Cryptoshit. This thing is crazy to buy.

Charlie Munger is revered and powerful in finance.

Munger, vice chairman of Berkshire Hathaway, is noted for his wit, no-nonsense attitude to investment, and ability to spot promising firms and markets.

Munger's crypto views have upset some despite his reputation as a straight shooter.

“There’s only one correct answer for intelligent people, just totally avoid all the people that are promoting it.” — Charlie Munger

The Munger Interview on CNBC (4:48 secs)

This Monday, CNBC co-anchor Rebecca Quick interviewed Munger and brought up his 2007 statement, "I'm not allowed to have an opinion on this subject until I can present the arguments against my viewpoint better than the folks who are supporting it."

Great investing and life advice!

If you can't explain the opposing reasons, you're not informed enough to have an opinion.

In today's world, it's important to grasp both sides of a debate before supporting one.

Rebecca inquired:

Does your Wall Street Journal article on banning cryptocurrency apply? If so, would you like to present the counterarguments?

Mungers reply:

I don't see any viable counterarguments. I think my opponents are idiots, hence there is no sensible argument against my position.

Consider his words.

Do you believe Munger has studied both sides?

He said, "I assume my opponents are idiots, thus there is no sensible argument against my position."

This is worrisome, especially from a guy who once encouraged studying both sides before forming an opinion.

Munger said:

National currencies have benefitted humanity more than almost anything else.

Hang on, I think we located the perpetrator.

Munger thinks crypto will replace currencies.

False.

I doubt he studied cryptocurrencies because the name is deceptive.

He misread a headline as a Dollar destroyer.

Cryptocurrencies are speculations.

Like Tesla, Amazon, Apple, Google, Microsoft, etc.

Crypto won't replace dollars.

In the interview with CNBC, Munger continued:

“I’m not proud of my country for allowing this crap, what I call the cryptoshit. It’s worthless, it’s no good, it’s crazy, it’ll do nothing but harm, it’s anti-social to allow it.” — Charlie Munger

Not entirely inaccurate.

Daily cryptos are established solely to pump and dump regular investors.

Let's get into Munger's crypto aversion.

Rat poison is bitcoin.

Munger famously dubbed Bitcoin rat poison and a speculative bubble that would implode.

Partially.

But the bubble broke. Since 2021, the market has fallen.

Scam currencies and NFTs are being eliminated, which I like.

Whoa.

Why does Munger doubt crypto?

Mungers thinks cryptocurrencies has no intrinsic value.

He worries about crypto fraud and money laundering.

Both are valid issues.

Yet grouping crypto is intellectually dishonest.

Ethereum, Bitcoin, Solana, Chainlink, Flow, and Dogecoin have different purposes and values (not saying they’re all good investments).

Fraudsters who hurt innocents will be punished.

Therefore, complaining is useless.

Why not stop it? Repair rather than complain.

Regrettably, individuals today don't offer solutions.

Blind Areas for Mungers

As with everyone, Mungers' bitcoin views may be impacted by his biases and experiences.

OK.

But Munger has always advocated classic value investing and may be wary of investing in an asset outside his expertise.

Mungers' banking and insurance investments may influence his bitcoin views.

Could a coworker or acquaintance have told him crypto is bad and goes against traditional finance?

Right?

Takeaways

Do you respect Charlie Mungers?

Yes and no, like any investor or individual.

To understand Mungers' bitcoin beliefs, you must be critical.

Mungers is a successful investor, but his views about bitcoin should be considered alongside other viewpoints.

Munger’s success as an investor has made him an influencer in the space.

Influence gives power.

He controls people's thoughts.

Munger's ok. He will always be heard.

I'll do so cautiously.

James Howells lost 8,000 bitcoins. He has $11 million to get them back.

His life altered when he threw out an iPhone-sized hard drive.

Howells, from the city of Newport in southern Wales, had two identical laptop hard drives squirreled away in a drawer in 2013. One was blank; the other had 8,000 bitcoins, currently worth around $181 million.

He wanted to toss out the blank one, but the drive containing the Bitcoin went to the dump.

He's determined to reclaim his 2009 stash.

Howells, 36, wants to arrange a high-tech treasure hunt for bitcoins. He can't enter the landfill.

