Bernard Lawrence "Bernie" Madoff, the largest Ponzi scheme in history
Madoff who?
Bernie Madoff ran the largest Ponzi scheme in history, defrauding thousands of investors over at least 17 years, and possibly longer. He pioneered electronic trading and chaired Nasdaq in the 1990s. On April 14, 2021, he died while serving a 150-year sentence for money laundering, securities fraud, and other crimes.
Understanding Madoff
Madoff claimed to generate large, steady returns through a trading strategy called split-strike conversion, but he simply deposited client funds into a single bank account and paid out existing clients. He funded redemptions by attracting new investors and their capital, but the market crashed in late 2008. He confessed to his sons, who worked at his firm, on Dec. 10, 2008. Next day, they turned him in. The fund reported $64.8 billion in client assets.
Madoff pleaded guilty to 11 federal felony counts, including securities fraud, wire fraud, mail fraud, perjury, and money laundering. Ponzi scheme became a symbol of Wall Street's greed and dishonesty before the financial crisis. Madoff was sentenced to 150 years in prison and ordered to forfeit $170 billion, but no other Wall Street figures faced legal ramifications.
Bernie Madoff's Brief Biography
Bernie Madoff was born in Queens, New York, on April 29, 1938. He began dating Ruth (née Alpern) when they were teenagers. Madoff told a journalist by phone from prison that his father's sporting goods store went bankrupt during the Korean War: "You watch your father, who you idolize, build a big business and then lose everything." Madoff was determined to achieve "lasting success" like his father "whatever it took," but his career had ups and downs.
Early Madoff investments
At 22, he started Bernard L. Madoff Investment Securities LLC. First, he traded penny stocks with $5,000 he earned installing sprinklers and as a lifeguard. Family and friends soon invested with him. Madoff's bets soured after the "Kennedy Slide" in 1962, and his father-in-law had to bail him out.
Madoff felt he wasn't part of the Wall Street in-crowd. "We weren't NYSE members," he told Fishman. "It's obvious." According to Madoff, he was a scrappy market maker. "I was happy to take the crumbs," he told Fishman, citing a client who wanted to sell eight bonds; a bigger firm would turn it down.
Recognition
Success came when he and his brother Peter built electronic trading capabilities, or "artificial intelligence," that attracted massive order flow and provided market insights. "I had all these major banks coming down, entertaining me," Madoff told Fishman. "It was mind-bending."
By the late 1980s, he and four other Wall Street mainstays processed half of the NYSE's order flow. Controversially, he paid for much of it, and by the late 1980s, Madoff was making in the vicinity of $100 million a year. He was Nasdaq chairman from 1990 to 1993.
Madoff's Ponzi scheme
It is not certain exactly when Madoff's Ponzi scheme began. He testified in court that it began in 1991, but his account manager, Frank DiPascali, had been at the firm since 1975.
Why Madoff did the scheme is unclear. "I had enough money to support my family's lifestyle. "I don't know why," he told Fishman." Madoff could have won Wall Street's respect as a market maker and electronic trading pioneer.
Madoff told Fishman he wasn't solely responsible for the fraud. "I let myself be talked into something, and that's my fault," he said, without saying who convinced him. "I thought I could escape eventually. I thought it'd be quick, but I couldn't."
Carl Shapiro, Jeffry Picower, Stanley Chais, and Norm Levy have been linked to Bernard L. Madoff Investment Securities LLC for years. Madoff's scheme made these men hundreds of millions of dollars in the 1960s and 1970s.
Madoff told Fishman, "Everyone was greedy, everyone wanted to go on." He says the Big Four and others who pumped client funds to him, outsourcing their asset management, must have suspected his returns or should have. "How can you make 15%-18% when everyone else is making less?" said Madoff.
How Madoff Got Away with It for So Long
Madoff's high returns made clients look the other way. He deposited their money in a Chase Manhattan Bank account, which merged to become JPMorgan Chase & Co. in 2000. The bank may have made $483 million from those deposits, so it didn't investigate.
When clients redeemed their investments, Madoff funded the payouts with new capital he attracted by promising unbelievable returns and earning his victims' trust. Madoff created an image of exclusivity by turning away clients. This model let half of Madoff's investors profit. These investors must pay into a victims' fund for defrauded investors.
