He kept it under wraps for years until he legally couldn’t.

His shirt is incomplete. I can’t stop thinking about this…

Actually, ignore the article. Look at it. JUST LOOK at it… It’s quite disturbing, isn’t it?

Ughh…

Me: “Hey, what up?” Friend: “All good, watching lord of the rings on amazon prime video.” Me: “Oh, do you know how Amazon grew and became famous?” Friend: “Geek alert…Can I just watch in peace?” Me: “But… Bezos?” Friend: “Let it go, just let it go…”

I can question you, the reader, and start answering instantly without his consent. This far.

Reader, how did Amazon succeed? You'll say, Of course, it was an internet bookstore, then it sold everything.

Mistaken. They moved from zero to one because of this. How did they get from one to thousand? AWS-some. Understand? It's geeky and lame. If not, I'll explain my geekiness.

Over an extended period of time, Amazon was not profitable.

Business basics. You want customers if you own a bakery, right?

Well, 100 clients per day order $5 cheesecakes (because cheesecakes are awesome.)

$5 x 100 consumers x 30 days Equals $15,000 monthly revenue. You proudly work here.

Now you have to pay the barista (unless ChatGPT is doing it haha? Nope..)

• The barista is requesting $5000 a month.

• Each cheesecake costs the cheesecake maker $2.5 ($2.5 × 100 x 30 = $7500).

• The monthly cost of running your bakery, including power, is about $5000.

Assume no extra charges. Your operating costs are $17,500.

Just $15,000? You have income but no profit. You might make money selling coffee with your cheesecake next month.

Is losing money bad? You're broke. Losing money. It's bad for financial statements.

It's almost a business ultimatum. Most startups fail. Amazon took nine years.

I'm reading Amazon Unbound: Jeff Bezos and the Creation of a Global Empire to comprehend how a company has a $1 trillion market cap.

Many things made Amazon big. The book claims that Bezos and Amazon kept a specific product secret for a long period.

Clouds above the bald head.

In 2006, Bezos started a cloud computing initiative. They believed many firms like Snapchat would pay for reliable servers.

In 2006, cloud computing was not what it is today. I'll simplify. 2006 had no iPhone.

Bezos invested in Amazon Web Services (AWS) without disclosing its revenue. That's permitted till a certain degree.

Google and Microsoft would realize Amazon is heavily investing in this market and worry.

Bezos anticipated high demand for this product. Microsoft built its cloud in 2010, and Google in 2008.

If you managed Google or Microsoft, you wouldn't know how much Amazon makes from their cloud computing service. It's enough. Yet, Amazon is an internet store, so they'll focus on that.

All but Bezos were wrong.

Time to come clean now.

They revealed AWS revenue in 2015. Two things were apparent:

1. Bezos made the proper decision to bet on the cloud and keep it a secret.

2. In this race, Amazon is in the lead.

They continued. Let me list some AWS users today.

• Netflix

• Airbnb

• Twitch

More. Amazon was unprofitable for nine years, remember? This article's main graph.

AWS accounted for 74% of Amazon's profit in 2021. This 74% might not exist if they hadn't invested in AWS.

Bring this with you home.

Amazon predated AWS. Yet, it helped the giant reach $1 trillion. Bezos' secrecy? Perhaps, until a time machine is invented (they might host the time machine software on AWS, though.)

Without AWS, Amazon would have been profitable but unimpressive. They may have invested in anything else that would have returned more (like crypto? No? Ok.)

Bezos has business flaws. His success. His failures include:

• introducing the Fire Phone and suffering a $170 million loss.

• Amazon's failure in China In 2011, Amazon had a about 15% market share in China. 2019 saw a decrease of about 1%.

• not offering a higher price to persuade the creator of Netflix to sell the company to him. He offered a rather reasonable $15 million in his proposal. But what if he had offered $30 million instead (Amazon had over $100 million in revenue at the time)? He might have owned Netflix, which has a $156 billion market valuation (and saved billions rather than invest in Amazon Prime Video).

Some he could control. Some were uncontrollable. Nonetheless, every action he made in the foregoing circumstances led him to invest in AWS.

The VP has revealed a secret that should frighten the rest of the EV world.

Tesla led the EV revolution. Elon Musk's invention offers a viable alternative to gas-guzzlers. Tesla has lost ground in recent years. VW, BMW, Mercedes, and Ford offer EVs with similar ranges, charging speeds, performance, and cost. Tesla's next-generation 4680 battery pack, Roadster, Cybertruck, and Semi were all delayed. CATL offers superior batteries than the 4680. Martin Viecha, Tesla's Vice President, recently told Business Insider something that startled the EV world and will establish Tesla as the EV king.

