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Matthew O'Riordan

Matthew O'Riordan

3 years ago

Trends in SaaS Funding from 2016 to 2022

More on Entrepreneurship/Creators

Jared Heyman

Jared Heyman

3 years ago

The survival and demise of Y Combinator startups

I've written a lot about Y Combinator's success, but as any startup founder or investor knows, many startups fail.

Rebel Fund invests in the top 5-10% of new Y Combinator startups each year, so we focus on identifying and supporting the most promising technology startups in our ecosystem. Given the power law dynamic and asymmetric risk/return profile of venture capital, we worry more about our successes than our failures. Since the latter still counts, this essay will focus on the proportion of YC startups that fail.

Since YC's launch in 2005, the figure below shows the percentage of active, inactive, and public/acquired YC startups by batch.

As more startups finish, the blue bars (active) decrease significantly. By 12 years, 88% of startups have closed or exited. Only 7% of startups reach resolution each year.

YC startups by status after 12 years:

Half the startups have failed, over one-third have exited, and the rest are still operating.

In venture investing, it's said that failed investments show up before successful ones. This is true for YC startups, but only in their early years.

Below, we only present resolved companies from the first chart. Some companies fail soon after establishment, but after a few years, the inactive vs. public/acquired ratio stabilizes around 55:45. After a few years, a YC firm is roughly as likely to quit as fail, which is better than I imagined.

I prepared this post because Rebel investors regularly question me about YC startup failure rates and how long it takes for them to exit or shut down.

Early-stage venture investors can overlook it because 100x investments matter more than 0x investments.

YC founders can ignore it because it shouldn't matter if many of their peers succeed or fail ;)

ʟ ᴜ ᴄ ʏ

ʟ ᴜ ᴄ ʏ

3 years ago

The Untapped Gold Mine of Inspiration and Startup Ideas

I joined the 1000 Digital Startups Movement (Gerakan 1000 Startup Digital) in 2017 and learned a lot about the startup sector. My previous essay outlined what a startup is and what must be prepared. Here I'll offer raw ideas for better products.

Image by macrovector on Freepik

Intro

A good startup solves a problem. These can include environmental, economic, energy, transportation, logistics, maritime, forestry, livestock, education, tourism, legal, arts and culture, communication, and information challenges. Everything I wrote is simply a basic idea (as inspiration) and requires more mapping and validation. Learn how to construct a startup to maximize launch success.

Adrian Gunadi (Investree Co-Founder) taught me that a Founder or Co-Founder must be willing to be CEO (Chief Everything Officer). Everything is independent, including drafting a proposal, managing finances, and scheduling appointments. The best individuals will come to you if you're the best. It's easier than consulting Andy Zain (Kejora Capital Founder).

Description

To help better understanding from your idea, try to answer this following questions:

- Describe your idea/application
Maximum 1000 characters.

- Background
Explain the reasons that prompted you to realize the idea/application.

- Objective
Explain the expected goals of the creation of the idea/application.

- Solution
A solution that tells your idea can be the right solution for the problem at hand.

- Uniqueness
What makes your idea/app unique?

- Market share
Who are the people who need and are looking for your idea?

- Marketing Ways and Business Models
What is the best way to sell your idea and what is the business model?

Not everything here is a startup idea. It's meant to inspire creativity and new perspectives.

Ideas

#Application

1. Medical students can operate on patients or not. Applications that train prospective doctors to distinguish body organs and their placement are useful. In the advanced stage, the app can be built with numerous approaches so future doctors can practice operating on patients based on their ailments. If they made a mistake, they'd start over. Future doctors will be more assured and make fewer mistakes this way.

2. VR (virtual reality) technology lets people see 3D space from afar. Later, similar technology was utilized to digitally sell properties, so buyers could see the inside and room contents. Every gadget has flaws. It's like a gold mine for robbers. VR can let prospective students see a campus's facilities. This facility can also help hotels promote their products.

