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.

More retail traders means faster, more sophisticated, and more successful methods.

Tech specifications

Only requires a laptop and an internet connection.

We'll use OpenBB's research platform for data/analysis.

Pricing and execution on Options-Quant

Background

You don't need to know the arithmetic details to use this method.

Black-Scholes is a popular option pricing model. It's best for pricing European options. European options are only exercisable at expiration, unlike American options. American options are always exercisable.

American options carry a premium to cover for the risk of early exercise. The Black-Scholes model doesn't account for this premium, hence it can't price genuine, traded American options.

Barone-Adesi-Whaley (BAW) model. BAW modifies Black-Scholes. It accounts for exercise risk premium and stock dividends. It adds the option's early exercise value to the Black-Scholes value.

The trader need not know the formulaic derivations of this model.

https://ir.nctu.edu.tw/bitstream/11536/14182/1/000264318900005.pdf

Strategy

This strategy targets implied volatility. First, we'll locate liquid options that expire within 30 days and have minimal implied volatility.

After selecting the option that meets the requirements, we price it to get the BAW implied volatility (we choose BAW because it's a more accurate Black-Scholes model). If estimated implied volatility is larger than market volatility, we'll capture the spread.

(Calculated IV — Market IV) = (Profit)

Some approaches to target implied volatility are pricey and inaccessible to individual investors. The best and most cost-effective alternative is to acquire a straddle and delta hedge. This may sound terrifying and pricey, but as shown below, it's much less so.

The Trade

First, we want to find our ideal option, so we use OpenBB terminal to screen for options that:

• Have an IV at least 5% lower than the 20-day historical IV

• Are no more than 5% out-of-the-money

• Expire in less than 30 days

We query:

stocks/options/screen/set low_IV/scr --export Output.csv

This uses the screener function to screen for options that satisfy the above criteria, which we specify in the low IV preset (more on custom presets here). It then saves the matching results to a csv(Excel) file for viewing and analysis.

Stick to liquid names like SPY, AAPL, and QQQ since getting out of a position is just as crucial as getting in. Smaller, illiquid names have higher inefficiencies, which could restrict total profits.

We calculate IV using the BAWbisection model (the bisection is a method of calculating IV, more can be found here.) We price the IV first.

According to the BAW model, implied volatility at this level should be priced at 26.90%. When re-pricing the put, IV is 24.34%, up 3%.

Now it's evident. We must purchase the straddle (long the call and long the put) assuming the computed implied volatility is more appropriate and efficient than the market's. We just want to speculate on volatility, not price fluctuations, thus we delta hedge.

The Fun Starts

We buy both options for $7.65. (x100 multiplier). Initial delta is 2. For every dollar the stock price swings up or down, our position value moves $2.

We want delta to be 0 to avoid price vulnerability. A delta of 0 suggests our position's value won't change from underlying price changes. Being delta-hedged allows us to profit/lose from implied volatility. Shorting 2 shares makes us delta-neutral.

That's delta hedging. (Share price * shares traded) = $330.7 to become delta-neutral. You may have noted that delta is not truly 0.00. This is common since delta-hedging means getting as near to 0 as feasible, since it is rare for deltas to align at 0.00.

Now we're vulnerable to changes in Vega (and Gamma, but given we're dynamically hedging, it's not a big risk), or implied volatility. We wanted to gamble that the position's IV would climb by at least 2%, so we'll maintain it delta-hedged and watch IV.

Because the underlying moves continually, the option's delta moves continuously. A trader can short/long 5 AAPL shares at most. Paper trading lets you practice delta-hedging. Being quick-footed will help with this tactic.

Profit-Closing

As expected, implied volatility rose. By 10 minutes before market closure, the call's implied vol rose to 27% and the put's to 24%. This allowed us to sell the call for $4.95 and the put for $4.35, creating a profit of $165.

You may pull historical data to see how this trade performed. Note the implied volatility and pricing in the final options chain for August 5, 2022 (the position date).

