What An Inverted Yield Curve Means For Investors
The yield spread between 10-year and 2-year US Treasury bonds has fallen below 0.2 percent, its lowest level since March 2020. A flattening or negative yield curve can be a bad sign for the economy.
What Is An Inverted Yield Curve?
In the yield curve, bonds of equal credit quality but different maturities are plotted. The most commonly used yield curve for US investors is a plot of 2-year and 10-year Treasury yields, which have yet to invert.
A typical yield curve has higher interest rates for future maturities. In a flat yield curve, short-term and long-term yields are similar. Inverted yield curves occur when short-term yields exceed long-term yields. Inversions of yield curves have historically occurred during recessions.
Inverted yield curves have preceded each of the past eight US recessions. The good news is they're far leading indicators, meaning a recession is likely not imminent.
Every US recession since 1955 has occurred between six and 24 months after an inversion of the two-year and 10-year Treasury yield curves, according to the San Francisco Fed. So, six months before COVID-19, the yield curve inverted in August 2019.
Looking Ahead
The spread between two-year and 10-year Treasury yields was 0.18 percent on Tuesday, the smallest since before the last US recession. If the graph above continues, a two-year/10-year yield curve inversion could occur within the next few months.
According to Bank of America analyst Stephen Suttmeier, the S&P 500 typically peaks six to seven months after the 2s-10s yield curve inverts, and the US economy enters recession six to seven months later.
Investors appear unconcerned about the flattening yield curve. This is in contrast to the iShares 20+ Year Treasury Bond ETF TLT +2.19% which was down 1% on Tuesday.
Inversion of the yield curve and rising interest rates have historically harmed stocks. Recessions in the US have historically coincided with or followed the end of a Federal Reserve rate hike cycle, not the start.
More on Economics & Investing

Justin Kuepper
3 years ago
Day Trading Introduction
Historically, only large financial institutions, brokerages, and trading houses could actively trade in the stock market. With instant global news dissemination and low commissions, developments such as discount brokerages and online trading have leveled the playing—or should we say trading—field. It's never been easier for retail investors to trade like pros thanks to trading platforms like Robinhood and zero commissions.
Day trading is a lucrative career (as long as you do it properly). But it can be difficult for newbies, especially if they aren't fully prepared with a strategy. Even the most experienced day traders can lose money.
So, how does day trading work?
Day Trading Basics
Day trading is the practice of buying and selling a security on the same trading day. It occurs in all markets, but is most common in forex and stock markets. Day traders are typically well educated and well funded. For small price movements in highly liquid stocks or currencies, they use leverage and short-term trading strategies.
Day traders are tuned into short-term market events. News trading is a popular strategy. Scheduled announcements like economic data, corporate earnings, or interest rates are influenced by market psychology. Markets react when expectations are not met or exceeded, usually with large moves, which can help day traders.
Intraday trading strategies abound. Among these are:
- Scalping: This strategy seeks to profit from minor price changes throughout the day.
- Range trading: To determine buy and sell levels, range traders use support and resistance levels.
- News-based trading exploits the increased volatility around news events.
- High-frequency trading (HFT): The use of sophisticated algorithms to exploit small or short-term market inefficiencies.
A Disputed Practice
Day trading's profit potential is often debated on Wall Street. Scammers have enticed novices by promising huge returns in a short time. Sadly, the notion that trading is a get-rich-quick scheme persists. Some daytrade without knowledge. But some day traders succeed despite—or perhaps because of—the risks.
Day trading is frowned upon by many professional money managers. They claim that the reward rarely outweighs the risk. Those who day trade, however, claim there are profits to be made. Profitable day trading is possible, but it is risky and requires considerable skill. Moreover, economists and financial professionals agree that active trading strategies tend to underperform passive index strategies over time, especially when fees and taxes are factored in.
Day trading is not for everyone and is risky. It also requires a thorough understanding of how markets work and various short-term profit strategies. Though day traders' success stories often get a lot of media attention, keep in mind that most day traders are not wealthy: Many will fail, while others will barely survive. Also, while skill is important, bad luck can sink even the most experienced day trader.
Characteristics of a Day Trader
Experts in the field are typically well-established professional day traders.
They usually have extensive market knowledge. Here are some prerequisites for successful day trading.