3. How can retail entrepreneurs maximize sales? Most popular goods' sales data. By using product and brand/type sales figures, entrepreneurs can avoid overstocking. Walmart computerized their procedures to track products from the manufacturer to the store. As Retail Link products sell out, suppliers can immediately step in.

4. Failing to marry is something to be avoided. But if it had to happen, the loss would be like the proverb “rub salt into the wound”.  On the I do Now I dont website, Americans who don't marry can resell their jewelry to other brides-to-be. If some want to cancel the wedding and receive their down money and dress back, others want a wedding with particular criteria, such as a quick date and the expected building. Create a DP takeover marketplace for both sides.

#Games

1. Like in the movie, players must exit the maze they enter within 3 minutes or the shape will change, requiring them to change their strategy. The maze's transformation time will shorten after a few stages.

2. Treasure hunts involve following clues to uncover hidden goods. Here, numerous sponsors are combined in one boat, and participants can choose a game based on the prizes. Let's say X-mart is a sponsor and provides riddles or puzzles to uncover the prize in their store. After gathering enough points, the player can trade them for a gift utilizing GPS and AR (augmented reality). Players can collaborate to increase their chances of success.

3. Where's Wally? Where’s Wally displays a thick image with several things and various Wally-like characters. We must find the actual Wally, his companions, and the desired object. Make a game with a map where players must find objects for the next level. The player must find 5 artifacts randomly placed in an Egyptian-style mansion, for example. In the room, there are standard tickets, pass tickets, and gold tickets that can be removed for safekeeping, as well as a wall-mounted carpet that can be stored but not searched and turns out to be a flying rug that can be used to cross/jump to a different place. Regular tickets are spread out since they can buy life or stuff. At a higher level, a black ticket can lower your ordinary ticket. Objects can explode, scattering previously acquired stuff. If a player runs out of time, they can exchange a ticket for more.

#TVprogram

1. At the airport there are various visitors who come with different purposes. Asking tourists to live for 1 or 2 days in the city will be intriguing to witness.

2. Many professions exist. Carpenters, cooks, and lawyers must have known about job desks. Does HRD (Human Resource Development) only recruit new employees? Many don't know how to become a CEO, CMO, COO, CFO, or CTO. Showing young people what a Program Officer in an NGO does can help them choose a career.

#StampsCreations

Philatelists know that only the government can issue stamps. I hope stamps are creative so they have more worth.

1. Thermochromic pigments (leuco dyes) are well-known for their distinctive properties. By putting pigments to black and white batik stamps, for example, the black color will be translucent and display the basic color when touched (at a hot temperature).

2. In 2012, Liechtenstein Post published a laser-art Chinese zodiac stamp. Belgium (Bruges Market Square 2012), Taiwan (Swallow Tail Butterfly 2009), etc. Why not make a stencil of the president or king/queen?

3. Each country needs its unique identity, like Taiwan's silk and bamboo stamps. Create from your country's history. Using traditional paper like washi (Japan), hanji (Korea), and daluang/saeh (Indonesia) can introduce a country's culture.

4. Garbage has long been a problem. Bagasse, banana fronds, or corn husks can be used as stamp material.

5. Austria Post published a stamp containing meteor dust in 2006. 2004 meteorite found in Morocco produced the dust. Gibraltar's Rock of Gilbraltar appeared on stamps in 2002. What's so great about your country? East Java is muddy (Lapindo mud). Lapindo mud stamps will be popular. Red sand at Pink Beach, East Nusa Tenggara, could replace the mud.

#PostcardCreations

1. Map postcards are popular because they make searching easier. Combining laser-cut road map patterns with perforated 200-gram paper glued on 400-gram paper as a writing medium. Vision-impaired people can use laser-cut maps.

2. Regional art can be promoted by tucking traditional textiles into postcards.

3. A thin canvas or plain paper on the card's front allows the giver to be creative.

4. What is local crop residue? Cork lids, maize husks, and rice husks can be recycled into postcard materials.

5. Have you seen a dried-flower bookmark? Cover the postcard with mica and add dried flowers. If you're worried about losing the flowers, you can glue them or make a postcard envelope.

