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David G Chen

David G Chen

3 years ago

If you want to earn money, stop writing for entertainment.

More on Productivity

Darshak Rana

Darshak Rana

3 years ago

17 Google Secrets 99 Percent of People Don't Know 

What can't Google do?
Seriously, nothing! Google rocks.
Google is a major player in online tools and services. We use it for everything, from research to entertainment.
Did I say entertain yourself?
Yes, with so many features and options, it can be difficult to fully utilize Google.

#1. Drive Google Mad

You can make Google's homepage dance if you want to be silly.
Just type “Google Gravity” into Google.com. Then select I'm lucky.
See the page unstick before your eyes!

#2 Play With Google Image

Google isn't just for work.
Then have fun with it!
You can play games right in your search results. When you need a break, google “Solitaire” or “Tic Tac Toe”. 

#3. Do a Barrel Roll

Need a little more excitement in your life? Want to see Google dance?
Type “Do a barrel roll” into the Google search bar.
Then relax and watch your screen do a 360. 

#4  No Internet?  No issue!

This is a fun trick to use when you have no internet.
If your browser shows a “No Internet” page, simply press Space.
Boom!
We have dinosaurs! Now use arrow keys to save your pixelated T-Rex from extinction.

#5 Google Can Help

Play this Google coin flip game to see if you're lucky.
Enter “Flip a coin” into the search engine.
You'll see a coin flipping animation. If you get heads or tails, click it. 

#6. Think with Google

My favorite Google find so far is the “Think with Google” website.
Think with Google is a website that offers marketing insights, research, and case studies.
I highly recommend it to entrepreneurs, small business owners, and anyone interested in online marketing. 

#7. Google Can Read Images!

This is a cool Google trick that few know about.
You can search for images by keyword or upload your own by clicking the camera icon on Google Images.
Google will then show you all of its similar images.

Caution: You should be fine with your uploaded images being public. 

#8. Modify the Google Logo!

Clicking on the “I'm Feeling Lucky” button on Google.com takes you to a random Google Doodle.
Each year, Google creates a Doodle to commemorate holidays, anniversaries, and other occasions.

#9. What is my IP?

Simply type “What is my IP” into Google to find out.
Your IP address will appear on the results page.

#10. Send a Self-Destructing Email With Gmail, 

Create a new message in Gmail. Find an icon that resembles a lock and a clock near the SEND button. That's where the Confidential Mode is.
By clicking it, you can set an expiration date for your email. Expiring emails are automatically deleted from both your and the recipient's inbox.

#11. Blink, Google Blink!

This is a unique Google trick.
Type “blink HTML” into Google. The words “blink HTML” will appear and then disappear.
The text is displayed for a split second before being deleted.
To make this work, Google reads the HTML code and executes the “blink” command. 

#12. The Answer To Everything

This is for all Douglas Adams fans.
The answer to life, the universe, and everything is 42, according to Google.
An allusion to Douglas Adams' Hitchhiker's Guide to the Galaxy, in which Ford Prefect seeks to understand life, the universe, and everything.

#13. Google in 1998

It's a blast!
Type “Google in 1998” into Google. "I'm feeling lucky"
You'll be taken to an old-school Google homepage.
It's a nostalgic trip for long-time Google users. 

#14. Scholarships and Internships

Google can help you find college funding!
Type “scholarships” or “internships” into Google.
The number of results will surprise you. 

#15. OK, Google. Dice!

To roll a die, simply type “Roll a die” into Google.
On the results page is a virtual dice that you can click to roll. 

#16. Google has secret codes!

Hit the nine squares on the right side of your Google homepage to go to My Account. Then Personal Info.
You can add your favorite language to the “General preferences for the web” tab. 

#17. Google Terminal 

You can feel like a true hacker.
Just type “Google Terminal” into Google.com. "I'm feeling lucky"
Voila~!
You'll be taken to an old-school computer terminal-style page.
You can then type commands to see what happens.

Have you tried any of these activities? Tell me in the comments.