Madoff wooed investors with his philanthropy. He defrauded nonprofits, including the Elie Wiesel Foundation for Peace and Hadassah. He approached congregants through his friendship with J. Ezra Merkin, a synagogue officer. Madoff allegedly stole $1 billion to $2 billion from his investors.
Investors believed Madoff for several reasons:
- His public portfolio seemed to be blue-chip stocks.
- His returns were high (10-20%) but consistent and not outlandish. In a 1992 interview with Madoff, the Wall Street Journal reported: "[Madoff] insists the returns were nothing special, given that the S&P 500-stock index returned 16.3% annually from 1982 to 1992. 'I'd be surprised if anyone thought matching the S&P over 10 years was remarkable,' he says.
- "He said he was using a split-strike collar strategy. A collar protects underlying shares by purchasing an out-of-the-money put option.
SEC inquiry
The Securities and Exchange Commission had been investigating Madoff and his securities firm since 1999, which frustrated many after he was prosecuted because they felt the biggest damage could have been prevented if the initial investigations had been rigorous enough.
Harry Markopolos was a whistleblower. In 1999, he figured Madoff must be lying in an afternoon. The SEC ignored his first Madoff complaint in 2000.
Markopolos wrote to the SEC in 2005: "The largest Ponzi scheme is Madoff Securities. This case has no SEC reward, so I'm turning it in because it's the right thing to do."
Many believed the SEC's initial investigations could have prevented Madoff's worst damage.
Markopolos found irregularities using a "Mosaic Method." Madoff's firm claimed to be profitable even when the S&P fell, which made no mathematical sense given what he was investing in. Markopolos said Madoff Securities' "undisclosed commissions" were the biggest red flag (1 percent of the total plus 20 percent of the profits).
Markopolos concluded that "investors don't know Bernie Madoff manages their money." Markopolos learned Madoff was applying for large loans from European banks (seemingly unnecessary if Madoff's returns were high).
The regulator asked Madoff for trading account documentation in 2005, after he nearly went bankrupt due to redemptions. The SEC drafted letters to two of the firms on his six-page list but didn't send them. Diana Henriques, author of "The Wizard of Lies: Bernie Madoff and the Death of Trust," documents the episode.
In 2008, the SEC was criticized for its slow response to Madoff's fraud.
Confession, sentencing of Bernie Madoff
Bernard L. Madoff Investment Securities LLC reported 5.6% year-to-date returns in November 2008; the S&P 500 fell 39%. As the selling continued, Madoff couldn't keep up with redemption requests, and on Dec. 10, he confessed to his sons Mark and Andy, who worked at his firm. "After I told them, they left, went to a lawyer, who told them to turn in their father, and I never saw them again. 2008-12-11: Bernie Madoff arrested.
Madoff insists he acted alone, but several of his colleagues were jailed. Mark Madoff died two years after his father's fraud was exposed. Madoff's investors committed suicide. Andy Madoff died of cancer in 2014.
2009 saw Madoff's 150-year prison sentence and $170 billion forfeiture. Marshals sold his three homes and yacht. Prisoner 61727-054 at Butner Federal Correctional Institution in North Carolina.
Madoff's lawyers requested early release on February 5, 2020, claiming he has a terminal kidney disease that may kill him in 18 months. Ten years have passed since Madoff's sentencing.
Bernie Madoff's Ponzi scheme aftermath
The paper trail of victims' claims shows Madoff's complexity and size. Documents show Madoff's scam began in the 1960s. His final account statements show $47 billion in "profit" from fake trades and shady accounting.
Thousands of investors lost their life savings, and multiple stories detail their harrowing loss.
Irving Picard, a New York lawyer overseeing Madoff's bankruptcy, has helped investors. By December 2018, Picard had recovered $13.3 billion from Ponzi scheme profiteers.
A Madoff Victim Fund (MVF) was created in 2013 to help compensate Madoff's victims, but the DOJ didn't start paying out the $4 billion until late 2017. Richard Breeden, a former SEC chair who oversees the fund, said thousands of claims were from "indirect investors"
Breeden and his team had to reject many claims because they weren't direct victims. Breeden said he based most of his decisions on one simple rule: Did the person invest more than they withdrew? Breeden estimated 11,000 "feeder" investors.
