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.

Why breakthrough technologies must be accessible

ChatGPT has exploded. Over 1 million people have used the app, and coding sites like Stack Overflow have banned its answers. It's huge.

I wouldn't have called that as an AI researcher. ChatGPT uses the same GPT-3 technology that's been around for over two years.

More than impressive technology, ChatGPT 3 shows how access makes breakthroughs usable. OpenAI has finally made people realize the power of AI by packaging GPT-3 for normal users.

We think of Thomas Edison as the inventor of the lightbulb, not because he invented it, but because he popularized it.

Going forward, AI companies that make using AI easy will thrive.

Use-case importance

Most modern AI systems use massive language models. These language models are trained on 6,000+ years of human text.

GPT-3 ate 8 billion pages, almost every book, and Wikipedia. It created an AI that can write sea shanties and solve coding problems.

Nothing new. I began beta testing GPT-3 in 2020, but the system's basics date back further.

Tools like GPT-3 are hidden in many apps. Many of the AI writing assistants on this platform are just wrappers around GPT-3.

Lots of online utilitarian text, like restaurant menu summaries or city guides, is written by AI systems like GPT-3. You've probably read GPT-3 without knowing it.

Accessibility

Why is ChatGPT so popular if the technology is old?

ChatGPT makes the technology accessible. Free to use, people can sign up and text with the chatbot daily. ChatGPT isn't revolutionary. It does it in a way normal people can access and be amazed by.

Accessibility isn't easy. OpenAI's Sam Altman tweeted that opening ChatGPT to the public increased computing costs.

Each chat costs "low-digit cents" to process. OpenAI probably spends several hundred thousand dollars a day to keep ChatGPT running, with no immediate business case.

Academic researchers and others who developed GPT-3 couldn't afford it. Without resources to make technology accessible, it can't be used.

Retrospective

This dynamic is old. In the history of science, a researcher with a breakthrough idea was often overshadowed by an entrepreneur or visionary who made it accessible to the public.

We think of Thomas Edison as the inventor of the lightbulb. But really, Vasilij Petrov, Thomas Wright, and Joseph Swan invented the lightbulb. Edison made technology visible and accessible by electrifying public buildings, building power plants, and wiring.

Edison probably lost a ton of money on stunts like building a power plant to light JP Morgan's home, the NYSE, and several newspaper headquarters.

People wanted electric lights once they saw their benefits. By making the technology accessible and visible, Edison unlocked a hugely profitable market.

Similar things are happening in AI. ChatGPT shows that developing breakthrough technology in the lab or on B2B servers won't change the culture.

AI must engage people's imaginations to become mainstream. Before the tech impacts the world, people must play with it and see its revolutionary power.

As the field evolves, companies that make the technology widely available, even at great cost, will succeed.

OpenAI's compute fees are eye-watering. Revolutions are costly.

It's cheaper, faster charging, longer lasting, safer, and better for the environment.

Batteries are the future. Next-gen and planet-saving technology, including solar power and EVs, require batteries. As these smart technologies become more popular, we find that our batteries can't keep up. Lithium-ion batteries are expensive, slow to charge, big, fast to decay, flammable, and not environmentally friendly. MIT just created a new battery that eliminates all of these problems.  So, is this the battery of the future? Or is there a catch?

When I say entirely new, I mean it. This battery employs no currently available materials. Its electrodes are constructed of aluminium and pure sulfur instead of lithium-complicated ion's metals and graphite. Its electrolyte is formed of molten chloro-aluminate salts, not an organic solution with lithium salts like lithium-ion batteries.

How does this change in materials help?

Aluminum, sulfur, and chloro-aluminate salts are abundant, easy to acquire, and cheap. This battery might be six times cheaper than a lithium-ion battery and use less hazardous mining. The world and our wallets will benefit.

But don’t go thinking this means it lacks performance.

This battery charged in under a minute in tests. At 25 degrees Celsius, the battery will charge 25 times slower than at 110 degrees Celsius. This is because the salt, which has a very low melting point, is in an ideal state at 110 degrees and can carry a charge incredibly quickly. Unlike lithium-ion, this battery self-heats when charging and discharging, therefore no external heating is needed.

Anyone who's seen a lithium-ion battery burst might be surprised. Unlike lithium-ion batteries, none of the components in this new battery can catch fire. Thus, high-temperature charging and discharging speeds pose no concern.

These batteries are long-lasting. Lithium-ion batteries don't last long, as any iPhone owner can attest. During charging, metal forms a dendrite on the electrode. This metal spike will keep growing until it reaches the other end of the battery, short-circuiting it. This is why phone batteries only last a few years and why electric car range decreases over time. This new battery's molten salt slows deposition, extending its life. This helps the environment and our wallets.

These batteries are also energy dense. Some lithium-ion batteries have 270 Wh/kg energy density (volume and mass). Aluminum-sulfur batteries could have 1392 Wh/kg, according to calculations. They'd be 5x more energy dense. Tesla's Model 3 battery would weigh 96 kg instead of 480 kg if this battery were used. This would improve the car's efficiency and handling.

