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.

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.

Four times the energy density and a fraction of lithium-cost ion's

As the globe abandons fossil fuels, batteries become more important. EVs, solar, wind, tidal, wave, and even local energy grids will use them. We need a battery revolution since our present batteries are big, expensive, and detrimental to the environment. A recent publication describes a battery that solves these problems. But will it be enough?

Sodium-sulfur molten salt battery. It has existed for a long time and uses molten salt as an electrolyte (read more about molten salt batteries here). These batteries are cheaper, safer, and more environmentally friendly because they use less eco-damaging materials, are non-toxic, and are non-flammable.

Previous molten salt batteries used aluminium-sulphur chemistries, which had a low energy density and required high temperatures to keep the salt liquid. This one uses a revolutionary sodium-sulphur chemistry and a room-temperature-melting salt, making it more useful, affordable, and eco-friendly. To investigate this, researchers constructed a button-cell prototype and tested it.

First, the battery was 1,017 mAh/g. This battery is four times as energy dense as high-density lithium-ion batteries (250 mAh/g).

No one knows how much this battery would cost. A more expensive molten-salt battery costs $15 per kWh. Current lithium-ion batteries cost $132/kWh. If this new molten salt battery costs the same as present cells, it will be 90% cheaper.

This room-temperature molten salt battery could be utilized in an EV. Cold-weather heaters just need a modest backup battery.

The ultimate EV battery? If used in a Tesla Model S, you could install four times the capacity with no weight gain, offering a 1,620-mile range. This huge battery pack would cost less than Tesla's. This battery would nearly perfect EVs.

Or would it?

The battery's capacity declined by 50% after 1,000 charge cycles. This means that our hypothetical Model S would suffer this decline after 1.6 million miles, but for more cheap vehicles that use smaller packs, this would be too short. This test cell wasn't supposed to last long, so this is shocking. Future versions of this cell could be modified to live longer.

This affordable and eco-friendly cell is best employed as a grid-storage battery for renewable energy. Its safety and affordable price outweigh its short lifespan. Because this battery is made of easily accessible materials, it may be utilized to boost grid-storage capacity without causing supply chain concerns or EV battery prices to skyrocket.

Researchers are designing a bigger pouch cell (like those in phones and laptops) for this purpose. The battery revolution we need could be near. Let’s just hope it isn’t too late.

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?

The internet is a massive information resource. With so much stuff, it's easy to forget about useful websites. Here are five essential websites you may not have known about.

1. Companies.tools

Companies.tools are what successful startups employ. This website offers a curated selection of design, research, coding, support, and feedback resources. Ct has the latest app development platform and greatest client feedback method.

2. Excel Formula Bot

Excel Formula Bot can help if you forget a formula. Formula Bot uses AI to convert text instructions into Excel formulas, so you don't have to remember them.

Just tell the Bot what to do, and it will do it. Excel Formula Bot can calculate sales tax and vacation days. When you're stuck, let the Bot help.

3.TypeLit

TypeLit helps you improve your typing abilities while reading great literature.

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Goals and progress can be tracked. Why not improve your typing and learn great literature with TypeLit?

4. Calm Schedule

Finding a meeting time that works for everyone is difficult. Personal and business calendars might be difficult to coordinate.

Synchronize your two calendars to save time and avoid problems. You may avoid searching through many calendars for conflicts and keep your personal information secret. Having one source of truth for personal and work occasions will help you never miss another appointment.
https://calmcalendar.com/

5. myNoise

myNoise makes the outside world quieter. myNoise is the right noise for a noisy office or busy street.

If you can't locate the right noise, make it. MyNoise unlocks the world. Shut out distractions. Thank your ears.

6. Synthesia

Professional videos require directors, filmmakers, editors, and animators. Now, thanks to AI, you can generate high-quality videos without video editing experience.

AI avatars are crucial. You can design a personalized avatar using a web-based software like synthesia.io. Our avatars can lip-sync in over 60 languages, so you can make worldwide videos. There's an AI avatar for every video goal.

Not free. Amazing service, though.

7. Cleaning-up-images

Have you shot a wonderful photo just to notice something in the background? You may have a beautiful headshot but wish to erase an imperfection.

Cleanup.pictures removes undesirable objects from photos. Our algorithms will eliminate the selected object.

Cleanup.pictures can help you obtain the ideal shot every time. Next time you take images, let Cleanup.pictures fix any flaws.

8. PDF24 Tools

Editing a PDF can be a pain. Most of us don't know Adobe Acrobat's functionalities. Why buy something you'll rarely use? Better options exist.

PDF24 is an online PDF editor that's free and subscription-free. Rotate, merge, split, compress, and convert PDFs in your browser. PDF24 makes document signing easy.

Upload your document, sign it (or generate a digital signature), and download it. It's easy and free. PDF24 is a free alternative to pricey PDF editing software.

9. Class Central

Finding online classes is much easier. Class Central has classes from Harvard, Stanford, Coursera, Udemy, and Google, Amazon, etc. in one spot.

Whether you want to acquire a new skill or increase your knowledge, you'll find something. New courses bring variety.

10. Rome2rio

Foreign travel offers countless transport alternatives. How do you get from A to B? It’s easy!

Rome2rio will show you the best method to get there, including which mode of transport is ideal.

• Plane

• Car

• Train

• Bus

• Ferry

• Driving

• Shared bikes

• Walking

Do you know any free, useful websites?