Do what you're already doing, but with NFTs, make it bigger and better.

You shouldn't copy a project's roadmap just because it was profitable.

This will lead to over-promising, team burnout, and an RUG NFT project.

OFFER VALUE

Building a great community starts with giving.

Why are musicians popular?

Because they offer entertainment for everyone, a random person becomes a fan, and more fans become a cult.

That's how you should approach your community.

TEAM UP

A great team helps.

An NFT project could have 3 or 2 people.

Credibility trumps team size.

Make sure your team can answer community questions, resolve issues, and constantly attend to them.

Don't overwork and burn out.

Your community will be able to recognize that you are trying too hard and give up on the project.

BUILD A GREAT PRODUCT

Bored Ape Yacht Club altered the NFT space.

Cryptopunks transformed NFTs.

Many others did, including Okay Bears.

What made them that way?

Because they answered a key question.

What is my NFT supposed to be?

Before planning art, this question must be answered.

NFTs can't be just jpegs.

What does it represent?

Is it a Metaverse-ready project?

What blockchain are you going to be using and why?

Set some ground rules for yourself. This helps your project's direction.

These questions will help you and your team set a direction for blockchain, NFT, and Web3 technology.

EDUCATE ON WEB3

The more the team learns about Web3 technology, the more they can offer their community.

Think tokens, metaverse, cross-chain interoperability and more.

BUILD A GREAT COMMUNITY

Several projects mistreat their communities.

They treat their community like "customers" and try to sell them NFT.

Providing Whitelists and giveaways aren't your only community-building options.

Think bigger.

Consider them family and friends, not wallets.

Consider them fans.

These are some tips to start your NFT project.

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.

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.