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.

It's cheaper, faster charging, longer lasting, safer, and better for the environment.

Batteries are the future. Next-gen and planet-saving technology, including solar power and EVs, require batteries. As these smart technologies become more popular, we find that our batteries can't keep up. Lithium-ion batteries are expensive, slow to charge, big, fast to decay, flammable, and not environmentally friendly. MIT just created a new battery that eliminates all of these problems.  So, is this the battery of the future? Or is there a catch?

When I say entirely new, I mean it. This battery employs no currently available materials. Its electrodes are constructed of aluminium and pure sulfur instead of lithium-complicated ion's metals and graphite. Its electrolyte is formed of molten chloro-aluminate salts, not an organic solution with lithium salts like lithium-ion batteries.

How does this change in materials help?

Aluminum, sulfur, and chloro-aluminate salts are abundant, easy to acquire, and cheap. This battery might be six times cheaper than a lithium-ion battery and use less hazardous mining. The world and our wallets will benefit.

But don’t go thinking this means it lacks performance.

This battery charged in under a minute in tests. At 25 degrees Celsius, the battery will charge 25 times slower than at 110 degrees Celsius. This is because the salt, which has a very low melting point, is in an ideal state at 110 degrees and can carry a charge incredibly quickly. Unlike lithium-ion, this battery self-heats when charging and discharging, therefore no external heating is needed.

Anyone who's seen a lithium-ion battery burst might be surprised. Unlike lithium-ion batteries, none of the components in this new battery can catch fire. Thus, high-temperature charging and discharging speeds pose no concern.

These batteries are long-lasting. Lithium-ion batteries don't last long, as any iPhone owner can attest. During charging, metal forms a dendrite on the electrode. This metal spike will keep growing until it reaches the other end of the battery, short-circuiting it. This is why phone batteries only last a few years and why electric car range decreases over time. This new battery's molten salt slows deposition, extending its life. This helps the environment and our wallets.

These batteries are also energy dense. Some lithium-ion batteries have 270 Wh/kg energy density (volume and mass). Aluminum-sulfur batteries could have 1392 Wh/kg, according to calculations. They'd be 5x more energy dense. Tesla's Model 3 battery would weigh 96 kg instead of 480 kg if this battery were used. This would improve the car's efficiency and handling.

These calculations were for batteries without molten salt electrolyte. Because they don't reflect the exact battery chemistry, they aren't a surefire prediction.

This battery seems great. It will take years, maybe decades, before it reaches the market and makes a difference. Right?

Nope. The project's scientists founded Avanti to develop and market this technology.

So we'll soon be driving cheap, durable, eco-friendly, lightweight, and ultra-safe EVs? Nope.

This battery must be kept hot to keep the salt molten; otherwise, it won't work and will expand and contract, causing damage. This issue could be solved by packs that can rapidly pre-heat, but that project is far off.

Rapid and constant charge-discharge cycles make these batteries ideal for solar farms, homes, and EV charging stations. The battery is constantly being charged or discharged, allowing it to self-heat and maintain an ideal temperature.

These batteries aren't as sexy as those making EVs faster, more efficient, and cheaper. Grid batteries are crucial to our net-zero transition because they allow us to use more low-carbon energy. As we move away from fossil fuels, we'll need millions of these batteries, so the fact that they're cheap, safe, long-lasting, and environmentally friendly will be huge. Who knows, maybe EVs will use this technology one day. MIT has created another world-changing technology.

Leonardo—The New Midjourney?

Users are comparing the new cowboy to Midjourney.

Leonardo.AI creates great photographs and has several unique capabilities I haven't seen in other AI image systems.

Midjourney's quality photographs are evident in the community feed.

Create Pictures Using Models

You can make graphics using platform models when you first enter the app (website):

Luma, Leonardo creative, Deliberate 1.1.

Clicking a model displays its description and samples:

Click Generate With This Model.

Then you can add your prompt, alter models, photos, sizes, and guide scale in a sleek UI.

Changing Pictures

Leonardo's Canvas editor lets you change created images by hovering over them:

The editor opens with masking, erasing, and picture download.

Develop Your Own Models

I've never seen anything like Leonardo's model training feature.

Upload a handful of similar photographs and save them as a model for future images. Share your model with the community.

You can make photos using your own model and a community-shared set of fine-tuned models:

Obtain Leonardo access

Leonardo is currently free.

Visit Leonardo.ai and click "Get Early Access" to receive access.

Add your email to receive a link to join the discord channel. Simply describe yourself and fill out a form to join the discord channel.

Please go to 👑│introductions to make an introduction and ✨│priority-early-access will be unlocked, you must fill out a form and in 24 hours or a little more (due to demand), the invitation will be sent to you by email.

I got access in two hours, so hopefully you can too.

Last Words

I know there are many AI generative platforms, some free and some expensive, but Midjourney produces the most artistically stunning images and art.

