Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.

Great News about the new Google Business Intelligence Solution

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

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

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

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

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

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

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

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

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

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

Sources and Further Readings

Google, Release Notes (2022)

Google, Looker (2022)

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.

What they'll do is scarier.

My acquaintance recently joined a VC-funded startup. Money, equity, and upside possibilities were nice, but he had a nagging dread.

They just secured a $40M round and are hiring like crazy to prepare for their IPO in two years. All signals pointed to this startup's (a B2B IT business in a stable industry) success, and its equity-holding workers wouldn't pass that up.

Five months after starting the work, my friend struggled with leaving. We might overlook the awful culture and long hours at the proper price. This price plus the company's fate and survival abilities sent my friend departing in an unpleasant unplanned resignation before jumping on yet another sinking ship.

This affects founders. This affects VC-backed companies (and all businesses). This affects anyone starting, buying, or running a business.

Here's the under-the-table approach that's draining VC capital, leaving staff terrified (or jobless), founders rattled, and investors upset. How to recognize, solve, and avoid it

The unsettling reality behind door #1

You can't raise money off just your looks, right? If "looks" means your founding team's expertise, then maybe. In my friend's case, the founding team's strong qualifications and track records won over investors before talking figures.

They're hardly the only startup to raise money without a profitable customer acquisition strategy. Another firm raised money for an expensive sleep product because it's eco-friendly. They were off to the races with a few keywords and key players.

Both companies, along with numerous others, elected to invest on product development first. Company A employed all the tech, then courted half their market (they’re a tech marketplace that connects two parties). Company B spent millions on R&D to create a palatable product, then flooded the world with marketing.

My friend is on Company B's financial team, and he's seen where they've gone wrong. It's terrible.

Company A (tech market): Growing? Not quite. To achieve the ambitious expansion they (and their investors) demand, they've poured much of their little capital into salespeople: Cold-calling commission and salary salesmen. Is it working? Considering attrition and companies' dwindling capital, I don't think so.

Company B (green sleep) has been hiring, digital marketing, and opening new stores like crazy. Growing expenses should result in growing revenues and a favorable return on investment; if you grow too rapidly, you may neglect to check that ROI.

Once Company A cut headcount and Company B declared “going concerned”, my friend realized both startups had the same ailment and didn't recognize it.

I shouldn't have to ask a friend to verify a company's cash reserves and profitability to spot a financial problem. It happened anyhow.

The frightening part isn't that investors were willing to invest millions without product-market fit, CAC, or LTV estimates. That's alarming, but not as scary as the fact that startups aren't understanding the problem until VC rounds have dried up.

When they question consultants if their company will be around in 6 months. It’s a red flag. How will they stretch $20M through a 2-year recession with a $3M/month burn rate and no profitability? Alarms go off.

Who's in danger?

In a word, everyone who raised money without a profitable client acquisition strategy or enough resources to ride out dry spells.

Money mismanagement and poor priorities affect every industry (like sinking all your capital into your product, team, or tech, at the expense of probing what customer acquisition really takes and looks like).

This isn't about tech, real estate, or recession-proof luxury products. Fast, cheap, easy money flows into flashy-looking teams with buzzwords, trending industries, and attractive credentials.

If these companies can't show progress or get a profitable CAC, they can't raise more money. They die if they can't raise more money (or slash headcount and find shoestring budget solutions until they solve the real problem).

The kiss of death (and how to avoid it)

If you're running a startup and think raising VC is the answer, pause and evaluate. Do you need the money now?

I'm not saying VC is terrible or has no role. Founders have used it as a Band-Aid for larger, pervasive problems. Venture cash isn't a crutch for recruiting consumers profitably; it's rocket fuel to get you what and who you need.

Pay-to-play isn't a way to throw money at the wall and hope for a return. Pay-to-play works until you run out of money, and if you haven't mastered client acquisition, your cash will diminish quickly.

How can you avoid this bottomless pit? Tips:

• Understand your burn rate

• Keep an eye on your growth or profitability.

• Analyze each and every marketing channel and initiative.

• Make lucrative customer acquisition strategies and satisfied customers your top two priorities. not brand-new products. not stellar hires. avoid the fundraising rollercoaster to save time. If you succeed in these two tasks, investors will approach you with their thirsty offers rather than the other way around, and your cash reserves won't diminish as a result.

