Expulsion of ten million Ukrainians
According to recent data from two UN agencies, ten million Ukrainians have been displaced.
The International Organization for Migration (IOM) estimates nearly 6.5 million Ukrainians have relocated. Most have fled the war zones around Kyiv and eastern Ukraine, including Dnipro, Zhaporizhzhia, and Kharkiv. Most IDPs have fled to western and central Ukraine.
Since Russia invaded on Feb. 24, 3.6 million people have crossed the border to seek refuge in neighboring countries, according to the latest UN data. While most refugees have fled to Poland and Romania, many have entered Russia.
Internally displaced figures are IOM estimates as of March 19, based on 2,000 telephone interviews with Ukrainians aged 18 and older conducted between March 9-16. The UNHCR compiled the figures for refugees to neighboring countries on March 21 based on official border crossing data and its own estimates. The UNHCR's top-line total is lower than the country totals because Romania and Moldova totals include people crossing between the two countries.
Sources: IOM, UNHCR
According to IOM estimates based on telephone interviews with a representative sample of internally displaced Ukrainians, over 53% of those displaced are women, and over 60% of displaced households have children.
More on Current Events
Steve QJ
3 years ago
Putin's War On Reality
The dictator's playbook.
Stalin's successor, Nikita Khrushchev, delivered a speech titled "On The Cult Of Personality And Its Consequences" in 1956, three years after Stalin’s death.
It was Stalin's grave abuse of power that caused untold harm to our party.
Stalin acted not by persuasion, explanation, or patient cooperation, but by imposing his ideas and demanding absolute obedience. […]
See where Stalin's mania for greatness led? He had lost all sense of reality.
The speech, which was never made public, shook the Soviet Union and the Soviet Bloc. After Stalin's "cult of personality" was exposed as a lie, only reality remained.
As I've watched the nightmare unfold in Ukraine, I'm reminded of that question. Primarily by Putin's repeated denials.
His odd claim that Ukraine is run by drug addicts and Nazis (especially strange given that Volodymyr Zelenskyy, the Ukrainian president, is Jewish). Others attempt to portray Russia as liberators rather than occupiers. For example, he portrays Luhansk and Donetsk as plucky, newly independent states when they have been totalitarian statelets for 8 years.
Putin seemed to have lost all sense of reality.
Maybe that's why his remarks to an oligarchs' gathering stood out:
Everything is a desperate measure. They gave us no choice. We couldn't do anything about their security risks. […] They could have put the country in jeopardy.
This is almost certainly true from Putin's perspective. Even for Putin, a military invasion seems unlikely. So, what exactly is putting Russia's security in jeopardy? How could Ukraine's independence endanger Russia's existence?
The truth is the only thing that truly terrifies leaders like these.
Trump, the president of “alternative facts,” "and “fake news” praised Putin's fabricated justifications for the Ukraine invasion. Russia tightened news censorship as news of their losses came in. It's no accident that modern dictatorships like Russia (and China and North Korea) restrict citizens' access to information.
Controlling what people see, hear, and think is the simplest method. And Ukraine's recent efforts to join the European Union showed a country whose thoughts Putin couldn't control. With the Russian and Ukrainian peoples so close, he could not control their reality.
He appears to think this is a threat worth fighting NATO over.
It's easy to disown history's great dictators. By the magnitude of their harm. But the strategy they used is still in use today, albeit not to the same devastating effect.
The Kim dynasty in North Korea has ruled for 74 years, Putin has ruled Russia for 19 years (using loopholes and even rewriting the constitution).
“Politicians and diapers must be changed frequently,” said Mark Twain. "And for the same reason.”
When their egos are threatened, they sabre-rattle, as in Kim Jong-un and Donald Trump's famous spat about the size of their...ahem, “nuclear buttons”." Or Putin's threats of mutual destruction this weekend.
Most importantly, they have cult-like control over their followers.
When a leader whose power is built on lies feels he is losing control of the narrative, things like Trump's Jan. 6 meltdown and Putin's current actions in Ukraine are unavoidable.
Leaders who try to control their people's reality will have to die to keep the illusion alive.
Long version of this post available here
Gill Pratt
3 years ago
War's Human Cost
War's Human Cost
I didn't start crying until I was outside a McDonald's in an Olempin, Poland rest area on highway S17.
