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.

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.

They depend heavily on open source..

Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?

Let’s find out.

1. Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
   

2. How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
   

3. How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.

4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.

1. Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.

6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.

1. Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?

8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.

1. Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
   

A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.

New Stiglitz just dropped.

Here's the inflation story everyone believes (warning: it's false): America gave the poor too much money during the recession, and now the economy is awash with free money, which made them so rich they're refusing to work, meaning the economy isn't making anything. Prices are soaring due to increased cash and missing labor.

Lawrence Summers says there's only one answer. We must impoverish the poor: raise interest rates, cause a recession, and eliminate millions of jobs, until the poor are stripped of their underserved fortunes and return to work.

https://pluralistic.net/2021/11/20/quiet-part-out-loud/#profiteering

This is nonsense. Countries around the world suffered inflation during and after lockdowns, whether they gave out humanitarian money to keep people from starvation. America has slightly greater inflation than other OECD countries, but it's not due to big relief packages.

The Causes of and Responses to Today's Inflation, a Roosevelt Institute report by Nobel-winning economist Joseph Stiglitz and macroeconomist Regmi Ira, debunks this bogus inflation story and offers a more credible explanation for inflation.

https://rooseveltinstitute.org/wp-content/uploads/2022/12/RI CausesofandResponsestoTodaysInflation Report 202212.pdf

Sharp interest rate hikes exacerbate the slump and increase inflation, the authors argue. They compare monetary policy inflation cures to medieval bloodletting, where doctors repeated the same treatment until the patient recovered (for which they received credit) or died (which was more likely).

Let's discuss bloodletting. Inflation hawks warn of the wage price spiral, when inflation rises and powerful workers bargain for higher pay, driving up expenses, prices, and wages. This is the fairy-tale narrative of the 1970s, and it's true except that OPEC's embargo drove up oil prices, which produced inflation. Oh well.

Let's be generous to seventies-haunted inflation hawks and say we're worried about a wage-price spiral. Fantastic! No. Real wages are 2.3% lower than they were in Oct 2021 after peaking in June at 4.8%.

Why did America's powerful workers take a paycut rather than demand inflation-based pay? Weak unions, globalization, economic developments.

Workers don't expect inflation to rise, so they're not requesting inflationary hikes. Inflationary expectations have remained moderate, consistent with our data interpretation.

https://www.newyorkfed.org/microeconomics/sce#/

Neither are workers. Working people see surplus savings as wealth and spend it gradually over their lives, despite rising demand. People may have saved money by staying in during the lockdown, but they don't eat out every night to make up for it. Instead, they keep those savings as precautionary balances. This is why the economy is lagging.

People don't buy non-traded goods with pandemic savings (basically, imports). Imports don't multiply like domestic purchases. If you buy a loaf of bread from the corner baker for $1 and they spend it at the tavern across the street, that dollar generates $3 in economic activity. Spending a dollar on foreign goods leaves the country and any multiplier effect happens there, not in the US.

Only marginally higher wages. The ECI is up 1.6% from 2019. Almost all gains went to the 25% lowest-paid Americans. Contrary to the inflation worry about too much savings, these workers don't make enough to save, even post-pandemic.

Recreation and transit spending are at or below pre-pandemic levels. Higher food and hotel prices (which doesn’t mean we’re buying more food than we were in 2019, just that it costs more).

What causes inflation if not greedy workers, free money, and high demand? The most expensive domestic goods produce the biggest revenues for their manufacturers. They charge you more without paying their workers or suppliers more.

The largest price-gougers are funneling their earnings to rich people who store it offshore through stock buybacks and dividends. A $1 billion stock buyback doesn't buy $1 billion in bread.

Five factors influence US inflation today:

I. Price rises for energy and food

II. shifts in consumer tastes

III. supply interruptions (mainly autos);

IV. increased rents (due to telecommuting);

V. monopoly (AKA price-gouging).

None can be remedied by raising interest rates or laying off workers.

Russia's invasion of Ukraine, omicron, and China's Zero Covid policy all disrupted the flow of food, energy, and production inputs. The price went higher because we made less.

After Russia invaded Ukraine, oil prices spiked, and sanctions made it worse. But that was February. By October, oil prices had returned to pre-pandemic, 2015 levels attributable to global economic adjustments, including a shift to renewables. Every new renewable installation reduces oil consumption and affects oil prices.

High food prices have a simple solution. The US and EU have bribed farmers not to produce for 50 years. If the war continues, this program may end, and food prices may decline.

Demand changes. We want different things than in 2019, not more. During the lockdown, people substituted goods. Half of the US toilet-paper supply in 2019 was on commercial-sized rolls. This is created from different mills and stock than our toilet paper.

Lockdown pushed toilet paper demand to residential rolls, causing shortages (the TP hoarding story was just another pandemic urban legend). Because supermarket stores don't have accounts with commercial paper distributors, ordering from languishing stores was difficult. Kleenex and paper towel substitutions caused greater shortages.

All that drove increased costs in numerous product categories, and there were more cases. These increases are transient, caused by supply chain inefficiencies that are resolving.

