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.

Ethereum is the second-largest cryptocurrency. The Merge, a mid-September event that will convert Ethereum's consensus process from proof-of-work to proof-of-stake if all goes according to plan, will be a game changer.

Why is Ethereum ditching proof-of-work? Because it can. We're talking about a fully functioning, open-source ecosystem with a capacity for evolution that other cryptocurrencies lack, a change that would allow it to scale up its performance from 15 transactions per second to 100,000 as its blockchain is used for more and more things. It would reduce its energy consumption by 99.95%. Vitalik Buterin, the system's founder, would play a less active role due to decentralization, and miners, who validated transactions through proof of work, would be far less important.

Why has this conversion taken so long and been so cautious? Because it involves modifying a core process while it's running to boost its performance. It requires running the new mechanism in test chains on an ever-increasing scale, assessing participant reactions, and checking for issues or restrictions. The last big test was in early June and was successful. All that's left is to converge the mechanism with the Ethereum blockchain to conclude the switch.

What's stopping Bitcoin, the leader in market capitalization and the cryptocurrency that began blockchain's appeal, from doing the same? Satoshi Nakamoto, whoever he or she is, departed from public life long ago, therefore there's no community leadership. Changing it takes a level of consensus that is impossible to achieve without strong leadership, which is why Bitcoin's evolution has been sluggish and conservative, with few modifications.

Secondly, The Merge will balance the consensus mechanism (proof-of-work or proof-of-stake) and the system decentralization or centralization. Proof-of-work prevents double-spending, thus validators must buy hardware. The system works, but it requires a lot of electricity and, as it scales up, tends to re-centralize as validators acquire more hardware and the entire network activity gets focused in a few nodes. Larger operations save more money, which increases profitability and market share. This evolution runs opposed to the concept of decentralization, and some anticipate that any system that uses proof of work as a consensus mechanism will evolve towards centralization, with fewer large firms able to invest in efficient network nodes.

Yet radical bitcoin enthusiasts share an opposite argument. In proof-of-stake, transaction validators put their funds at stake to attest that transactions are valid. The algorithm chooses who validates each transaction, giving more possibilities to nodes that put more coins at stake, which could open the door to centralization and government control.

In both cases, we're talking about long-term changes, but Bitcoin's proof-of-work has been evolving longer and seems to confirm those fears, while proof-of-stake is only employed in coins with a minuscule volume compared to Ethereum and has no predictive value.

As of mid-September, we will have two significant cryptocurrencies, each with a different consensus mechanisms and equally different characteristics: one is intrinsically conservative and used only for economic transactions, while the other has been evolving in open source mode, and can be used for other types of assets, smart contracts, or decentralized finance systems. Some even see it as the foundation of Web3.

Many things could change before September 15, but The Merge is likely to be a turning point. We'll have to follow this closely.

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.

If you're not genuine, you'll be revealed.

Sam Bankman-Fried (SBF) was called the Cryptocurrency Warren Buffet.

No wonder.

SBF's trading expertise, Blockchain knowledge, and ability to construct FTX attracted mainstream investors.

He had a fantastic worldview, donating much of his riches to charity.

As the onion layers peel back, it's clear he wasn't the altruistic media figure he portrayed.

SBF's mistakes were disastrous.

• Customer deposits were traded and borrowed by him.

• With ten other employees, he shared a $40 million mansion where they all had polyamorous relationships.

• Tone-deaf and wasteful marketing expenditures, such as the $200 million spent to change the name of the Miami Heat stadium to the FTX Arena

• Democrats received a $40 million campaign gift.

• And now there seems to be no regret.

FTX was a 32-billion-dollar cryptocurrency exchange.

It went bankrupt practically overnight.

SBF, FTX's creator, exploited client funds to leverage trade.

FTX had $1 billion in customer withdrawal reserves against $9 billion in liabilities in sister business Alameda Research.

Bloomberg Billionaire Index says it's the largest and fastest net worth loss in history.

It gets worse.

SBF's net worth is $900 Million, however he must still finalize FTX's bankruptcy.

SBF's arrest in the Bahamas and SEC inquiry followed news that his cryptocurrency exchange had crashed, losing billions in customer deposits.

A journalist contacted him on Twitter D.M., and their exchange is telling.

His ideas are revealed.

Kelsey Piper says they didn't expect him to answer because people under investigation don't comment.

Bankman-Fried wanted to communicate, and the interaction shows he has little remorse.

