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.

The brand-new USB Rubber Ducky is much riskier than before.

With its own programming language, the well-liked hacking tool may now pwn you.

With a vengeance, the USB Rubber Ducky is back.

This year's Def Con hacking conference saw the release of a new version of the well-liked hacking tool, and its author, Darren Kitchen, was on hand to explain it. We put a few of the new features to the test and discovered that the most recent version is riskier than ever.

WHAT IS IT?

The USB Rubber Ducky seems to the untrained eye to be an ordinary USB flash drive. However, when you connect it to a computer, the computer recognizes it as a USB keyboard and will accept keystroke commands from the device exactly like a person would type them in.

Kitchen explained to me, "It takes use of the trust model built in, where computers have been taught to trust a human, in that anything it types is trusted to the same degree as the user is trusted. And a computer is aware that clicks and keystrokes are how people generally connect with it.

Over ten years ago, the first Rubber Ducky was published, quickly becoming a hacker favorite (it was even featured in a Mr. Robot scene). Since then, there have been a number of small upgrades, but the most recent Rubber Ducky takes a giant step ahead with a number of new features that significantly increase its flexibility and capability.

WHERE IS ITS USE?

The options are nearly unlimited with the proper strategy.

The Rubber Ducky has already been used to launch attacks including making a phony Windows pop-up window to collect a user's login information or tricking Chrome into sending all saved passwords to an attacker's web server. However, these attacks lacked the adaptability to operate across platforms and had to be specifically designed for particular operating systems and software versions.

The nuances of DuckyScript 3.0 are described in a new manual. 

The most recent Rubber Ducky seeks to get around these restrictions. The DuckyScript programming language, which is used to construct the commands that the Rubber Ducky will enter into a target machine, receives a significant improvement with it. DuckyScript 3.0 is a feature-rich language that allows users to write functions, store variables, and apply logic flow controls, in contrast to earlier versions that were primarily limited to scripting keystroke sequences (i.e., if this... then that).

This implies that, for instance, the new Ducky can check to see if it is hooked into a Windows or Mac computer and then conditionally run code specific to each one, or it can disable itself if it has been attached to the incorrect target. In order to provide a more human effect, it can also generate pseudorandom numbers and utilize them to add a configurable delay between keystrokes.

The ability to steal data from a target computer by encoding it in binary code and transferring it through the signals intended to instruct a keyboard when the CapsLock or NumLock LEDs should light up is perhaps its most astounding feature. By using this technique, a hacker may plug it in for a brief period of time, excuse themselves by saying, "Sorry, I think that USB drive is faulty," and then take it away with all the credentials stored on it.

HOW SERIOUS IS THE RISK?

In other words, it may be a significant one, but because physical device access is required, the majority of people aren't at risk of being a target.

The 500 or so new Rubber Duckies that Hak5 brought to Def Con, according to Kitchen, were his company's most popular item at the convention, and they were all gone on the first day. It's safe to suppose that hundreds of hackers already possess one, and demand is likely to persist for some time.

Additionally, it has an online development toolkit that can be used to create attack payloads, compile them, and then load them onto the target device. A "payload hub" part of the website makes it simple for hackers to share what they've generated, and the Hak5 Discord is also busy with conversation and helpful advice. This makes it simple for users of the product to connect with a larger community.

It's too expensive for most individuals to distribute in volume, so unless your favorite cafe is renowned for being a hangout among vulnerable targets, it's doubtful that someone will leave a few of them there. To that end, if you intend to plug in a USB device that you discovered outside in a public area, pause to consider your decision.

WOULD IT WORK FOR ME?

Although the device is quite straightforward to use, there are a few things that could cause you trouble if you have no prior expertise writing or debugging code. For a while, during testing on a Mac, I was unable to get the Ducky to press the F4 key to activate the launchpad, but after forcing it to identify itself using an alternative Apple keyboard device ID, the problem was resolved.

From there, I was able to create a script that, when the Ducky was plugged in, would instantly run Chrome, open a new browser tab, and then immediately close it once more without requiring any action from the laptop user. Not bad for only a few hours of testing, and something that could be readily changed to perform duties other than reading technology news.

Would you abandon your bank for Apple?

Banks are struggling.

• not as a result of inflation

• not due to the economic downturn.

• not due to the conflict in Ukraine.

But because they’re underestimating Apple.

Slowly but surely, Apple is looking more like a bank.

An easy new savings account like Apple

Apple has a new savings account.

Apple says Apple Card users may set up and manage savings straight in Wallet.

• No more charges

• Colorfully high yields

• With no minimum balance

• No minimal down payments

Most consumer-facing banks will have to match Apple's offer or suffer disruption.

