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.

Believe what you see, what people say

It’s sad that we never get trained to leave assumptions behind. - Sebastian Thrun

Many problems in software development are not because of code but because developers create the wrong software. This isn't rare because software is emergent and most individuals only realize what they want after it's built.

Inquisitive developers who pass the yellow cat test can improve the process.

Carpenters measure twice and cut the wood once. Developers are rarely so careful.

The Yellow Cat Test

Game of Thrones made dragons cool again, so I am reading The Game of Thrones book.

The yellow cat exam is from Syrio Forel, Arya Stark's fencing instructor.

Syrio tells Arya he'll strike left when fencing. He hits her after she dodges left. Arya says “you lied”. Syrio says his words lied, but his eyes and arm told the truth.

Arya learns how Syrio became Bravos' first sword.

“On the day I am speaking of, the first sword was newly dead, and the Sealord sent for me. Many bravos had come to him, and as many had been sent away, none could say why. When I came into his presence, he was seated, and in his lap was a fat yellow cat. He told me that one of his captains had brought the beast to him, from an island beyond the sunrise. ‘Have you ever seen her like?’ he asked of me.

“And to him I said, ‘Each night in the alleys of Braavos I see a thousand like him,’ and the Sealord laughed, and that day I was named the first sword.”

Arya screwed up her face. “I don’t understand.”

Syrio clicked his teeth together. “The cat was an ordinary cat, no more. The others expected a fabulous beast, so that is what they saw. How large it was, they said. It was no larger than any other cat, only fat from indolence, for the Sealord fed it from his own table. What curious small ears, they said. Its ears had been chewed away in kitten fights. And it was plainly a tomcat, yet the Sealord said ‘her,’ and that is what the others saw. Are you hearing?” Reddit discussion.

Development teams should not believe what they are told.

We created an appointment booking system. We thought it was an appointment-booking system. Later, we realized the software's purpose was to book the right people for appointments and discourage the unneeded ones.

The first 3 months of the project had half-correct requirements and software understanding.

Open your eyes

“Open your eyes is all that is needed. The heart lies and the head plays tricks with us, but the eyes see true. Look with your eyes, hear with your ears. Taste with your mouth. Smell with your nose. Feel with your skin. Then comes the thinking afterwards, and in that way, knowing the truth” Syrio Ferel

We must see what exists, not what individuals tell the development team or how developers think the software should work. Initial criteria cover 50/70% and change.

Developers build assumptions problems by assuming how software should work. Developers must quickly explain assumptions.

When a development team's assumptions are inaccurate, they must alter the code, DevOps, documentation, and tests.

It’s always faster and easier to fix requirements before code is written.

First-draft requirements can be based on old software. Development teams must grasp corporate goals and consider needs from many angles.

Testers help rethink requirements. They look at how software requirements shouldn't operate.

Technical features and benefits might misdirect software projects.

The initiatives that focused on technological possibilities developed hard-to-use software that needed extensive rewriting following user testing.

Software development

High-level criteria are different from detailed ones.

• The interpretation of words determines their meaning.

• Presentations are lofty, upbeat, and prejudiced.

• People's perceptions may be unclear, incorrect, or just based on one perspective (half the story)

• Developers can be misled by requirements, circumstances, people, plans, diagrams, designs, documentation, and many other things.

Developers receive misinformation, misunderstandings, and wrong assumptions. The development team must avoid building software with erroneous specifications.

Once code and software are written, the development team changes and fixes them.

Developers create software with incomplete information, they need to fill in the blanks to create the complete picture.

Conclusion

Yellow cats are often inaccurate when communicating requirements.

Before writing code, clarify requirements, assumptions, etc.

Everyone will pressure the development team to generate code rapidly, but this will slow down development.

Code changes are harder than requirements.

The trick Notion could use is simply Facebook-ing the hell out of them.

*Time travel to fifteen years ago.* Future-Me: “Hey! What are you up to?” Old-Me: “I am proofreading an article. It’s taking a few hours, but I will be done soon.” Future-Me: “You know, in the future, you will be using a google chrome plugin called Grammarly that will help you easily proofread articles in half that time.” Old-Me: “What is… Google Chrome?” Future-Me: “Gosh…”

I love Grammarly. It’s one of those products that I personally feel the effects of. I mean, Space X is a great company. But I am not a rocket writing this article in space (or am I?)…

No, I’m not. So I don’t personally feel a connection to Space X. So, if a company collapse occurs in the morning, I might write about it. But I will have zero emotions regarding it.