Leonardo is the closest I've seen to Midjourney, but Midjourney is still the leader.

It's free now.

Leonardo's fine-tuned model selections, model creation, image manipulation, and output speed and quality make it a great AI image toolbox addition.

Offices without books are like bodies without souls.

After 10 years, my CEO sold his company for $30 million. I've shared many of his lessons on medium. You could ask him anything at his always-open office. He also said we could use his office for meetings while he was away. When I used his office for work, I was always struck by how many books he had.

Books are useful in almost every aspect of learning. Building a business, improving family relationships, learning a new language, a new skill... Books teach, guide, and structure. Whether fiction or nonfiction, books inspire, give ideas, and develop critical thinking skills.

My CEO prefers non-fiction and attends a Friday book club. This article discusses 5 books I found in his office that impacted my life/business. My CEO sold his company for $30 million, but I've built a steady business through blogging and video making.

I recall events and lessons I learned from my CEO and how they relate to each book, and I explain how I applied the book's lessons to my business and life.

Note: This post has no affiliate links.

1. The One Thing — Gary Keller

Gary Keller, a real estate agent, wanted more customers. So he and his team brainstormed ways to get more customers. They decided to write a bestseller about work and productivity. The more people who saw the book, the more customers they'd get.

Gary Keller focused on writing the best book on productivity, work, and efficiency for months. His business experience. Keller's business grew after the book's release.

The author summarizes the book in one question.

"What's the one thing that will make everything else easier or unnecessary?"

When I started my blog and business alongside my 9–5, I quickly identified my one thing: writing. My business relied on it, so it had to be great. Without writing, there was no content, traffic, or business.

My CEO focused on funding when he started his business. Even in his final years, he spent a lot of time on the phone with investors, either to get more money or to explain what he was doing with it. My CEO's top concern was money, and the other super important factors were handled by separate teams.

• Product tech and design

• Incredible customer support team

• Excellent promotion team

• Profitable sales team

My CEO didn't always focus on one thing and ignore the rest. He was on all of those teams when I started my job. He'd start his day in tech, have lunch with marketing, and then work in sales. He was in his office on the phone at night.

He eventually realized his errors. Investors told him he couldn't do everything for the company. If needed, he had to change internally. He learned to let go, mind his own business, and focus for the next four years. Then he sold for $30 million.

The bigger your project/company/idea, the more you'll need to delegate to stay laser-focused. I started something new every few months for 10 years before realizing this. So much to do makes it easy to avoid progress. Once you identify the most important aspect of your project and enlist others' help, you'll be successful.

2. Eat That Frog — Brian Tracy

The author quote sums up book's essence:

Mark Twain said that if you eat a live frog in the morning, it's probably the worst thing that will happen to you all day. Your "frog" is the biggest, most important task you're most likely to procrastinate on.

"Frog" and "One Thing" are both about focusing on what's most important. Eat That Frog recommends doing the most important task first thing in the morning.

I shared my CEO's calendar in an article 10 months ago. Like this:

CEO's average week (some information crossed out for confidentiality)

Notice anything about 8am-8:45am? Almost every day is the same (except Friday). My CEO started his day with a management check-in for 2 reasons:

• Checking in with all managers is cognitively demanding, and my CEO is a morning person.

• In a young startup where everyone is busy, the morning management check-in was crucial. After 10 am, you couldn't gather all managers.

When I started my blog, writing was my passion. I'm a morning person, so I woke up at 6 am and started writing by 6:30 am every day for a year. This allowed me to publish 3 articles a week for 52 weeks to build my blog and audience. After 2 years, I'm not stopping.

3. Deep Work — Cal Newport

Deep work is focusing on a cognitively demanding task without distractions (like a morning management meeting). It helps you master complex information quickly and produce better results faster. In a competitive world 10 or 20 years ago, focus wasn't a huge advantage. Smartphones, emails, and social media made focus a rare, valuable skill.

Most people can't focus anymore. Screens light up, notifications buzz, emails arrive, Instagram feeds... Many people don't realize they're interrupted because it's become part of their normal workflow.

Cal Newport mentions Bill Gates' "Think Weeks" in Deep Work.

Microsoft CEO Bill Gates would isolate himself (often in a lakeside cottage) twice a year to read and think big thoughts.

Inside Bill's Brain on Netflix shows Newport's lakeside cottage. I've always wanted a lakeside cabin to work in. My CEO bought a lakehouse after selling his company, but now he's retired.

As a company grows, you can focus less on it. In a previous section, I said investors told my CEO to get back to basics and stop micromanaging. My CEO's commitment and ability to get work done helped save the company. His deep work and new frameworks helped us survive the corona crisis (more on this later).

The ability to deep work will be a huge competitive advantage in the next century. Those who learn to work deeply will likely be successful while everyone else is glued to their screens, Bluetooth-synced to their watches, and playing Candy Crush on their tablets.