Children pick toys at a refugee center, Olempin, Poland, March 4, 2022.
Refugee children, mostly alone with their mothers, but occasionally with a gray-haired grandfather or non-Ukrainian father, were coaxed into picking a toy from boxes provided by a kind-hearted company and volunteers.
I went to Warsaw to continue my research on my family's history during the Holocaust. In light of the ongoing Ukrainian conflict, I asked former colleagues in the US Department of Defense and Intelligence Community if it was safe to travel there. They said yes, as Poland was a NATO member.
I stayed in a hotel in the Warsaw Ghetto, where 90% of my mother's family was murdered in the Holocaust. Across the street was the first Warsaw Judenrat. It was two blocks away from the apartment building my mother's family had owned and lived in, now dilapidated and empty.
Building of my great-grandfather, December 2021.
A mass grave of thousands of rocks for those killed in the Warsaw Ghetto, I didn't cry when I touched its cold walls.
Warsaw Jewish Cemetery, 200,000–300,000 graves.
Mass grave, Warsaw Jewish Cemetery.
My mother's family had two homes, one in Warszawa and the rural one was a forest and sawmill complex in Western Ukraine. For the past half-year, a local Ukrainian historian had been helping me discover faint traces of her family’s life there — in fact, he had found some people still alive who remembered the sawmill and that it belonged to my mother’s grandfather. The historian was good at his job, and we had become close.
My historian friend, December 2021, talking to a Ukrainian.
With war raging, my second trip to Warsaw took on a different mission. To see his daughter and one-year-old grandson, I drove east instead of to Ukraine. They had crossed the border shortly after the war began, leaving men behind, and were now staying with a friend on Poland's eastern border.
I entered after walking up to the house and settling with the dog. The grandson greeted me with a huge smile and the Ukrainian word for “daddy,” “Tato!” But it was clear he was awaiting his real father's arrival, and any man he met would be so tentatively named.
After a few moments, the boy realized I was only a stranger. He had musical talent, like his mother and grandfather, both piano teachers, as he danced to YouTube videos of American children's songs dubbed in Ukrainian, picking the ones he liked and crying when he didn't.
Songs chosen by my historian friend's grandson, March 4, 2022
He had enough music and began crying regardless of the song. His mother picked him up and started nursing him, saying she was worried about him. She had no idea where she would live or how she would survive outside Ukraine. She showed me her father's family history of losses in the Holocaust, which matched my own research.
After an hour of drinking tea and trying to speak of hope, I left for the 3.5-hour drive west to Warsaw.
It was unlike my drive east. It was reminiscent of the household goods-filled carts pulled by horses and people fleeing war 80 years ago.
Jewish refugees relocating, USHMM Holocaust Encyclopaedia, 1939.
The carefully chosen trinkets by children to distract them from awareness of what is really happening and the anxiety of what lies ahead, made me cry despite all my research on the Holocaust. There is no way for them to communicate with their mothers, who are worried, absent, and without their fathers.
It's easy to see war as a contest of nations' armies, weapons, and land. The most costly aspect of war is its psychological toll. My father screamed in his sleep from nightmares of his own adolescent trauma in Warsaw 80 years ago.
Survivor father studying engineering, 1961.
In the airport, I waited to return home while Ukrainian public address systems announced refugee assistance. Like at McDonald's, many mothers were alone with their children, waiting for a flight to distant relatives.
That's when I had my worst trip experience.
A woman near me, clearly a refugee, answered her phone, cried out, and began wailing.
The human cost of war descended like a hammer, and I realized that while I was going home, she never would
Jared A. Brock
3 years ago
Here is the actual reason why Russia invaded Ukraine
Democracy's demise
Our Ukrainian brothers and sisters are being attacked by a far superior force.
It's the biggest invasion since WWII.
43.3 million peaceful Ukrainians awoke this morning to tanks, mortars, and missiles. Russia is already 15 miles away.
America and the West will not deploy troops.
They're sanctioning. Except railways. And luxuries. And energy. Diamonds. Their dependence on Russian energy exports means they won't even cut Russia off from SWIFT.
Ukraine is desperate enough to hand out guns on the street.