Read full article here

Pen Magnet

Pen Magnet

3 years ago

Why Google Staff Doesn't Work

Photo by Rajeshwar Bachu on Unsplash

Sundar Pichai unveiled Simplicity Sprint at Google's latest all-hands conference.

To boost employee efficiency.

Not surprising. Few envisioned Google declaring a productivity drive.

Sunder Pichai's speech:

“There are real concerns that our productivity as a whole is not where it needs to be for the head count we have. Help me create a culture that is more mission-focused, more focused on our products, more customer focused. We should think about how we can minimize distractions and really raise the bar on both product excellence and productivity.”

The primary driver driving Google's efficiency push is:

Google's efficiency push follows 13% quarterly revenue increase. Last year in the same quarter, it was 62%.

Market newcomers may argue that the previous year's figure was fuelled by post-Covid reopening and growing consumer spending. Investors aren't convinced. A promising company like Google can't afford to drop so quickly.

Google’s quarterly revenue growth stood at 13%, against 62% in last year same quarter.

Google isn't alone. In my recent essay regarding 2025 programmers, I warned about the economic downturn's effects on FAAMG's workforce. Facebook had suspended hiring, and Microsoft had promised hefty bonuses for loyal staff.

In the same article, I predicted Google's troubles. Online advertising, especially the way Google and Facebook sell it using user data, is over.

FAAMG and 2nd rung IT companies could be the first to fall without Post-COVID revival and uncertain global geopolitics.

Google has hardly ever discussed effectiveness:

Apparently openly.

Amazon treats its employees like robots, even in software positions. It has significant turnover and a terrible reputation as a result. Because of this, it rarely loses money due to staff productivity.

Amazon trumps Google. In reality, it treats its employees poorly.

Google was the founding father of the modern-day open culture.

Larry and Sergey Google founded the IT industry's Open Culture. Silicon Valley called Google's internal democracy and transparency near anarchy. Management rarely slammed decisions on employees. Surveys and internal polls ensured everyone knew the company's direction and had a vote.

20% project allotment (weekly free time to build own project) was Google's open-secret innovation component.

After Larry and Sergey's exit in 2019, this is Google's first profitability hurdle. Only Google insiders can answer these questions.

  • Would Google's investors compel the company's management to adopt an Amazon-style culture where the developers are treated like circus performers?

  • If so, would Google follow suit?

  • If so, how does Google go about doing it?

Before discussing Google's likely plan, let's examine programming productivity.

What determines a programmer's productivity is simple:

How would we answer Google's questions?

As a programmer, I'm more concerned about Simplicity Sprint's aftermath than its economic catalysts.

Large organizations don't care much about quarterly and annual productivity metrics. They have 10-year product-launch plans. If something seems horrible today, it's likely due to someone's lousy judgment 5 years ago who is no longer in the blame game.

Deconstruct our main question.

  • How exactly do you change the culture of the firm so that productivity increases?

  • How can you accomplish that without affecting your capacity to profit? There are countless ways to increase output without decreasing profit.

  • How can you accomplish this with little to no effect on employee motivation? (While not all employers care about it, in this case we are discussing the father of the open company culture.)

  • How do you do it for a 10-developer IT firm that is losing money versus a 1,70,000-developer organization with a trillion-dollar valuation?

When implementing a large-scale organizational change, success must be carefully measured.

The fastest way to do something is to do it right, no matter how long it takes.

You require clearly-defined group/team/role segregation and solid pass/fail matrices to:

  • You can give performers rewards.

  • Ones that are average can be inspired to improve

  • Underachievers may receive assistance or, in the worst-case scenario, rehabilitation

As a 20-year programmer, I associate productivity with greatness.

Doing something well, no matter how long it takes, is the fastest way to do it.

Let's discuss a programmer's productivity.

Why productivity is a strange term in programming:

Productivity is work per unit of time.

Money=time This is an economic proverb. More hours worked, more pay. Longer projects cost more.

