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.

Monkeypox was rare until recently. In 2005, a research called a cluster of six monkeypox cases in the Republic of Congo "the longest reported chain to date."

That's changed. This year, over 25,000 monkeypox cases have been reported in 83 countries, indicating widespread human-to-human transmission.

What spreads monkeypox? Monkeypox transmission research is ongoing; findings may change. But science says...

Most cases were formerly animal-related.

According to the WHO, monkeypox was first diagnosed in an infant in the DRC in 1970. After that, instances were infrequent and often tied to animals. In 2003, 47 Americans contracted rabies from pet prairie dogs.

In 2017, Nigeria saw a significant outbreak. NPR reported that doctors diagnosed young guys without animal exposure who had genital sores. Nigerian researchers highlighted the idea of sexual transmission in a 2019 study, but the theory didn't catch on. “People tend to cling on to tradition, and the idea is that monkeypox is transmitted from animals to humans,” explains research co-author Dr. Dimie Ogoina.

Most monkeypox cases are sex-related.

Human-to-human transmission of monkeypox occurs, and sexual activity plays a role.

Joseph Osmundson, a clinical assistant professor of biology at NYU, says most transmission occurs in queer and gay sexual networks through sexual or personal contact.

Monkeypox spreads by skin-to-skin contact, especially with its blister-like rash, explains Ogoina. Researchers are exploring whether people can be asymptomatically contagious, but they are infectious until their rash heals and fresh skin forms, according to the CDC.

A July research in the New England Journal of Medicine reported that of more than 500 monkeypox cases in 16 countries as of June, 95% were linked to sexual activity and 98% were among males who have sex with men. WHO Director-General Tedros Adhanom Ghebreyesus encouraged males to temporarily restrict their number of male partners in July.

Is monkeypox a sexually transmitted infection (STI)?

Skin-to-skin contact can spread monkeypox, not simply sexual activities. Dr. Roy Gulick, infectious disease chief at Weill Cornell Medicine and NewYork-Presbyterian, said monkeypox is not a "typical" STI. Monkeypox isn't a STI, claims the CDC.

Most cases in the current outbreak are tied to male sexual behavior, but Osmundson thinks the virus might also spread on sports teams, in spas, or in college dorms.

Can you get monkeypox from surfaces?

Monkeypox can be spread by touching infected clothing or bedding. According to a study, a U.K. health care worker caught monkeypox in 2018 after handling ill patient's bedding.

Angela Rasmussen, a virologist at the University of Saskatchewan in Canada, believes "incidental" contact seldom distributes the virus. “You need enough virus exposure to get infected,” she says. It's conceivable after sharing a bed or towel with an infectious person, but less likely after touching a doorknob, she says.

Dr. Müge evik, a clinical lecturer in infectious diseases at the University of St. Andrews in Scotland, says there is a "spectrum" of risk connected with monkeypox. "Every exposure isn't equal," she explains. "People must know where to be cautious. Reducing [sexual] partners may be more useful than cleaning coffee shop seats.

Is monkeypox airborne?

Exposure to an infectious person's respiratory fluids can cause monkeypox, but the WHO says it needs close, continuous face-to-face contact. CDC researchers are still examining how often this happens.

Under precise laboratory conditions, scientists have shown that monkeypox can spread via aerosols, or tiny airborne particles. But there's no clear evidence that this is happening in the real world, Rasmussen adds. “This is expanding predominantly in communities of males who have sex with men, which suggests skin-to-skin contact,” she explains. If airborne transmission were frequent, she argues, we'd find more occurrences in other demographics.

In the shadow of COVID-19, people are worried about aerosolized monkeypox. Rasmussen believes the epidemiology is different. Different viruses.

Can kids get monkeypox?

More than 80 youngsters have contracted the virus thus far, mainly through household transmission. CDC says pregnant women can spread the illness to their fetus.

Among the 1970s, monkeypox predominantly affected children, but by the 2010s, it was more common in adults, according to a February study. The study's authors say routine smallpox immunization (which protects against monkeypox) halted when smallpox was eradicated. Only toddlers were born after smallpox vaccination halted decades ago. More people are vulnerable now.