SBF talks honestly about FTX gaming customers' money and insults his competition.

Reporter Kelsey Piper was outraged by what he said and felt the mistakes SBF says plague him didn't evident in the messages.

Before FTX's crash, SBF was a poster child for Cryptocurrency regulation and avoided criticizing U.S. regulators.

He tells Piper that his lobbying is just excellent PR.

It shows his genuine views and supports cynics' opinions that his attempts to win over U.S. authorities were good for his image rather than Crypto.

SBF’s responses are in Grey, and Pipers are in Blue.

It's unclear if SBF cut corners for his gain. In their Twitter exchange, Piper revisits an interview question about ethics.

SBF says, "All the foolish sh*t I said"

SBF claims FTX has never invested customer monies.

Piper challenged him on Twitter.

While he insisted FTX didn't use customer deposits, he said sibling business Alameda borrowed too much from FTX's balance sheet.

He did, basically.

When consumers tried to withdraw money, FTX was short.

SBF thought Alameda had enough money to cover FTX customers' withdrawals, but life sneaks up on you.

SBF believes most exchanges have done something similar to FTX, but they haven't had a bank run (a bunch of people all wanting to get their deposits out at the same time).

SBF believes he shouldn't have consented to the bankruptcy and kept attempting to raise more money because withdrawals would be open in a month with clients whole.

If additional money came in, he needed $8 billion to bridge the creditors' deficit, and there aren't many corporations with $8 billion to spare.

Once clients feel protected, they will continue to leave their assets on the exchange, according to one idea.

Kevin OLeary, a world-renowned hedge fund manager, says not all investors will walk through the open gate once the company is safe, therefore the $8 Billion wasn't needed immediately.

SBF claims the bankruptcy was his biggest error because he could have accumulated more capital.

Final Reflections

Sam Bankman-Fried, 30, became the world's youngest billionaire in four years.

Never listen to what people say about investing; watch what they do.

SBF is a trader who gets wrecked occasionally.

Ten first-time entrepreneurs ran FTX, screwing each other with no risk management.

It prevents opposing or challenging perspectives and echo chamber highs.

Twitter D.M. conversation with a journalist is the final nail.

He lacks an experienced crew.

This event will surely speed up much-needed regulation.

It's also prompted cryptocurrency exchanges to offer proof of reserves to calm customers.

Let's see this once-dominant IT corporation crumble.

What's the capital of Kazakhstan? If you don't know the answer, you can probably find it by Googling. Google Search returned results for Nur-Sultan in 0.66 seconds.

Google is the best search engine I've ever used. Did you know another search engine ruled the Internet? I'm sure you guessed Yahoo!

Google's friendly UI and wide selection of services make it my top choice. Let's explore Yahoo's decline.

Yahoo!

YAHOO stands for Yet Another Hierarchically Organized Oracle. Jerry Yang and David Filo established Yahoo.

Yahoo is primarily a search engine and email provider. It offers News and an advertising platform. It was a popular website in 1995 that let people search the Internet directly. Yahoo began offering free email in 1997 by acquiring RocketMail.

According to a study, Yahoo used Google Search Engine technology until 2000 and then developed its own in 2004.

Yahoo! rejected buying Google for $1 billion

Larry Page and Sergey Brin, Google's founders, approached Yahoo in 1998 to sell Google for $1 billion so they could focus on their studies. Yahoo denied the offer, thinking it was overvalued at the time.

Yahoo realized its error and offered Google $3 billion in 2002, but Google demanded $5 billion since it was more valuable. Yahoo thought $5 billion was overpriced for the existing market.

In 2022, Google is worth $1.56 Trillion.

What happened to Yahoo!

Yahoo refused to buy Google, and Google's valuation rose, making a purchase unfeasible.

Yahoo started losing users when Google launched Gmail. Google's UI was far cleaner than Yahoo's.

Yahoo offered $1 billion to buy Facebook in July 2006, but Zuckerberg and the board sought $1.1 billion. Yahoo rejected, and Facebook's valuation rose, making it difficult to buy.

Yahoo was losing users daily while Google and Facebook gained many. Google and Facebook's popularity soared. Yahoo lost value daily.

Microsoft offered $45 billion to buy Yahoo in February 2008, but Yahoo declined. Microsoft increased its bid to $47 billion after Yahoo said it was too low, but Yahoo rejected it. Then Microsoft rejected Yahoo’s 10% bid increase in May 2008.