Viecha mentioned that Tesla's production costs have dropped 57% since 2017. This isn't due to cheaper batteries or devices like Model 3. No, this is due to amazing factory efficiency gains.

Musk wasn't crazy to want a nearly 100% automated production line, and Tesla's strategy of sticking with one model and improving it has paid off. Others change models every several years. This implies they must spend on new R&D, set up factories, and modernize service and parts systems. All of this costs a ton of money and prevents them from refining production to cut expenses.

Meanwhile, Tesla updates its vehicles progressively. Everything from the backseats to the screen has been enhanced in a 2022 Model 3. Tesla can refine, standardize, and cheaply produce every part without changing the production line.

In 2017, Tesla's automobile production averaged $84,000. In 2022, it'll be $36,000.

Mr. Viecha also claimed that new factories in Shanghai and Berlin will be significantly cheaper to operate once fully operating.

Tesla's hand is visible. Tesla selling $36,000 cars for $60,000 This barely beats the competition. Model Y long-range costs just over $60,000. Tesla makes $24,000+ every sale, giving it a 40% profit margin, one of the best in the auto business.

VW I.D4 costs about the same but makes no profit. Tesla's rivals face similar challenges. Their EVs make little or no profit.

Tesla costs the same as other EVs, but they're in a different league.

But don't forget that the battery pack accounts for 40% of an EV's cost. Tesla may soon fully utilize its 4680 battery pack.

The 4680 battery pack has larger cells and a unique internal design. This means fewer cells are needed for a car, making it cheaper to assemble and produce (per kWh). Energy density and charge speeds increase slightly.

Tesla underestimated the difficulty of making this revolutionary new cell. Each time they try to scale up production, quality drops and rejected cells rise.

Tesla recently installed this battery pack in Model Ys and is scaling production. If they succeed, Tesla battery prices will plummet.

Tesla's Model Ys 2170 battery costs $11,000. The same size pack with 4680 cells costs $3,400 less. Once scaled, it could be $5,500 (50%) less. The 4680 battery pack could reduce Tesla production costs by 20%.

With these cost savings, Tesla could sell Model Ys for $40,000 while still making a profit. They could offer a $25,000 car.

Even with new battery technology, it seems like other manufacturers will struggle to make EVs profitable.

Teslas cost about the same as competitors, so don't be fooled. Behind the scenes, they're still years ahead, and the 4680 battery pack and new factories will only increase that lead. Musk faces a first. He could sell Teslas at current prices and make billions while other manufacturers struggle. Or, he could massively undercut everyone and crush the competition once and for all. Tesla and Elon win.

Hiring is difficult, but you shouldn't compromise on team members. Or it may suggest you need to look beyond years in a similar role/function.

Every hire should be someone we'd want as one of our first ten employees.

If you hire such people, your team will adapt, initiate, and problem-solve, and your company will grow. You'll stay nimble even as you scale, and you'll learn from your colleagues.

If you only hire for a specific role or someone who can execute the job, you'll become a cluster of optimizers, and talent will depart for a more fascinating company. A startup is continually changing, therefore you want individuals that embrace it.

As a leader, establishing ideal conditions for talent and having a real ideology should be high on your agenda. You can't eliminate attrition, nor would you want to, but you can hire people who will become your company's leaders.

In my last four jobs I was employee 2, 5, 3, and 5. So while this is all a bit self serving, you’re the one reading my writing — and I have some experience with who works out in the first ten!

First, we'll examine what they do well (and why they're beneficial for startups), then what they don't, and how to hire them.

First 10 are:

• Business partners: Because it's their company, they take care of whatever has to be done and have ideas about how to do it. You can rely on them to always put the success of the firm first because it is their top priority (company success is strongly connected with success for early workers). This approach will eventually take someone to leadership positions.
  

• High Speed Learners: They process knowledge quickly and can reach 80%+ competency in a new subject matter rather quickly. A growing business that is successful tries new things frequently. We have all lost a lot of money and time on employees who follow the wrong playbook or who wait for someone else within the company to take care of them.
  

• Autodidacts learn by trial and error, osmosis, networking with others, applying first principles, and reading voraciously (articles, newsletters, books, and even social media). Although teaching is wonderful, you won't have time.
  

• Self-scaling: They figure out a means to deal with issues and avoid doing the grunt labor over the long haul, increasing their leverage. Great people don't keep doing the same thing forever; as they expand, they use automation and delegation to fill in their lower branches. This is a crucial one; even though you'll still adore them, you'll have to manage their scope or help them learn how to scale on their own.
  