Newport's city council has rebuffed Howells' requests to dig for his hard drive for almost a decade, stating it would be expensive and environmentally destructive.

I got an early look at his $11 million idea to search 110,000 tons of trash. He expects submitting it to the council would convince it to let him recover the hard disk.

110,000 tons of trash, 1 hard drive

Finding a hard disk among heaps of trash may seem Herculean.

Former IT worker Howells claims it's possible with human sorters, robot dogs, and an AI-powered computer taught to find hard drives on a conveyor belt.

His idea has two versions, depending on how much of the landfill he can search.

His most elaborate solution would take three years and cost $11 million to sort 100,000 metric tons of waste. Scaled-down version costs $6 million and takes 18 months.

He's created a team of eight professionals in AI-powered sorting, landfill excavation, garbage management, and data extraction, including one who recovered Columbia's black box data.

The specialists and their companies would be paid a bonus if they successfully recovered the bitcoin stash.

Howells: "We're trying to commercialize this project."

Howells claimed rubbish would be dug up by machines and sorted near the landfill.

Human pickers and a Max-AI machine would sort it. The machine resembles a scanner on a conveyor belt.

Remi Le Grand of Max-AI told us it will train AI to recognize Howells-like hard drives. A robot arm would select candidates.

Howells has added security charges to his scheme because he fears people would steal the hard drive.

He's budgeted for 24-hour CCTV cameras and two robotic "Spot" canines from Boston Dynamics that would patrol at night and look for his hard drive by day.

Howells said his crew met in May at the Celtic Manor Resort outside Newport for a pitch rehearsal.

Richard Hammond's narrative swings from banal to epic.

Richard Hammond filmed the meeting and created a YouTube documentary on Howells.

Hammond said of Howells' squad, "They're committed and believe in him and the idea."

Hammond: "It goes from banal to gigantic." "If I were in his position, I wouldn't have the strength to answer the door."

Howells said trash would be cleaned and repurposed after excavation. Reburying the rest.

"We won't pollute," he declared. "We aim to make everything better."

After the project is finished, he hopes to develop a solar or wind farm on the dump site. The council is unlikely to accept his vision soon.

A council representative told us, "Mr. Howells can't convince us of anything." "His suggestions constitute a significant ecological danger, which we can't tolerate and are forbidden by our permit."

Will the recovered hard drive work?

The "platter" is a glass or metal disc that holds the hard drive's data. Howells estimates 80% to 90% of the data will be recoverable if the platter isn't damaged.

Phil Bridge, a data-recovery expert who consulted Howells, confirmed these numbers.

If the platter is broken, Bridge adds, data recovery is unlikely.

Bridge says he was intrigued by the proposal. "It's an intriguing case," he added. Helping him get it back and proving everyone incorrect would be a great success story.

Who'd pay?

Swiss and German venture investors Hanspeter Jaberg and Karl Wendeborn told us they would fund the project if Howells received council permission.

Jaberg: "It's a needle in a haystack and a high-risk investment."

Howells said he had no contract with potential backers but had discussed the proposal in Zoom meetings. "Until Newport City Council gives me something in writing, I can't commit," he added.

Suppose he finds the bitcoins.

Howells said he would keep 30% of the data, worth $54 million, if he could retrieve it.

A third would go to the recovery team, 30% to investors, and the remainder to local purposes, including gifting £50 ($61) in bitcoin to each of Newport's 150,000 citizens.

Howells said he opted to spend extra money on "professional firms" to help convince the council.

What if the council doesn't approve?

If Howells can't win the council's support, he'll sue, claiming its actions constitute a "illegal embargo" on the hard drive. "I've avoided that path because I didn't want to cause complications," he stated. I wanted to cooperate with Newport's council.

Howells never met with the council face-to-face. He mentioned he had a 20-minute Zoom meeting in May 2021 but thought his new business strategy would help.

He met with Jessica Morden on June 24. Morden's office confirmed meeting.

After telling the council about his proposal, he can only wait. "I've never been happier," he said. This is our most professional operation, with the best employees.

The "crypto proponent" buys bitcoin every month and sells it for cash.

Howells tries not to think about what he'd do with his part of the money if the hard disk is found functional. "Otherwise, you'll go mad," he added.

This post is a summary. Read the full article here.

