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.

Las Vegas hosted CES 2023. This third and last look at CES 2023 previews upcoming consumer electronics trends that will be crucial for market share.

Definitely start with ICT. Qualcomm CEO Cristiano Amon spoke to CNBC from Las Vegas on China's crackdown and the company's automated driving systems for electric vehicles (EV). The business showed a concept car and its latest Snapdragon processor designs, which offer expanded digital interactions through SalesForce-partnered CRM platforms.

Qualcomm CEO Meets SK Hynix Vice Chairman at CES 2023 On Jan. 6, SK hynix Inc.'s vice chairman and co-CEO Park Jung-ho discussed strengthening www.businesskorea.co.kr.

Electrification is reviving Michigan's automobile industry. Michigan Local News reports that $14 billion in EV and battery manufacturing investments will benefit the state. The report also revealed that the Strategic Outreach and Attraction Reserve (SOAR) fund had generated roughly $1 billion for the state's automotive sector.

Michigan to "dominate" EV battery manufacturing after $2B investment. Michigan spent $2 billion to safeguard www.mlive.com.

Ars Technica is great for technology, society, and the future. After CES 2023, Jonathan M. Gitlin published How many electric car chargers are enough? Read about EV charging network issues and infrastructure spending. Politics aside, rapid technological advances enable EV charging network expansion in American cities and abroad.

New research says US needs 8x more EV chargers by 2030. Electric vehicle skepticism—which is widespread—is fundamentally about infrastructure. arstechnica.com

Finally, the UNEP's The Future of Electric Vehicles and Material Resources: A Foresight Brief. Understanding how lithium-ion batteries will affect EV sales is crucial. Climate change affects EVs in various ways, but electrification and mining trends stand out because more EVs demand more energy-intensive metals and rare earths. Areas & Producers has been publishing my electrification and mining trends articles. Follow me if you wish to write for the publication.

Producers This magazine analyzes medium.com-related corporate, legal, and international news to examine a paradigm shift.

The Weekend Brief (TWB) will routinely cover tech, industrials, and global commodities in global markets, including stock markets. Read more about the future of key areas and critical producers of the global economy in Areas & Producers.

TotalEnergies, Stellantis Form Automotive Cells Company (ACC) A joint-venture to design and build electric vehicles (EVs) was formed in 2020.

Apple's search engine has long been rumored. Recent Google developments may confirm the rumor. Is Apple about to become Google's biggest rival?

Here's a video:

People noted Apple's changes in 2020. AppleBot, a web crawler that downloads and caches Internet content, was more active than in the last five years.

Apple hired search engine developers, including ex-Googlers, such as John Giannandrea, Google's former search chief.

Apple also changed the way iPhones search. With iOS 14, Apple's search results arrived before Google's.

These facts fueled rumors that Apple was developing a search engine.

Apple and Google Have a Contract

Many skeptics said Apple couldn't compete with Google. This didn't affect the company's competitiveness.

Apple is the only business with the resources and scale to be a Google rival, with 1.8 billion active devices and a $2 trillion market cap.

Still, people doubted that due to a license deal. Google pays Apple $8 to $12 billion annually to be the default iPhone and iPad search engine.

Apple can't build an independent search product under this arrangement.

Why would Apple enter search if it's being paid to stay out?

Ironically, this partnership has many people believing Apple is getting into search.

A New Default Search Engine May Be Needed

Google was sued for antitrust in 2020. It is accused of anticompetitive and exclusionary behavior. Justice wants to end Google's monopoly.

Authorities could restrict Apple and Google's licensing deal due to its likely effect on market competitiveness. Hence Apple needs a new default search engine.

Apple Already Has a Search Engine

The company already has a search engine, Spotlight.

Since 2004, Spotlight has aired. It was developed to help users find photos, documents, apps, music, and system preferences.

Apple's search engine could do more than organize files, texts, and apps.

Spotlight Search was updated in 2014 with iOS 8. Web, App Store, and iTunes searches became available. You could find nearby places, movie showtimes, and news.

This search engine has subsequently been updated and improved. Spotlight added rich search results last year.

If you search for a TV show, movie, or song, photos and carousels will appear at the top of the page.