As a buyer, you desire a quick supply. As a business owner, you want employees who perform at full capacity, creating more products to transport and boosting your profits.

All economic matrices encourage production because of our obsession with it. Productivity is the only organic way a nation may increase its GDP.

Time is money — is not just a proverb, but an economical fact.

Applying the same productivity theory to programming gets problematic. An automating computer. Its capacity depends on the software its master writes.

Today, a sophisticated program can process a billion records in a few hours. Creating one takes a competent coder and the necessary infrastructure. Learning, designing, coding, testing, and iterations take time.

Programming productivity isn't linear, unlike manufacturing and maintenance.

Average programmers produce code every day yet miss deadlines. Expert programmers go days without coding. End of sprint, they often surprise themselves by delivering fully working solutions.

Reversing the programming duties has no effect. Experts aren't needed for productivity.

These patterns remind me of an XKCD comic.

Source: XKCD

Programming productivity depends on two factors:

  • The capacity of the programmer and his or her command of the principles of computer science

  • His or her productive bursts, how often they occur, and how long they last as they engineer the answer

At some point, productivity measurement becomes Schrödinger’s cat.

Product companies measure productivity using use cases, classes, functions, or LOCs (lines of code). In days of data-rich source control systems, programmers' merge requests and/or commits are the most preferred yardstick. Companies assess productivity by tickets closed.

Every organization eventually has trouble measuring productivity. Finer measurements create more chaos. Every measure compares apples to oranges (or worse, apples with aircraft.) On top of the measuring overhead, the endeavor causes tremendous and unnecessary stress on teams, lowering their productivity and defeating its purpose.

Macro productivity measurements make sense. Amazon's factory-era management has done it, but at great cost.

Google can pull it off if it wants to.

What Google meant in reality when it said that employee productivity has decreased:

When Google considers its employees unproductive, it doesn't mean they don't complete enough work in the allotted period.

They can't multiply their work's influence over time.

  • Programmers who produce excellent modules or products are unsure on how to use them.

  • The best data scientists are unable to add the proper parameters in their models.

  • Despite having a great product backlog, managers struggle to recruit resources with the necessary skills.

  • Product designers who frequently develop and A/B test newer designs are unaware of why measures are inaccurate or whether they have already reached the saturation point.

  • Most ignorant: All of the aforementioned positions are aware of what to do with their deliverables, but neither their supervisors nor Google itself have given them sufficient authority.

So, Google employees aren't productive.

How to fix it?

  • Business analysis: White suits introducing novel items can interact with customers from all regions. Track analytics events proactively, especially the infrequent ones.

  • SOLID, DRY, TEST, and AUTOMATION: Do less + reuse. Use boilerplate code creation. If something already exists, don't implement it yourself.

  • Build features-building capabilities: N features are created by average programmers in N hours. An endless number of features can be built by average programmers thanks to the fact that expert programmers can produce 1 capability in N hours.

  • Work on projects that will have a positive impact: Use the same algorithm to search for images on YouTube rather than the Mars surface.

  • Avoid tasks that can only be measured in terms of time linearity at all costs (if a task can be completed in N minutes, then M copies of the same task would cost M*N minutes).

In conclusion:

Software development isn't linear. Why should the makers be measured?

Notation for The Big O

I'm discussing a new way to quantify programmer productivity. (It applies to other professions, but that's another subject)

The Big O notation expresses the paradigm (the algorithmic performance concept programmers rot to ace their Google interview)

Google (or any large corporation) can do this.

  1. Sort organizational roles into categories and specify their impact vs. time objectives. A CXO role's time vs. effect function, for instance, has a complexity of O(log N), meaning that if a CEO raises his or her work time by 8x, the result only increases by 3x.

  2. Plot the influence of each employee over time using the X and Y axes, respectively.

  3. Add a multiplier for Y-axis values to the productivity equation to make business objectives matter. (Example values: Support = 5, Utility = 7, and Innovation = 10).

  4. Compare employee scores in comparable categories (developers vs. devs, CXOs vs. CXOs, etc.) and reward or help employees based on whether they are ahead of or behind the pack.