Not as much as your grandfather

My family friend always justified expensive, impractical expenditures by saying it was only monopoly money. In business, startups, and especially with money from investors expecting a return, that's not true.

More founders could understand that there isn't always another round if they viewed VC money as their own limited pool. When the well runs dry, you must refill it or save the day.

Venture financing isn't your grandpa's money. A discerning investor has entrusted you with dry powder in the hope that you'll use it wisely, strategically, and thoughtfully. Use it well.

Economic mutual destruction.

Multibillion-dollar corporations never bothered with an independent audit, and they all lied about their balance sheets.

It's easy to forget that the Big Four accounting firms are lousy fraud enablers. Just because they sign off on your books doesn't mean you're not a hoax waiting to erupt.

This is *crazy* Capitalism depends on independent auditors. Rich folks need to know their financial advisers aren't lying. Rich folks usually succeed.

No accounting. EY, KPMG, PWC, and Deloitte make more money consulting firms than signing off on their accounts.

The Big Four sign off on phony books because failing to make friends with unscrupulous corporations may cost them consulting contracts.

The Big Four are the only firms big enough to oversee bankruptcy when they sign off on fraudulent books, as they did for Carillion in 2018. All four profited from Carillion's bankruptcy.

The Big Four are corrupt without any consequences for misconduct. Who can forget when KPMG's top management was fined millions for helping auditors cheat on ethics exams?

Consulting and auditing conflict. Consultants help a firm cover its evil activities, such as tax fraud or wage theft, whereas auditors add clarity to a company's finances. The Big Four make more money from cooking books than from uncooking them, thus they are constantly embroiled in scandals.

If a major scandal breaks, it may bring down the entire sector and substantial parts of the economy. Jim Peterson explains system risk for The Dig.

The Big Four are voluntary private partnerships where accountants invest their time, reputations, and money. If a controversy threatens the business, partners who depart may avoid scandal and financial disaster.

When disaster looms, each partner should bolt for the door, even if a disciplined stay-and-hold posture could weather the storm. This happened to Arthur Andersen during Enron's collapse, and a 2006 EU report recognized the risk to other corporations.

Each partner at a huge firm knows how much dirty laundry they've buried in the company's garden, and they have well-founded suspicions about what other partners have buried, too. When someone digs, everyone runs.

If a firm confronts substantial litigation damages or enforcement penalties, it could trigger the collapse of one of the Big Four. That would be bad news for the firm's clients, who would have trouble finding another big auditor.

Most of the world's auditing capacity is concentrated in four enormous, brittle, opaque, compromised organizations. If one of them goes bankrupt, the other three won't be able to take on its clients.

Peterson: Another collapse would strand many of the world's large public businesses, leaving them unable to obtain audit views for their securities listings and regulatory compliance.

Count Down: The Past, Present, and Uncertain Future of the Big Four Accounting Firms is in its second edition.

https://www.emerald.com/insight/publication/doi/10.1108/9781787147003

40 years pass. After 14 years of retirement, you die. Am I the only one who sees the problem?

I’m the Jedi master of escaping the rat race.

Not to impress. I know this works since I've tried it. Quitting a job to make money online is worse than Kim Kardashian's internet-burning advice.

Let me help you rethink the move from a career to online income to f*ck you money.

To understand why a job is a joke, do some life math.

Without a solid why, nothing makes sense.

The retirement age is 65. Our processed food consumption could shorten our 79-year average lifespan.

You spend 40 years working.

After 14 years of retirement, you die.

Am I alone in seeing the problem?

Life is too short to work a job forever, especially since most people hate theirs. After-hours skills are vital.

Money equals unrestricted power, f*ck you.

F*ck you money is the answer.

Jack Raines said it first. He says we can do anything with the money. Jack, a young rebel straight out of college, can travel and try new foods.

F*ck you money signifies not checking your bank account before buying.

F*ck you” money is pure, unadulterated freedom with no strings attached.

Jack claims you're rich when you rarely think about money.

Avoid confusion.

This doesn't imply you can buy a Lamborghini. It indicates your costs, income, lifestyle, and bank account are balanced.

Jack established an online portfolio while working for UPS in Atlanta, Georgia. So he gained boundless power.

The portion that many erroneously believe

Yes, you need internet abilities to make money, but they're not different from 9-5 talents.