These calculations were for batteries without molten salt electrolyte. Because they don't reflect the exact battery chemistry, they aren't a surefire prediction.

This battery seems great. It will take years, maybe decades, before it reaches the market and makes a difference. Right?

Nope. The project's scientists founded Avanti to develop and market this technology.

So we'll soon be driving cheap, durable, eco-friendly, lightweight, and ultra-safe EVs? Nope.

This battery must be kept hot to keep the salt molten; otherwise, it won't work and will expand and contract, causing damage. This issue could be solved by packs that can rapidly pre-heat, but that project is far off.

Rapid and constant charge-discharge cycles make these batteries ideal for solar farms, homes, and EV charging stations. The battery is constantly being charged or discharged, allowing it to self-heat and maintain an ideal temperature.

These batteries aren't as sexy as those making EVs faster, more efficient, and cheaper. Grid batteries are crucial to our net-zero transition because they allow us to use more low-carbon energy. As we move away from fossil fuels, we'll need millions of these batteries, so the fact that they're cheap, safe, long-lasting, and environmentally friendly will be huge. Who knows, maybe EVs will use this technology one day. MIT has created another world-changing technology.

I've always bucked social media norms. YouTube doesn't compare. Traditional video made me zig when everyone zagged. Audio, picture personality animation, thought movies, and slide show videos are most popular and profitable.

YouTube's business is shifting. While most video experts swear by the idea that YouTube success is all about making personal and professional Face-Share-Videos, those who use YouTube for business know things are different.

In this article, I will share concepts from my mini master class Figures to Followers: Prioritizing Purposeful Profits Over Popularity on YouTube to Create the Win-Win for You, Your Audience & More and my forthcoming publication The WOWTUBE-PRENEUR FACTOR EVOLUTION: The Basics of Powerfully & Profitably Positioning Yourself as a Video Communications Authority to Broadcast Your WOW Effect as a Video Entrepreneur.

I've researched the psychology, anthropology, and anatomy of significant social media platforms as an entrepreneur and social media marketing expert. While building my YouTube empire, I've paid particular attention to what works for short, mid, and long-term success, whether it's a niche-focused, lifestyle, or multi-interest channel.

Most new, semi-new, and seasoned YouTubers feel vlog-style or live-on-camera videos are popular. Faceless, animated, music-text-based, and slideshow videos do well for businesses.

Buyer-consumer vs. content-consumer thinking is totally different when absorbing content. Profitability and popularity are closely related, however most people become popular with traditional means but not profitable.

In my experience, Faceless videos are more profitable, although it depends on the channel's style. Several professionals are now teaching in their courses that non-traditional films are making the difference in their business success and popularity.

Face-Share-Personal-Touch videos make audiences feel like they know the personality, but they're not profitable.

Most spend hours creating articles, videos, and thumbnails to seem good. That's how most YouTubers gained their success in the past, but not anymore.

Looking the part and performing a typical role in videos doesn't convert well, especially for newbie channels.

Working with video marketers and YouTubers for years, I've noticed that most struggle to be consistent with content publishing since they exclusively use formats that need extensive development. Camera and green screen set ups, shooting/filming, and editing for post productions require their time, making it less appealing to post consistently, especially if they're doing all the work themselves.

Because they won't make simple format videos or audio videos with an overlay image, they overcomplicate the procedure (even with YouTube Shorts), and they leave their channels for weeks or months. Again, they believe YouTube only allows specific types of videos. Even though this procedure isn't working, they plan to keep at it.

A successful YouTube channel needs multiple video formats to suit viewer needs, I teach. Face-Share-Personal Touch and Faceless videos are both useful.

How people engage with YouTube content has changed over the years, and the average customer is no longer interested in an all-video channel.

Face-Share-Personal-Touch videos are great

• Google Live

• Online training

• Giving listeners a different way to access your podcast that is being broadcast on sites like Anchor, BlogTalkRadio, Spreaker, Google, Apple Store, and others Many people enjoy using a video camera to record themselves while performing the internet radio, Facebook, or Instagram Live versions of their podcasts.

• Video Blog Updates

• even more

Faceless videos are popular for business and benefit both entrepreneurs and audiences.

For the business owner/entrepreneur…

• Less production time results in time dollar savings.

• enables the business owner to demonstrate the diversity of content development

For the Audience…

• The channel offers a variety of appealing content options.

• The same format is not monotonous or overly repetitive for the viewers.

Below are a couple videos from YouTube guru Make Money Matt's channel, which has over 347K subscribers.

Enjoy

24 Best Niches to Make Money on YouTube Without Showing Your Face

Make Money on YouTube Without Making Videos (Free Course)

In conclusion, you have everything it takes to build your own YouTube brand and empire. Learn the rules, then adapt them to succeed.

Please reread this and the other suggested articles for optimal benefit.

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