After measuring every employee's inventiveness, it's straightforward to help underachievers and praise achievers.

Example of a Big(O) Category:

If I ran Google (God forbid, its worst days are far off), here's how I'd classify it. You can categorize Google employees whichever you choose.

The Google interview truth:

O(1) < O(log n) < O(n) < O(n log n) < O(n^x) where all logarithmic bases are < n.

O(1): Customer service workers' hours have no impact on firm profitability or customer pleasure.

CXOs Most of their time is spent on travel, strategic meetings, parties, and/or meetings with minimal floor-level influence. They're good at launching new products but bad at pivoting without disaster. Their directions are being followed.

Devops, UX designers, testers Agile projects revolve around deployment. DevOps controls the levers. Their automation secures results in subsequent cycles.

UX/UI Designers must still prototype UI elements despite improved design tools.

All test cases are proportional to use cases/functional units, hence testers' work is O(N).

Architects Their effort improves code quality. Their right/wrong interference affects product quality and rollout decisions even after the design is set.

Core Developers Only core developers can write code and own requirements. When people understand and own their labor, the output improves dramatically. A single character error can spread undetected throughout the SDLC and cost millions.

Core devs introduce/eliminate 1000x bugs, refactoring attempts, and regression. Following our earlier hypothesis.

The fastest way to do something is to do it right, no matter how long it takes.

Conclusion:

Google is at the liberal extreme of the employee-handling spectrum

Microsoft faced an existential crisis after 2000. It didn't choose Amazon's data-driven people management to revitalize itself.

Instead, it entrusted developers. It welcomed emerging technologies and opened up to open source, something it previously opposed.

Google is too lax in its employee-handling practices. With that foundation, it can only follow Amazon, no matter how carefully.

Any attempt to redefine people's measurements will affect the organization emotionally.

The more Google compares apples to apples, the higher its chances for future rebirth.

Jano le Roux

Jano le Roux

3 years ago

My Top 11 Tools For Building A Modern Startup, With A Free Plan

The best free tools are probably unknown to you.

Webflow

Modern startups are easy to build.

Start with free tools.

Let’s go.

Web development — Webflow

Code-free HTML, CSS, and JS.

Webflow isn't like Squarespace, Wix, or Shopify.

It's a super-fast no-code tool for professionals to construct complex, highly-responsive websites and landing pages.

Webflow can help you add animations like those on Apple's website to your own site.

I made the jump from WordPress a few years ago and it changed my life.

No damn plugins. No damn errors. No damn updates.

The best, you can get started on Webflow for free.

Data tracking — Airtable

Spreadsheet wings.

Airtable combines spreadsheet flexibility with database power without code.

  • Airtable is modern.

  • Airtable has modularity.

  • Scaling Airtable is simple.

Airtable, one of the most adaptable solutions on this list, is perfect for client data management.

Clients choose customized service packages. Airtable consolidates data so you can automate procedures like invoice management and focus on your strengths.

Airtable connects with so many tools that rarely creates headaches. Airtable scales when you do.

Airtable's flexibility makes it a potential backend database.

Design — Figma

Better, faster, easier user interface design.

Figma rocks!

  • It’s fast.

  • It's free.

  • It's adaptable

First, design in Figma.

Iterate.

Export development assets.

Figma lets you add more team members as your company grows to work on each iteration simultaneously.

Figma is web-based, so you don't need a powerful PC or Mac to start.

Task management — Trello

Unclock jobs.

Tacky and terrifying task management products abound. Trello isn’t.

Those that follow Marie Kondo will appreciate Trello.

  • Everything is clean.

  • Nothing is complicated.

  • Everything has a place.

Compared to other task management solutions, Trello is limited. And that’s good. Too many buttons lead to too many decisions lead to too many hours wasted.

Trello is a must for teamwork.

Domain email — Zoho

Free domain email hosting.

Professional email is essential for startups. People relied on monthly payments for too long. Nope.

