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.

A TECHNICAL THOUGHT

The IT giant is seeding the digital Great Renaissance.

Recently, technology has been dull.

We're still fascinated by processing speeds. Wearables are no longer an engineer's dream.

Apple has been quiet and avoided huge announcements. Slowness speaks something. Everything in the spaceship HQ seems to be turning slowly, unlike competitors around buzzwords.

Is this a sign of the impending storm?

Metas stock has fallen while Google milks dumb people. Microsoft steals money from corporations and annexes platforms like Linkedin.

Just surface bubbles?

Is Apple, one of the technology continents, pushing against all others to create a paradigm shift?

The fundamental human right to privacy

Apple's unusual remarks emphasize privacy. They incorporate it into their business models and judgments.

Apple believes privacy is a human right. There are no compromises.

This makes it hard for other participants to gain Apple's ecosystem's efficiencies.

Other players without hardware platforms lose.

Apple delivers new kidneys without rejection, unlike other software vendors. Nothing compromises your privacy.

Corporate citizenship will become more popular.

Apples have full coffers. They've started using that flow to better communities, which is great.

Apple's $2.5B home investment is one example. Google and Facebook are building or proposing to build workforce housing.

Apple's funding helps marginalized populations in more than 25 California counties, not just Apple employees.

Is this a trend, and does Apple keep giving back? Hope so.

I'm not cynical enough to suspect these investments have malicious motives.

The last frontier is the environment.

Climate change is a battle-to-win.

Long-term winners will be companies that protect the environment, turning climate change dystopia into sustainable growth.

Apple has been quietly changing its supply chain to be carbon-neutral by 2030.

“Apple is dedicated to protecting the planet we all share with solutions that are supporting the communities where we work.” Lisa Jackson, Apple’s vice president of environment.

Apple's $4.7 billion Green Bond investment will produce 1.2 gigawatts of green energy for the corporation and US communities. Apple invests $2.2 billion in Europe's green energy. In the Philippines, Thailand, Nigeria, Vietnam, Colombia, Israel, and South Africa, solar installations are helping communities obtain sustainable energy.

Apple is already carbon neutral today for its global corporate operations, and this new commitment means that by 2030, every Apple device sold will have net zero climate impact. -Apple.

Apple invests in green energy and forests to reduce its paper footprint in China and the US. Apple and the Conservation Fund are safeguarding 36,000 acres of US working forest, according to GreenBiz.

Apple's packaging paper is recycled or from sustainably managed forests.

What matters is the scale.

$1 billion is a rounding error for Apple.

These small investments originate from a tree with deep, spreading roots.

Apple's genes are anchored in building the finest products possible to improve consumers' lives.

I felt it when I switched to my iPhone while waiting for a train and had to pack my Macbook. iOS 16 dictation makes writing more enjoyable. Small change boosts productivity. Smooth transition from laptop to small screen and dictation.

Apples' tiny, well-planned steps have great growth potential for all consumers in everything they do.

There is clearly disruption, but it doesn't have to be violent

Digital channels, methods, and technologies have globalized human consciousness. One person's responsibility affects many.

Apple gives us tools to be privately connected. These technologies foster creativity, innovation, fulfillment, and safety.

Apple has invented a mountain of technologies, services, and channels to assist us adapt to the good future or combat evil forces who cynically aim to control us and ruin the environment and communities. Apple has quietly disrupted sectors for decades.

Google, Microsoft, and Meta, among others, should ride this wave. It's a tsunami, but it doesn't have to be devastating if we care, share, and cooperate with political decision-makers and community leaders worldwide.

A fresh Renaissance

Renaissance geniuses Michelangelo and Da Vinci. Different but seeing something no one else could yet see. Both were talented in many areas and could discover art in science and science in art.

These geniuses exemplified a period that changed humanity for the better. They created, used, and applied new, valuable things. It lives on.

Apple is a digital genius orchard. Wozniak and Jobs offered us fertile ground for the digital renaissance. We'll build on their legacy.

We may put our seeds there and see them bloom despite corporate greed and political ignorance.

I think the coming tsunami will illuminate our planet like the Renaissance.

Few sentences can have global significance.

Ethan Zuckerman invented the pop-up commercial in 1997.

He was working for Tripod.com, an online service that let people make little web pages for free. Tripod offered advertising to make money. Advertisers didn't enjoy seeing their advertising next to filthy content, like a user's anal sex website.

Zuckerman's boss wanted a solution. Wasn't there a way to move the ads away from user-generated content?