Final Thoughts

Congratulations, that was a doozy. To reiterate, we identified tickers prone to increased implied volatility by screening OpenBB's low IV setting. We double-checked the IV by plugging the price into Options-BAW Quant's model. When volatility was off, we bought a straddle and delta-hedged it. Finally, implied volatility returned to a normal level, and we profited on the spread.

The retail trading space is very quickly catching up to that of institutions.  Commissions and fees used to kill this method, but now they cost less than $5. Watching momentum, technical analysis, and now quantitative strategies evolve is intriguing.

I'm not linked with these sites and receive no financial benefit from my writing.

Tell me how your experience goes and how I helped; I love success tales.

Every week I meet many people interested in VC. Many of them ask me what it's like to be a junior analyst in VC or what I've learned so far.

Looking back, I've learned many things as a junior VC, having gone through an almost-euphoric peak bull market, failed tech IPOs of 2019 including WeWorks' catastrophic fall, and the beginnings of a bearish market.

1. Network, network, network!

VCs spend 80% of their time networking. Junior VCs source deals or manage portfolios. You spend your time bringing startups to your fund or helping existing portfolio companies grow. Knowing stakeholders (corporations, star talent, investors) in your particular areas of investment helps you develop your portfolio.

Networking was one of my strengths. When I first started in the industry, I'd go to startup events and meet 50 people a month. Over time, I realized these relationships were shallow and I was only getting business cards. So I stopped seeing networking as a transaction. VC is a long-term game, so you should work with people you like. Now I know who I click with and can build deeper relationships with them. My network is smaller but more valuable than before.

2. The Most Important Metric Is Founder

People often ask how we pick investments. Why some companies can raise money and others can't is a mystery. The founder is the most important metric for VCs. When a company is young, the product, environment, and team all change, but the founder remains constant. VCs bet on the founder, not the company.

How do we decide which founders are best after 2-3 calls? When looking at a founder's profile, ask why this person can solve this problem. The founders' track record will tell. If the founder is a serial entrepreneur, you know he/she possesses the entrepreneur DNA and will likely succeed again. If it's his/her first startup, focus on industry knowledge to deliver the best solution.

3. A company's fate can be determined by macrotrends.

Macro trends are crucial. A company can have the perfect product, founder, and team, but if it's solving the wrong problem, it won't succeed. I've also seen average companies ride the wave to success. When you're on the right side of a trend, there's so much demand that more companies can get a piece of the pie.

In COVID-19, macro trends made or broke a company. Ed-tech and health-tech companies gained unicorn status and raised funding at inflated valuations due to sudden demand. With the easing of pandemic restrictions and the start of a bear market, many of these companies' valuations are in question.

4. Look for methods to ACTUALLY add value.

You only need to go on VC twitter (read: @vcstartterkit and @vcbrags) for 5 minutes or look at fin-meme accounts on Instagram to see how much VCs claim to add value but how little they actually do. VC is a long-term game, though. Long-term, founders won't work with you if you don't add value.

How can we add value when we're young and have no network? Leaning on my strengths helped me. Instead of viewing my age and limited experience as a disadvantage, I realized that I brought a unique perspective to the table.

As a VC, you invest in companies that will be big in 5-7 years, and millennials and Gen Z will have the most purchasing power. Because you can relate to that market, you can offer insights that most Partners at 40 can't. I added value by helping with hiring because I had direct access to university talent pools and by finding university students for product beta testing.

5. Develop your personal brand.

Generalists or specialists run most funds. This means that funds either invest across industries or have a specific mandate. Most funds are becoming specialists, I've noticed. Top-tier founders don't lack capital, so funds must find other ways to attract them. Why would a founder work with a generalist fund when a specialist can offer better industry connections and partnership opportunities?

Same for fund members. Founders want quality investors. Become a thought leader in your industry to meet founders. Create content and share your thoughts on industry-related social media. When I first started building my brand, I found it helpful to interview industry veterans to create better content than I could on my own. Over time, my content attracted quality founders so I didn't have to look for them.

These are my biggest VC lessons. This list isn't exhaustive, but it's my industry survival guide.

For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.

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.