• Free Range: You can direct them toward objectives rather than specific chores. Check-ins can be used to keep them generally on course without stifling invention instead of giving them precise instructions because doing so will obscure their light.
  

• When people are inspired, they bring their own ideas about what a firm can be and become animated during discussions about how to get there.
  

• Novelty Seeking: They look for business and personal growth chances. Give them fresh assignments and new directions to follow around once every three months.

Here’s what the First Ten types may not be:

• Domain specialists. When you look at their resumes, you'll almost certainly think they're unqualified. Fortunately, a few strategically positioned experts may empower a number of First Ten types by serving on a leadership team or in advising capacities.
  

• Balanced. These people become very invested, and they may be vulnerable to many types of stress. You may need to assist them in managing their own stress and coaching them through obstacles. If you are reading this and work at Banza, I apologize for not doing a better job of supporting this. I need to be better at it.
  

• Able to handle micromanagement with ease. People who like to be in charge will suppress these people. Good decision-making should be delegated to competent individuals. Generally speaking, if you wish to scale.

Great startup team members have versatility, learning, innovation, and energy. When we hire for the function, not the person, we become dull and staid. Could this person go to another department if needed? Could they expand two levels in a few years?

First Ten qualities and experience level may have a weak inverse association. People with 20+ years of experience who had worked at larger organizations wanted to try something new and had a growth mentality. College graduates may want to be told what to do and how to accomplish it so they can stay in their lane and do what their management asks.

Does the First Ten archetype sound right for your org? Cool, let’s go hiring. How will you know when you’ve found one?

• They exhibit adaptive excellence, excelling at a variety of unrelated tasks. It could be hobbies or professional talents. This suggests that they will succeed in the next several endeavors they pursue.
  

• Successful risk-taking is doing something that wasn't certain to succeed, sometimes more than once, and making it do so. It's an attitude.
  

• Rapid Rise: They regularly change roles and get promoted. However, they don't leave companies when the going gets tough. Look for promotions at every stop and at least one position with three or more years of experience.

You can ask them:

• Tell me about a time when you started from scratch or achieved success. What occurred en route? You might request a variety of tales from various occupations or even aspects of life. They ought to be energized by this.
  

• What new skills have you just acquired? It is not required to be work-related. They must be able to describe it and unintentionally become enthusiastic about it.
  

• Tell me about a moment when you encountered a challenge and had to alter your strategy. The core of a startup is reinventing itself when faced with obstacles.
  

• Tell me about a moment when you eliminated yourself from a position at work. They've demonstrated they can permanently solve one issue and develop into a new one, as stated above.
  

• Why do you want to leave X position or Y duty? These people ought to be moving forward, not backward, all the time. Instead, they will discuss what they are looking forward to visiting your location.
  

• Any questions? Due to their inherent curiosity and desire to learn new things, they should practically never run out of questions. You can really tell if they are sufficiently curious at this point.

People who see their success as being the same as the success of the organization are the best-case team members, in any market. They’ll grow and change with the company, and always try to prioritize what matters. You’ll find yourself more energized by your work because you’re surrounded by others who are as well. Happy teambuilding!

Don't say this in public!

Want to wow your audience? Want to deliver a successful presentation? Do you want practical takeaways from your presentation?

Then avoid these phrases.

Public speaking is difficult. People fear public speaking, according to research.

"Public speaking is people's biggest fear, according to studies. Number two is death. "Sounds right?" — Comedian Jerry Seinfeld

Yes, public speaking is scary. These words and phrases will make your presentation harder.

Using unnecessary words can weaken your message.

You may have prepared well for your presentation and feel confident. During your presentation, you may freeze up. You may blank or forget.

Effective delivery is even more important than skillful public speaking.

Here are 10 presentation pitfalls.

1. I or Me

Presentations are about the audience, not you. Replace "I or me" with "you, we, or us." Focus on your audience. Reward them with expertise and intriguing views about your issue.

Serve your audience actionable items during your presentation, and you'll do well. Your audience will have a harder time listening and engaging if you're self-centered.

2. Sorry if/for

Your presentation is fine. These phrases make you sound insecure and unprepared. Don't pressure the audience to tell you not to apologize. Your audience should focus on your presentation and essential messages.

3. Excuse the Eye Chart, or This slide's busy

Why add this slide if you're utilizing these phrases? If you don't like this slide, change it before presenting. After the presentation, extra data can be provided.

Don't apologize for unclear slides. Hide or delete a broken PowerPoint slide. If so, divide your message into multiple slides or remove the "business" slide.

4. Sorry I'm Nervous

Some think expressing yourself will win over the audience. Nerves are horrible. Even public speakers are nervous.