6. Wood may be ubiquitous; try a 0.2-mm copper plate engraved with an image and connected to a postcard as a writing medium.

7. Utilized paper pulp can be used to hold eggs, smartphones, and food. Form a smooth paper pulp on the plate with the desired image, the Golden Gate bridge, and paste it on your card.

8. Postcards can promote perfume. When customers rub their hands on the card with the perfume image, they'll smell the aroma.

#Tour #Travel

Tourism activities can be tailored to tourists' interests or needs. Each tourist benefits from tourism's distinct aim.

Let's define tourism's objective and purpose.

  • Holiday Tour is a tour that its participants plan and do in order to relax, have fun, and amuse themselves.

  • A familiarization tour is a journey designed to help travelers learn more about (survey) locales connected to their line of work.

  • An educational tour is one that aims to give visitors knowledge of the field of work they are visiting or an overview of it.

  • A scientific field is investigated and knowledge gained as the major goal of a scientific tour.

  • A pilgrimage tour is one designed to engage in acts of worship.

  • A special mission tour is one that has a specific goal, such a commerce mission or an artistic endeavor.

  • A hunting tour is a destination for tourists that plans organized animal hunting that is only allowed by local authorities for entertainment purposes.

Every part of life has tourism potential. Activities include:

1. Those who desire to volunteer can benefit from the humanitarian theme and collaboration with NGOs. This activity's profit isn't huge but consider the environmental impact.

2. Want to escape the city? Meditation travel can help. Beautiful spots around the globe can help people forget their concerns. A certified yoga/meditation teacher can help travelers release bad energy.

3. Any prison visitors? Some prisons, like those for minors under 17, are open to visitors. This type of tourism helps mental convicts reach a brighter future.

4. Who has taken a factory tour/study tour? Outside-of-school study tour (for ordinary people who have finished their studies). Not everyone in school could tour industries, workplaces, or embassies to learn and be inspired. Shoyeido (an incense maker) and Royce (a chocolate maker) offer factory tours in Japan.

5. Develop educational tourism like astronomy and archaeology. Until now, only a few astronomy enthusiasts have promoted astronomy tourism. In Indonesia, archaeology activities focus on site preservation, and to participate, office staff must undertake a series of training (not everyone can take a sabbatical from their routine). Archaeological tourist activities are limited, whether held by history and culture enthusiasts or in regional tours.

6. Have you ever longed to observe a film being made or your favorite musician rehearsing? Such tours can motivate young people to pursue entertainment careers.

7. Pamper your pets to reduce stress. Many pet owners don't have time for walks or treats. These premium services target the wealthy.

8. A quirky idea to provide tours for imaginary couples or things. Some people marry inanimate objects or animals and seek to make their lover happy; others cherish their ashes after death.

#MISCideas

1. Fashion is a lifestyle, thus people often seek fresh materials. Chicken claws, geckos, snake skin casings, mice, bats, and fish skins are also used. Needs some improvement, definitely.

2. As fuel supplies become scarcer, people hunt for other energy sources. Sound is an underutilized renewable energy. The Batechsant technology converts environmental noise into electrical energy, according to study (Battery Technology Of Sound Power Plant). South Korean researchers use Sound-Driven Piezoelectric Nanowire based on Nanogenerators to recharge cell phone batteries. The Batechsant system uses existing noise levels to provide electricity for street lamp lights, aviation, and ships. Using waterfall sound can also energize hard-to-reach locations.

3. A New York Times reporter said IQ doesn't ensure success. Our school system prioritizes IQ above EQ (Emotional Quotient). EQ is a sort of human intelligence that allows a person to perceive and analyze the dynamics of his emotions when interacting with others (and with himself). EQ is suspected of being a bigger source of success than IQ. EQ training can gain greater attention to help people succeed. Prioritize role models from school stakeholders, teachers, and parents to improve children' EQ.