France, Austria, Turkey, and the EU are considering military aid, but Ukraine will fall without America or NATO.
The Russian goal is likely to encircle Kyiv and topple Zelenskyy's government. A proxy power will be reinstated once Russia has total control.
“Western security services believe Putin intends to overthrow the government and install a puppet regime,” says Financial Times foreign affairs commentator Gideon Rachman. This “decapitation” strategy includes municipalities. Ukrainian officials are being targeted for arrest or death.”
Also, Putin has never lost a war.
Why is Russia attacking Ukraine?
Putin, like a snowflake college student, “feels unsafe.”
Why?
Because Ukraine is full of “Nazi ideas.”
Putin claims he has felt threatened by Ukraine since the country's pro-Putin leader was ousted and replaced by a popular Jewish comedian.
Hee hee
He fears a full-scale enemy on his doorstep if Ukraine joins NATO. But he refuses to see it both ways. NATO has never invaded Russia, but Russia has always stolen land from its neighbors. Can you blame them for joining a mutual defense alliance when a real threat exists?
Nations that feel threatened can join NATO. That doesn't justify an attack by Russia. It allows them to defend themselves. But NATO isn't attacking Moscow. They aren't.
Russian President Putin's "special operation" aims to de-Nazify the Jewish-led nation.
To keep Crimea and the other two regions he has already stolen, he wants Ukraine undefended by NATO.
(Warlords have fought for control of the strategically important Crimea for over 2,000 years.)
Putin wants to own all of Ukraine.
Why?
The Black Sea is his goal.
Ports bring money and power, and Ukraine pipelines transport Russian energy products.
Putin wants their wheat, too — with 70% crop coverage, Ukraine would be their southern breadbasket, and Russia has no qualms about starving millions of Ukrainians to death to feed its people.
In the end, it's all about greed and power.
Putin wants to own everything Russia has ever owned. This year he turns 70, and he wants to be remembered like his hero Peter the Great.
In order to get it, he's willing to kill thousands of Ukrainians
Art imitates life
This story began when a Jewish TV comedian portrayed a teacher elected President after ranting about corruption.
Servant of the People, the hit sitcom, is now the leading centrist political party.
Right, President Zelenskyy won the hearts and minds of Ukrainians by imagining a fairer world.
A fair fight is something dictators, corporatists, monopolists, and warlords despise.
Now Zelenskyy and his people will die, allowing one of history's most corrupt leaders to amass even more power.
The poor always lose
Meanwhile, the West will impose economic sanctions on Russia.
China is likely to step in to help Russia — or at least the wealthy.
The poor and working class in Russia will suffer greatly if there is a hard crash or long-term depression.
Putin's friends will continue to drink champagne and eat caviar.
Russia cutting off oil, gas, and fertilizer could cause more inflation and possibly a recession if it cuts off supplies to the West. This causes more suffering and hardship for the Western poor and working class.
Why? a billionaire sociopath gets his dirt.
Yes, Russia is simply copying America. Some of us think all war is morally wrong, regardless of who does it.
But let's not kid ourselves right now.
The markets rallied after the biggest invasion in Europe since WWII.
Investors hope Ukraine collapses and Russian oil flows.
Unbridled capitalists value lifeless.
What we can do about Ukraine
When the Russian army invaded eastern Finland, my wife's grandmother fled as a child. 80 years later, Russia still has Karelia.
Russia invaded Ukraine today to retake two eastern provinces.
History has taught us nothing.
Past mistakes won't fix the future.
Instead, we should try:
- Pray and/or meditate on our actions with our families.
- Stop buying Russian products (vodka, obviously, but also pay more for hydro/solar/geothermal/etc.)
- Stop wasting money on frivolous items and donate it to Ukrainian charities.
Here are 35+ places to donate.
- To protest, gather a few friends, contact the media, and shake signs in front of the Russian embassy.
- Prepare to welcome refugees.
More war won't save the planet or change hearts.
Only love can work.
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SAHIL SAPRU
3 years ago
Growth tactics that grew businesses from 1 to 100
Everyone wants a scalable startup.
Innovation helps launch a startup. The secret to a scalable business is growth trials (from 1 to 100).
Growth marketing combines marketing and product development for long-term growth.