Demand for frontline staff saw a one-time repricing of pay, which is being recouped as we speak.

Illnesses. Brittle, hollowed-out global supply chains aggravated this. The constant pursuit of cheap labor and minimal regulation by monopolies that dominate most sectors means things are manufactured in far-flung locations. Financialization means any surplus capital assets were sold off years ago, leaving firms with little production slack. After the epidemic, several of these systems took years to restart.

Automobiles are to blame. Financialization and monopolization consolidated microchip and auto production in Taiwan and China. When the lockdowns came, these worldwide corporations cancelled their chip orders, and when they placed fresh orders, they were at the back of the line.

That drove up car prices, which is why the US has slightly higher inflation than other wealthy countries: the economy is car-centric. Automobile prices account for 9% of the CPI. France: 3.6%

Rent shocks and telecommuting. After the epidemic, many professionals moved to exurbs, small towns, and the countryside to work from home. As commercial properties were vacated, it was impractical to adapt them for residential use due to planning restrictions. Addressing these restrictions will cut rent prices more than raising inflation rates, which halts housing construction.

Statistical mirages cause some rent inflation. The CPI estimates what homeowners would pay to rent their properties. When rents rise in your neighborhood, the CPI believes you're spending more on rent even if you have a 30-year fixed-rate mortgage.

Market dominance. Almost every area of the US economy is dominated by monopolies, whose CEOs disclose on investor calls that they use inflation scares to jack up prices and make record profits.

https://pluralistic.net/2022/02/02/its-the-economy-stupid/#overinflated

Long-term profit margins are rising. Markups averaged 26% from 1960-1980. 2021: 72%. Market concentration explains 81% of markup increases (e.g. monopolization). Profit margins reach a 70-year high in 2022. These elements interact. Monopolies thin out their sectors, making them brittle and sensitive to shocks.

If we're worried about a shrinking workforce, there are more humanitarian and sensible solutions than causing a recession and mass unemployment. Instead, we may boost US production capacity by easing workers' entry into the workforce.

https://pluralistic.net/2022/06/01/factories-to-condos-pipeline/#stuff-not-money

US female workforce participation ranks towards the bottom of developed countries. Many women can't afford to work due to America's lack of daycare, low earnings, and bad working conditions in female-dominated fields. If America doesn't have enough workers, childcare subsidies and minimum wages can help.

By contrast, driving the country into recession with interest-rate hikes will reduce employment, and the last recruited (women, minorities) are the first fired and the last to be rehired. Forcing America into recession won't enhance its capacity to create what its people want; it will degrade it permanently.

Nothing the Fed does can stop price hikes from international markets, lack of supply chain investment, COVID-19 disruptions, climate change, the Ukraine war, or market power. They can worsen it. When supply problems generate inflation, raising interest rates decreases investments that can remedy shortages.

Increasing interest rates won't cut rents since landlords pass on the expenses and high rates restrict investment in new dwellings where tenants could escape the costs.

Fixing the supply fixes supply-side inflation. Increase renewables investment (as the Inflation Reduction Act does). Monopolies can be busted (as the IRA does). Reshore key goods (as the CHIPS Act does). Better pay and child care attract employees.

Windfall taxes can claw back price-gouging corporations' monopoly earnings.

https://pluralistic.net/2022/03/15/sanctions-financing/#soak-the-rich

In 2008, we ruled out fiscal solutions (bailouts for debtors) and turned to monetary policy (bank bailouts). This preserved the economy but increased inequality and eroded public trust.

Monetary policy won't help. Even monetary policy enthusiasts recognize an 18-month lag between action and result. That suggests monetary tightening is unnecessary. Like the medieval bloodletter, central bankers whose interest rate hikes don't work swiftly may do more of the same, bringing the economy to its knees.

Interest rates must rise. Zero-percent interest fueled foolish speculation and financialization. Increasing rates will stop this. Increasing interest rates will destroy the economy and dampen inflation.

Then what? All recent evidence indicate to inflation decreasing on its own, as the authors argue. Supply side difficulties are finally being overcome, evidence shows. Energy and food prices are showing considerable mean reversion, which is disinflationary.

The authors don't recommend doing nothing. Best case scenario, they argue, is that the Fed won't keep raising interest rates until morale improves.

He’s not the President. Stop treating him like one.

Elon Musk tweeted from Qatar, where he was watching the World Cup Final with Jared Kushner.

Musk's subsequent Tweets were as normal, basic, and bland as anyone's from a World Cup Final: It's depressing to see the world's richest man looking at his phone during a grand ceremony. Rich guy goes to rich guy event didn't seem important.

Before Musk posted his should-I-step-down-at-Twitter poll, CNN ran a long segment asking if it was hypocritical for him to reveal his real-time location after defending his (very dumb) suspension of several journalists for (supposedly) revealing his assassination coordinates by linking to a site that tracks Musks private jet. It was hard to ignore CNN's hypocrisy: It covered Musk as Twitter CEO like President Trump. EVERY TRUMP STORY WAS BASED ON HIM SAYING X, THEN DOING Y. Trump would do something horrific, lie about it, then pretend it was fine, then condemn a political rival who did the same thing, be called hypocritical, and so on. It lasted four years. Exhausting.