Sahil Lavingia, Gumroad's creator, explains.

A job is a way to get paid to learn.

Mistreat your boss 9-5. Drain his skills. Defuse him. Love and leave him (eventually).

Find another employment if yours is hazardous. Pick an easy job. Make sure nothing sneaks into your 6-12 time slot.

The dumb game that makes you a sheep

A 9-5 job requires many job interviews throughout life.

You email your résumé to employers and apply for jobs through advertisements. This game makes you a sheep.

You're competing globally. Work-from-home makes the competition tougher. If you're not the cheapest, employers won't hire you.

After-hours online talents (say, 6 pm-12 pm) change the game. This graphic explains it better:

Online talents boost after-hours opportunities.

You go from wanting to be picked to picking yourself. More chances equal more money. Your f*ck you fund gets the extra cash.

A novel method of learning is essential.

College costs six figures and takes a lifetime to repay.

Informal learning is distinct. 6-12pm:

• Observe the carefully controlled Twitter newsfeed.

• Make use of Teachable and Gumroad's online courses.

• Watch instructional YouTube videos

• Look through the top Substack newsletters.

Informal learning is more effective because it's not obvious. It's fun to follow your curiosity and hobbies.

The majority of people lack one attitude. It's simple to learn.

One big impediment stands in the way of f*ck you money and time independence. So often.

Too many people plan after 6-12 hours. Dreaming. Big-thinkers. Strategically. They fill their calendar with meetings.

This is after-hours masturb*tion.

Sahil Bloom reminded me that a bias towards action will determine if this approach works for you.

The key isn't knowing what to do from 6-12 a.m. Trust yourself and develop abilities as you go. It's for building the parachute after you jump.

Sounds risky. We've eliminated the risk by finishing this process after hours while you work 9-5.

With no risk, you can have an I-don't-care attitude and still be successful.

When you choose to move forward, this occurs.

Once you try 9-5/6-12, you'll tell someone.

It's bad.

Few of us hang out with problem-solvers.

It's how much of society operates. So they make reasons so they can feel better about not giving you money.

Matthew Kobach told me chasing f*ck you money is easier with like-minded folks.

Without f*ck you money friends, loneliness will take over and you'll think you've messed up when you just need to keep going.

Steal this easy guideline

Let's act. No more fluffing and caressing.

1. Learn

If you detest your 9-5 talents or don't think they'll work online, get new ones. If you're skilled enough, continue.

Easlo recommends these skills:

• Designer for Figma

• Designer Canva

• bubble creators

• editor in Photoshop

• Automation consultant for Zapier

• Designer of Webflow

• video editor Adobe

• Ghostwriter for Twitter

• Idea consultant

• Artist in Blender Studio

2. Develop the ability

Every night from 6-12, apply the skill.

Practicing ghostwriting? Write someone's tweets for free. Do someone's website copy to learn copywriting. Get a website to the top of Google for a keyword to understand SEO.

Free practice is crucial. Your 9-5 pays the money, so work for free.

3. Take off stealthily like a badass

Another mistake. Sell to few. Don't be the best. Don't claim expertise.

Sell your new expertise to others behind you.

Two ways:

• Using a digital good

• By providing a service,

Point 1 also includes digital service examples. Digital products include eBooks, communities, courses, ad-supported podcasts, and templates. It's easy. Your 9-5 job involves one of these.

Take ideas from work.

Why? They'll steal your time for profit.

4. Iterate while feeling awful

First-time launches always fail. You'll feel terrible. Okay. Remember your 9-5?

Find improvements. Ask free and paying consumers what worked.

Multiple relaunches, each 1% better.

5. Discover more

Never stop learning. Improve your skill. Add a relevant skill. Learn copywriting if you write online.

After-hours students earn the most.

6. Continue

Repetition is key.

7. Make this one small change.

Consistently. The 6-12 momentum won't make you rich in 30 days; that's success p*rn.

Consistency helps wage slaves become f*ck you money. Most people can't switch between the two.

Putting everything together

It's easy. You're probably already doing some.

This formula explains why, how, and what to do. It's a 5th-grade-friendly blueprint. Good.

Reduce financial risk with your 9-to-5. Replace Netflix with 6-12 money-making talents.

Life is short; do whatever you want. Today.