When you visited a Tripod page, a pop-up ad page appeared. So, the ad isn't officially tied to any user page. It'd float onscreen.

Here’s the thing, though: Zuckerman’s bit of Javascript, that created the popup ad? It was incredibly short — a single line of code:

window.open('http://tripod.com/navbar.html'
"width=200, height=400, toolbar=no, scrollbars=no, resizable=no, target=_top");

Javascript tells the browser to open a 200-by-400-pixel window on top of any other open web pages, without a scrollbar or toolbar.

Simple yet harmful! Soon, commercial websites mimicked Zuckerman's concept, infesting the Internet with pop-up advertising. In the early 2000s, a coder for a download site told me that most of their revenue came from porn pop-up ads.

Pop-up advertising are everywhere. You despise them. Hopefully, your browser blocks them.

Zuckerman wrote a single line of code that made the world worse.

I read Zuckerman's story in How 26 Lines of Code Changed the World. Torie Bosch compiled a humorous anthology of short writings about code that tipped the world.

Most of these samples are quite short. Pop-cultural preconceptions about coding say that important code is vast and expansive. Hollywood depicts programmers as blurs spouting out Niagaras of code. Google's success was formerly attributed to its 2 billion lines of code.

It's usually not true. Google's original breakthrough, the piece of code that propelled Google above its search-engine counterparts, was its PageRank algorithm, which determined a web page's value based on how many other pages connected to it and the quality of those connecting pages. People have written their own Python versions; it's only a few dozen lines.

Google's operations, like any large tech company's, comprise thousands of procedures. So their code base grows. The most impactful code can be brief.

The examples are fascinating and wide-ranging, so read the whole book (or give it to nerds as a present). Charlton McIlwain wrote a chapter on the police beat algorithm developed in the late 1960s to anticipate crime hotspots so law enforcement could dispatch more officers there. It created a racial feedback loop. Since poor Black neighborhoods were already overpoliced compared to white ones, the algorithm directed more policing there, resulting in more arrests, which convinced it to send more police; rinse and repeat.

Kelly Chudler's You Are Not Expected To Understand This depicts the police-beat algorithm.

Even shorter code changed the world: the tracking pixel.

Lily Hay Newman's chapter on monitoring pixels says you probably interact with this code every day. It's a snippet of HTML that embeds a single tiny pixel in an email. Getting an email with a tracking code spies on me. As follows: My browser requests the single-pixel image as soon as I open the mail. My email sender checks to see if Clives browser has requested that pixel. My email sender can tell when I open it.

Adding a tracking pixel to an email is easy:

<img src="URL LINKING TO THE PIXEL ONLINE" width="0" height="0">

An older example: Ellen R. Stofan and Nick Partridge wrote a chapter on Apollo 11's lunar module bailout code. This bailout code operated on the lunar module's tiny on-board computer and was designed to prioritize: If the computer grew overloaded, it would discard all but the most vital work.

When the lunar module approached the moon, the computer became overloaded. The bailout code shut down anything non-essential to landing the module. It shut down certain lunar module display systems, scaring the astronauts. Module landed safely.

22-line code

POODOO    INHINT
    CA  Q
    TS  ALMCADR

    TC  BANKCALL
    CADR  VAC5STOR  # STORE ERASABLES FOR DEBUGGING PURPOSES.

    INDEX  ALMCADR
    CAF  0
ABORT2    TC  BORTENT

OCT77770  OCT  77770    # DONT MOVE
    CA  V37FLBIT  # IS AVERAGE G ON
    MASK  FLAGWRD7
    CCS  A
    TC  WHIMPER -1  # YES.  DONT DO POODOO.  DO BAILOUT.

    TC  DOWNFLAG
    ADRES  STATEFLG

    TC  DOWNFLAG
    ADRES  REINTFLG

    TC  DOWNFLAG
    ADRES  NODOFLAG

    TC  BANKCALL
    CADR  MR.KLEAN
    TC  WHIMPER

This fun book is worth reading.

I'm a contributor to the New York Times Magazine, Wired, and Mother Jones. I've also written Coders: The Making of a New Tribe and the Remaking of the World and Smarter Than You Think: How Technology is Changing Our Minds. Twitter and Instagram: @pomeranian99; Mastodon: @clive@saturation.social.

After a crazy second half of 2021 and significant trade volumes into 2022, the market for NFT artworks like Bored Ape Yacht Club, CryptoPunks, and Pudgy Penguins has begun a sharp collapse as market downturns hit token values.

DappRadar data shows NFT monthly sales have fallen below $1 billion since June 2021. OpenSea, the world's largest NFT exchange, has seen sales volume decline 75% since May and is trading like July 2021.