Market knowledge and experience
Those who try to day-trade without understanding market fundamentals frequently lose. Day traders should be able to perform technical analysis and read charts. Charts can be misleading if not fully understood. Do your homework and know the ins and outs of the products you trade.
Enough capital
Day traders only use risk capital they can lose. This not only saves them money but also helps them trade without emotion. To profit from intraday price movements, a lot of capital is often required. Most day traders use high levels of leverage in margin accounts, and volatile market swings can trigger large margin calls on short notice.
Strategy
A trader needs a competitive advantage. Swing trading, arbitrage, and trading news are all common day trading strategies. They tweak these strategies until they consistently profit and limit losses.
Strategy Breakdown:
Type | Risk | Reward
Swing Trading | High | High
Arbitrage | Low | Medium
Trading News | Medium | Medium
Mergers/Acquisitions | Medium | High
Discipline
A profitable strategy is useless without discipline. Many day traders lose money because they don't meet their own criteria. “Plan the trade and trade the plan,” they say. Success requires discipline.
Day traders profit from market volatility. For a day trader, a stock's daily movement is appealing. This could be due to an earnings report, investor sentiment, or even general economic or company news.
Day traders also prefer highly liquid stocks because they can change positions without affecting the stock's price. Traders may buy a stock if the price rises. If the price falls, a trader may decide to sell short to profit.
A day trader wants to trade a stock that moves (a lot).
Day Trading for a Living
Professional day traders can be self-employed or employed by a larger institution.
Most day traders work for large firms like hedge funds and banks' proprietary trading desks. These traders benefit from direct counterparty lines, a trading desk, large capital and leverage, and expensive analytical software (among other advantages). By taking advantage of arbitrage and news events, these traders can profit from less risky day trades before individual traders react.
Individual traders often manage other people’s money or simply trade with their own. They rarely have access to a trading desk, but they frequently have strong ties to a brokerage (due to high commissions) and other resources. However, their limited scope prevents them from directly competing with institutional day traders. Not to mention more risks. Individuals typically day trade highly liquid stocks using technical analysis and swing trades, with some leverage.
Day trading necessitates access to some of the most complex financial products and services. Day traders usually need:
Access to a trading desk
Traders who work for large institutions or manage large sums of money usually use this. The trading or dealing desk provides these traders with immediate order execution, which is critical during volatile market conditions. For example, when an acquisition is announced, day traders interested in merger arbitrage can place orders before the rest of the market.
News sources
The majority of day trading opportunities come from news, so being the first to know when something significant happens is critical. It has access to multiple leading newswires, constant news coverage, and software that continuously analyzes news sources for important stories.
Analytical tools
Most day traders rely on expensive trading software. Technical traders and swing traders rely on software more than news. This software's features include:
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Automatic pattern recognition: It can identify technical indicators like flags and channels, or more complex indicators like Elliott Wave patterns.
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Genetic and neural applications: These programs use neural networks and genetic algorithms to improve trading systems and make more accurate price predictions.
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Broker integration: Some of these apps even connect directly to the brokerage, allowing for instant and even automatic trade execution. This reduces trading emotion and improves execution times.
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Backtesting: This allows traders to look at past performance of a strategy to predict future performance. Remember that past results do not always predict future results.
Together, these tools give traders a competitive advantage. It's easy to see why inexperienced traders lose money without them. A day trader's earnings potential is also affected by the market in which they trade, their capital, and their time commitment.
Day Trading Risks
Day trading can be intimidating for the average investor due to the numerous risks involved. The SEC highlights the following risks of day trading:
Because day traders typically lose money in their first months of trading and many never make profits, they should only risk money they can afford to lose.
Trading is a full-time job that is stressful and costly: Observing dozens of ticker quotes and price fluctuations to spot market trends requires intense concentration. Day traders also spend a lot on commissions, training, and computers.
Day traders heavily rely on borrowing: Day-trading strategies rely on borrowed funds to make profits, which is why many day traders lose everything and end up in debt.
Avoid easy profit promises: Avoid “hot tips” and “expert advice” from day trading newsletters and websites, and be wary of day trading educational seminars and classes.
Should You Day Trade?
As stated previously, day trading as a career can be difficult and demanding.
- First, you must be familiar with the trading world and know your risk tolerance, capital, and goals.