Breeden wrote in a November 2018 update for the Madoff Victim Fund, "We've paid over 27,300 victims 56.65% of their losses, with thousands more to come." In December 2018, 37,011 Madoff victims in the U.S. and around the world received over $2.7 billion. Breeden said the fund expected to make "at least one more significant distribution in 2019"
This post is a summary. Read full article here
More on Economics & Investing
Sam Hickmann
3 years ago
What is this Fed interest rate everybody is talking about that makes or breaks the stock market?
The Federal Funds Rate (FFR) is the target interest rate set by the Federal Reserve System (Fed)'s policy-making body (FOMC). This target is the rate at which the Fed suggests commercial banks borrow and lend their excess reserves overnight to each other.
The FOMC meets 8 times a year to set the target FFR. This is supposed to promote economic growth. The overnight lending market sets the actual rate based on commercial banks' short-term reserves. If the market strays too far, the Fed intervenes.
Banks must keep a certain percentage of their deposits in a Federal Reserve account. A bank's reserve requirement is a percentage of its total deposits. End-of-day bank account balances averaged over two-week reserve maintenance periods are used to determine reserve requirements.
If a bank expects to have end-of-day balances above what's needed, it can lend the excess to another institution.
The FOMC adjusts interest rates based on economic indicators that show inflation, recession, or other issues that affect economic growth. Core inflation and durable goods orders are indicators.
In response to economic conditions, the FFR target has changed over time. In the early 1980s, inflation pushed it to 20%. During the Great Recession of 2007-2009, the rate was slashed to 0.15 percent to encourage growth.
Inflation picked up in May 2022 despite earlier rate hikes, prompting today's 0.75 percent point increase. The largest increase since 1994. It might rise to around 3.375% this year and 3.1% by the end of 2024.

Cody Collins
2 years ago
The direction of the economy is as follows.
What quarterly bank earnings reveal
Big banks know the economy best. Unless we’re talking about a housing crisis in 2007…
Banks are crucial to the U.S. economy. The Fed, communities, and investments exchange money.
An economy depends on money flow. Banks' views on the economy can affect their decision-making.
Most large banks released quarterly earnings and forward guidance last week. Others were pessimistic about the future.
What Makes Banks Confident
Bank of America's profit decreased 30% year-over-year, but they're optimistic about the economy. Comparatively, they're bullish.
Who banks serve affects what they see. Bank of America supports customers.
They think consumers' future is bright. They believe this for many reasons.
The average customer has decent credit, unless the system is flawed. Bank of America's new credit card and mortgage borrowers averaged 771. New-car loan and home equity borrower averages were 791 and 797.
2008's housing crisis affected people with scores below 620.
Bank of America and the economy benefit from a robust consumer. Major problems can be avoided if individuals maintain spending.
Reasons Other Banks Are Less Confident
Spending requires income. Many companies, mostly in the computer industry, have announced they will slow or freeze hiring. Layoffs are frequently an indication of poor times ahead.
BOA is positive, but investment banks are bearish.
Jamie Dimon, CEO of JPMorgan, outlined various difficulties our economy could confront.
But geopolitical tension, high inflation, waning consumer confidence, the uncertainty about how high rates have to go and the never-before-seen quantitative tightening and their effects on global liquidity, combined with the war in Ukraine and its harmful effect on global energy and food prices are very likely to have negative consequences on the global economy sometime down the road.
That's more headwinds than tailwinds.
JPMorgan, which helps with mergers and IPOs, is less enthusiastic due to these concerns. Incoming headwinds signal drying liquidity, they say. Less business will be done.
Final Reflections
I don't think we're done. Yes, stocks are up 10% from a month ago. It's a long way from old highs.
I don't think the stock market is a strong economic indicator.
Many executives foresee a 2023 recession. According to the traditional definition, we may be in a recession when Q2 GDP statistics are released next week.
Regardless of criteria, I predict the economy will have a terrible year.