Yet, if Grammarly fails tomorrow, I will feel 1% emotionally distressed. So looking at the title of this article, you’d realize that I am betting against them. This is how much I believe in the critical business model that’s taking over the world, the one of Notion.

Notion How frequently do you go through your notes?

Grammarly is everywhere, which helps its success. Grammarly is available when you update LinkedIn on Chrome. Grammarly prevents errors in Google Docs.

My internal concentration isn't apparent in the previous paragraph. Not Grammarly. I should have used Chrome to make a Google doc and LinkedIn update. Without this base, Grammarly will be useless.

So, welcome to this business essay.

• Grammarly provides a solution.

• Another issue is resolved by Jasper.

• Your entire existence is supposed to be contained within Notion.

New Google Chrome is offline. It's an all-purpose notepad (in the near future.)

• How should I start my blog? Enter it in Note.

• an update on LinkedIn? If you mention it, it might be automatically uploaded there (with little help from another app.)

• An advanced thesis? You can brainstorm it with your coworkers.

This ad sounds great! I won't cry if Notion dies tomorrow.

I'll reread the following passages to illustrate why I think Notion could kill Grammarly and Jasper.

Notion is a fantastic app that incubates your work.

Smartly, they began with note-taking.

Hopefully, your work will be on Notion. Grammarly and Jasper are still must-haves.

Grammarly will proofread your typing while Jasper helps with copywriting and AI picture development.

They're the best, therefore you'll need them. Correct? Nah.

Notion might bombard them with Facebook posts.

Notion: “Hi Grammarly, do you want to sell your product to us?” Grammarly: “Dude, we are more valuable than you are. We’ve even raised $400m, while you raised $342m. Our last valuation round put us at $13 billion, while yours put you at $10 billion. Go to hell.” Notion: “Okay, we’ll speak again in five years.”

Notion: “Jasper, wanna sell?” Jasper: “Nah, we’re deep into AI and the field. You can’t compete with our people.” Notion: “How about you either sell or you turn into a Snapchat case?” Jasper: “…”

Notion is your home. Grammarly is your neighbor. Your track is Jasper.

What if you grew enough vegetables in your backyard to avoid the supermarket? No more visits.

What if your home had a beautiful treadmill? You won't rush outside as much (I disagree with my own metaphor). (You get it.)

It's Facebooking. Instagram Stories reduced your Snapchat usage. Notion will reduce your need to use Grammarly.

The Final Piece of the AI Puzzle

Let's talk about Notion first, since you've probably read about it everywhere.

• They raised $343 million, as I previously reported, and bought four businesses

• According to Forbes, Notion will have more than 20 million users by 2022. The number of users is up from 4 million in 2020.

If raising $1.8 billion was impressive, FTX wouldn't have fallen.

This article compares the basic product to two others. Notion is a day-long app.

Notion has released Notion AI to support writers. It's early, so it's not as good as Jasper. Then-Jasper isn't now-Jasper. In five years, Notion AI will be different.

With hard work, they may construct a Jasper-like writing assistant. They have resources and users.

At this point, it's all speculation. Jasper's copywriting is top-notch. Grammarly's proofreading is top-notch. Businesses are constrained by user activities.

If Notion's future business movements are strategic, they might become a blue ocean shark (or get acquired by an unbelievable amount.)

I love business mental teasers, so tell me:

• How do you feel? Are you a frequent Notion user?

• Do you dispute my position? I enjoy hearing opposing viewpoints.

Ironically, I proofread this with Grammarly.

900K impressions, 8K clicks, and $$$ orders…

I recently started dropshipping. Now that I own my business and can charge it as a business expense, it feels less like money wasted if it doesn't work. I also made t-shirts to sell. I intended to open a t-shirt store and had many designs on a hard drive. I read that Tiktok advertising had a high conversion rate and low cost because they were new. According to many, the advertising' cost/efficiency ratio would plummet and become as bad as Google or Facebook Ads. Now felt like the moment to try Tiktok marketing and dropshipping. I work in marketing for a SaaS firm and have seen how poorly ads perform. I wanted to try it alone.

I set up $250 and ran advertising for a week. Before that, I made my own products, store, and marketing. In this post, I'll show you my process and results.

Setting up the store

Dropshipping is a sort of retail business in which the manufacturer ships the product directly to the client through an online platform maintained by a seller. The seller takes orders but has no stock. The manufacturer handles all orders. This no-stock concept increases profitability and flexibility.

In my situation, I used previous t-shirt designs to make my own product. I didn't want to handle order fulfillment logistics, so I looked for a way to print my designs on demand, ship them, and handle order tracking/returns automatically. So I found Printful.