- Day trading also takes a lot of time. You'll need to put in a lot of time if you want to perfect your strategies and make money. Part-time or whenever isn't going to cut it. You must be fully committed.
- If you decide trading is for you, remember to start small. Concentrate on a few stocks rather than jumping into the market blindly. Enlarging your trading strategy can result in big losses.
- Finally, keep your cool and avoid trading emotionally. The more you can do that, the better. Keeping a level head allows you to stay focused and on track.
If you follow these simple rules, you may be on your way to a successful day trading career.
Is Day Trading Illegal?
Day trading is not illegal or unethical, but it is risky. Because most day-trading strategies use margin accounts, day traders risk losing more than they invest and becoming heavily in debt.
How Can Arbitrage Be Used in Day Trading?
Arbitrage is the simultaneous purchase and sale of a security in multiple markets to profit from small price differences. Because arbitrage ensures that any deviation in an asset's price from its fair value is quickly corrected, arbitrage opportunities are rare.
Why Don’t Day Traders Hold Positions Overnight?
Day traders rarely hold overnight positions for several reasons: Overnight trades require more capital because most brokers require higher margin; stocks can gap up or down on overnight news, causing big trading losses; and holding a losing position overnight in the hope of recovering some or all of the losses may be against the trader's core day-trading philosophy.
What Are Day Trader Margin Requirements?
Regulation D requires that a pattern day trader client of a broker-dealer maintain at all times $25,000 in equity in their account.
How Much Buying Power Does Day Trading Have?
Buying power is the total amount of funds an investor has available to trade securities. FINRA rules allow a pattern day trader to trade up to four times their maintenance margin excess as of the previous day's close.
The Verdict
Although controversial, day trading can be a profitable strategy. Day traders, both institutional and retail, keep the markets efficient and liquid. Though day trading is still popular among novice traders, it should be left to those with the necessary skills and resources.
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.
Chritiaan Hetzner
3 years ago
Mystery of the $1 billion'meme stock' that went to $400 billion in days
Who is AMTD Digital?
An unknown Hong Kong corporation joined the global megacaps worth over $500 billion on Tuesday.
The American Depository Share (ADS) with the ticker code HKD gapped at the open, soaring 25% over the previous closing price as trading began, before hitting an intraday high of $2,555.
At its peak, its market cap was almost $450 billion, more than Facebook parent Meta or Alibaba.
Yahoo Finance reported a daily volume of 350,500 shares, the lowest since the ADS began trading and much below the average of 1.2 million.
Despite losing a fifth of its value on Wednesday, it's still worth more than Toyota, Nike, McDonald's, or Walt Disney.
The company sold 16 million shares at $7.80 each in mid-July, giving it a $1 billion market valuation.
Why the boom?
That market cap seems unjustified.
According to SEC reports, its income-generating assets barely topped $400 million in March. Fortune's emails and calls went unanswered.
Website discloses little about company model. Its one-minute business presentation film uses a Star Wars–like design to sell the company as a "one-stop digital solutions platform in Asia"
The SEC prospectus explains.
AMTD Digital sells a "SpiderNet Ecosystems Solutions" kind of club membership that connects enterprises. This is the bulk of its $25 million annual revenue in April 2021.
Pretax profits have been higher than top line over the past three years due to fair value accounting gains on Appier, DayDayCook, WeDoctor, and five Asian fintechs.
AMTD Group, the company's parent, specializes in investment banking, hotel services, luxury education, and media and entertainment. AMTD IDEA, a $14 billion subsidiary, is also traded on the NYSE.
“Significant volatility”
Why AMTD Digital listed in the U.S. is unknown, as it informed investors in its share offering prospectus that could delist under SEC guidelines.
Beijing's red tape prevents the Sarbanes-Oxley Board from inspecting its Chinese auditor.
This frustrates Chinese stock investors. If the U.S. and China can't achieve a deal, 261 Chinese companies worth $1.3 trillion might be delisted.
Calvin Choi left UBS to become AMTD Group's CEO.
His capitalist background and status as a Young Global Leader with the World Economic Forum don't stop him from praising China's Communist party or celebrating the "glory and dream of the Great Rejuvenation of the Chinese nation" a century after its creation.