Weekly layoffs are announced. Inflation persists. Will prices return to 2020 levels if inflation cools? Perhaps. Still expensive energy. Ukraine's war has global repercussions.
I predict BOA's next quarter earnings won't be as bullish about the consumer's strength.

Desiree Peralta
2 years ago
How to Use the 2023 Recession to Grow Your Wealth Exponentially
This season's three best money moves.
“Millionaires are made in recessions.” — Time Capital
We're in a serious downturn, whether or not we're in a recession.
97% of business owners are decreasing costs by more than 10%, and all markets are down 30%.
If you know what you're doing and analyze the markets correctly, this is your chance to become a millionaire.
In any recession, there are always excellent possibilities to seize. Real estate, crypto, stocks, enterprises, etc.
What you do with your money could influence your future riches.
This article analyzes the three key markets, their circumstances for 2023, and how to profit from them.
Ways to make money on the stock market.
If you're conservative like me, you should invest in an index fund. Most of these funds are down 10-30% of ATH:
In earlier recessions, most money index funds lost 20%. After this downturn, they grew and passed the ATH in subsequent months.
Now is the greatest moment to invest in index funds to grow your money in a low-risk approach and make 20%.
If you want to be risky but wise, pick companies that will get better next year but are struggling now.
Even while we can't be 100% confident of a company's future performance, we know some are strong and will have a fantastic year.
Microsoft (down 22%), JPMorgan Chase (15.6%), Amazon (45%), and Disney (33.8%).
These firms give dividends, so you can earn passively while you wait.
So I consider that a good strategy to make wealth in the current stock market is to create two portfolios: one based on index funds to earn 10% to 20% profit when the corrections end, and the other based on individual stocks of popular and strong companies to earn 20%-30% return and dividends while you wait.
How to profit from the downturn in the real estate industry.
With rising mortgage rates, it's the worst moment to buy a home if you don't want to be eaten by banks. In the U.S., interest rates are double what they were three years ago, so buying now looks foolish.
Due to these rates, property prices are falling, but that won't last long since individuals will take advantage.
According to historical data, now is the ideal moment to buy a house for the next five years and perhaps forever.
If you can buy a house, do it. You can refinance the interest at a lower rate with acceptable credit, but not the house price.
Take advantage of the housing market prices now because you won't find a decent deal when rates normalize.
How to profit from the cryptocurrency market.
This is the riskiest market to tackle right now, but it could offer the most opportunities if done appropriately.
The most powerful cryptocurrencies are down more than 60% from last year: $68,990 for BTC and $4,865 for ETH.
If you focus on those two coins, you can make 30%-60% without waiting for them to return to their ATH, and they're low enough to be a solid investment.
I don't encourage trying other altcoins because the crypto market is in crisis and you can lose everything if you're greedy.
Still, the main Cryptos are a good investment provided you store them in an external wallet and follow financial gurus' security advice.
Last thoughts
We can't anticipate a recession until it ends. We can't forecast a market or asset's lowest point, therefore waiting makes little sense.
If you want to develop your wealth, assess the money prospects on all the marketplaces and initiate long-term trades.
Many millionaires are made during recessions because they don't fear negative figures and use them to scale their money.
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Guillaume Dumortier
2 years ago
Mastering the Art of Rhetoric: A Guide to Rhetorical Devices in Successful Headlines and Titles
Unleash the power of persuasion and captivate your audience with compelling headlines.
As the old adage goes, "You never get a second chance to make a first impression."
In the world of content creation and social ads, headlines and titles play a critical role in making that first impression.
A well-crafted headline can make the difference between an article being read or ignored, a video being clicked on or bypassed, or a product being purchased or passed over.
To make an impact with your headlines, mastering the art of rhetoric is essential. In this post, we'll explore various rhetorical devices and techniques that can help you create headlines that captivate your audience and drive engagement.
tl;dr : Headline Magician will help you craft the ultimate headline titles powered by rhetoric devices
Example with a high-end luxury organic zero-waste skincare brand
✍️ The Power of Alliteration
Alliteration is the repetition of the same consonant sound at the beginning of words in close proximity. This rhetorical device lends itself well to headlines, as it creates a memorable, rhythmic quality that can catch a reader's attention.