OpenAI's ChatGPT is an amazing AI-powered chatbot. It can write poetry, fiction, and marketing ideas. I was impressed how well ChatGPT followed the interview, albeit there were a few classics “I’m afraid I can’t do that”.

Full interview below.

Me: I'm your interviewer. We'll discuss crypto. Thanks for being interviewed. What do you think about cryptocurrency?

CGPT: Cryptocurrency is an innovative technology that could transform money and financial activities. It might boost the efficiency and security of financial institutions and let consumers deal directly without banks. Cryptocurrency is still a new and untested technology with many unknowns and hurdles before it can be broadly accepted.

Me: Over 22,000 cryptocurrencies exist, and many have little use. We need how much cryptocurrencies?

CGPT: The appropriate quantity will rely on a multitude of factors, including each cryptocurrency's use cases, adoption rate, and market rivalry. Only a few cryptocurrencies will likely receive widespread adoption and be successful. Many existing cryptocurrencies may not survive since they can't deliver new or valued solutions or compete with more established cryptocurrencies.

Me: Will cryptocurrencies grow? What's next for worldwide adoption?

CGPT: It's hard to forecast the future of cryptocurrencies because the acceptance of new technologies is unpredictable. I believe cryptocurrencies will expand and acquire popularity in the future years. Regulatory ambiguity, security concerns, and scalability issues must be overcome for this to happen. Cryptocurrency companies and organizations must engage together with governments and authorities to address these obstacles and establish a growth-friendly climate. Continued innovation and improvement of the technology, including public education and awareness, will drive acceptance.

Me: Do bear markets affect bitcoin adoption?

CGPT: On the one hand, a bear market might induce uncertainty and hesitation among potential consumers. Bear markets can present opportunities for long-term investors who can acquire cryptocurrencies at cheaper prices and are more likely to hang onto their assets. A bear market can also test the tenacity and power of the underlying technology and community, which can boost long-term confidence and adoption. A bear market might have profound and nuanced effects on bitcoin adoption.

Me: What are some likely outcomes if Bitcoin reaches $100,000 by next year?

CGPT: If Bitcoin saw rapid growth, it would undoubtedly have repercussions for the cryptocurrency market and economy. Possible scenarios include increased public interest and awareness of cryptocurrency, a surge in demand for Bitcoin and other cryptocurrencies, and a growth in the cryptocurrency industry's market value. By shifting their focus and cash to the cryptocurrency market, investors and traders may also affect other asset classes, such as traditional equities and commodities. Governments and financial organizations may focus more on the cryptocurrency sector as they try to grasp Bitcoin's rapid rise.

Me: Will other countries accept crypto as currency?

CGPT: It's hard to say if additional governments will adopt cryptocurrencies as legal tender. Some countries have recognized the promise of bitcoin and are exploring its use, while others are cautious. Adoption of bitcoin as legal cash may vary by country, based on financial infrastructure, rules, and political atmosphere. As cryptocurrency technology evolves and becomes more accepted, more governments may embrace it as legal tender.

Me: Final question: will the recent cryptocurrency hacks affect long term adoption?

CGPT: Hacks might tarnish cryptocurrency's reputation and public faith in its security, the technology underpinning it is continually improving. Many cryptocurrency projects have developed strong security mechanisms to prevent hacks and other dangers, and these safeguards will undoubtedly improve over time. The decentralized nature of cryptocurrency makes it more resistant to attacks. Hacks and other security breaches are a concern, but they may not affect cryptocurrency adoption.

One-hour ebook sales, affiliate relationships, and more.

If you follow me, you may know I started a new ebook in August 2022.

Despite publishing on this platform, my website, and Quora, I'm not a writer.

My writing speed is slow, 2,000 words a day, and I struggle to communicate cohesively.

In April 2022, I wrote a successful guide on How to Write Google-Friendly Blog Posts.

I had no email list or social media presence. I've made $1,600+ selling ebooks.

Evidence:

My first digital offering isn't a book.

It's an actionable guide with my tried-and-true process for writing Google-friendly content.

I'm not bragging.

Established authors like Tim Denning make more from my ebook sales with one newsletter.

This experience taught me writing isn't a privilege.

Writing a book and making money online doesn't require expertise.

Many don't consult experts. They want someone approachable.

Two years passed before I realized my own limits.