Zoho offers 5 free professional emails.

It doesn't have Google's UI, but it works.

VPN — Proton VPN

Fast Swiss VPN protects your data and privacy.

Proton VPN is secure.

  • Proton doesn't record any data.

  • Proton is based in Switzerland.

Swiss privacy regulation is among the most strict in the world, therefore user data are protected. Switzerland isn't a 14 eye country.

Journalists and activists trust Proton to secure their identities while accessing and sharing information authoritarian governments don't want them to access.

Web host — Netlify

Free fast web hosting.

Netlify is a scalable platform that combines your favorite tools and APIs to develop high-performance sites, stores, and apps through GitHub.

Serverless functions and environment variables preserve API keys.

Netlify's free tier is unmissable.

  • 100GB of free monthly bandwidth.

  • Free 125k serverless operations per website each month.

Database — MongoDB

Create a fast, scalable database.

MongoDB is for small and large databases. It's a fast and inexpensive database.

  • Free for the first million reads.

  • Then, for each million reads, you must pay $0.10.

MongoDB's free plan has:

  • Encryption from end to end

  • Continual authentication

  • field-level client-side encryption

If you have a large database, you can easily connect MongoDB to Webflow to bypass CMS limits.

Automation — Zapier

Time-saving tip: automate repetitive chores.

Zapier simplifies life.

Zapier syncs and connects your favorite apps to do impossibly awesome things.

If your online store is connected to Zapier, a customer's purchase can trigger a number of automated actions, such as:

  1. The customer is being added to an email chain.

  2. Put the information in your Airtable.

  3. Send a pre-programmed postcard to the customer.

  4. Alexa, set the color of your smart lights to purple.

Zapier scales when you do.

Email & SMS marketing — Omnisend

Email and SMS marketing campaigns.

Omnisend

This is an excellent Mailchimp option for magical emails. Omnisend's processes simplify email automation.

I love the interface's cleanliness.

Omnisend's free tier includes web push notifications.

Send up to:

  • 500 emails per month

  • 60 maximum SMSs

  • 500 Web Push Maximum

Forms and surveys — Tally

Create flexible forms that people enjoy.

Typeform is clean but restricting. Sometimes you need to add many questions. Tally's needed sometimes.

Tally is flexible and cheaper than Typeform.

99% of Tally's features are free and unrestricted, including:

  • Unlimited forms

  • Countless submissions

  • Collect payments

  • File upload

Tally lets you examine what individuals contributed to forms before submitting them to see where they get stuck.

Airtable and Zapier connectors automate things further. If you pay, you can apply custom CSS to fit your brand.

See.

Free tools are the greatest.

Let's use them to launch a startup.

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Desiree Peralta

Desiree Peralta

3 years ago

Why Now Is Your Chance To Create A Millionaire Career

People don’t believe in influencers anymore; they need people like you.

Photo by Ivan Samkov

Social media influencers have dominated for years. We've seen videos, images, and articles of *famous* individuals unwrapping, reviewing, and endorsing things.

This industry generates billions. This year, marketers spent $2.23 billion on Instagram, $1 million on Youtube, and $775 million on Tiktok. This marketing has helped start certain companies.

Influencers are dying, so ordinary people like us may take over this billion-dollar sector. Why?

Why influencers are perishing

Most influencers lie to their fans, especially on Instagram. Influencers' first purpose was to make their lives so flawless that others would want to buy their stuff.

In 2015, an Australian influencer with 600,000 followers went viral for revealing all her photos and everything she did to seem great before deleting her account.

“I dramatically edited the pictures, I manipulated the environements, and made my life look perfect in social media… I remember I obsessively checked the like count for a full week since uploading it, a selfie that now has close to 2,500 likes. It got 5 likes. This was when I was so hungry for social media validation … This was the reason why I quit social media: for me, personally, it consumed me. I wasn’t living in a 3D world.”

Influencers then lost credibility.

Influencers seem to live in a bubble, separate from us. Thanks to self-popularity love's and constant awareness campaigns, people find these people ridiculous.