Despite having an executive vice chairman with a record of battling corruption and ties to Carrie Lam, Beijing's previous proconsul in Hong Kong, Choi is apparently being targeted for a two-year industry ban by the city's securities regulator after an investor accused Choi of malfeasance.
Some CMIG-funded initiatives produced money, but he didn't give us the proceeds, a corporate official told China's Caixin in October 2020. We don't know if he misappropriated or lost some money.
A seismic anomaly
In fundamental analysis, where companies are valued based on future cash flows, AMTD Digital's mind-boggling market cap is a statistical aberration that should occur once every hundred years.
AMTD Digital doesn't know why it's so valuable. In a thank-you letter to new shareholders, it said it was confused by the stock's performance.
Since its IPO, the company has seen significant ADS price volatility and active trading volume, it said Tuesday. "To our knowledge, there have been no important circumstances, events, or other matters since the IPO date."
Permabears awoke after the jump. Jim Chanos asked if "we're all going to ignore the $400 billion meme stock in the room," while Nate Anderson called AMTD Group "sketchy."
It happened the same day SEC Chair Gary Gensler praised the 20th anniversary of the Sarbanes-Oxley Act, aimed to restore trust in America's financial markets after the Enron and WorldCom accounting fraud scandals.
The run-up revived unpleasant memories of Robinhood's decision to limit retail investors' ability to buy GameStop, regarded as a measure to protect hedge funds invested in the meme company.
Why wasn't HKD's buy button removed? Because retail wasn't behind it?" tweeted Gensler on Tuesday. "Real stock fraud. "You're worthless."
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ANTHONY P.
3 years ago
Startups are difficult. Streamlining the procedure for creating the following unicorn.
New ventures are exciting. It's fun to imagine yourself rich, successful, and famous (if that's your thing). How you'll help others and make your family proud. This excitement can pull you forward for years, even when you intuitively realize that the path you're on may not lead to your desired success.
Know when to change course. Switching course can mean pivoting or changing direction.
In this not-so-short blog, I'll describe the journey of building your dream. And how the journey might look when you think you're building your dream, but fall short of that vision. Both can feel similar in the beginning, but there are subtle differences.
Let’s dive in.
How an exciting journey to a dead end looks and feels.
You want to help many people. You're business-minded, creative, and ambitious. You jump into entrepreneurship. You're excited, free, and in control.
I'll use tech as an example because that's what I know best, but this applies to any entrepreneurial endeavor.
So you start learning the basics of your field, say coding/software development. You read books, take courses, and may even join a bootcamp. You start practicing, and the journey begins. Once you reach a certain level of skill (which can take months, usually 12-24), you gain the confidence to speak with others in the field and find common ground. You might attract a co-founder this way with time. You and this person embark on a journey (Tip: the idea you start with is rarely the idea you end with).
Amateur mistake #1: You spend months building a product before speaking to customers.
Building something pulls you forward blindly. You make mistakes, avoid customers, and build with your co-founder or small team in the dark for months, usually 6-12 months.
You're excited when the product launches. We'll be billionaires! The market won't believe it. This excites you and the team. Launch.
….
Nothing happens.
Some people may sign up out of pity, only to never use the product or service again.
You and the team are confused, discouraged and in denial. They don't get what we've built yet. We need to market it better, we need to talk to more investors, someone will understand our vision.
This is a hopeless path, and your denial could last another 6 months. If you're lucky, while talking to consumers and investors (which you should have done from the start), someone who has been there before would pity you and give you an idea to pivot into that can create income.
Suppose you get this idea and pivot your business. Again, you've just pivoted into something limited by what you've already built. It may be a revenue-generating idea, but it's rarely new. Now you're playing catch-up, doing something others are doing but you can do better. (Tip #2: Don't be late.) Your chances of winning are slim, and you'll likely never catch up.
You're finally seeing revenue and feel successful. You can compete, but if you're not a first mover, you won't earn enough over time. You'll get by or work harder than ever to earn what a skilled trade could provide. You didn't go into business to stress out and make $100,000 or $200,000 a year. When you can make the same amount by becoming a great software developer, electrician, etc.
You become stuck. Either your firm continues this way for years until you realize there isn't enough growth to recruit a strong team and remove yourself from day-to-day operations due to competition. Or a catastrophic economic event forces you to admit that what you were building wasn't new and unique and wouldn't get you where you wanted to be.