I have a brain, two hands, and Internet to spread my message.

I wrote and published a second ebook after the first's success.

On Gumroad, I released my second digital product.

Here's my complete Gumroad evaluation.

Gumroad is a marketplace for content providers to develop and sell sales pages.

Gumroad handles payments and client requests. It's helpful when someone sends a bogus payment receipt requesting an ebook (actual story!).

You'll forget administrative concerns after your first ebook sale.

After my first ebook sale, I did this: I made additional cash!

After every sale, I tell myself, "I built a new semi-passive revenue source."

This thinking shift helps me become less busy while increasing my income and quality of life.

Besides helping others, folks sell evergreen digital things to earn passive money.

It's in my second ebook.

I explain how I built and sold 50+ copies of my SEO writing ebook without being an influencer.

I show how anyone can sell ebooks on Gumroad and automate their sales process.

This is my ebook.

After publicizing the ebook release, I sold three copies within an hour.

Wow, or meh?

I don’t know.

The answer is different for everyone.

These three sales came from a small email list of 40 motivated fans waiting for my ebook release.

I had bigger plans.

I'll market my ebook on Medium, my website, Quora, and email.

I'm testing affiliate partnerships this time.

One of my ebook buyers is now promoting it for 40% commission.

Become my affiliate if you think your readers would like my ebook.

My ebook is a few days old, but I'm interested to see where it goes.

My SEO writing book started without an email list, affiliates, or 4,000 website visitors. I've made four figures.

I'm slowly expanding my communication avenues to have more impact.

Even a small project can open doors you never knew existed.

So began my writing career.

In summary

If you dare, every concept can become a profitable trip.

Before, I couldn't conceive of creating an ebook.

How to Sell eBooks on Gumroad is my second digital product.

Marketing and writing taught me that anything can be sold online.

Many people find the internet's various business models bewildering.

This article summarizes 31 startup e-books.

1. Using the freemium business model (free plus premium),

The freemium business model offers basic software, games, or services for free and charges for enhancements.

Examples include Slack, iCloud, and Google Drive

Provide a rudimentary, free version of your product or service to users.

Google Drive and Dropbox offer 15GB and 2GB of free space but charge for more.

Freemium business model details (Click here)

2. The Business Model of Subscription

Subscription business models sell a product or service for recurring monthly or yearly revenue.

Examples: Tinder, Netflix, Shopify, etc

It's the next step to Freemium if a customer wants to pay monthly for premium features.

Subscription Business Model (Click here)

3. A market-based business strategy

It's an e-commerce site or app where third-party sellers sell products or services.

Examples are Amazon and Fiverr.

• On Amazon's marketplace, a third-party vendor sells a product.

• Freelancers on Fiverr offer specialized skills like graphic design.

Marketplace's business concept is explained.

4. Business plans using aggregates

In the aggregator business model, the service is branded.

Uber, Airbnb, and other examples

Marketplace and Aggregator business models differ.

Amazon and Fiverr link merchants and customers and take a 10-20% revenue split.

Uber and Airbnb-style aggregator Join these businesses and provide their products.

5. The pay-as-you-go concept of business

This is a consumption-based pricing system. Cloud companies use it.

Example: Amazon Web Service and Google Cloud Platform (GCP) (AWS)

AWS, an Amazon subsidiary, offers over 200 pay-as-you-go cloud services.

“In short, the more you use the more you pay”

When it's difficult to divide clients into pricing levels, pay-as-you is employed.

6. The business model known as fee-for-service (FFS)

FFS charges fixed and variable fees for each successful payment.

For instance, PayU, Paypal, and Stripe

Stripe charges 2.9% + 30 per payment.

These firms offer a payment gateway to take consumer payments and deposit them to a business account.

Fintech business model

7. EdTech business strategy

In edtech, you generate money by selling material or teaching as a service.

edtech business models

Freemium When course content is free but certification isn't, e.g. Coursera

FREE TRIAL SkillShare offers free trials followed by monthly or annual subscriptions.

Self-serving marketplace approach where you pick what to learn.

Ad-revenue model The company makes money by showing adverts to its huge user base.

Lock-in business strategy

Lock in prevents customers from switching to a competitor's brand or offering.

It uses switching costs or effort to transmit (soft lock-in), improved brand experience, or incentives.