Influencers are praised more for showing themselves as natural and common than for showing luxuries and lies.

Influencer creating self-awareness

Little by little, they are dying, making room for a new group to take advantage of this multi-million dollar business, which gives us (ordinary people) a big opportunity to grow on any content creation platform we want.

Why this is your chance to develop on any platform for creating content

In 2021, I wroteNot everyone who talks about money is a Financial Advisor, be careful of who you take advice from,”. In it, I warned that not everyone with a large following is a reputable source of financial advice.

Other writers hated this post and said I was wrong.

People don't want Jeff Bezos or Elon Musk's counsel, they said. They prefer to hear about their neighbor's restroom problems or his closest friend's terrible business.

Real advice from regular folks.

And I found this was true when I returned to my independent YouTube channel and had more than 1000 followers after having abandoned it with fewer than 30 videos in 2021 since there were already many personal finance and travel channels and I thought mine wasn't special.

People appreciated my videos because I was a 20-something girl trying to make money online, and they believed my advice more than that of influencers with thousands of followers.

I think today is the greatest time to grow on any platform as an ordinary person. Normal individuals give honest recommendations about what works for them and look easier to make because they have the same options as us.

Nobody cares how a millionaire acquired a Lamborghini unless it's entertaining. Education works now. Real counsel from average people is replicable.

Many individuals don't appreciate how false influencers seem (unreal bodies and excessive surgery and retouching) since it makes them feel uneasy.

That's why body-positive advertisements have been so effective, but they've lost ground in places like Tiktok, where the audience wants more content from everyday people than influencers living amazing lives. More people will relate to your content if you appear genuine.

Last thoughts

Influencers are dwindling. People want more real people to give real advice and demonstrate an ordinary life.

People will enjoy anything you tell about your daily life as long as you provide value, and you can build a following rapidly if you're honest.

This is a millionaire industry that is getting more expensive and will go with what works, so stand out immediately.

Sammy Abdullah

Sammy Abdullah

3 years ago

SaaS payback period data

It's ok and even desired to be unprofitable if you're gaining revenue at a reasonable cost and have 100%+ net dollar retention, meaning you never lose customers and expand them. To estimate the acceptable cost of new SaaS revenue, we compare new revenue to operating loss and payback period. If you pay back the customer acquisition cost in 1.5 years and never lose them (100%+ NDR), you're doing well.

To evaluate payback period, we compared new revenue to net operating loss for the last 73 SaaS companies to IPO since October 2017. (55 out of 73). Here's the data. 1/(new revenue/operating loss) equals payback period. New revenue/operating loss equals cost of new revenue.

Payback averages a year. 55 SaaS companies that weren't profitable at IPO got a 1-year payback. Outstanding. If you pay for a customer in a year and never lose them (100%+ NDR), you're establishing a valuable business. The average was 1.3 years, which is within the 1.5-year range.

New revenue costs $0.96 on average. These SaaS companies lost $0.96 every $1 of new revenue last year. Again, impressive. Average new revenue per operating loss was $1.59.

Loss-in-operations definition. Operating loss revenue COGS S&M R&D G&A (technical point: be sure to use the absolute value of operating loss). It's wrong to only consider S&M costs and ignore other business costs. Operating loss and new revenue are measured over one year to eliminate seasonality.

Operating losses are desirable if you never lose a customer and have a quick payback period, especially when SaaS enterprises are valued on ARR. The payback period should be under 1.5 years, the cost of new income < $1, and net dollar retention 100%.

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

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.

A mathematical expression/formula in the Linux codebase, a screenshot by the author

Inbuilt max and min functions can minimize verbose if statements.

Reducing a verbose nested-if with the min function in Neutralinojs, a screenshot by the author

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.

GetWindowRect outputs an LPRECT geometric object, a screenshot by the author

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):

The Git codebase defines a function with logarithmic time complexity, a screenshot by the author

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

A utility function that uses ceil, a screenshot by the author

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.