Users may set it up from their iPhones without traveling to a bank or filling out paperwork.

It’s built into the iPhone in your pocket.

So now more waiting for slow approval processes.

Once the savings account is set up, Apple will automatically transfer all future Daily Cash into it. Users may also add these cash to an Apple Cash card in their Apple Wallet app and adjust where Daily Cash is paid at any time.

Apple Pay and Apple Wallet VP Jennifer Bailey:

Savings enables Apple Card users to grow their Daily Cash rewards over time, while also saving for the future.

Bailey says Savings adds value to Apple Card's Daily Cash benefit and offers another easy-to-use tool to help people lead healthier financial lives.

Transfer money from a linked bank account or Apple Cash to a Savings account. Users can withdraw monies to a connected bank account or Apple Cash card without costs.

Once set up, Apple Card customers can track their earnings via Wallet's Savings dashboard. This dashboard shows their account balance and interest.

This product targets younger people as the easiest way to start a savings account on the iPhone.

Why would a Gen Z account holder travel to the bank if their iPhone could be their bank?

Using this concept, Apple will transform the way we think about banking by 2030.

Two other nightmares keep bankers awake at night

Apple revealed two new features in early 2022 that banks and payment gateways hated.

• Tap to Pay with Apple

• Late Apple Pay

They startled the industry.

Tap To Pay converts iPhones into mobile POS card readers. Apple Pay Later is pushing the BNPL business in a consumer-friendly direction, hopefully ending dodgy lending practices.

Tap to Pay with Apple

iPhone POS

Millions of US merchants, from tiny shops to huge establishments, will be able to accept Apple Pay, contactless credit and debit cards, and other digital wallets with a tap.

No hardware or payment terminal is needed.

Revolutionary!

Stripe has previously launched this feature.

Tap to Pay on iPhone will provide companies with a secure, private, and quick option to take contactless payments and unleash new checkout experiences, said Bailey.

Apple's solution is ingenious. Brilliant!

Bailey says that payment platforms, app developers, and payment networks are making it easier than ever for businesses of all sizes to accept contactless payments and thrive.

I admire that Apple is offering this up to third-party services instead of closing off other functionalities.

Slow POS terminals, farewell.

Late Apple Pay

Pay Apple later.

Apple Pay Later enables US consumers split Apple Pay purchases into four equal payments over six weeks with no interest or fees.

The Apple ecosystem integration makes this BNPL scheme unique. Nonstick. No dumb forms.

Frictionless.

Just double-tap the button.

Apple Pay Later was designed with users' financial well-being in mind. Apple makes it easy to use, track, and pay back Apple Pay Later from Wallet.

Apple Pay Later can be signed up in Wallet or when using Apple Pay. Apple Pay Later can be used online or in an app that takes Apple Pay and leverages the Mastercard network.

Apple Pay Order Tracking helps consumers access detailed receipts and order tracking in Wallet for Apple Pay purchases at participating stores.

Bad BNPL suppliers, goodbye.

Most bankers will be caught in Apple's eye playing mini golf in high-rise offices.

The big problem:

• Banks still think about features and big numbers just like other smartphone makers did not too long ago.

• Apple thinks about effortlessness, seamlessness, and frictionlessness that just work through integrated hardware and software.

Let me know what you think Apple’s next power moves in the banking industry could be.

Niches are rich, as the adage goes.

Micro SaaS requires a great micro-niche; otherwise, it's merely plain old SaaS with a large audience.

Instead of targeting broad markets with few identifying qualities, specialise down to a micro-niche. How would you target these users?

Better go tiny. You'll locate and engage new consumers more readily and serve them better with a customized solution.

Imagine you're a real estate lawyer looking for a case management solution. Because it's so specific to you, you'd be lured to this link:

instead of below:

Next, locate mini SaaS niches that could work for you. You're not yet looking at the problems/solutions in these areas, merely shortlisting them.

The market should be growing, not shrinking

We shouldn't design apps for a declining niche. We intend to target stable or growing niches for the next 5 to 10 years.

If it's a developing market, you may be able to claim a stake early. You must balance this strategy with safer, longer-established niches (accountancy, law, health, etc).

First Micro SaaS apps I designed were for Merch By Amazon creators, a burgeoning niche. I found this niche when searching for passive income.

Graphic designers and entrepreneurs post their art to Amazon to sell on clothes. When Amazon sells their design, they get a royalty. Since 2015, this platform and specialty have grown dramatically.

Amazon doesn't publicize the amount of creators on the platform, but it's possible to approximate by looking at Facebook groups, Reddit channels, etc.

I could see the community growing week by week, with new members joining. Merch was an up-and-coming niche, and designers made money when their designs sold. All I had to do was create tools that let designers focus on making bestselling designs.