Schools and daycares could become monkeypox hotspots, according to pediatric instances. Ogoina adds this hasn't happened in Nigeria's outbreaks, which is encouraging. He says, "I'm not sure if we should worry." We must be careful and seek evidence.

He explained everything.

A drinking buddy confessed. Alexander. He says he works at a startup based on a scam, which appears too clever to be a lie.

Alexander (assuming he developed the story) or the startup's creator must have been a genius.

This is the story of an Internet scam that targets older individuals and generates tens of millions of dollars annually.

The business sells authentic things at 10% of their market value. This firm cannot be lucrative, but the entrepreneur has a plan: monthly subscriptions to a worthless service.

The firm can then charge the customer's credit card to settle the gap. The buyer must subscribe without knowing it. What's their strategy?

How does the con operate?

Imagine a website with a split homepage. On one page, the site offers an attractive goods at a ridiculous price (from 1 euro to 10% of the product's market worth).

Same product, but with a stupid monthly subscription. Business is unsustainable. They buy overpriced products and resell them too cheaply, hoping customers will subscribe to a useless service.

No customer will want this service. So they create another illegal homepage that hides the monthly subscription offer. After an endless scroll, a box says Yes, I want to subscribe to a service that costs x dollars per month.

Unchecking the checkbox bugs. When a customer buys a product on this page, he's enrolled in a monthly subscription. Not everyone should see it because it's illegal. So what does the startup do?

A page that varies based on the sort of website visitor, a possible consumer or someone who might be watching the startup's business

Startup technicians make sure the legal page is displayed when the site is accessed normally. Typing the web address in the browser, using Google, etc. The page crashes when buying a goods, preventing the purchase.

This avoids the startup from selling a product at a loss because the buyer won't subscribe to the worthless service and charge their credit card each month.

The illegal page only appears if a customer clicks on a Google ad, indicating interest in the offer.

Alexander says that a banker, police officer, or anyone else who visits the site (maybe for control) will only see a valid and buggy site as purchases won't be possible.

The latter will go to the site in the regular method (by typing the address in the browser, using Google, etc.) and not via an online ad.

Those who visit from ads are likely already lured by the site's price. They'll be sent to an illegal page that requires a subscription.

Laziness is humanity's secret weapon. The ordinary person ignores tiny monthly credit card charges. The subscription lasts around a year before the customer sees an unexpected deduction.

After-sales service (ASS) is useful in this situation.

After-sales assistance begins when a customer notices slight changes on his credit card, usually a year later.

The customer will search Google for the direct debit reference. How he'll complain to after-sales service.

It's crucial that ASS appears in the top 4/5 Google search results. This site must be clear, and offer chat, phone, etc., he argues.

The pigeon must be comforted after waking up. The customer learns via after-sales service that he subscribed to a service while buying the product, which justifies the debits on his card.

The customer will then clarify that he didn't intend to make the direct debits. The after-sales care professional will pretend to listen to the customer's arguments and complaints, then offer to unsubscribe him for free because his predicament has affected him.

In 99% of cases, the consumer is satisfied since the after-sales support unsubscribed him for free, and he forgets the debited amounts.

The remaining 1% is split between 0.99% who are delighted to be reimbursed and 0.01%. We'll pay until they're done. The customer should be delighted, not object or complain, and keep us beneath the radar (their situation is resolved, the rest, they don’t care).

It works, so we expand our thinking.

Startup has considered industrialization. Since this fraud is working, try another. Automate! So they used a site generator (only for product modifications), underpaid phone operators for after-sales service, and interns for fresh product ideas.

The company employed a data scientist. This has allowed the startup to recognize that specific customer profiles can be re-registered in the database and that it will take X months before they realize they're subscribing to a worthless service. Customers are re-subscribed to another service, then unsubscribed before realizing it.

Alexander took months to realize the deception and leave. Lawyers and others apparently threatened him and former colleagues who tried to talk about it.

The startup would have earned prizes and competed in contests. He adds they can provide evidence to any consumer group, media, police/gendarmerie, or relevant body. When I submitted my information to the FBI, I was told, "We know, we can't do much.", he says.