Today, I'll explain growth hacking strategies popular startups used to scale.
1/ A Facebook user's social value is proportional to their friends.
Facebook built its user base using content marketing and paid ads. Mark and his investors feared in 2007 when Facebook's growth stalled at 90 million users.
Chamath Palihapitiya was brought in by Mark.
The team tested SEO keywords and MAU chasing. The growth team introduced “people you may know”
This feature reunited long-lost friends and family. Casual users became power users as the retention curve flattened.
Growth Hack Insights: With social network effect the value of your product or platform increases exponentially if you have users you know or can relate with.
2/ Airbnb - Focus on your value propositions
Airbnb nearly failed in 2009. The company's weekly revenue was $200 and they had less than 2 months of runway.
Enter Paul Graham. The team noticed a pattern in 40 listings. Their website's property photos sucked.
Why?
Because these photos were taken with regular smartphones. Users didn't like the first impression.
Graham suggested traveling to New York to rent a camera, meet with property owners, and replace amateur photos with high-resolution ones.
A week later, the team's weekly revenue doubled to $400, indicating they were on track.
Growth Hack Insights: When selling an “online experience” ensure that your value proposition is aesthetic enough for users to enjoy being associated with them.
3/ Zomato - A company's smartphone push ensured growth.
Zomato delivers food. User retention was a challenge for the founders. Indian food customers are notorious for switching brands at the drop of a hat.
Zomato wanted users to order food online and repeat orders throughout the week.
Zomato created an attractive website with “near me” keywords for SEO indexing.
Zomato gambled to increase repeat orders. They only allowed mobile app food orders.
Zomato thought mobile apps were stickier. Product innovations in search/discovery/ordering or marketing campaigns like discounts/in-app notifications/nudges can improve user experience.
Zomato went public in 2021 after users kept ordering food online.
Growth Hack Insights: To improve user retention try to build platforms that build user stickiness. Your product and marketing team will do the rest for them.
4/ Hotmail - Signaling helps build premium users.
Ever sent or received an email or tweet with a sign — sent from iPhone?
Hotmail did it first! One investor suggested Hotmail add a signature to every email.
Overnight, thousands joined the company. Six months later, the company had 1 million users.
When serving an existing customer, improve their social standing. Signaling keeps the top 1%.
5/ Dropbox - Respect loyal customers
Dropbox is a company that puts people over profits. The company prioritized existing users.
Dropbox rewarded loyal users by offering 250 MB of free storage to anyone who referred a friend. The referral hack helped Dropbox get millions of downloads in its first few months.
Growth Hack Insights: Think of ways to improve the social positioning of your end-user when you are serving an existing customer. Signaling goes a long way in attracting the top 1% to stay.
These experiments weren’t hacks. Hundreds of failed experiments and user research drove these experiments. Scaling up experiments is difficult.
Contact me if you want to grow your startup's user base.
Pen Magnet
3 years ago
Why Google Staff Doesn't Work
Sundar Pichai unveiled Simplicity Sprint at Google's latest all-hands conference.
To boost employee efficiency.
Not surprising. Few envisioned Google declaring a productivity drive.
Sunder Pichai's speech:
“There are real concerns that our productivity as a whole is not where it needs to be for the head count we have. Help me create a culture that is more mission-focused, more focused on our products, more customer focused. We should think about how we can minimize distractions and really raise the bar on both product excellence and productivity.”
The primary driver driving Google's efficiency push is:
Google's efficiency push follows 13% quarterly revenue increase. Last year in the same quarter, it was 62%.
Market newcomers may argue that the previous year's figure was fuelled by post-Covid reopening and growing consumer spending. Investors aren't convinced. A promising company like Google can't afford to drop so quickly.
Google’s quarterly revenue growth stood at 13%, against 62% in last year same quarter.
Google isn't alone. In my recent essay regarding 2025 programmers, I warned about the economic downturn's effects on FAAMG's workforce. Facebook had suspended hiring, and Microsoft had promised hefty bonuses for loyal staff.
In the same article, I predicted Google's troubles. Online advertising, especially the way Google and Facebook sell it using user data, is over.
FAAMG and 2nd rung IT companies could be the first to fall without Post-COVID revival and uncertain global geopolitics.