4. The 7 Habits of Highly Effective People — Stephen R. Covey

It took me a while to start reading this book because it seemed like another shallow self-help bible. I kept finding this book when researching self-improvement. I tried it because it was everywhere.

Stephen Covey taught me 2 years ago to have a personal mission statement.

A 7 Habits mission statement describes the life you want to lead, the character traits you want to embody, and the impact you want to have on others. shortform.com

I've had many lunches with my CEO and talked about Vipassana meditation and Sunday forest runs, but I've never seen his mission statement. I'm sure his family is important, though. In the above calendar screenshot, you can see he always included family events (in green) so we could all see those time slots. We couldn't book him then. Although he never spent as much time with his family as he wanted, he always made sure to be on time for his kid's birthday rather than a conference call.

My CEO emphasized his company's mission. Your mission statement should answer 3 questions.

• What does your company do?

• How does it do it?

• Why does your company do it?

As a graphic designer, I had to create mission-statement posters. My CEO hung posters in each office.

5. Measure What Matters — John Doerr

This book is about Andrew Grove's OKR strategy, developed in 1968. When he joined Google's early investors board, he introduced it to Larry Page and Sergey Brin. Google still uses OKR.

Objective Key Results

• Objective: It explains your goals and desired outcome. When one goal is reached, another replaces it. OKR objectives aren't technical, measured, or numerical. They must be clear.

• Key Result should be precise, technical, and measurable, unlike the Objective. It shows if the Goal is being worked on. Time-bound results are quarterly or yearly.

Our company almost sank several times. Sales goals were missed, management failed, and bad decisions were made. On a Monday, our CEO announced we'd implement OKR to revamp our processes.

This was a year before the pandemic, and I'm certain we wouldn't have sold millions or survived without this change. This book impacted the company the most, not just management but all levels. Organization and transparency improved. We reached realistic goals. Happy investors. We used the online tool Gtmhub to implement OKR across the organization.

My CEO's company went from near bankruptcy to being acquired for $30 million in 2 years after implementing OKR.

I hope you enjoyed this booklist. Here's a recap of the 5 books and the lessons I learned from each.

1. The 7 Habits of Highly Effective People — Stephen R. Covey

Have a mission statement that outlines your goals, character traits, and impact on others.

1. Deep Work — Cal Newport

Focus is a rare skill; master it. Deep workers will succeed in our hyper-connected, distracted world.

1. The One Thing — Gary Keller

What can you do that will make everything else easier or unnecessary? Once you've identified it, focus on it.

1. Eat That Frog — Brian Tracy

Identify your most important task the night before and do it first thing in the morning. You'll have a lighter day.

1. Measure What Matters — John Doerr

On a timeline, divide each long-term goal into chunks. Divide those slices into daily tasks (your goals). Time-bound results are quarterly or yearly. Objectives aren't measured or numbered.

Thanks for reading. Enjoy the ride!

Don’t give a number

Google pays its software engineers generously. While many of their employees are competent, they disregard a critical skill to maximize their pay.

Negotiation.

If Google employees have never negotiated, they're as helpless as anyone else.

In this piece, I'll reveal a compensation negotiation tip that will set you apart.

The Fallacy of Negotiating

How do you negotiate your salary? “Just give them a number twice the amount you really want”. - Someplace on the internet

Above is typical negotiation advice. If you ask for more than you want, the recruiter may meet you halfway.

It seems logical and great, but here's why you shouldn't follow that advice.

Haitian hostage rescue

In 1977, an official's aunt was kidnapped in Haiti. The kidnappers demanded $150,000 for the aunt's life. It seems reasonable until you realize why kidnappers want $150,000.

FBI detective and negotiator Chris Voss researched why they demanded so much.

“So they could party through the weekend”

When he realized their ransom was for partying, he offered $4,751 and a CD stereo. Criminals freed the aunt.

These thieves gave 31.57x their estimated amount and got a fraction. You shouldn't trust these thieves to negotiate your compensation.

What happened?

Negotiating your offer and Haiti

This narrative teaches you how to negotiate with a large number.

You can and will be talked down.

If a recruiter asks your wage expectation and you offer double, be ready to explain why.

If you can't justify your request, you may be offered less. The recruiter will notice and talk you down.

Reasonably,

• a tiny bit more than the present amount you earn

• a small premium over an alternative offer

• a little less than the role's allotted amount

Real-World Illustration

Recruiter: What’s your expected salary? Candidate: (I know the role is usually $100,000) $200,000 Recruiter: How much are you compensated in your current role? Candidate: $90,000 Recruiter: We’d be excited to offer you $95,000 for your experiences for the role.

So Why Do They Even Ask?

Recruiters ask for a number to negotiate a lower one. Asking yourself limits you.

You'll rarely get more than you asked for, and your request can be lowered.

The takeaway from all of this is to never give an expected compensation.

Tell them you haven't thought about it when you applied.