Apple, SAP, and other examples

Apple offers an iPhone and then locks you in with extra hardware (Watch, Airpod) and platform services (Apple Store, Apple Music, cloud, etc.).

9. Business Model for API Licensing

APIs let third-party apps communicate with your service.

Uber and Airbnb use Google Maps APIs for app navigation.

Examples are Google Map APIs (Map), Sendgrid (Email), and Twilio (SMS).

Business models for APIs

1. Free: The simplest API-driven business model that enables unrestricted API access for app developers. Google Translate and Facebook are two examples.

2. Developer Pays: Under this arrangement, service providers such as AWS, Twilio, Github, Stripe, and others must be paid by application developers.

3. The developer receives payment: These are the compensated content producers or developers who distribute the APIs utilizing their work. For example, Amazon affiliate programs

10. Open-source enterprise

Open-source software can be inspected, modified, and improved by anybody.

For instance, use Firefox, Java, or Android.

Google paid Mozilla $435,702 million to be their primary search engine in 2018.

Open-source software profits in six ways.

1. Paid assistance The Project Manager can charge for customization because he is quite knowledgeable about the codebase.

2. A full database solution is available as a Software as a Service (MongoDB Atlas), but there is a fee for the monitoring tool.

3. Open-core design R studio is a better GUI substitute for open-source applications.

4. sponsors of GitHub Sponsorships benefit the developers in full.

5. demands for paid features Earn Money By Developing Open Source Add-Ons for Current Products

Open-source business model

11. The business model for data

If the software or algorithm collects client data to improve or monetize the system.

Open AI GPT3 gets smarter with use.

Foursquare allows users to exchange check-in locations.

Later, they compiled large datasets to enable retailers like Starbucks launch new outlets.

12. Business Model Using Blockchain

Blockchain is a distributed ledger technology that allows firms to deploy smart contracts without a central authority.

Examples include Alchemy, Solana, and Ethereum.

Business models using blockchain

1. Economy of tokens or utility When a business uses a token business model, it issues some kind of token as one of the ways to compensate token holders or miners. For instance, Solana and Ethereum

2. Bitcoin Cash P2P Business Model Peer-to-peer (P2P) blockchain technology permits direct communication between end users. as in IPFS

3. Enterprise Blockchain as a Service (Baas) BaaS focuses on offering ecosystem services similar to those offered by Amazon (AWS) and Microsoft (Azure) in the web 3 sector. Example: Ethereum Blockchain as a Service with Bitcoin (EBaaS).

4. Blockchain-Based Aggregators With AWS for blockchain, you can use that service by making an API call to your preferred blockchain. As an illustration, Alchemy offers nodes for many blockchains.

13. The free-enterprise model

In the freeterprise business model, free professional accounts are led into the funnel by the free product and later become B2B/enterprise accounts.

For instance, Slack and Zoom

Freeterprise companies flourish through collaboration.

Start with a free professional account to build an enterprise.

14. Business plan for razor blades

It's employed in hardware where one piece is sold at a loss and profits are made through refills or add-ons.

Gillet razor & blades, coffee machine & beans, HP printer & cartridge, etc.

Sony sells the Playstation console at a loss but makes up for it by selling games and charging for online services.

Advantages of the Razor-Razorblade Method

1. lowers the risk a customer will try a product. enables buyers to test the goods and services without having to pay a high initial investment.

2. The product's ongoing revenue stream has the potential to generate sales that much outweigh the original investments.

Razor blade business model

15. The business model of direct-to-consumer (D2C)

In D2C, the company sells directly to the end consumer through its website using a third-party logistic partner.

Examples include GymShark and Kylie Cosmetics.

D2C brands can only expand via websites, marketplaces (Amazon, eBay), etc.

D2C benefits

• Lower reliance on middlemen = greater profitability

• You now have access to more precise demographic and geographic customer data.

• Additional space for product testing

• Increased customisation throughout your entire product line-Inventory Less

16. Business model: White Label vs. Private Label

Private label/White label products are made by a contract or third-party manufacturer.

Most amazon electronics are made in china and white-labeled.

Amazon supplements and electronics.

Contract manufacturers handle everything after brands select product quantities on design labels.

17. The franchise model

The franchisee uses the franchisor's trademark, branding, and business strategy (company).