This resembles Google's rich search results.

When Will the Apple Search Engine Be Available?

When will Apple's search launch? Robert Scoble says it's near.

Scoble tweeted a number of hints before this year's Worldwide Developer Conference.

Scoble bases his prediction on insider information and deductive reasoning. January 2023 is expected.

Will you use Apple's search engine?

I've worked in a People role at seven early-stage firms for over 15 years (I enjoy chasing a dream!). Few of the seven achieved profitability, including unicorn status or acquisition.

Did early-stage startups share anything? Was there a difference between winners and losers? YES.

I support founders and entrepreneurs building financially sustainable enterprises with a compelling cause. This isn't something everyone would do. A company's success demands more than guts. Founders drive startup success.

Six Qualities of Successful Startups

Successful startup founders either innately grasped the correlation between strong team engagement and a well-executed business model, or they knew how to ask and listen to others (executive coaches, other company leaders, the team itself) to learn about it.

Successful startups:

1. Co-founders agreed and got along personally.

Multi-founder startups are common. When co-founders agree on strategic decisions and are buddies, there's less friction and politics at work.

As a co-founder, ask your team if you're aligned. They'll explain.

I've seen C-level leaders harbor personal resentments over disagreements. A co-departure founder's caused volatile leadership and work disruptions that the team struggled to manage during and after.

2. Team stayed.

Successful startups have low turnover. Nobody is leaving. There may be a termination for performance, but other team members will have observed the issues and agreed with the decision.

You don't want organizational turnover of 30%+, with leaders citing performance issues but the team not believing them. This breeds suspicion.

Something is wrong if many employees leave voluntarily or involuntarily. You may hear about lack of empowerment, support, or toxic leadership in exit interviews and from the existing team. Intellectual capital loss and resource instability harm success.

3. Team momentum.

A successful startup's team is excited about its progress. Consistently achieving goals and having trackable performance metrics. Some describe this period of productivity as magical, with great talents joining the team and the right people in the right places. Increasing momentum.

I've also seen short-sighted decisions where only some departments, like sales and engineering, had goals. Lack of a unified goals system created silos and miscommunication. Some employees felt apathetic because they didn't know how they contributed to team goals.

4. Employees advanced in their careers.

Even if you haven't created career pathing or professional development programs, early-stage employees will grow and move into next-level roles. If you hire more experienced talent and leaders, expect them to mentor existing team members. Growing companies need good performers.

New talent shouldn't replace and discard existing talent. This creates animosity and makes existing employees feel unappreciated for their early contributions to the company.

5. The company lived its values.

Culture and identity are built on lived values. A company's values affect hiring, performance management, rewards, and other processes. Identify, practice, and believe in company values. Starting with team values instead of management or consultants helps achieve this. When a company's words and actions match, it builds trust.

When company values are beautifully displayed on a wall but few employees understand them, the opposite is true. If an employee can't name the company values, they're useless.

6. Communication was clear.

When necessary information is shared with the team, they feel included, trusted, and like owners. Transparency means employees have the needed information to do their jobs. Disclosure builds trust. The founders answer employees' questions honestly.

Information accessibility decreases office politics. Without transparency, even basic information is guarded and many decisions are made in secret. I've seen founders who don't share financial, board meeting, or compensation and equity information. The founders' lack of trust in the team wasn't surprising, so it was reciprocated.

The Choices

Finally. All six of the above traits (leadership alignment, minimal turnover, momentum, professional advancement, values, and transparency) were high in the profitable startups I've worked at, including unicorn status or acquisition.

I've seen these as the most common and constant signals of startup success or failure.

These characteristics are the product of founders' choices. These decisions lead to increased team engagement and business execution.

Here's something to consider for startup employees and want-to-bes. 90% of startups fail, despite the allure of building something new and gaining ownership. With the emotional and time investment in startup formation, look for startups with these traits to reduce your risk.

Both you and the startup will thrive in these workplaces.

People-first update.

Every Google upgrade causes website owners to panic.

Some have just recovered from previous algorithm tweaks and resumed content development.

If you follow Google's Webmaster rules, you shouldn't fear its adjustments.

Everyone has a view of them. Miscommunication and confusion result.

