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.

Great News about the new Google Business Intelligence Solution

Google has renamed Data Studio to Looker Studio and Looker Studio Pro.

Now, Google releases Looker Studio Pro. Similar to the move from Data Studio to Looker Studio, Looker Studio Pro is basically what Looker was previously, but both solutions will merge. Google says the Pro edition will acquire new enterprise management features, team collaboration capabilities, and SLAs.

In addition to Google's announcements and sales methods, additional features include:

Looker Studio assets can now have organizational ownership. Customers can link Looker Studio to a Google Cloud project and migrate existing assets once. This provides:

• Your users' created Looker Studio assets are all kept in a Google Cloud project.

• When the users who own assets leave your organization, the assets won't be removed.

• Using IAM, you may provide each Looker Studio asset in your company project-level permissions.

• Other Cloud services can access Looker Studio assets that are owned by a Google Cloud project.

Looker Studio Pro clients may now manage report and data source access at scale using team workspaces.

Google announcing these features for the pro version is fascinating. Both products will likely converge, but Google may only release many features in the premium version in the future. Microsoft with Power BI and its free and premium variants already achieves this.

Sources and Further Readings

Google, Release Notes (2022)

Google, Looker (2022)

In this essay, I studied REAL NFT use examples and their potential uses.

Knowledge of the Hype Cycle

Gartner's Hype Cycle.

It proposes 5 phases for disruptive technology.

1. Technology Trigger: the emergence of potentially disruptive technology.

2. Peak of Inflated Expectations: Early publicity creates hype. (Ex: 2021 Bubble)

3. Trough of Disillusionment: Early projects fail to deliver on promises and the public loses interest. I suspect NFTs are somewhere around this trough of disillusionment now.

4. Enlightenment slope: The tech shows successful use cases.

5. Plateau of Productivity: Mainstream adoption has arrived and broader market applications have proven themselves. Here’s a more detailed visual of the Gartner Hype Cycle from Wikipedia.

In the speculative NFT bubble of 2021, @beeple sold Everydays: the First 5000 Days for $69 MILLION in 2021's NFT bubble.

@nbatopshot sold millions in video collectibles.

This is when expectations peaked.

Let's examine NFTs' real-world applications.

Watch this video if you're unfamiliar with NFTs.

Online Art

Most people think NFTs are rich people buying worthless JPEGs and MP4s.

Digital artwork and collectibles are revolutionary for creators and enthusiasts.

NFT Profile Pictures

You might also have seen NFT profile pictures on Twitter.

My profile picture is an NFT I coined with @skogards factoria app, which helps me avoid bogus accounts.

Profile pictures are a good beginning point because they're unique and clearly yours.

NFTs are a way to represent proof-of-ownership. It’s easier to prove ownership of digital assets than physical assets, which is why artwork and pfps are the first use cases.

They can do much more.

NFTs can represent anything with a unique owner and digital ownership certificate. Domains and usernames.

Usernames & Domains

@unstoppableweb, @ensdomains, @rarible sell NFT domains.

NFT domains are transferable, which is a benefit.

Godaddy and other web2 providers have difficult-to-transfer domains. Domains are often leased instead of purchased.

Tickets

NFTs can also represent concert tickets and event passes.

There's a limited number, and entry requires proof.

NFTs can eliminate the problem of forgery and make it easy to verify authenticity and ownership.

NFT tickets can be traded on the secondary market, which allows for:

1. marketplaces that are uniform and offer the seller and buyer security (currently, tickets are traded on inefficient markets like FB & craigslist)

2. unbiased pricing

3. Payment of royalties to the creator

4. Historical ticket ownership data implies performers can airdrop future passes, discounts, etc.

5. NFT passes can be a fandom badge.

The $30B+ online tickets business is increasing fast.

NFT-based ticketing projects:

• @GetProtocol

• @SeatlabNFT

• @YellowHeartNFT

• @GUTStickets

• @WicketEvents

Gaming Assets

NFTs also help in-game assets.

Imagine someone spending five years collecting a rare in-game blade, then outgrowing or quitting the game. Gamers value that collectible.

The gaming industry is expected to make $200 BILLION in revenue this year, a significant portion of which comes from in-game purchases.

Royalties on secondary market trading of gaming assets encourage gaming businesses to develop NFT-based ecosystems.

Digital assets are the start. On-chain NFTs can represent real-world assets effectively.

Real estate has a unique owner and requires ownership confirmation.

Real Estate

Tokenizing property has many benefits.

1. Can be fractionalized to increase access, liquidity

2. Can be collateralized to increase capital efficiency and access to loans backed by an on-chain asset

3. Allows investors to diversify or make bets on specific neighborhoods, towns or cities +++

I've written about this thought exercise before.

I made an animated video explaining this.

We've just explored NFTs for transferable assets. But what about non-transferrable NFTs?

SBTs are Soul-Bound Tokens. Vitalik Buterin (Ethereum co-founder) blogged about this.

NFTs are basically verifiable digital certificates.

Diplomas & Degrees

That fits Degrees & Diplomas. These shouldn't be marketable, thus they can be non-transferable SBTs.

Anyone can verify the legitimacy of on-chain credentials, degrees, abilities, and achievements.

The same goes for other awards.

For example, LinkedIn could give you a verified checkmark for your degree or skills.

Authenticity Protection

NFTs can also safeguard against counterfeiting.

Counterfeiting is the largest criminal enterprise in the world, estimated to be $2 TRILLION a year and growing.

Anti-counterfeit tech is valuable.

This is one of @ORIGYNTech's projects.

Identity

Identity theft/verification is another real-world problem NFTs can handle.

In the US, 15 million+ citizens face identity theft every year, suffering damages of over $50 billion a year.

