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.

After viewing its insanity, I had to leave this platform.

I joined LinkedIn recently. That's how I aim to increase my readership and gain recognition. LinkedIn's premise appealed to me: a Facebook-like platform for professional networking.

I don't use Facebook since it's full of propaganda. It seems like a professional, apolitical space, right?

I expected people to:

• be more formal and respectful than on Facebook.

• Talk about the inclusiveness of the workplace. Studies consistently demonstrate that inclusive, progressive workplaces outperform those that adhere to established practices.

• Talk about business in their industry. Yep. I wanted to read articles with advice on how to write better and reach a wider audience.

Oh, sh*t. I hadn't anticipated that.

After posting and reading about inclusivity and pro-choice, I was startled by how many professionals acted unprofessionally. I've seen:

• Men have approached me in the DMs in a really aggressive manner. Yikes. huge yikes Not at all professional.

• I've heard pro-choice women referred to as infant killers by many people. If I were the CEO of a company and I witnessed one of my employees acting that poorly, I would immediately fire them.

• Many posts are anti-LGBTQIA+, as I've noticed. a lot, like, a lot. Some are subtly stating that the world doesn't need to know, while others are openly making fun of transgender persons like myself.

• Several medical professionals were posting explicitly racist comments. Even if you are as white as a sheet like me, you should be alarmed by this. Who's to guarantee a patient who is black won't unintentionally die?

• I won't even get into how many men in STEM I observed pushing for the exclusion of women from their fields. I shouldn't be surprised considering the majority of those men I've encountered have a passionate dislike for women, but goddamn, dude.

Many people appear entirely too at ease displaying their bigotry on their professional profiles.

As a white female, I'm always shocked by people's open hostility. Professional environments are very important.

I don't know if this is still true (people seem too politicized to care), but if I heard many of these statements in person, I'd suppose they feel ashamed. Really.

Are you not ashamed of being so mean? Are you so weak that competing with others terrifies you? Isn't this embarrassing?

LinkedIn isn't great at censoring offensive comments. These people aren't getting warnings. So they were safe while others were unsafe.

The CEO in me would want to know if I had placed a bigot on my staff.

I always wondered if people's employers knew about their online behavior. If they know how horrible they appear, they don't care.

As a manager, I was picky about hiring. Obviously. In most industries, it costs $1,000 or more to hire a full-time employee, so be sure it pays off.

Companies that embrace diversity and tolerance (and are intolerant of intolerance) are more profitable, likely to recruit top personnel, and successful.

People avoid businesses that alienate them. That's why I don't eat at Chic-Fil-A and why folks avoid MyPillow. Being inclusive is good business.

CEOs are harmed by online bigots. Image is an issue. If you're a business owner, you can fire staff who don't help you.

On the one hand, I'm delighted it makes it simpler to identify those with whom not to do business.

Don’t get me wrong. I'm glad I know who to avoid when hiring, getting references, or searching for a job. When people are bad, it saves me time.

What's up with professionalism?

Really. I need to know. I've crossed the boundary between acceptable and unacceptable behavior, but never on a professional platform. I got in trouble for not wearing bras even though it's not part of my gender expression.

If I behaved like that at my last two office jobs, my supervisors would have fired me immediately. Some of the behavior I've seen is so outrageous, I can't believe these people have employment. Some are even leaders.

Like…how? Is hatred now normalized?

Please pay attention whether you're seeking for a job or even simply a side gig.

Do not add to the tragedy that LinkedIn comments can be, or at least don't make uninformed comments. Even if you weren't banned, the site may still bite you.

Recruiters can and do look at your activity. Your writing goes on your résumé. The wrong comment might lose you a job.

Recruiters and CEOs might reject candidates whose principles contradict with their corporate culture. Bigotry will get you banned from many companies, especially if others report you.

If you want a high-paying job, avoid being a LinkedIn asshole. People care even if you think no one does. Before speaking, ponder. Is this how you want to be perceived?

Better advice:

If your politics might turn off an employer, stop posting about them online and ask yourself why you hold such objectionable ideas.

Ethereum is the second-largest cryptocurrency. The Merge, a mid-September event that will convert Ethereum's consensus process from proof-of-work to proof-of-stake if all goes according to plan, will be a game changer.

Why is Ethereum ditching proof-of-work? Because it can. We're talking about a fully functioning, open-source ecosystem with a capacity for evolution that other cryptocurrencies lack, a change that would allow it to scale up its performance from 15 transactions per second to 100,000 as its blockchain is used for more and more things. It would reduce its energy consumption by 99.95%. Vitalik Buterin, the system's founder, would play a less active role due to decentralization, and miners, who validated transactions through proof of work, would be far less important.

Why has this conversion taken so long and been so cautious? Because it involves modifying a core process while it's running to boost its performance. It requires running the new mechanism in test chains on an ever-increasing scale, assessing participant reactions, and checking for issues or restrictions. The last big test was in early June and was successful. All that's left is to converge the mechanism with the Ethereum blockchain to conclude the switch.

What's stopping Bitcoin, the leader in market capitalization and the cryptocurrency that began blockchain's appeal, from doing the same? Satoshi Nakamoto, whoever he or she is, departed from public life long ago, therefore there's no community leadership. Changing it takes a level of consensus that is impossible to achieve without strong leadership, which is why Bitcoin's evolution has been sluggish and conservative, with few modifications.