Now, for some (hopefully) exciting news.

Google tweeted on August 18, 2022 about a fresh content update.

This change is another Google effort to remove low-quality, repetitive, and AI-generated content.

The algorithm generates and analyzes search results, not humans.

Google spends a lot to teach its algorithm what searchers want. Intent isn't always clear.

Google's content update aims to:

“… ensure people see more original, helpful content written by people, for people, in search results.”

Isn't it a noble goal?

However, what does it mean for content creators and website owners?

How can you ensure you’re creating content that will be successful after the updates roll out?

Let's first define people-first content.

What does "people-first-content" mean?

If asked, I'd say information written to answer queries and solve problems.

Like others, I read it from the term.

Content creators and marketers disagree. They need more information to follow recommendations.

Google gives explicit instructions for creating people-first content.

According to Google, if you answer yes to the following questions, you have a people-first attitude.

1. Do you have customers who might find your content useful if they contacted you directly?

2. Does your content show the breadth of your knowledge?

3. Do you have a niche or a focus for your website?

4. After reading your content, will readers learn something new to aid them in achieving their goals?

5. Are readers happy after reading your content?

6. Have you been adhering to Google's fundamental updates and product reviews?

As an SEO writer, I'm not scared.

I’ve been following these rules consciously while creating content for my website. That’s why it’s been steadily growing despite me publishing just one or two stories a month.

If you avoid AI-generated text and redundant, shallow material, your website won't suffer.

If you use unscrupulous methods to boost your website's traffic, including link buying or keyword stuffing, stop. Google is getting smarter and will find and punish your site eventually.

For those who say, “SEO is no longer working,” I dedicated the whole paragraph below.

This does not imply that SEO is obsolete.

Google:

“People-first content creators focus on creating satisfying content, while also utilizing SEO best practices to bring searchers additional value.”

The official helpful content update page lists two people-first content components:

• meeting user needs

• best practices for SEO

Always read official guidelines, not unsolicited suggestions.

SEO will work till search engines die.

How to use the update

Google said the changes will arrive in August 2022.

They pledged to post updates on Google's search ranking updates page.

Google also tweets this info. If you haven't followed it already, I recommend it.

Ranking adjustments could take two weeks and will affect English searches internationally initially.

Google affirmed plans to extend to other languages.

If you own a website, monitor your rankings and traffic to see if it's affected.

If you think NFTs are awful, check out the art market.

The fervor around NFTs has subsided in recent months due to the crypto market crash and the media's short attention span. They were all anyone could talk about earlier this spring. Last semester, when passions were high and field luminaries were discussing "slurp juices," I asked my students and students from over 20 other universities what they thought of NFTs.

According to many, NFTs were either tasteless pyramid schemes or a new way for artists to make money. NFTs contributed to the climate crisis and harmed the environment, but so did air travel, fast fashion, and smartphones. Some students complained that NFTs were cheap, tasteless, algorithmically generated schlock, but others asked how this was different from other art.

I'm not sure what I expected, but the intensity of students' reactions surprised me. They had strong, emotional opinions about a technology I'd always considered administrative. NFTs address ownership and accounting, like most crypto/blockchain projects.

Art markets can be irrational, arbitrary, and subject to the same scams and schemes as any market. And maybe a few shenanigans that are unique to the art world.

The Fairness Question

Fairness, a deflating moral currency, was the general sentiment (the less of it in circulation, the more ardently we clamor for it.) These students, almost all of whom are artists, complained to the mismatch between the quality of the work in some notable NFT collections and the excessive amounts these items were fetching on the market. They can sketch a Bored Ape or Lazy Lion in their sleep. Why should they buy ramen with school loans while certain swindlers get rich?

I understand students. Art markets are unjust. They can be irrational, arbitrary, and governed by chance and circumstance, like any market. And art-world shenanigans.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets

Over 50% of artworks in circulation are fake, say experts. Sincere art collectors and institutions are upset by the prevalence of fake goods on the market. Not everyone. Wealthy people and companies use art as investments. They can use cultural institutions like museums and galleries to increase the value of inherited art collections. People sometimes buy artworks and use family ties or connections to museums or other cultural taste-makers to hype the work in their collection, driving up the price and allowing them to sell for a profit. Money launderers can disguise capital flows by using market whims, hype, and fluctuating asset prices.