Look at the Google Trends graph below to see how this niche has evolved and when I released my apps and resigned my job.

Are the users able to afford the tools?

Who's your average user? Consumer or business? Is your solution budgeted?

If they're students, you'll struggle to convince them to subscribe to your study-system app (ahead of video games and beer).

Let's imagine you designed a Shopify plugin that emails customers when a product is restocked. If your plugin just needs 5 product sales a month to justify its cost, everyone wins (just be mindful that one day Shopify could potentially re-create your plugins functionality within its core offering making your app redundant ).

Do specialized users buy tools? If so, that's comforting. If not, you'd better have a compelling value proposition for your end customer if you're the first.

This should include how much time or money your program can save or make the user.

Are you able to understand the Micro SaaS market?

Ideally, you're already familiar about the industry/niche. Maybe you're fixing a challenge from your day job or freelance work.

If not, evaluate how long it would take to learn the niche's users. Health & Fitness is easier to relate to and understand than hedge fund derivatives trading.

Competing in these complex (and profitable) fields might offer you an edge.

B2C, B2M, or B2B?

Consider your user base's demographics. Will you target businesses, consumers, or both? Let's examine the different consumer types:

• B2B refers to business-to-business transactions where customers are other businesses. UpVoty, Plutio, Slingshot, Salesforce, Atlassian, and Hubspot are a few examples of SaaS, ranging from Micro SaaS to SaaS.

• Business to Consumer (B2C), in which your clients are people who buy things. For instance, Duolingo, Canva, and Nomad List.

• For instance, my tool KDP Wizard has a mixed user base of publishing enterprises and also entrepreneurial consumers selling low-content books on Amazon. This is a case of business to many (B2M), where your users are a mixture of businesses and consumers. There is a large SaaS called Dropbox that offers both personal and business plans.

Targeting a B2B vs. B2C niche is very different. The sales cycle differs.

• A B2B sales staff must make cold calls to potential clients' companies. Long sales, legal, and contractual conversations are typically required for each business to get the go-ahead. The cost of obtaining a new customer is substantially more than it is for B2C, despite the fact that the recurring fees are significantly higher.

• Since there is typically only one individual making the purchasing decision, B2C signups are virtually always self-service with reduced recurring fees. Since there is typically no outbound sales staff in B2C, acquisition costs are significantly lower than in B2B.

User Characteristics for B2B vs. B2C

Consider where your niche's users congregate if you don't already have a presence there.

B2B users frequent LinkedIn and Twitter. B2C users are on Facebook/Instagram/Reddit/Twitter, etc.

Churn is higher in B2C because consumers haven't gone through all the hoops of a B2B sale. Consumers are more unpredictable than businesses since they let their bank cards exceed limitations or don't update them when they expire.

With a B2B solution, there's a contractual arrangement and the firm will pay the subscription as long as they need it.

Depending on how you feel about the above (sales team vs. income vs. churn vs. targeting), you'll know which niches to pursue.

You ought to respect potential customers.

Would you hang out with customers?

You'll connect with users at conferences (in-person or virtual), webinars, seminars, screenshares, Facebook groups, emails, support calls, support tickets, etc.

If talking to a niche's user base makes you shudder, you're in for a tough road. Whether they're demanding or dull, avoid them if possible.

Merch users are mostly graphic designers, side hustlers, and entrepreneurs. These laid-back users embrace technologies that assist develop their Merch business.

I discovered there was only one annual conference for this specialty, held in Seattle, USA. I decided to organize a conference for UK/European Merch designers, despite never having done so before.

Hosting a conference for over 80 people was stressful, and it turned out to be much bigger than expected, with attendees from the US, Europe, and the UK.

I met many specialized users, built relationships, gained trust, and picked their brains in person. Many of the attendees were already Merch Wizard users, so hearing their feedback and ideas for future features was invaluable.

focused and specific

Instead of building for a generic, hard-to-reach market, target a specific group.

I liken it to fishing in a little, hidden pond. This small pond has only one species of fish, so you learn what bait it likes. Contrast that with trawling for hours to catch as many fish as possible, even if some aren't what you want.

In the case management scenario, it's difficult to target leads because several niches could use the app. Where do your potential customers hang out? Your generic solution: No.

It's easier to join a community of Real Estate Lawyers and see if your software can answer their pain points.

My Success with Micro SaaS

In my case, my Micro SaaS apps have been my chrome extensions. Since I launched them, they've earned me an average $10k MRR, allowing me to quit my lousy full-time job years ago.

I sold my apps after scaling them for a life-changing lump amount. Since then, I've helped unfulfilled software developers escape the 9-5 through Micro SaaS.