4. Teaching focuses more on theory than practice, so students are less eager to explore and easily forget if they don't pay attention. Has an engineer ever made bricks from arid red soil? Morocco's non-college-educated builders can create weatherproof bricks from red soil without equipment. Can mechanical engineering grads create a water pump to solve water shortages in remote areas? Art graduates can innovate beyond only painting. Artists may create kinetic sculpture by experimenting so much. Young people should understand these sciences so they can be more creative with their potential. These might be extracurricular activities in high school and university.

5. People have been trying to recycle agricultural waste for a long time. Mycelium helps replace light, easily crushed tiles and bricks (a collection of hyphae like in the manufacture of tempe). Waste must contain lignocellulose. In this vein, anti-mainstream painting canvases can be made. The goal is to create the canvas uneven like an amoeba outline, not square or spherical. The resulting canvas is lightweight and needs no frame. Then what? Open source your idea like Precious Plastic to establish a community. By propagating this notion, many knowledgeable people will help improve your product's quality and impact.

6. As technology and humans adapt, fraud increases. Making phony doctor's letters to fool superiors, fake credentials to get hired, fraudulent land certificates to make money, and fake news (hoax). The existence of a Wikimedia can aid the community by comparing bogus and original information.

7. Do you often hit a problem-solving impasse? Since the Doraemon bag hasn't been made, construct an Idea Bank. Everyone can contribute to solving problems here. How do you recruit volunteers? Obviously, a reward is needed. Contributors can become moderators or gain complimentary tickets to TIA (Tech in Asia) conferences. Idea Bank-related concepts: the rise of startups without a solid foundation generates an age as old as corn that does not continue. Those with startup ideas should describe them here so they can be validated by other users. Other users can contribute input if a comparable notion is produced to improve the product or integrate it. Similar-minded users can become Co-Founders.

8. Why not invest in fruit/vegetables, inspired by digital farming? The landowner obtains free fruit without spending much money on maintenance. Investors can get fruits/vegetables in larger quantities, fresher, and cheaper during harvest. Fruits and vegetables are often harmed if delivered too slowly. Rich investors with limited land can invest in teak, agarwood, and other trees. When harvesting, investors might choose raw results or direct wood sales earnings. Teak takes at least 7 years to harvest, therefore long-term wood investments carry the risk of crop failure.

9. Teenagers in distant locations can't count, read, or write. Many factors hinder locals' success. Life's demands force them to work instead of study. Creating a learning playground may attract young people to learning. Make a skatepark at school. Skateboarders must learn in school. Donations buy skateboards.

10. Globally, online taxi-bike is known. By hiring a motorcycle/car online, people no longer bother traveling without a vehicle. What if you wish to cross the island or visit remote areas? Is online boat or helicopter rental possible like online taxi-bike? Such a renting process has been done independently thus far and cannot be done quickly.

11. What do startups need now? A startup or investor consultant. How many startups fail to become Unicorns? Many founders don't know how to manage investor money, therefore they waste it on promotions and other things. Many investors only know how to invest and can't guide a struggling firm.

“In times of crisis, the wise build bridges, while the foolish build barriers.” — T’Challa [Black Panther]

Don't chase cash. Money is a byproduct. Profit-seeking is stressful. Market requirements are opportunities. If you have something to say, please comment.

This is only informational. Before implementing ideas, do further study.

Eitan Levy

Eitan Levy

4 years ago

The Top 8 Growth Hacking Techniques for Startups

The Top 8 Growth Hacking Techniques for Startups

These startups, and how they used growth-hack marketing to flourish, are some of the more ethical ones, while others are less so.

Before the 1970 World Cup began, Puma paid footballer Pele $120,000 to tie his shoes. The cameras naturally focused on Pele and his Pumas, causing people to realize that Puma was the top football brand in the world.

Early workers of Uber canceled over 5,000 taxi orders made on competing applications in an effort to financially hurt any of their rivals.

PayPal developed a bot that advertised cheap goods on eBay, purchased them, and paid for them with PayPal, fooling eBay into believing that customers preferred this payment option. Naturally, Paypal became eBay's primary method of payment.