Google has hardly ever discussed effectiveness:
Apparently openly.
Amazon treats its employees like robots, even in software positions. It has significant turnover and a terrible reputation as a result. Because of this, it rarely loses money due to staff productivity.
Amazon trumps Google. In reality, it treats its employees poorly.
Google was the founding father of the modern-day open culture.
Larry and Sergey Google founded the IT industry's Open Culture. Silicon Valley called Google's internal democracy and transparency near anarchy. Management rarely slammed decisions on employees. Surveys and internal polls ensured everyone knew the company's direction and had a vote.
20% project allotment (weekly free time to build own project) was Google's open-secret innovation component.
After Larry and Sergey's exit in 2019, this is Google's first profitability hurdle. Only Google insiders can answer these questions.
Would Google's investors compel the company's management to adopt an Amazon-style culture where the developers are treated like circus performers?
If so, would Google follow suit?
If so, how does Google go about doing it?
Before discussing Google's likely plan, let's examine programming productivity.
What determines a programmer's productivity is simple:
How would we answer Google's questions?
As a programmer, I'm more concerned about Simplicity Sprint's aftermath than its economic catalysts.
Large organizations don't care much about quarterly and annual productivity metrics. They have 10-year product-launch plans. If something seems horrible today, it's likely due to someone's lousy judgment 5 years ago who is no longer in the blame game.
Deconstruct our main question.
How exactly do you change the culture of the firm so that productivity increases?
How can you accomplish that without affecting your capacity to profit? There are countless ways to increase output without decreasing profit.
How can you accomplish this with little to no effect on employee motivation? (While not all employers care about it, in this case we are discussing the father of the open company culture.)
How do you do it for a 10-developer IT firm that is losing money versus a 1,70,000-developer organization with a trillion-dollar valuation?
When implementing a large-scale organizational change, success must be carefully measured.
The fastest way to do something is to do it right, no matter how long it takes.
You require clearly-defined group/team/role segregation and solid pass/fail matrices to:
You can give performers rewards.
Ones that are average can be inspired to improve
Underachievers may receive assistance or, in the worst-case scenario, rehabilitation
As a 20-year programmer, I associate productivity with greatness.
Doing something well, no matter how long it takes, is the fastest way to do it.
Let's discuss a programmer's productivity.
Why productivity is a strange term in programming:
Productivity is work per unit of time.
Money=time This is an economic proverb. More hours worked, more pay. Longer projects cost more.
As a buyer, you desire a quick supply. As a business owner, you want employees who perform at full capacity, creating more products to transport and boosting your profits.
All economic matrices encourage production because of our obsession with it. Productivity is the only organic way a nation may increase its GDP.
Time is money — is not just a proverb, but an economical fact.
Applying the same productivity theory to programming gets problematic. An automating computer. Its capacity depends on the software its master writes.
Today, a sophisticated program can process a billion records in a few hours. Creating one takes a competent coder and the necessary infrastructure. Learning, designing, coding, testing, and iterations take time.
Programming productivity isn't linear, unlike manufacturing and maintenance.
Average programmers produce code every day yet miss deadlines. Expert programmers go days without coding. End of sprint, they often surprise themselves by delivering fully working solutions.
Reversing the programming duties has no effect. Experts aren't needed for productivity.
These patterns remind me of an XKCD comic.
Programming productivity depends on two factors:
The capacity of the programmer and his or her command of the principles of computer science
His or her productive bursts, how often they occur, and how long they last as they engineer the answer
At some point, productivity measurement becomes Schrödinger’s cat.
Product companies measure productivity using use cases, classes, functions, or LOCs (lines of code). In days of data-rich source control systems, programmers' merge requests and/or commits are the most preferred yardstick. Companies assess productivity by tickets closed.
Every organization eventually has trouble measuring productivity. Finer measurements create more chaos. Every measure compares apples to oranges (or worse, apples with aircraft.) On top of the measuring overhead, the endeavor causes tremendous and unnecessary stress on teams, lowering their productivity and defeating its purpose.
Macro productivity measurements make sense. Amazon's factory-era management has done it, but at great cost.
Google can pull it off if it wants to.
