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.

As technology develops, you should stay up to date

You don't want to fall behind, do you? This post covers 7 tech-related things you should know.

You'll learn how to operate your computer (and other electronic devices) like an expert and how to leverage the Internet and social media to create your brand and business. Read on to stay relevant in today's tech-driven environment.

You must learn how to code.

Future-language is coding. It's how we and computers talk. Learn coding to keep ahead.

Try Codecademy or Code School. There are also numerous free courses like Coursera or Udacity, but they take a long time and aren't necessarily self-paced, so it can be challenging to find the time.

Artificial intelligence (AI) will transform all jobs.

Our skillsets must adapt with technology. AI is a must-know topic. AI will revolutionize every employment due to advances in machine learning.

Here are seven AI subjects you must know.

What is artificial intelligence?

How does artificial intelligence work?

What are some examples of AI applications?

How can I use artificial intelligence in my day-to-day life?

What jobs have a high chance of being replaced by artificial intelligence and how can I prepare for this?

Can machines replace humans? What would happen if they did?

How can we manage the social impact of artificial intelligence and automation on human society and individual people?

Blockchain Is Changing the Future

Few of us know how Bitcoin and blockchain technology function or what impact they will have on our lives. Blockchain offers safe, transparent, tamper-proof transactions.

It may alter everything from business to voting. Seven must-know blockchain topics:

1. Describe blockchain.

2. How does the blockchain function?

3. What advantages does blockchain offer?

4. What possible uses for blockchain are there?

5. What are the dangers of blockchain technology?

6. What are my options for using blockchain technology?

7. What does blockchain technology's future hold?

Cryptocurrencies are here to stay

Cryptocurrencies employ cryptography to safeguard transactions and manage unit creation. Decentralized cryptocurrencies aren't controlled by governments or financial institutions.

Bitcoin, the first cryptocurrency, was launched in 2009. Cryptocurrencies can be bought and sold on decentralized exchanges.

Bitcoin is here to stay.

Bitcoin isn't a fad, despite what some say. Since 2009, Bitcoin's popularity has grown. Bitcoin is worth learning about now. Since 2009, Bitcoin has developed steadily.

With other cryptocurrencies emerging, many people are wondering if Bitcoin still has a bright future. Curiosity is natural. Millions of individuals hope their Bitcoin investments will pay off since they're popular now.

Thankfully, they will. Bitcoin is still running strong a decade after its birth. Here's why.

The Internet of Things (IoT) is no longer just a trendy term.

IoT consists of internet-connected physical items. These items can share data. IoT is young but developing fast.

20 billion IoT-connected devices are expected by 2023. So much data! All IT teams must keep up with quickly expanding technologies. Four must-know IoT topics:

1. Recognize the fundamentals: Priorities first! Before diving into more technical lingo, you should have a fundamental understanding of what an IoT system is. Before exploring how something works, it's crucial to understand what you're working with.

2. Recognize Security: Security does not stand still, even as technology advances at a dizzying pace. As IT professionals, it is our duty to be aware of the ways in which our systems are susceptible to intrusion and to ensure that the necessary precautions are taken to protect them.

3. Be able to discuss cloud computing: The cloud has seen various modifications over the past several years once again. The use of cloud computing is also continually changing. Knowing what kind of cloud computing your firm or clients utilize will enable you to make the appropriate recommendations.

4. Bring Your Own Device (BYOD)/Mobile Device Management (MDM) is a topic worth discussing (MDM). The ability of BYOD and MDM rules to lower expenses while boosting productivity among employees who use these services responsibly is a major factor in their continued growth in popularity.

IoT Security is key

As more gadgets connect, they must be secure. IoT security includes securing devices and encrypting data. Seven IoT security must-knows:

1. fundamental security ideas

2. Authorization and identification

3. Cryptography

4. electronic certificates

5. electronic signatures

6. Private key encryption

7. Public key encryption

Final Thoughts

With so much going on in the globe, it can be hard to stay up with technology. We've produced a list of seven tech must-knows.

Massive Layoffs, record low VC investment, debate over crash... why is it happening and what’s the endgame?

This article generalizes a diverse industry. For objectivity, specific tech company challenges like growing competition within named segments won't be considered. Please comment on the posts.

According to Layoffs.fyi, nearly 120.000 people have been fired from startups since March 2020. More than 700 startups have fired 1% to 100% of their workforce. "The tech market is crashing"

Venture capital investment dropped 19% QoQ in the first four months of 2022, a 2018 low. Since January 2022, Nasdaq has dropped 27%. Some believe the tech market is collapsing.