Anyone renting a space on Craigslist had their emails collected by AirBnB, who then urged them to use their service instead. A one-click interface was also created to list immediately on AirBnB from Craigslist.

To entice potential single people looking for love, Tinder developed hundreds of bogus accounts of attractive people. Additionally, for at least a year, users were "accidentally" linked.

Reddit initially created a huge number of phony accounts and forced them all to communicate with one another. It eventually attracted actual users—the real meaning of "fake it 'til you make it"! Additionally, this gave Reddit control over the tone of voice they wanted for their site, which is still present today.

To disrupt the conferences of their main rival, Salesforce recruited fictitious protestors. The founder then took over all of the event's taxis and gave a 45-minute pitch for his startup. No place to hide!

When a wholesaler required a minimum purchase of 10, Amazon CEO Jeff Bezos wanted a way to purchase only one book from them. A wholesaler would deliver the one book he ordered along with an apology for the other eight books after he discovered a loophole and bought the one book before ordering nine books about lichens. On Amazon, he increased this across all of the users.


Original post available here

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Ren & Heinrich

Ren & Heinrich

3 years ago

200 DeFi Projects were examined. Here is what I learned.

Photo by Luke Chesser on Unsplash

I analyze the top 200 DeFi crypto projects in this article.

This isn't a study. The findings benefit crypto investors.

Let’s go!

A set of data

I analyzed data from defillama.com. In my analysis, I used the top 200 DeFis by TVL in October 2022.

Total Locked Value

The chart below shows platform-specific locked value.

14 platforms had $1B+ TVL. 65 platforms have $100M-$1B TVL. The remaining 121 platforms had TVLs below $100 million, with the lowest being $23 million.

TVLs are distributed Pareto. Top 40% of DeFis account for 80% of TVLs.

Compliant Blockchains

Ethereum's blockchain leads DeFi. 96 of the examined projects offer services on Ethereum. Behind BSC, Polygon, and Avalanche.

Five platforms used 10+ blockchains. 36 between 2-10 159 used 1 blockchain.

Use Cases for DeFi

The chart below shows platform use cases. Each platform has decentralized exchanges, liquid staking, yield farming, and lending.

These use cases are DefiLlama's main platform features.

Which use case costs the most? Chart explains. Collateralized debt, liquid staking, dexes, and lending have high TVLs.

The DeFi Industry

I compared three high-TVL platforms (Maker DAO, Balancer, AAVE). The columns show monthly TVL and token price changes. The graph shows monthly Bitcoin price changes.

Each platform's market moves similarly.

Probably because most DeFi deposits are cryptocurrencies. Since individual currencies are highly correlated with Bitcoin, it's not surprising that they move in unison.

Takeaways

This analysis shows that the most common DeFi services (decentralized exchanges, liquid staking, yield farming, and lending) also have the highest average locked value.

Some projects run on one or two blockchains, while others use 15 or 20. Our analysis shows that a project's blockchain count has no correlation with its success.

It's hard to tell if certain use cases are rising. Bitcoin's price heavily affects the entire DeFi market.

TVL seems to be a good indicator of a DeFi platform's success and quality. Higher TVL platforms are cheaper. They're a better long-term investment because they gain or lose less value than DeFis with lower TVLs.

Coinbase

Coinbase

4 years ago

10 Predictions for Web3 and the Cryptoeconomy for 2022

By Surojit Chatterjee, Chief Product Officer

2021 proved to be a breakout year for crypto with BTC price gaining almost 70% yoy, Defi hitting $150B in value locked, and NFTs emerging as a new category. Here’s my view through the crystal ball into 2022 and what it holds for our industry:

1. Eth scalability will improve, but newer L1 chains will see substantial growth — As we welcome the next hundred million users to crypto and Web3, scalability challenges for Eth are likely to grow. I am optimistic about improvements in Eth scalability with the emergence of Eth2 and many L2 rollups. Traction of Solana, Avalanche and other L1 chains shows that we’ll live in a multi-chain world in the future. We’re also going to see newer L1 chains emerge that focus on specific use cases such as gaming or social media.