Prices of popular non-fungible tokens have also decreased. Bored Ape Yacht Club (BAYC) has witnessed volume and sales drop 63% and 15%, respectively, in the past month.

BeInCrypto analysis shows market decline. May 2022 cryptocurrency marketplace volume was $4 billion, according to a news platform. This is a sharp drop from April's $7.18 billion.

OpenSea, a big marketplace, contributed $2.6 billion, while LooksRare, Magic Eden, and Solanart also contributed.

NFT markets are digital platforms for buying and selling tokens, similar stock trading platforms. Although some of the world's largest exchanges offer NFT wallets, most users store their NFTs on their favorite marketplaces.

In January 2022, overall NFT sales volume was $16.57 billion, with LooksRare contributing $11.1 billion. May 2022's volume was $12.57 less than January, a 75% drop, and June's is expected to be considerably smaller.

A World Based on Utility

Despite declines in NFT trading volumes, not all investors are negative on NFTs. Although there are uncertainties about the sustainability of NFT-based art collections, there are fewer reservations about utility-based tokens and their significance in technology's future.

In June, business CEO Christof Straub said NFTs may help artists monetize unreleased content, resuscitate catalogs, establish deeper fan connections, and make processes more efficient through technology.

We all know NFTs can't be JPEGs. Straub noted that NFT music rights can offer more equitable rewards to musicians.

Music NFTs are here to stay if they have real value, solve real problems, are trusted and lawful, and have fair and sustainable business models.

NFTs can transform numerous industries, including music. Market opinion is shifting towards tokens with more utility than the social media artworks we're used to seeing.

While the major NFT names remain dominant in terms of volume, new utility-based initiatives are emerging as top 20 collections.

Otherdeed, Sorare, and NBA Top Shot are NFT-based games that rank above Bored Ape Yacht Club and Cryptopunks.

Users can switch video NFTs of basketball players in NBA Top Shot. Similar efforts are emerging in the non-fungible landscape.

Sorare shows how NFTs can support a new way of playing fantasy football, where participants buy and swap trading cards to create a 5-player team that wins rewards based on real-life performances.

Sorare raised 579.7 million in one of Europe's largest Series B financing deals in September 2021. Recently, the platform revealed plans to expand into Major League Baseball.

Strong growth indications suggest a promising future for NFTs. The value of art-based collections like BAYC and CryptoPunks may be questioned as markets become diluted by new limited collections, but the potential for NFTs to become intrinsically linked to tangible utility like online gaming, music and art, and even corporate reward schemes shows the industry has a bright future.

I've been pondering product strategy and how to articulate it. Frameworks helped guide our thinking.

If your teams aren't working together or there's no clear path to victory, your product strategy may not be well-articulated or communicated (if you have one).

Before diving into a product strategy's details, it's important to understand its role in the bigger picture — the pieces that move your organization forward.

the overall picture

A product strategy is crucial, in my opinion. It's part of a successful product or business. It's the showpiece.

To simplify, we'll discuss four main components:

1. Vision

2. Product Management

3. Goals

4. Roadmap

Vision

Your company's mission? Your company/product in 35 years? Which headlines?

The vision defines everything your organization will do in the long term. It shows how your company impacted the world. It's your organization's rallying cry.

An ambitious but realistic vision is needed.

Without a clear vision, your product strategy may be inconsistent.

Product Management

Our main subject. Product strategy connects everything. It fulfills the vision.

In Part 2, we'll discuss product strategy.

Goals

This component can be goals, objectives, key results, targets, milestones, or whatever goal-tracking framework works best for your organization.

These product strategy metrics will help your team prioritize strategies and roadmaps.

Your company's goals should be unified. This fuels success.

Roadmap

The roadmap is your product strategy's timeline. It provides a prioritized view of your team's upcoming deliverables.

A roadmap is time-bound and includes measurable goals for your company. Your team's steps and capabilities for executing product strategy.

If your team has trouble prioritizing or defining a roadmap, your product strategy or vision is likely unclear.

Formulation of a Product Strategy

Now that we've discussed where your product strategy fits in the big picture, let's look at a framework.

A product strategy should include challenges, an approach, and actions.

Challenges

First, analyze the problems/situations you're solving. It can be customer- or company-focused.

The analysis should explain the problems and why they're important. Try to simplify the situation and identify critical aspects.

Some questions:

• What issues are we attempting to resolve?

• What obstacles—internal or otherwise—are we attempting to overcome?

• What is the opportunity, and why should we pursue it, in your opinion?