Almost every mainstream critique leveled against NFTs applies just as easily to art markets.

Art has always been this way. Edward Kienholz's 1989 print series satirized art markets. He stamped 395 identical pieces of paper from $1 to $395. Each piece was initially priced as indicated. Kienholz was joking about a strange feature of art markets: once the last print in a series sells for $395, all previous works are worth at least that much. The entire series is valued at its highest auction price. I don't know what a Kienholz print sells for today (inquire with the gallery), but it's more than $395.

I love Lee Lozano's 1969 "Real Money Piece." Lozano put cash in various denominations in a jar in her apartment and gave it to visitors. She wrote, "Offer guests coffee, diet pepsi, bourbon, half-and-half, ice water, grass, and money." "Offer real money as candy."

Lee Lozano kept track of who she gave money to, how much they took, if any, and how they reacted to the offer of free money without explanation. Diverse reactions. Some found it funny, others found it strange, and others didn't care. Lozano rarely says:

Apr 17 Keith Sonnier refused, later screws lid very tightly back on. Apr 27 Kaltenbach takes all the money out of the jar when I offer it, examines all the money & puts it all back in jar. Says he doesn’t need money now. Apr 28 David Parson refused, laughing. May 1 Warren C. Ingersoll refused. He got very upset about my “attitude towards money.” May 4 Keith Sonnier refused, but said he would take money if he needed it which he might in the near future. May 7 Dick Anderson barely glances at the money when I stick it under his nose and says “Oh no thanks, I intend to earn it on my own.” May 8 Billy Bryant Copley didn’t take any but then it was sort of spoiled because I had told him about this piece on the phone & he had time to think about it he said.

Smart Contracts (smart as in fair, not smart as in Blockchain)

Cornell University's Cheryl Finley has done a lot of research on secondary art markets. I first learned about her research when I met her at the University of Florida's Harn Museum, where she spoke about smart contracts (smart as in fair, not smart as in Blockchain) and new protocols that could help artists who are often left out of the economic benefits of their own work, including women and women of color.

Her talk included findings from her ArtNet op-ed with Lauren van Haaften-Schick, Christian Reeder, and Amy Whitaker.

NFTs allow us to think about and hack on formal contractual relationships outside a system of laws that is currently not set up to service our community.

The ArtNet article The Recent Sale of Amy Sherald's ‘Welfare Queen' Symbolizes the Urgent Need for Resale Royalties and Economic Equity for Artists discussed Sherald's 2012 portrait of a regal woman in a purple dress wearing a sparkling crown and elegant set of pearls against a vibrant red background.

Amy Sherald sold "Welfare Queen" to Princeton professor Imani Perry. Sherald agreed to a payment plan to accommodate Perry's budget.

Amy Sherald rose to fame for her 2016 portrait of Michelle Obama and her full-length portrait of Breonna Taylor, one of the most famous works of the past decade.

As is common, Sherald's rising star drove up the price of her earlier works. Perry's "Welfare Queen" sold for $3.9 million in 2021.

Imani Perry's early investment paid off big-time. Amy Sherald, whose work directly increased the painting's value and who was on an artist's shoestring budget when she agreed to sell "Welfare Queen" in 2012, did not see any of the 2021 auction money. Perry and the auction house got that money.

Sherald sold her Breonna Taylor portrait to the Smithsonian and Louisville's Speed Art Museum to fund a $1 million scholarship. This is a great example of what an artist can do for the community if they can amass wealth through their work.

NFTs haven't solved all of the art market's problems — fakes, money laundering, market manipulation — but they didn't create them. Blockchain and NFTs are credited with making these issues more transparent. More ideas emerge daily about what a smart contract should do for artists.

NFTs are a copyright solution. They allow us to hack formal contractual relationships outside a law system that doesn't serve our community.

Amy Sherald shows the good smart contracts can do (as in, well-considered, self-determined contracts, not necessarily blockchain contracts.) Giving back to our community, deciding where and how our work can be sold or displayed, and ensuring artists share in the equity of our work and the economy our labor creates.