By using alliteration, you can make your headlines more engaging and easier to remember.
Examples:
"Crafting Compelling Content: A Comprehensive Course"
"Mastering the Art of Memorable Marketing"
🔁 The Appeal of Anaphora
Anaphora is the repetition of a word or phrase at the beginning of successive clauses. This rhetorical device emphasizes a particular idea or theme, making it more memorable and persuasive.
In headlines, anaphora can be used to create a sense of unity and coherence, which can draw readers in and pique their interest.
Examples:
"Create, Curate, Captivate: Your Guide to Social Media Success"
"Innovation, Inspiration, and Insight: The Future of AI"
🔄 The Intrigue of Inversion
Inversion is a rhetorical device where the normal order of words is reversed, often to create an emphasis or achieve a specific effect.
In headlines, inversion can generate curiosity and surprise, compelling readers to explore further.
Examples:
"Beneath the Surface: A Deep Dive into Ocean Conservation"
"Beyond the Stars: The Quest for Extraterrestrial Life"
⚖️ The Persuasive Power of Parallelism
Parallelism is a rhetorical device that involves using similar grammatical structures or patterns to create a sense of balance and symmetry.
In headlines, parallelism can make your message more memorable and impactful, as it creates a pleasing rhythm and flow that can resonate with readers.
Examples:
"Eat Well, Live Well, Be Well: The Ultimate Guide to Wellness"
"Learn, Lead, and Launch: A Blueprint for Entrepreneurial Success"
⏭️ The Emphasis of Ellipsis
Ellipsis is the omission of words, typically indicated by three periods (...), which suggests that there is more to the story.
In headlines, ellipses can create a sense of mystery and intrigue, enticing readers to click and discover what lies behind the headline.
Examples:
"The Secret to Success... Revealed"
"Unlocking the Power of Your Mind... A Step-by-Step Guide"
🎭 The Drama of Hyperbole
Hyperbole is a rhetorical device that involves exaggeration for emphasis or effect.
In headlines, hyperbole can grab the reader's attention by making bold, provocative claims that stand out from the competition. Be cautious with hyperbole, however, as overuse or excessive exaggeration can damage your credibility.
Examples:
"The Ultimate Guide to Mastering Any Skill in Record Time"
"Discover the Revolutionary Technique That Will Transform Your Life"
❓The Curiosity of Questions
Posing questions in your headlines can be an effective way to pique the reader's curiosity and encourage engagement.
Questions compel the reader to seek answers, making them more likely to click on your content. Additionally, questions can create a sense of connection between the content creator and the audience, fostering a sense of dialogue and discussion.
Examples:
"Are You Making These Common Mistakes in Your Marketing Strategy?"
"What's the Secret to Unlocking Your Creative Potential?"
💥 The Impact of Imperatives
Imperatives are commands or instructions that urge the reader to take action. By using imperatives in your headlines, you can create a sense of urgency and importance, making your content more compelling and actionable.
Examples:
"Master Your Time Management Skills Today"
"Transform Your Business with These Innovative Strategies"
💢 The Emotion of Exclamations
Exclamations are powerful rhetorical devices that can evoke strong emotions and convey a sense of excitement or urgency.
Including exclamations in your headlines can make them more attention-grabbing and shareable, increasing the chances of your content being read and circulated.
Examples:
"Unlock Your True Potential: Find Your Passion and Thrive!"
"Experience the Adventure of a Lifetime: Travel the World on a Budget!"
🎀 The Effectiveness of Euphemisms
Euphemisms are polite or indirect expressions used in place of harsher, more direct language.
In headlines, euphemisms can make your message more appealing and relatable, helping to soften potentially controversial or sensitive topics.
Examples:
"Navigating the Challenges of Modern Parenting"
"Redefining Success in a Fast-Paced World"
⚡Antithesis: The Power of Opposites
Antithesis involves placing two opposite words side-by-side, emphasizing their contrasts. This device can create a sense of tension and intrigue in headlines.
Examples:
"Once a day. Every day"
"Soft on skin. Kill germs"
"Mega power. Mini size."
To utilize antithesis, identify two opposing concepts related to your content and present them in a balanced manner.