It made sense because Trump was the President of the United States. The press's main purpose is to relentlessly cover and question the president.

It's strange to say this out. Twitter isn't America. Elon Musk isn't a president. He maintains a money-losing social media service to harass and mock people he doesn't like. Treating Musk like Trump, as if he should be held accountable like Trump, shows a startling lack of perspective. Some journalists treat Twitter like a country.

The compulsive, desperate way many journalists utilize the site suggests as much. Twitter isn't the town square, despite popular belief. It's a place for obsessives to meet and converse. Journalists say they're breaking news. Their careers depend on it. They can argue it's a public service. Nope. It's a place lonely people go to speak all day. Twitter. So do journalists, Trump, and Musk. Acting as if it has a greater purpose, as if it's impossible to break news without it, or as if the republic is in peril is ludicrous. Only 23% of Americans are on Twitter, while 25% account for 97% of Tweets. I'd think a large portion of that 25% are journalists (or attention addicts) chatting to other journalists. Their loudness makes Twitter seem more important than it is. Nope. It's another stupid website. They were there before Twitter; they will be there after Twitter. It’s just a website. We can all get off it if we want. Most of us aren’t even on it in the first place.

Musk is a website-owner. No world leader. He's not as accountable as Trump was. Musk is cable news's primary character now that Trump isn't (at least for now). Becoming a TV news anchor isn't as significant as being president. Elon Musk isn't as important as we all pretend, and Twitter isn't even close. Twitter is a dumb website, Elon Musk is a rich guy going through a midlife crisis, and cable news is lazy because its leaders thought the entire world was on Twitter and are now freaking out that their playground is being disturbed.

I’ve said before that you need to leave Twitter, now. But even if you’re still on it, we need to stop pretending it matters more than it does. It’s a site for lonely attention addicts, from the man who runs it to the journalists who can’t let go of it. It’s not a town square. It’s not a country. It’s not even a successful website. Let’s stop pretending any of it’s real. It’s not.

Here is the ugly stuff, read this if you have a founder in your life or are trying to become one. Your call.

#1 You'll try to talk yourself to sleep, but it won't always work.

As founders, we're all driven. Good and bad, you're restless. Success requires resistance and discipline. Your startup will be on your mind 24/7, and not everyone will have the patience to listen to your worries, ideas, and coffee runs. You become more self-sufficient than ever before.

#2 No one will understand what you're going through unless they've been a founder.

Some of my closest friends don't understand the work that goes into starting a business, and we can't blame them.

#3 You'll feel alienated.

Your problems aren't common; calling your bestie won't help. You must search hard for the right resources. It alienates you from conversations you no longer relate to. (No 4th of July, no long weekends!)

#4 Since you're your "own boss," people assume you have lots of free time.

Do you agree? I was on a webinar with lots of new entrepreneurs, and one woman said, "I started my own business so I could have more time for myself." This may be true for some lucky people, and you can be flexible with your schedule. If you want your business to succeed, you'll probably be its slave for a while.

#5 No time for illness or family emergencies.

Both last month. Oh, no! Physically and emotionally withdrawing at the worst times will give you perspective. I learned this the hard way because I was too stubborn to postpone an important interview. I thought if I rested all day and only took one call, I'd be fine. Nope. I had a fever and my mind wasn't as sharp, so my performance and audience interaction suffered. Nope. Better to delay than miss out.

Oh, and setting a "OoO" makes you cringe.

#6 Good luck with your mental health, perfectionists.

When building a startup, it's difficult to accept that there won't be enough time to do everything. You can't make them all, not perfectly. You must learn to accept things that are done but not perfect.

#7 As a founder, you'll make mistakes, but you'll want to make them quickly so you can learn.

Hard lessons are learned quicker. You'll need to pivot and try new things often; some won't work, and it's best to discover them sooner rather than later.

#8 Pyramid schemes abound.

I didn't realize how bad it was until I started a company. You must spy and constantly research. As a founder, you'll receive many emails from people claiming to "support" you. Be wary and keep your eyes open. When it's too good to be true. Some "companies" will try to get you to pay for "competitions" to "pitch at events." Don't do it.

#9 Keep your competitor research to a minimum.

Actually, competition is good. It means there's a market for those solutions. However, this can be mentally exhausting too. Learn about their geography and updates, but that's it.

#10 You'll feel guilty taking vacation.

I don't know what to say, but I no longer enjoy watching TV, and that's okay. Pay attention to things that enrich you, bring you joy, and have fun. It boosts creativity.

Being a startup founder may be one of the hardest professional challenges you face, but it's also a great learning experience. Your passion will take you places you never imagined and open doors to opportunities you wouldn't have otherwise. You'll meet amazing people. No regrets, no complaints. It's a roller coaster, but the good days are great.

Miss anything? Comment below