Secondly, The Merge will balance the consensus mechanism (proof-of-work or proof-of-stake) and the system decentralization or centralization. Proof-of-work prevents double-spending, thus validators must buy hardware. The system works, but it requires a lot of electricity and, as it scales up, tends to re-centralize as validators acquire more hardware and the entire network activity gets focused in a few nodes. Larger operations save more money, which increases profitability and market share. This evolution runs opposed to the concept of decentralization, and some anticipate that any system that uses proof of work as a consensus mechanism will evolve towards centralization, with fewer large firms able to invest in efficient network nodes.

Yet radical bitcoin enthusiasts share an opposite argument. In proof-of-stake, transaction validators put their funds at stake to attest that transactions are valid. The algorithm chooses who validates each transaction, giving more possibilities to nodes that put more coins at stake, which could open the door to centralization and government control.

In both cases, we're talking about long-term changes, but Bitcoin's proof-of-work has been evolving longer and seems to confirm those fears, while proof-of-stake is only employed in coins with a minuscule volume compared to Ethereum and has no predictive value.

As of mid-September, we will have two significant cryptocurrencies, each with a different consensus mechanisms and equally different characteristics: one is intrinsically conservative and used only for economic transactions, while the other has been evolving in open source mode, and can be used for other types of assets, smart contracts, or decentralized finance systems. Some even see it as the foundation of Web3.

Many things could change before September 15, but The Merge is likely to be a turning point. We'll have to follow this closely.

A fascinating business conversation.

This week at Web Summit, I had mentor hour.

Mentor hour connects startups with experienced entrepreneurs.

The YC-selected founder who mentored me had grown his company to $100 million in 18 months.

I had 45 minutes to question him.

I've compiled this.

Context

Founder's name is Zack.

After working in private equity, Zack opted to acquire an MBA.

Surrounded by entrepreneurs at a prominent school, he decided to become one himself.

Unsure how to proceed, he bet on two horses.

On one side, he received an offer from folks who needed help running their startup owing to lack of time. On the other hand, he had an idea for a SaaS to start himself.

He just needed to validate it.

Validating

Since Zack's proposal helped companies, he contacted university entrepreneurs for comments.

He contacted university founders.

Once he knew he'd correctly identified the problem and that people were willing to pay to address it, he started developing.

He earned $100k in a university entrepreneurship competition.

His plan was evident by then.

The other startup's founders saw his potential and granted him $400k to launch his own SaaS.

Hiring

He started looking for a tech co-founder because he lacked IT skills.

He interviewed dozens and picked the finest.

As he didn't want to wait for his program to be ready, he contacted hundreds of potential clients and got 15 letters of intent promising they'd join up when it was available.

YC accepted him by then.

He had enough positive signals to raise.

Raising

He didn't say how many VCs he called, but he indicated 50 were interested.

He jammed meetings into two weeks to generate pressure and encourage them to invest.

Seed raise: $11 million.

Selling

His objective was to contact as many entrepreneurs as possible to promote his product.

He first contacted startups by scraping CrunchBase data.

Once he had more money, he started targeting companies with ZoomInfo.

His VC urged him not to hire salespeople until he closed 50 clients himself.

He closed 100 and hired a CRO through a headhunter.

Scaling

Three persons started the business.

1. He primarily works in sales.

2. Coding the product was done by his co-founder.

3. Another person performing operational duties.

He regretted recruiting the third co-founder, who was ineffective (could have hired an employee instead).

He wanted his company to be big, so he hired two young marketing people from a competing company.

After validating several marketing channels, he chose PR.

$100 Million and under

He developed a sales team and now employs 30 individuals.

He raised a $100 million Series A.

Additionally, he stated

• He’s been rejected a lot. Like, a lot.

• Two great books to read: Steve Jobs by Isaacson, and Why Startups Fail by Tom Eisenmann.

• The best skill to learn for non-tech founders is “telling stories”, which means sales. A founder’s main job is to convince: co-founders, employees, investors, and customers. Learn code, or learn sales.

Conclusion

I often read about these stories but hardly take them seriously.

Zack was amazing.

Three things about him stand out:

1. His vision. He possessed a certain amount of fire.

2. His vitality. The man had a lot of enthusiasm and spoke quickly and decisively. He takes no chances and pushes the envelope in all he does.

3. His Rolex.

He didn't do all this in 18 months.

Not really.

He couldn't launch his company without private equity experience.

These accounts disregard entrepreneurs' original knowledge.

Hormozi will tell you how he founded Gym Launch, but he won't tell you how he had a gym first, how he worked at uni to pay for his gym, or how he went to the gym and learnt about fitness, which gave him the idea to open his own.

Nobody knows nothing. If you scale quickly, it's probable because you gained information early.

Lincoln said, "Give me six hours to chop down a tree, and I'll spend four sharpening the axe."

Sharper axes cut trees faster.

The Habit of Learning implies constantly learning something new. One daily habit will make you successful. Learning will help you succeed.

Most successful people continually learn. Success requires this behavior. Daily learning.

Success loves books. Books offer expert advice. Everything is online today. Most books are online, so you can skip the library. You must download it and study for 15-30 minutes daily. This habit changes your thinking.

Typical Successful People

• Warren Buffett reads 500 pages of corporate reports and five newspapers for five to six hours each day.

• Each year, Bill Gates reads 50 books.

• Every two weeks, Mark Zuckerberg reads at least one book.

• According to his brother, Elon Musk studied two books a day as a child and taught himself engineering and rocket design.

Learning & Making Money Online

No worries if you can't afford books. Everything is online. YouTube, free online courses, etc.

How can you create this behavior in yourself?

1) Consider what you want to know

Before learning, know what's most important. So, move together.

Set a goal and schedule learning.

After deciding what you want to study, create a goal and plan learning time.

3) GATHER RESOURCES

Get the most out of your learning resources. Online or offline.