Nerves aren't noticeable. What's the point? Let the audience judge your nervousness. Please don't make this obvious.

5. I'm not a speaker or I've never done this before.

These phrases destroy credibility. People won't listen and will check their phones or computers.

Why present if you use these phrases?

Good speakers aren't necessarily public speakers. Be confident in what you say. When you're confident, many people will like your presentation.

6. Our Key Differentiators Are

Overused term. It's widely utilized. This seems "salesy," and your "important differentiators" are probably like a competitor's.

This statement has been diluted; say, "what makes us different is..."

7. Next Slide

Many slides or stories? Your presentation needs transitions. They help your viewers understand your argument.

You didn't transition well when you said "next slide." Think about organic transitions.

8. I Didn’t Have Enough Time, or I’m Running Out of Time

The phrase "I didn't have enough time" implies that you didn't care about your presentation. This shows the viewers you rushed and didn't care.

Saying "I'm out of time" shows poor time management. It means you didn't rehearse enough and plan your time well.

9. I've been asked to speak on

This phrase is used to emphasize your importance. This phrase conveys conceit.

When you say this sentence, you tell others you're intelligent, skilled, and appealing. Don't utilize this term; focus on your topic.

10. Moving On, or All I Have

These phrases don't consider your transitions or presentation's end. People recall a presentation's beginning and end.

How you end your discussion affects how people remember it. You must end your presentation strongly and use natural transitions.

Conclusion

10 phrases to avoid in a presentation. I or me, sorry if or sorry for, pardon the Eye Chart or this busy slide, forgive me if I appear worried, or I'm really nervous, and I'm not good at public speaking, I'm not a speaker, or I've never done this before.

Please don't use these phrases: next slide, I didn't have enough time, I've been asked to speak about, or that's all I have.

We shouldn't make public speaking more difficult than it is. We shouldn't exacerbate a difficult issue. Better public speakers avoid these words and phrases.

“Remember not only to say the right thing in the right place, but far more difficult still, to leave unsaid the wrong thing at the tempting moment.” — Benjamin Franklin, Founding Father

This is a summary. See the original post here.

I use a conceptual and practical system I developed decades ago as an example.

Since childhood, I've been interested in the brain-mind connection, so I developed a system using scientific breakthroughs, experiments, and the experiences of successful people in my circles.

This story provides a high-level overview of a custom system to inform and inspire readers. Creating a mind gym was one of my best personal and professional investments.

Such a complex system may not be possible for everyone or appear luxurious at first. However, the process and approach may help you find more accessible and viable solutions.

Visualizing the brain as a muscle, I learned to stimulate it with physical and mental exercises, applying a new mindset and behavioral changes.

My methods and practices may not work for others because we're all different. I focus on the approach's principles and highlights so you can create your own program.

Some create a conceptual and practical system intuitively, and others intellectually. Both worked. I see intellect and intuition as higher selves.

The mental tools I introduce are based on lifestyle changes and can be personalized by anyone, barring physical constraints or underlying health conditions.

Some people can't meditate despite wanting to due to mental constraints. This story lacks exceptions.

People's systems may vary. Many have used my tools successfully. All have scientific backing because their benefits attracted scientists. None are unethical or controversial.

My focus is cognition, which is the neocortex's ability. These practices and tools can affect the limbic and reptilian brain regions.

A previous article discussed brain health's biological aspects. This article focuses on psychology.

Thinking, learning, and remembering are cognitive abilities. Cognitive abilities determine our health and performance.

Cognitive health is the ability to think, concentrate, learn, and remember. Cognitive performance boosting involves various tools and processes. My system and protocols address cognitive health and performance.

As a biological organ, the brain's abilities decline with age, especially if not used regularly. Older people have more neurodegenerative disorders like dementia.

As aging is inevitable, I focus on creating cognitive reserves to remain mentally functional as we age and face mental decline or cognitive impairment.

My protocols focus on neurogenesis, or brain growth and maintenance. Neurons and connections can grow at any age.

Metacognition refers to knowing our cognitive abilities, like thinking about thinking and learning how to learn.

In the following sections, I provide an overview of my system, mental tools, and protocols.

This system summarizes my 50-year career. Some may find it too abstract, so I give examples.

First, explain the system. Section 2 introduces activities. Third, how to measure and maintain mental growth.

1 — Developed a practical mental gym.

The mental gym is a metaphor for the physical fitness gym to improve our mental muscles.

This concept covers brain and mind functionality. Integrated biological and psychological components.

I'll describe my mental gym so my other points make sense. My mental gym has physical and mental tools.