🎨 Scesis Onomaton: The Art of Verbless Copy
Scesis onomaton is a rhetorical device that involves writing verbless copy, which quickens the pace and adds emphasis.
Example:
"7 days. 7 dollars. Full access."
To use scesis onomaton, remove verbs and focus on the essential elements of your headline.
🌟 Polyptoton: The Charm of Shared Roots
Polyptoton is the repeated use of words that share the same root, bewitching words into memorable phrases.
Examples:
"Real bread isn't made in factories. It's baked in bakeries"
"Lose your knack for losing things."
To employ polyptoton, identify words with shared roots that are relevant to your content.
✨ Asyndeton: The Elegance of Omission
Asyndeton involves the intentional omission of conjunctions, adding crispness, conviction, and elegance to your headlines.
Examples:
"You, Me, Sushi?"
"All the latte art, none of the environmental impact."
To use asyndeton, eliminate conjunctions and focus on the core message of your headline.
🔮 Tricolon: The Magic of Threes
Tricolon is a rhetorical device that uses the power of three, creating memorable and impactful headlines.
Examples:
"Show it, say it, send it"
"Eat Well, Live Well, Be Well."
To use tricolon, craft a headline with three key elements that emphasize your content's main message.
🔔 Epistrophe: The Chime of Repetition
Epistrophe involves the repetition of words or phrases at the end of successive clauses, adding a chime to your headlines.
Examples:
"Catch it. Bin it. Kill it."
"Joint friendly. Climate friendly. Family friendly."
To employ epistrophe, repeat a key phrase or word at the end of each clause.

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.

Sammy Abdullah
24 years ago
How to properly price SaaS
Price Intelligently put out amazing content on pricing your SaaS product. This blog's link to the whole report is worth reading. Our key takeaways are below.
Don't base prices on the competition. Competitor-based pricing has clear drawbacks. Their pricing approach is yours. Your company offers customers something unique. Otherwise, you wouldn't create it. This strategy is static, therefore you can't add value by raising prices without outpricing competitors. Look, but don't touch is the competitor-based moral. You want to know your competitors' prices so you're in the same ballpark, but they shouldn't guide your selections. Competitor-based pricing also drives down prices.
Value-based pricing wins. This is customer-based pricing. Value-based pricing looks outward, not inward or laterally at competitors. Your clients are the best source of pricing information. By valuing customer comments, you're focusing on buyers. They'll decide if your pricing and packaging are right. In addition to asking consumers about cost savings or revenue increases, look at data like number of users, usage per user, etc.
Value-based pricing increases prices. As you learn more about the client and your worth, you'll know when and how much to boost rates. Every 6 months, examine pricing.
Cloning top customers. You clone your consumers by learning as much as you can about them and then reaching out to comparable people or organizations. You can't accomplish this without knowing your customers. Segmenting and reproducing them requires as much detail as feasible. Offer pricing plans and feature packages for 4 personas. The top plan should state Contact Us. Your highest-value customers want more advice and support.
Question your 4 personas. What's the one item you can't live without? Which integrations matter most? Do you do analytics? Is support important or does your company self-solve? What's too cheap? What's too expensive?
Not everyone likes per-user pricing. SaaS organizations often default to per-user analytics. About 80% of companies utilizing per-user pricing should use an alternative value metric because their goods don't give more value with more users, so charging for them doesn't make sense.
At least 3:1 LTV/CAC. Break even on the customer within 2 years, and LTV to CAC is greater than 3:1. Because customer acquisition costs are paid upfront but SaaS revenues accrue over time, SaaS companies face an early financial shortfall while paying back the CAC.
ROI should be >20:1. Indeed. Ensure the customer's ROI is 20x the product's cost. Microsoft Office costs $80 a year, but consumers would pay much more to maintain it.
A/B Testing. A/B testing is guessing. When your pricing page varies based on assumptions, you'll upset customers. You don't have enough customers anyway. A/B testing optimizes landing pages, design decisions, and other site features when you know the problem but not pricing.
Don't discount. It cheapens the product, makes it permanent, and increases churn. By discounting, you're ruining your pricing analysis.
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