What Google meant in reality when it said that employee productivity has decreased:
When Google considers its employees unproductive, it doesn't mean they don't complete enough work in the allotted period.
They can't multiply their work's influence over time.
Programmers who produce excellent modules or products are unsure on how to use them.
The best data scientists are unable to add the proper parameters in their models.
Despite having a great product backlog, managers struggle to recruit resources with the necessary skills.
Product designers who frequently develop and A/B test newer designs are unaware of why measures are inaccurate or whether they have already reached the saturation point.
Most ignorant: All of the aforementioned positions are aware of what to do with their deliverables, but neither their supervisors nor Google itself have given them sufficient authority.
So, Google employees aren't productive.
How to fix it?
Business analysis: White suits introducing novel items can interact with customers from all regions. Track analytics events proactively, especially the infrequent ones.
SOLID, DRY, TEST, and AUTOMATION: Do less + reuse. Use boilerplate code creation. If something already exists, don't implement it yourself.
Build features-building capabilities: N features are created by average programmers in N hours. An endless number of features can be built by average programmers thanks to the fact that expert programmers can produce 1 capability in N hours.
Work on projects that will have a positive impact: Use the same algorithm to search for images on YouTube rather than the Mars surface.
Avoid tasks that can only be measured in terms of time linearity at all costs (if a task can be completed in N minutes, then M copies of the same task would cost M*N minutes).
In conclusion:
Software development isn't linear. Why should the makers be measured?
Notation for The Big O
I'm discussing a new way to quantify programmer productivity. (It applies to other professions, but that's another subject)
The Big O notation expresses the paradigm (the algorithmic performance concept programmers rot to ace their Google interview)
Google (or any large corporation) can do this.
Sort organizational roles into categories and specify their impact vs. time objectives. A CXO role's time vs. effect function, for instance, has a complexity of O(log N), meaning that if a CEO raises his or her work time by 8x, the result only increases by 3x.
Plot the influence of each employee over time using the X and Y axes, respectively.
Add a multiplier for Y-axis values to the productivity equation to make business objectives matter. (Example values: Support = 5, Utility = 7, and Innovation = 10).
Compare employee scores in comparable categories (developers vs. devs, CXOs vs. CXOs, etc.) and reward or help employees based on whether they are ahead of or behind the pack.
After measuring every employee's inventiveness, it's straightforward to help underachievers and praise achievers.
Example of a Big(O) Category:
If I ran Google (God forbid, its worst days are far off), here's how I'd classify it. You can categorize Google employees whichever you choose.
The Google interview truth:
O(1) < O(log n) < O(n) < O(n log n) < O(n^x) where all logarithmic bases are < n.
O(1): Customer service workers' hours have no impact on firm profitability or customer pleasure.
CXOs Most of their time is spent on travel, strategic meetings, parties, and/or meetings with minimal floor-level influence. They're good at launching new products but bad at pivoting without disaster. Their directions are being followed.
Devops, UX designers, testers Agile projects revolve around deployment. DevOps controls the levers. Their automation secures results in subsequent cycles.
UX/UI Designers must still prototype UI elements despite improved design tools.
All test cases are proportional to use cases/functional units, hence testers' work is O(N).
Architects Their effort improves code quality. Their right/wrong interference affects product quality and rollout decisions even after the design is set.
Core Developers Only core developers can write code and own requirements. When people understand and own their labor, the output improves dramatically. A single character error can spread undetected throughout the SDLC and cost millions.
Core devs introduce/eliminate 1000x bugs, refactoring attempts, and regression. Following our earlier hypothesis.
The fastest way to do something is to do it right, no matter how long it takes.
Conclusion:
Google is at the liberal extreme of the employee-handling spectrum
Microsoft faced an existential crisis after 2000. It didn't choose Amazon's data-driven people management to revitalize itself.
Instead, it entrusted developers. It welcomed emerging technologies and opened up to open source, something it previously opposed.
Google is too lax in its employee-handling practices. With that foundation, it can only follow Amazon, no matter how carefully.
Any attempt to redefine people's measurements will affect the organization emotionally.
The more Google compares apples to apples, the higher its chances for future rebirth.
Shalitha Suranga
3 years ago
The Top 5 Mathematical Concepts Every Programmer Needs to Know
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.