Whether it's a profitable side hustle or a liferaft to quit their job and become their own Micro SaaS boss.

Having built my apps to the point where I could quit my job, then scaled and sold them, I feel I can share my skills with software developers worldwide.

Read my free guide on self-funded SaaS to discover more about Micro SaaS, or download your own copy. 12 chapters cover everything from Idea to Exit.

Watch my YouTube video to learn how to construct a Micro SaaS app in 10 steps.

Homeownership isn't the only life pattern.

Want to irritate people?

My party trick is to say I used to own a house but no longer do.

I no longer wish to own a home, not because I lost it or because I'm moving.

It was a long-term plan. It was more deliberate than buying a home. Many people are committed for this reason.

Poppycock.

Anyone who told me that owning a house (or striving to do so) is a must is wrong.

Because, URGH.

One pattern for life is to own a home, but there are millions of others.

You can afford to buy a home? Go, buddy.

You think you need 1,000 square feet (or more)? You think it's non-negotiable in life?

Nope.

It's insane that society forces everyone to own real estate, regardless of income, wants, requirements, or situation. As if this trade brings happiness, stability, and contentment.

Take it from someone who thought this for years: drywall isn't happy. Living your way brings contentment.

That's in real estate. It may also be renting a small apartment in a city that makes your soul sing, but you can't afford the downpayment or mortgage payments.

Living or traveling abroad is difficult when your life savings are connected to something that eats your money the moment you sign.

#vanlife, which seems like torment to me, makes some people feel alive.

I've seen co-living, vacation rental after holiday rental, living with family, and more work.

Insisting that home ownership is the only path in life is foolish and reduces alternative options.

How little we question homeownership is a disgrace.

No one challenges a homebuyer's motives. We congratulate them, then that's it.

When you offload one, you must answer every question, even if you have a loose screw.

• Why do you want to sell?

• Do you have any concerns about leaving the market?

• Why would you want to renounce what everyone strives for?

• Why would you want to abandon a beautiful place like that?

• Why would you mismanage your cash in such a way?

• But surely it's only temporary? RIGHT??

Incorrect questions. Buying a property requires several inquiries.

• The typical American has $4500 saved up. When something goes wrong with the house (not if, it’s never if), can you actually afford the repairs?

• Are you certain that you can examine a home in less than 15 minutes before committing to buying it outright and promising to pay more than twice the asking price on a 30-year 7% mortgage?

• Are you certain you're ready to leave behind friends, family, and the services you depend on in order to acquire something?

• Have you thought about the connotation that moving to a suburb, which more than half of Americans do, means you will be dependent on a car for the rest of your life?

Plus:

Are you sure you want to prioritize home ownership over debt, employment, travel, raising kids, and daily routines?

Homeownership entails that. This ex-homeowner says it will rule your life from the time you put the key in the door.

This isn't questioned. We don't question enough. The holy home-ownership grail was set long ago, and we don't challenge it.

Many people question after signing the deeds. 70% of homeowners had at least one regret about buying a property, including the expense.

Exactly. Tragic.

Homes are different from houses

We've been fooled into thinking home ownership will make us happy.

Some may agree. No one.

Bricks and brick hindered me from living the version of my life that made me most comfortable, happy, and steady.

I'm spending the next month in a modest apartment in southern Spain. Even though it's late November, today will be 68 degrees. My spouse and I will soon meet his visiting parents. We'll visit a Sherry store. We'll eat, nap, walk, and drink Sherry. Writing. Jerez means flamenco.

That's my home. This is such a privilege. Living a fulfilling life brings me the contentment that buying a home never did.

I'm happy and comfortable knowing I can make almost all of my days good. Rejecting home ownership is partly to blame.

I'm broke like most folks. I had to choose between home ownership and comfort. I said, I didn't find them together.

Feeling at home trumps owning brick-and-mortar every day.

The following is the reality of what it's like to turn the American Dream around.

Leaving the housing market.

Sometimes I wish I owned a home.

I miss having my own yard and bed. My kitchen, cookbooks, and pizza oven are missed.

But I rarely do.

Someone else's life plan pushed home ownership on me. I'm grateful I figured it out at 35. Many take much longer, and some never understand homeownership stinks (for them).

It's confusing. People will think you're dumb or suicidal.

If you read what I write, you'll know. You'll realize that all you've done is choose to live intentionally. Find a home beyond four walls and a picket fence.

Miss? As I said, they're not home. If it were, a pizza oven, a good mattress, and a well-stocked kitchen would bring happiness.

No.

If you can afford a house and desire one, more power to you.

There are other ways to discover home. Find calm and happiness. For fun.

For it, look deeper than your home's foundation.