It's bad, but nothing has crashed yet. We're about to get super technical, so buckle up!

I've written a follow-up article about what's next. For a more optimistic view of the crisis' aftermath, see: Tech Diaspora and Silicon Valley crisis

What happened?

Insanity reigned. Last decade, everyone became a unicorn. Seed investments can be made without a product or team. While the "real world" economy suffered from the pandemic for three years, tech companies enjoyed the "new normal."

COVID sped up technology adoption on several fronts, but this "new normal" wasn't so new after many restrictions were lifted. Worse, it lived with disrupted logistics chains, high oil prices, and WW3. The consumer market has felt the industry's boom for almost 3 years. Inflation, unemployment, mental distress...what looked like a fast economic recovery now looks like unfulfilled promises.

People rethink everything they eat. Paying a Netflix subscription instead of buying beef is moronic if you can watch it for free on your cousin’s account. No matter how great your real estate app's UI is, buying a house can wait until mortgage rates drop. PLGProduct Led Growth (PLG) isn't the go-to strategy when consumers have more basic expense priorities.

Exponential growth and investment

Until recently, tech companies believed that non-exponential revenue growth was fatal. Exponential growth entails doing more with less. From Salim Ismail words:

An Exponential Organization (ExO) has 10x the impact of its peers.

Many tech companies' theories are far from reality.

Investors have funded (sometimes non-exponential) growth. Scale-driven companies throw people at problems until they're solved. Need an entire closing team because you’ve just bought a TV prime time add? Sure. Want gold-weight engineers to colorize buttons? Why not?

Tech companies don't need cash flow to do it; they can just show revenue growth and get funding. Even though it's hard to get funding, this was the market's momentum until recently.

The graph at the beginning of this section shows how industry heavyweights burned money until 2020, despite being far from their market-share seed stage. Being big and being sturdy are different things, and a lot of the tech startups out there are paper tigers. Without investor money, they have no foundation.

A little bit about interest rates

Inflation-driven high interest rates are said to be causing tough times. Investors would rather leave money in the bank than spend it (I myself said it some days ago). It’s not wrong, but it’s also not that simple.

The USA central bank (FED) is a good proxy of global economics. Dollar treasury bonds are the safest investment in the world. Buying U.S. debt, the only country that can print dollars, guarantees payment.

The graph above shows that FED interest rates are low and 10+ year bond yields are near 2018 levels. Nobody was firing at 2018. What’s with that then?

Full explanation is too technical for this article, so I'll just summarize: Bond yields rise due to lack of demand or market expectations of longer-lasting inflation. Safe assets aren't a "easy money" tactic for investors. If that were true, we'd have seen the current scenario before.

Long-term investors are protecting their capital from inflation.

Not a crash, a landing

I bombarded you with info... Let's review:

• Consumption is down, hurting revenue.

• Tech companies of all ages have been hiring to grow revenue at the expense of profit.

• Investors expect inflation to last longer, reducing future investment gains.

Inflation puts pressure on a wheel that was rolling full speed not long ago. Investment spurs hiring, growth, and more investment. Worried investors and consumers reduce the cycle, and hiring follows.

Long-term investors back startups. When the invested company goes public or is sold, it's ok to burn money. What happens when the payoff gets further away? What if all that money sinks? Investors want immediate returns.

Why isn't the market crashing? Technology is not losing capital. It’s expecting change. The market realizes it threw moderation out the window and is reversing course. Profitability is back on the menu.

People solve problems and make money, but they also cost money. Huge cost for the tech industry. Engineers, Product Managers, and Designers earn up to 100% more than similar roles. Businesses must be careful about who they keep and in what positions to avoid wasting money.

What the future holds

From here on, it's all speculation. I found many great articles while researching this piece. Some are cited, others aren't (like this and this). We're in an adjustment period that may or may not last long.

Big companies aren't laying off many workers. Netflix firing 100 people makes headlines, but it's only 1% of their workforce. The biggest seem to prefer not hiring over firing.

Smaller startups beyond the seeding stage may be hardest hit. Without structure or product maturity, many will die.

I expect layoffs to continue for some time, even at Meta or Amazon. I don't see any industry names falling like they did during the .com crisis, but the market will shrink.

If you are currently employed, think twice before moving out and where to.
If you've been fired, hurry, there are still many opportunities.
If you're considering a tech career, wait.
If you're starting a business, I respect you. Good luck.