This isn't surprising considering all you need for US identity theft is a 9-digit number handed around in emails, documents, on the phone, etc.

Identity NFTs can fix this.

• NFTs are one-of-a-kind and unforgeable.

• NFTs offer a universal standard.

• NFTs are simple to verify.

• SBTs, or non-transferrable NFTs, are tied to a particular wallet.

• In the event of wallet loss or theft, NFTs may be revoked.

This could be one of the biggest use cases for NFTs.

Imagine a global identity standard that is standardized across countries, cannot be forged or stolen, is digital, easy to verify, and protects your private details.

Since your identity is more than your government ID, you may have many NFTs.

@0xPolygon and @civickey are developing on-chain identity.

Memberships

NFTs can authenticate digital and physical memberships.

Voting

NFT IDs can verify votes.

If you remember 2020, you'll know why this is an issue.

Online voting's ease can boost turnout.

Informational property

NFTs can protect IP.

This can earn creators royalties.

NFTs have 2 important properties:

• Verifiability IP ownership is unambiguously stated and publicly verified.

• Platforms that enable authors to receive royalties on their IP can enter the market thanks to standardization.

Content Rights

Monetization without copyrighting = more opportunities for everyone.

This works well with the music.

Spotify and Apple Music pay creators very little.

Crowdfunding

Creators can crowdfund with NFTs.

NFTs can represent future royalties for investors.

This is particularly useful for fields where people who are not in the top 1% can’t make money. (Example: Professional sports players)

Mirror.xyz allows blog-based crowdfunding.

Financial NFTs

This introduces Financial NFTs (fNFTs). Unique financial contracts abound.

Examples:

• a person's collection of assets (unique portfolio)

• A loan contract that has been partially repaid with a lender

• temporal tokens (ex: veCRV)

Legal Agreements

Not just financial contracts.

NFT can represent any legal contract or document.

Messages & Emails

What about other agreements? Verbal agreements through emails and messages are likewise unique, but they're easily lost and fabricated.

Health Records

Medical records or prescriptions are another types of documentation that has to be verified but isn't.

Medical NFT examples:

• Immunization records

• Covid test outcomes

• Prescriptions

• health issues that may affect one's identity

• Observations made via health sensors

Existing systems of proof by paper / PDF have photoshop-risk.

I tried to include most use scenarios, but this is just the beginning.

NFTs have many innovative uses.

For example: @ShaanVP minted an NFT called “5 Minutes of Fame” 👇

Here are 2 Twitter threads about NFTs:

1. This piece of gold by @chriscantino

2. This conversation between @punk6529 and @RaoulGMI on @RealVision“The World According to @punk6529”

If you're wondering why NFTs are better than web2 databases for these use scenarios, see this Twitter thread I wrote:

If you liked this, please share it.

It’s only a loss if you sell, right?

Nayib Bukele proclaimed himself “the world’s coolest dictator”.

His jokes aren't clear.

El Salvador's 43rd president self-proclaimed “CEO of El Salvador” couldn't be less presidential.

His thin jeans, aviator sunglasses, and baseball caps like a cartel lord.

He's popular, though.

Bukele won 53% of the vote by fighting violent crime and opposition party corruption.

El Salvador's 6.4 million inhabitants are riding the cryptocurrency volatility wave.

They were powerless.

Their autocratic leader, a former Yamaha Motors salesperson and Bitcoin believer, wants to help 70% unbanked locals.

He intended to give the citizens a way to save money and cut the country's $200 million remittance cost.

Transfer and deposit costs.

This makes logical sense when the president’s theatrics don’t blind you.

El Salvador's Bukele revealed plans to make bitcoin legal tender.

Remittances total $5.9 billion (23%) of the country's expenses.

Anything that reduces costs could boost the economy.

The country’s unbanked population is staggering. Here’s the data by % of people who either have a bank account (Blue) or a mobile money account (Black).

According to Bukele, 46% of the population has downloaded the Chivo Bitcoin Wallet.

In 2021, 36% of El Salvadorans had bank accounts.

Large rural countries like Kenya seem to have resolved their unbanked dilemma.

An economy surfaced where village locals would sell, trade and store network minutes and data as a store of value.

Kenyan phone networks realized unbanked people needed a safe way to accumulate wealth and have an emergency fund.

96% of Kenyans utilize M-PESA, which doesn't require a bank account.

The software involves human agents who hang out with cash and a phone.

These people are like ATMs.

You offer them cash to deposit money in your mobile money account or withdraw cash.

In a country with a faulty banking system, cash availability and a safe place to deposit it are important.

William Jack and Tavneet Suri found that M-PESA brought 194,000 Kenyan households out of poverty by making transactions cheaper and creating a safe store of value.

2016 Science paper

Mobile money, a service that allows monetary value to be stored on a mobile phone and sent to other users via text messages, has been adopted by most Kenyan households. We estimate that access to the Kenyan mobile money system M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty.

The impacts, which are more pronounced for female-headed households, appear to be driven by changes in financial behaviour — in particular, increased financial resilience and saving. Mobile money has therefore increased the efficiency of the allocation of consumption over time while allowing a more efficient allocation of labour, resulting in a meaningful reduction of poverty in Kenya.

Currently, El Salvador has 2,301 Bitcoin.

At publication, it's worth $44 million. That remains 41% of Bukele's original $105.6 million.

Unknown if the country has sold Bitcoin, but Bukeles keeps purchasing the dip.

It's still falling.

This might be a fantastic move for the impoverished country over the next five years, if they can live economically till Bitcoin's price recovers.

The evidence demonstrates that a store of value pulls individuals out of poverty, but others say Bitcoin is premature.

You may regard it as an aggressive endeavor to front run the next wave of adoption, offering El Salvador a financial upside.