I needed to connect my backend and supplier to a storefront so visitors could buy. 99% of dropshippers use Shopify, but I didn't want to master the difficult application. I wanted a one-day project. I'd previously worked with Big Cartel, so I chose them.

Big Cartel doesn't collect commissions on sales, simply a monthly flat price ($9.99 to $19.99 depending on your plan).

After opening a Big Cartel account, I uploaded 21 designs and product shots, then synced each product with Printful.

Developing the ads

I mocked up my designs on cool people photographs from placeit.net, a great tool for creating product visuals when you don't have a studio, camera gear, or models to wear your t-shirts.

I opened an account on the website and had advertising visuals within 2 hours.

Because my designs are simple (black design on white t-shirt), I chose happy, stylish people on plain-colored backdrops. After that, I had to develop an animated slideshow.

Because I'm a graphic designer, I chose to use Adobe Premiere to create animated Tiktok advertising.

Premiere is a fancy video editing application used for more than advertisements. Premiere is used to edit movies, not social media marketing. I wanted this experiment to be quick, so I got 3 social media ad templates from motionarray.com and threw my visuals in. All the transitions and animations were pre-made in the files, so it only took a few hours to compile. The result:

I downloaded 3 different soundtracks for the videos to determine which would convert best.

After that, I opened a Tiktok business account, uploaded my films, and inserted ad info. They went live within one hour.

The (poor) outcomes

As a European company, I couldn't deliver ads in the US. All of my advertisements' material (title, description, and call to action) was in English, hence they continued getting rejected in Europe for countries that didn't speak English. There are a lot of them:

I lost a lot of quality traffic, but I felt that if the images were engaging, people would check out the store and buy my t-shirts. I was wrong.

• 51,071 impressions on Day 1. 0 orders after 411 clicks

• 114,053 impressions on Day 2. 1.004 clicks and no orders

• Day 3: 987 clicks, 103,685 impressions, and 0 orders

• 101,437 impressions on Day 4. 0 orders after 963 clicks

• 115,053 impressions on Day 5. 1,050 clicks and no purchases

• 125,799 impressions on day 6. 1,184 clicks, no purchases

• 115,547 impressions on Day 7. 1,050 clicks and no purchases

• 121,456 impressions on day 8. 1,083 clicks, no purchases

• 47,586 impressions on Day 9. 419 Clicks. No orders

My overall conversion rate for video advertisements was 0.9%. TikTok's paid ad formats all result in strong engagement rates (ads average 3% to 12% CTR to site), therefore a 1 to 2% CTR should have been doable.

My one-week experiment yielded 8,151 ad clicks but no sales. Even if 0.1% of those clicks converted, I should have made 8 sales. Even companies with horrible web marketing would get one download or trial sign-up for every 8,151 clicks. I knew that because my advertising were in English, I had no impressions in the main EU markets (France, Spain, Italy, Germany), and that this impacted my conversion potential. I still couldn't believe my numbers.

I dug into the statistics and found that Tiktok's stats didn't match my store traffic data.

Looking more closely at the numbers

My ads were approved on April 26 but didn't appear until April 27. My store dashboard showed 440 visitors but 1,004 clicks on Tiktok. This happens often while tracking campaign results since different platforms handle comparable user activities (click, view) differently. In online marketing, residual data won't always match across tools.

My data gap was too large. Even if half of the 1,004 persons who clicked closed their browser or left before the store site loaded, I would have gained 502 visitors. The significant difference between Tiktok clicks and Big Cartel store visits made me suspicious. It happened all week:

• Day 1: 440 store visits and 1004 ad clicks

• Day 2: 482 store visits, 987 ad clicks

• 3rd day: 963 hits on ads, 452 store visits

• 443 store visits and 1,050 ad clicks on day 4.

• Day 5: 459 store visits and 1,184 ad clicks

• Day 6: 430 store visits and 1,050 ad clicks

• Day 7: 409 store visits and 1,031 ad clicks

• Day 8: 166 store visits and 418 ad clicks

The disparity wasn't related to residual data or data processing. The disparity between visits and clicks looked regular, but I couldn't explain it.

After the campaign concluded, I discovered all my creative assets (the videos) had a 0% CTR and a $0 expenditure in a separate dashboard. Whether it's a dashboard reporting issue or a budget allocation bug, online marketers shouldn't see this.