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.

How to reframe irritation and go forward

“… before you can figure out where you are going, you need to know where you are, and once you know and accept where you are, you can design your way to where you want to be.” — Bill Burnett and Dave Evans

“You’ve been here before. But there are some new ingredients this time. What can tell yourself that will make you understand that now isn’t just like last year? That there’s something new in this August.”

My coach paused. I sighed, inhaled deeply, and considered her question.

What could I say? I simply needed a plan from her so everything would fall into place and I could be the happy, successful person I want to be.

Time passed. My mind was exhausted from running all morning, all summer, or the last five years, searching for what to do next and how to get there.

Calmer, I remembered that my coach's inquiry had benefited me throughout the summer. The month before our call, I read Designing Your Work Life — How to Thrive and Change and Find Happiness at Work from Standford University’s Bill Burnett and Dave Evans.

A passage in their book felt like a lifeline: “We have something important to say to you: Wherever you are in your work life, whatever job you are doing, it’s good enough. For now. Not forever. For now.”

As I remembered this book on the coaching call, I wondered if I could embrace where I am in August and say my job life is good enough for now. Only temporarily.

I've done that since. I'm getting unstuck.

Here's how you can take the first step in any area where you feel stuck.

How to acquire the perspective of "Good enough for now" for yourself

We’ve all heard the advice to just make the best of a bad situation. That´s not bad advice, but if you only make the best of a bad situation, you are still in a bad situation. It doesn’t get to the root of the problem or offer an opportunity to change the situation. You’re more cheerfully navigating lousiness, which is an improvement, but not much of one and rather hard to sustain over time.” — Bill Burnett and Dave Evans

Reframing Burnett at Evans says good enough for now is the key to being happier at work. Because, as they write, a designer always has options.

Choosing to believe things are good enough for now is liberating. It helps us feel less victimized and less judged. Accepting our situation helps us become unstuck.

Let's break down the process, which designers call constructing your way ahead, into steps you can take today.

Writing helps get started. First, write down your challenge and why it's essential to you. If pen and paper help, try this strategy:

• Make the decision to accept the circumstance as it is. Designers always begin by acknowledging the truth of the situation. You now refrain from passing judgment. Instead, you simply describe the situation as accurately as you can. This frees us from negative thought patterns that prevent us from seeing the big picture and instead keep us in a tunnel of negativity.

• Look for a reframing right now. Begin with good enough for the moment. Take note of how your body feels as a result. Tell yourself repeatedly that whatever is occurring is sufficient for the time being. Not always, but just now. If you want to, you can even put it in writing and repeatedly breathe it in, almost like a mantra.

• You can select a reframe that is more relevant to your situation once you've decided that you're good enough for now and have allowed yourself to believe it. Try to find another perspective that is possible, for instance, if you feel unappreciated at work and your perspective of I need to use and be recognized for all my new skills in my job is making you sad and making you want to resign. For instance, I can learn from others at work and occasionally put my new abilities to use.

• After that, leave your mind and act in accordance with your new perspective. Utilize the designer's bias for action to test something out and create a prototype that you can learn from. Your beginning point for creating experiences that will support the new viewpoint derived from the aforementioned point is the new perspective itself. By doing this, you recognize a circumstance at work where you can provide value to yourself or your workplace and then take appropriate action. Send two or three coworkers from whom you wish to learn anything an email, for instance, asking them to get together for coffee or a talk.

Choose tiny, doable actions. You prioritize them at work.

Let's assume you're feeling disconnected at work, so you make a list of folks you may visit each morning or invite to lunch. If you're feeling unmotivated and tired, take a daily walk and treat yourself to a decent coffee.

This may be plenty for now. If you want to take this procedure further, use Burnett and Evans' internet tools and frameworks.

Developing the daily practice of reframing

“We’re not discontented kids in the backseat of the family minivan, but how many of us live our lives, especially our work lives, as if we are?” — Bill Burnett and Dave Evans

I choose the good enough for me perspective every day, often. No quick fix. Am a failing? Maybe a little bit, but I like to think of it more as building muscle.

This way, every time I tell myself it's ok, I hear you. For now, that muscle gets stronger.

Hopefully, reframing will become so natural for us that it will become a habit, and not a technique anymore.

If you feel like you’re stuck in your career or at work, the reframe of Good enough, for now, might be valuable, so just go ahead and try it out right now.

And while you’re playing with this, why not think of other areas of your life too, like your relationships, where you live — even your writing, and see if you can feel a shift?