In 2015, Verizon bought Yahoo for $4.5 billion, and Apollo Global Management bought 90% of Yahoo's shares for $5 billion in May 2021. Verizon kept 10%.

Yahoo's opportunity to acquire Google and Facebook could have been a turning moment. It declined Microsoft's $45 billion deal in 2008 and was sold to Verizon for $4.5 billion in 2015. Poor decisions and lack of vision caused its downfall. Yahoo's aim wasn't obvious and it didn't stick to a single domain.

Hence, a corporation needs a clear vision and a leader who can see its future.

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When it comes to building my business, I’m passionate about a lot of things. I love creating user experiences that simplify branding essentials. I love creating new typefaces and color combinations to inspire logo designers. I love fixing problems to improve my product.

Business marketing isn't my thing.

This is shared by many. Many solopreneurs, like me, struggle to advertise their business and drive themselves to work on it.

Without a lot of promotion, no company will succeed. Marketing is 80% of developing a firm, and when you're starting out, it's even more. Some believe that you shouldn't build anything until you've begun marketing your idea and found enough buyers.

Marketing your business without marketing experience is difficult. There are various outlets and techniques to learn. Instead of figuring out where to start, it's easier to return to your area of expertise, whether that's writing, designing product features, or improving your site's back end. Right?

First, realize that your role as a founder is to market your firm. Being a founder focused on product, I rarely work on it.

Secondly, use these basic methods that have helped me dedicate adequate time and focus to marketing. They're all simple to apply, and they've increased my business's visibility and success.

1. Establish buckets for every task.

You've probably heard to schedule tasks you don't like. As simple as it sounds, blocking a substantial piece of my workday for marketing duties like LinkedIn or Twitter outreach, AppSumo customer support, or SEO has forced me to spend time on them.

Giving me lots of room to focus on product development has helped even more. Sure, this means scheduling time to work on product enhancements after my four-hour marketing sprint.

It also involves making space to store product inspiration and ideas throughout the day so I don't get distracted. This is like the advice to keep a notebook beside your bed to write down your insomniac ideas. I keep fonts, color palettes, and product ideas in folders on my desktop. Knowing these concepts won't be lost lets me focus on marketing in the moment. When I have limited time to work on something, I don't have to conduct the research I've been collecting, so I can get more done faster.

2. Look for various accountability systems

Accountability is essential for self-discipline. To keep focused on my marketing tasks, I've needed various streams of accountability, big and little.

Accountability groups are great for bigger things. SaaS Camp, a sales outreach coaching program, is mine. We discuss marketing duties and results every week. This motivates me to do enough each week to be proud of my accomplishments. Yet hearing what works (or doesn't) for others gives me benchmarks for my own marketing outcomes and plenty of fresh techniques to attempt.

… say, I want to DM 50 people on Twitter about my product — I get that many Q-tips and place them in one pen holder on my desk.

The best accountability group can't watch you 24/7. I use a friend's simple method that shouldn't work (but it does). When I have a lot of marketing chores, like DMing 50 Twitter users about my product, That many Q-tips go in my desk pen holder. After each task, I relocate one Q-tip to an empty pen holder. When you have a lot of minor jobs to perform, it helps to see your progress. You might use toothpicks, M&Ms, or anything else you have a lot of.

3. Continue to monitor your feedback loops

Knowing which marketing methods work best requires monitoring results. As an entrepreneur with little go-to-market expertise, every tactic I pursue is an experiment. I need to know how each trial is doing to maximize my time.

I placed Google and Facebook advertisements on hold since they took too much time and money to obtain Return. LinkedIn outreach has been invaluable to me. I feel that talking to potential consumers one-on-one is the fastest method to grasp their problem areas, figure out my messaging, and find product market fit.

Data proximity offers another benefit. Seeing positive results makes it simpler to maintain doing a work you don't like. Why every fitness program tracks progress.

Marketing's goal is to increase customers and revenues, therefore I've found it helpful to track those metrics and celebrate monthly advances. I provide these updates for extra accountability.

Finding faster feedback loops is also motivating. Marketing brings more clients and feedback, in my opinion. Product-focused founders love that feedback. Positive reviews make me proud that my product is benefitting others, while negative ones provide me with suggestions for product changes that can improve my business.

The best advice I can give a lone creator who's afraid of marketing is to just start. Start early to learn by doing and reduce marketing stress. Start early to develop habits and successes that will keep you going. The sooner you start, the sooner you'll have enough consumers to return to your favorite work.