Tiktok can present any stats they want on their dashboard, just like any other platform that runs advertisements to promote content to its users. I can't verify that 895,687 individuals saw and clicked on my ad. I invested $200 for what appears to be around 900K impressions, which is an excellent ROI. No one bought a t-shirt, even an unattractive one, out of 900K people?

Would I do it again?

Nope. Whether I didn't make sales because Tiktok inflated the dashboard numbers or because I'm horrible at producing advertising and items that sell, I’ll stick to writing content and making videos. If setting up a business and ads in a few days was all it took to make money online, everyone would do it.

Video advertisements and dropshipping aren't dead. As long as the internet exists, people will click ads and buy stuff. Converting ads and selling stuff takes a lot of work, and I want to focus on other things.

I had always wanted to try dropshipping and I’m happy I did, I just won’t stick to it because that’s not something I’m interested in getting better at.

If I want to sell t-shirts again, I'll avoid Tiktok advertisements and find another route.

How I monetized and sold an abandoned side project for $20,000

The Origin Story

I've always wanted to be an entrepreneur but never succeeded. I often had business ideas, made a landing page, and told my buddies. Never got customers.

In April 2021, I decided to try again with a new strategy. I noticed that I had trouble acquiring an initial set of customers, so I wanted to start by acquiring a product that had a small user base that I could grow.

I found a SaaS marketplace called MicroAcquire.com where you could buy and sell SaaS products. I liked Shareit.video, an online Loom-like screen recorder.

Shareit.video didn't generate revenue, but 50 people visited daily to record screencasts.

Purchasing a Failed Side Project

I eventually bought Shareit.video for $12,000 from its owner.

$12,000 was probably too much for a website without revenue or registered users.

I thought time was most important. I could have recreated the website, but it would take months. $12,000 would give me an organized code base and a working product with a few users to monetize.

I considered buying a screen recording website and trying to grow it versus buying a new car or investing in crypto with the $12K.

Buying the website would make me a real entrepreneur, which I wanted more than anything.

Putting down so much money would force me to commit to the project and prevent me from quitting too soon.

A Year of Development

I rebranded the website to be called RecordJoy and worked on it with my cousin for about a year. Within a year, we made $5000 and had 3000 users.

We spent $3500 on ads, hosting, and software to run the business.

AppSumo promoted our $120 Life Time Deal in exchange for 30% of the revenue.

We put RecordJoy on maintenance mode after 6 months because we couldn't find a scalable user acquisition channel.

We improved SEO and redesigned our landing page, but nothing worked.

Despite not being able to grow RecordJoy any further, I had already learned so much from working on the project so I was fine with putting it on maintenance mode. RecordJoy still made $500 a month, which was great lunch money.

Getting Taken Over

One of our customers emailed me asking for some feature requests and I replied that we weren’t going to add any more features in the near future. They asked if we'd sell.

We got on a call with the customer and I asked if he would be interested in buying RecordJoy for 15k. The customer wanted around $8k but would consider it.

Since we were negotiating with one buyer, we put RecordJoy on MicroAcquire to see if there were other offers.

We quickly received 10+ offers. We got 18.5k. There was also about $1000 in AppSumo that we could not withdraw, so we agreed to transfer that over for $600 since about 40% of our sales on AppSumo usually end up being refunded.

Lessons Learned

First, create an acquisition channel

We couldn't discover a scalable acquisition route for RecordJoy. If I had to start another project, I'd develop a robust acquisition channel first. It might be LinkedIn, Medium, or YouTube.

Purchase Power of the Buyer Affects Acquisition Price

Some of the buyers we spoke to were individuals looking to buy side projects, as well as companies looking to launch a new product category. Individual buyers had less budgets than organizations.

Customers of AppSumo vary.

AppSumo customers value lifetime deals and low prices, which may not be a good way to build a business with recurring revenue. Designed for AppSumo users, your product may not connect with other users.

Try to increase acquisition trust

Acquisition often fails. The buyer can go cold feet, cease communicating, or run away with your stuff. Trusting the buyer ensures a smooth asset exchange. First acquisition meeting was unpleasant and price negotiation was tight. In later meetings, we spent the first few minutes trying to get to know the buyer’s motivations and background before jumping into the negotiation, which helped build trust.

Operating expenses can reduce your earnings.

Monitor operating costs. We were really happy when we withdrew the $5000 we made from AppSumo and Stripe until we realized that we had spent $3500 in operating fees. Spend money on software and consultants to help you understand what to build.

Don't overspend on advertising

We invested $1500 on Google Ads but made little money. For a side project, it’s better to focus on organic traffic from SEO rather than paid ads unless you know your ads are going to have a positive ROI.