2. There will be significant usability improvements in L1-L2 bridges — As more L1 networks gain traction and L2s become bigger, our industry will desperately seek improvements in speed and usability of cross-L1 and L1-L2 bridges. We’re likely to see interesting developments in usability of bridges in the coming year.

3. Zero knowledge proof technology will get increased traction — 2021 saw protocols like ZkSync and Starknet beginning to get traction. As L1 chains get clogged with increased usage, ZK-rollup technology will attract both investor and user attention. We’ll see new privacy-centric use cases emerge, including privacy-safe applications, and gaming models that have privacy built into the core. This may also bring in more regulator attention to crypto as KYC/AML could be a real challenge in privacy centric networks.

4. Regulated Defi and emergence of on-chain KYC attestation — Many Defi protocols will embrace regulation and will create separate KYC user pools. Decentralized identity and on-chain KYC attestation services will play key roles in connecting users’ real identity with Defi wallet endpoints. We’ll see more acceptance of ENS type addresses, and new systems from cross chain name resolution will emerge.

5. Institutions will play a much bigger role in Defi participation — Institutions are increasingly interested in participating in Defi. For starters, institutions are attracted to higher than average interest-based returns compared to traditional financial products. Also, cost reduction in providing financial services using Defi opens up interesting opportunities for institutions. However, they are still hesitant to participate in Defi. Institutions want to confirm that they are only transacting with known counterparties that have completed a KYC process. Growth of regulated Defi and on-chain KYC attestation will help institutions gain confidence in Defi.

6. Defi insurance will emerge — As Defi proliferates, it also becomes the target of security hacks. According to London-based firm Elliptic, total value lost by Defi exploits in 2021 totaled over $10B. To protect users from hacks, viable insurance protocols guaranteeing users’ funds against security breaches will emerge in 2022.

7. NFT Based Communities will give material competition to Web 2.0 social networks — NFTs will continue to expand in how they are perceived. We’ll see creator tokens or fan tokens take more of a first class seat. NFTs will become the next evolution of users’ digital identity and passport to the metaverse. Users will come together in small and diverse communities based on types of NFTs they own. User created metaverses will be the future of social networks and will start threatening the advertising driven centralized versions of social networks of today.

8. Brands will start actively participating in the metaverse and NFTs — Many brands are realizing that NFTs are great vehicles for brand marketing and establishing brand loyalty. Coca-Cola, Campbell’s, Dolce & Gabbana and Charmin released NFT collectibles in 2021. Adidas recently launched a new metaverse project with Bored Ape Yacht Club. We’re likely to see more interesting brand marketing initiatives using NFTs. NFTs and the metaverse will become the new Instagram for brands. And just like on Instagram, many brands may start as NFT native. We’ll also see many more celebrities jumping in the bandwagon and using NFTs to enhance their personal brand.

9. Web2 companies will wake up and will try to get into Web3 — We’re already seeing this with Facebook trying to recast itself as a Web3 company. We’re likely to see other big Web2 companies dipping their toes into Web3 and metaverse in 2022. However, many of them are likely to create centralized and closed network versions of the metaverse.

10. Time for DAO 2.0 — We’ll see DAOs become more mature and mainstream. More people will join DAOs, prompting a change in definition of employment — never receiving a formal offer letter, accepting tokens instead of or along with fixed salaries, and working in multiple DAO projects at the same time. DAOs will also confront new challenges in terms of figuring out how to do M&A, run payroll and benefits, and coordinate activities in larger and larger organizations. We’ll see a plethora of tools emerge to help DAOs execute with efficiency. Many DAOs will also figure out how to interact with traditional Web2 companies. We’re likely to see regulators taking more interest in DAOs and make an attempt to educate themselves on how DAOs work.

Thanks to our customers and the ecosystem for an incredible 2021. Looking forward to another year of building the foundations for Web3. Wagmi.

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.