Decided Method

Second, describe your approach. This can be a set of company policies for handling the challenge. It's the overall approach to the first part's analysis.

The approach can be your company's bets, the solutions you've found, or how you'll solve the problems you've identified.

Again, these questions can help:

• What is the value that we hope to offer to our clients?

• Which market are we focusing on first?

• What makes us stand out? Our benefit over rivals?

Actions

Third, identify actions that result from your approach. Second-part actions should be these.

Coordinate these actions. You may need to add products or features to your roadmap, acquire new capabilities through partnerships, or launch new marketing campaigns. Whatever fits your challenges and strategy.

Final questions:

• What skills do we need to develop or obtain?

• What is the chosen remedy? What are the main outputs?

• What else ought to be added to our road map?

Put everything together

… and iterate!

Strategy isn't one-and-done. Changes occur. Economies change. Competitors emerge. Customer expectations change.

One unexpected event can make strategies obsolete quickly. Muscle it. Review, evaluate, and course-correct your strategies with your teams. Quarterly works. In a new or unstable industry, more often.

What Is That?

Berkus is a pre-revenue valuation method based exclusively on qualitative criteria, like Scorecard.

Few firms match their financial estimates, especially in the early stages, so valuation methodologies like the Berkus method are a good way to establish a valuation when the economic measures are not reliable.

How does it work?

This technique evaluates five key success factors.

• Fundamental principle

• Technology

• Execution

• Strategic alliances in its primary market

• Production, followed by sales

The Berkus technique values the business idea and four success factors. As seen in the matrix below, each of these dimensions poses a danger to the startup's success.

It assigns $0-$500,000 to each of these beginning regions. This approach enables a maximum $2.5M pre-money valuation.

This approach relies significantly on geography and uses the US as a baseline, as it differs in every country in Europe.

A set of standards for analyzing each dimension individually

Fundamental principle (or strength of the idea)

Ideas are worthless; execution matters. Most of us can relate to seeing a new business open in our area or a startup get funded and thinking, "I had this concept years ago!" Someone did it.

The concept remains. To assess the idea's viability, we must consider several criteria.

• The concept's exclusivity It is necessary to protect a product or service's concept using patents and copyrights. Additionally, it must be capable of generating large profits.

• Planned growth and growth that goes in a specific direction have a lot of potential, therefore incorporating them into a business is really advantageous.

• The ability of a concept to grow A venture's ability to generate scalable revenue is a key factor in its emergence and continuation. A startup needs a scalable idea in order to compete successfully in the market.

• The attraction of a business idea to a broad spectrum of people is significantly influenced by the current socio-political climate. Thus, the requirement for the assumption of conformity.

• Concept Validation Ideas must go through rigorous testing with a variety of audiences in order to lower risk during the implementation phase.

Technology (Prototype)

This aspect reduces startup's technological risk. How good is the startup prototype when facing cyber threats, GDPR compliance (in Europe), tech stack replication difficulty, etc.?

Execution

Check the management team's efficacy. A potential angel investor must verify the founders' experience and track record with previous ventures. Good leadership is needed to chart a ship's course.

Strategic alliances in its primary market

Existing and new relationships will play a vital role in the development of both B2B and B2C startups. What are the startup's synergies? potential ones?

Production, followed by sales (product rollout)

Startup success depends on its manufacturing and product rollout. It depends on the overall addressable market, the startup's ability to market and sell their product, and their capacity to provide consistent, high-quality support.

Example

We're now founders of EyeCaramba, a machine vision-assisted streaming platform. My imagination always goes to poor puns when naming a startup.

Since we're first-time founders and the Berkus technique depends exclusively on qualitative methods and the evaluator's skill, we ask our angel-investor acquaintance for a pre-money appraisal of EyeCaramba.

Our friend offers us the following table:

Because we're first-time founders, our pal lowered our Execution score. He knows the idea's value and that the gaming industry is red-hot, with worse startup ideas getting funded, therefore he gave the Basic value the highest value (idea).

EyeCaramba's pre-money valuation is $400,000 + $250,000 + $75,000 + $275,000 + $164,000 (1.16M). Good.

References

• https://medium.com/humble-ventures/how-angel-investors-value-pre-revenue-startups-part-iii-8271405f0774#:~:text=pre%2Drevenue%20startups.-,Berkus%20Method,potential%20of%20the%20idea%20itself.%E2%80%9D

• https://eqvista.com/berkus-valuation-method-for-startups/

• https://www.venionaire.com/early-stage-startup-valuation-part-2-the-berkus-method/