For instance, KFC, Domino's, etc.

Subway, Domino, Burger King, etc. use this business strategy.

Many people pick a franchise because opening a restaurant is risky.

18. Ad-based business model

Social media and search engine giants exploit search and interest data to deliver adverts.

Google, Meta, TikTok, and Snapchat are some examples.

Users don't pay for the service or product given, e.g. Google users don't pay for searches.

In exchange, they collected data and hyper-personalized adverts to maximize revenue.

19. Business plan for octopuses

Each business unit functions separately but is connected to the main body.

Instance: Oyo

OYO is Asia's Airbnb, operating hotels, co-working, co-living, and vacation houses.

20, Transactional business model, number

Sales to customers produce revenue.

E-commerce sites and online purchases employ SSL.

Goli is an ex-GymShark.

21. The peer-to-peer (P2P) business model

In P2P, two people buy and sell goods and services without a third party or platform.

Consider OLX.

22. P2P lending as a manner of operation

In P2P lending, one private individual (P2P Lender) lends/invests or borrows money from another (P2P Borrower).

Instance: Kabbage

Social lending lets people lend and borrow money directly from each other without an intermediary financial institution.

23. A business model for brokers

Brokerages charge a commission or fee for their services.

Examples include eBay, Coinbase, and Robinhood.

Brokerage businesses are common in Real estate, finance, and online and operate on this model.

1. Buy/sell similar models Examples include financial brokers, insurance brokers, and others who match purchase and sell transactions and charge a commission.

2. These brokers charge an advertiser a fee based on the date, place, size, or type of an advertisement. This is known as the classified-advertiser model. For instance, Craiglist

24. Drop shipping as an industry

Dropshipping allows stores to sell things without holding physical inventories.

When a customer orders, use a third-party supplier and logistic partners.

Retailer product portfolio and customer experience Fulfiller The consumer places the order.

Dropshipping advantages

• Less money is needed (Low overhead-No Inventory or warehousing)

• Simple to start (costs under $100)

• flexible work environment

• New product testing is simpler

25. Business Model for Space as a Service

It's centered on a shared economy that lets millennials live or work in communal areas without ownership or lease.

Consider WeWork and Airbnb.

WeWork helps businesses with real estate, legal compliance, maintenance, and repair.

26. The business model for third-party logistics (3PL)

In 3PL, a business outsources product delivery, warehousing, and fulfillment to an external logistics company.

Examples include Ship Bob, Amazon Fulfillment, and more.

3PL partners warehouse, fulfill, and return inbound and outbound items for a charge.

Inbound logistics involves bringing products from suppliers to your warehouse.

Outbound logistics refers to a company's production line, warehouse, and customer.

27. The last-mile delivery paradigm as a commercial strategy

Last-mile delivery is the collection of supply chain actions that reach the end client.

Examples include Rappi, Gojek, and Postmates.

Last-mile is tied to on-demand and has a nighttime peak.

28. The use of affiliate marketing

Affiliate marketing involves promoting other companies' products and charging commissions.

Examples include Hubspot, Amazon, and Skillshare.

Your favorite youtube channel probably uses these short amazon links to get 5% of sales.

Affiliate marketing's benefits

• In exchange for a success fee or commission, it enables numerous independent marketers to promote on its behalf.

• Ensure system transparency by giving the influencers a specific tracking link and an online dashboard to view their profits.

• Learn about the newest bargains and have access to promotional materials.

29. The business model for virtual goods

This is an in-app purchase for an intangible product.

Examples include PubG, Roblox, Candy Crush, etc.

Consumables are like gaming cash that runs out. Non-consumable products provide a permanent advantage without repeated purchases.

30. Business Models for Cloud Kitchens

Ghost, Dark, Black Box, etc.

Delivery-only restaurant.

These restaurants don't provide dine-in, only delivery.

For instance, NextBite and Faasos

31. Crowdsourcing as a Business Model

Crowdsourcing = Using the crowd as a platform's source.

In crowdsourcing, you get support from people around the world without hiring them.

Crowdsourcing sites

1. Open-Source Software gives access to the software's source code so that developers can edit or enhance it. Examples include Firefox browsers and Linux operating systems.

2. Crowdfunding The oculus headgear would be an example of crowdfunding in essence, with no expectations.

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.