Mindfulness, meditation, visualization, self-conversations, breathing exercises, expressive writing, working in a flow state, reading, music, dance, isometric training, barefoot walking, cold/heat exposure, CBT, and social engagements are regular tools.

Dancing, walking, and thermogenesis are body-related tools. As the brain is part of the body and houses the mind, these tools can affect mental abilities such as attention, focus, memory, task switching, and problem-solving.

Different people may like different tools. I chose these tools based on my needs, goals, and lifestyle. They're just examples. You can choose tools that fit your goals and personality.

2 — Performed tasks regularly.

These tools gave me clarity. They became daily hobbies. Some I did alone, others with others.

Some examples: I meditate daily. Even though my overactive mind made daily meditation difficult at first, I now enjoy it. Meditation three times a day sharpens my mind.

Self-talk is used for self-therapy and creativity. Self-talk was initially difficult, but neurogenesis rewired my brain to make it a habit.

Cold showers, warm baths with Epsom salts, fasting, barefoot walks on the beach or grass, dancing, calisthenics, trampoline hopping, and breathing exercises increase my mental clarity, creativity, and productivity.

These exercises can increase BDNF, which promotes nervous system growth. They improve mental capacity and performance by increasing blood flow and brain oxygenation.

I use weekly and occasional activities like dry saunas, talking with others, and community activities.

These activities stimulate the brain and mind, improving performance and cognitive capacity.

3 — Measured progress, set growth goals.

Measuring progress helps us stay on track. Without data, it's hard to stay motivated. When we face inevitable setbacks, we may abandon our dreams.

I created a daily checklist for a spreadsheet with macros. I tracked how often and long I did each activity.

I measured my progress objectively and subjectively. In the progress spreadsheet, I noted my meditation hours and subjective feelings.

In another column, I used good, moderate, and excellent to get qualitative data. It took time and effort. Later, I started benefiting from this automated structure.

Creating a page for each activity, such as meditation, self-talk, cold showers, walking, expressive writing, personal interactions, etc., gave me empirical data I could analyze, modify, and graph to show progress.

Colored charts showed each area's strengths and weaknesses.

Strengths motivate me to continue them. Identifying weaknesses helped me improve them.

As the system matured, data recording became a habit and took less time. I saw the result immediately because I automated the charts when I entered daily data. Early time investment paid off later.

Mind Gym Benefits, Effective Use, and Progress Measuring

This concept helped me move from comfort to risk. I accept things as they are.

Turnarounds were made. I stopped feeling "Fight-Flight-Freeze" and maintained self-control.

I tamed my overactive amygdala by strengthening my brain. Stress and anxiety decreased. With these shifts, I accepted criticism and turned envy into admiration. Clarity improved.

When the cognitive part of the brain became stronger and the primitive part was tamed, managing thoughts and emotions became easier. My AQ increased. I learned to tolerate people, physical, mental, and emotional obstacles.

Accessing vast information sources in my subconscious mind through an improved RAS allowed me to easily tap into my higher self and recognize flaws in my lower self.

Summary

The brain loves patterns and routines, so habits help. Observing, developing, and monitoring habits mindfully can be beneficial. Mindfulness helps us achieve this goal systematically.

As body and mind are connected, we must consider both when building habits. Consistent and joyful practices can strengthen neurons and neural connections.

Habits help us accomplish more with less effort. Regularly using mental tools and processes can improve our cognitive health and performance as we age.

Creating daily habits to improve cognitive abilities can sharpen our minds and boost our well-being.

Some apps monitor our activities and behavior to help build habits. If you can't replicate my system, try these apps. Some smartwatches and fitness devices include them.

Set aside time each day for mental activities you enjoy. Regular scheduling and practice can strengthen brain regions and form habits. Once you form habits, tasks become easy.

Improving our minds is a lifelong journey. It's easier and more sustainable to increase our efforts daily, weekly, monthly, or annually.

Despite life's ups and downs, many want to remain calm and cheerful.

This valuable skill is unrelated to wealth or fame. It's about our mindset, fueled by our biological and psychological needs.

Here are some lessons I've learned about staying calm and composed despite challenges and setbacks.

1 — Tranquillity starts with observing thoughts and feelings.

2 — Clear the mental clutter and emotional entanglements with conscious breathing and gentle movements.

3 — Accept situations and events as they are with no resistance.

4 — Self-love can lead to loving others and increasing compassion.

5 — Count your blessings and cultivate gratitude.

Clear thinking can bring joy and satisfaction. It's a privilege to wake up with a healthy body and clear mind, ready to connect with others and serve them.

Thank you for reading my perspectives. I wish you a healthy and happy life.

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.