This realization could take 6-10 years. No kidding.
The good news is, you’ve learned a lot along the way and this information can be used towards your next venture (if you have the energy).
Key Lesson: Don’t build something if you aren’t one of the first in the space building it just for the sake of building something.
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Let's discuss what it's like to build something that can make your dream come true.
Case 2: Building something the market loves is difficult but rewarding.
It starts with a problem that hasn't been adequately solved for a long time but is now solvable due to technology. Or a new problem due to a change in how things are done.
Let's examine each example.
Example #1: Mass communication. The problem is now solvable due to some technological breakthrough.
Twitter — One of the first web 2 companies that became successful with the rise of smart mobile computing.
People can share their real-time activities via mobile device with friends, family, and strangers. Web 2 and smartphones made it easy and fun.
Example #2: A new problem has emerged due to some change in the way things are conducted.
Zoom- A web-conferencing company that reached massive success due to the movement towards “work from home”, remote/hybrid work forces.
Online web conferencing allows for face-to-face communication.
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These two examples show how to build a unicorn-type company. It's a mix of solving the right problem at the right time, either through a technological breakthrough that opens up new opportunities or by fundamentally changing how people do things.
Let's find these opportunities.
Start by examining problems, such as how the world has changed and how we can help it adapt. It can also be both. Start team brainstorming. Research technologies, current world-trends, use common sense, and make a list. Then, choose the top 3 that you're most excited about and seem most workable based on your skillsets, values, and passion.
Once you have this list, create the simplest MVP you can and test it with customers. The prototype can be as simple as a picture or diagram of user flow and end-user value. No coding required. Market-test. Twitter's version 1 was simple. It was a web form that asked, "What are you doing?" Then publish it from your phone. A global status update, wherever you are. Currently, this company has a $50 billion market cap.
Here's their MVP screenshot.
Small things grow. Tiny. Simplify.
Remember Frequency and Value when brainstorming. Your product is high frequency (Twitter, Instagram, Snapchat, TikTok) or high value (Airbnb for renting travel accommodations), or both (Gmail).
Once you've identified product ideas that meet the above criteria, they're simple, have a high frequency of use, or provide deep value. You then bring it to market in the simplest, most cost-effective way. You can sell a half-working prototype with imagination and sales skills. You need just enough of a prototype to convey your vision to a user or customer.
With this, you can approach real people. This will do one of three things: give you a green light to continue on your vision as is, show you that there is no opportunity and people won't use it, or point you in a direction that is a blend of what you've come up with and what the customer / user really wants, and you update the prototype and go back to the maze. Repeat until you have enough yeses and conviction to build an MVP.

Jay Peters
3 years ago
Apple AR/VR heaset
Apple is said to have opted for a standalone AR/VR headset over a more powerful tethered model.
It has had a tumultuous history.
Apple's alleged mixed reality headset appears to be the worst-kept secret in tech, and a fresh story from The Information is jam-packed with details regarding the device's rocky development.
Apple's decision to use a separate headgear is one of the most notable aspects of the story. Apple had yet to determine whether to pursue a more powerful VR headset that would be linked with a base station or a standalone headset. According to The Information, Apple officials chose the standalone product over the version with the base station, which had a processor that later arrived as the M1 Ultra. In 2020, Bloomberg published similar information.
That decision appears to have had a long-term impact on the headset's development. "The device's many processors had already been in development for several years by the time the choice was taken, making it impossible to go back to the drawing board and construct, say, a single chip to handle all the headset's responsibilities," The Information stated. "Other difficulties, such as putting 14 cameras on the headset, have given hardware and algorithm engineers stress."
Jony Ive remained to consult on the project's design even after his official departure from Apple, according to the story. Ive "prefers" a wearable battery, such as that offered by Magic Leap. Other prototypes, according to The Information, placed the battery in the headset's headband, and it's unknown which will be used in the final design.
The headset was purportedly shown to Apple's board of directors last week, indicating that a public unveiling is imminent. However, it is possible that it will not be introduced until later this year, and it may not hit shop shelves until 2023, so we may have to wait a bit to try it.
For further down the line, Apple is working on a pair of AR spectacles that appear like Ray-Ban wayfarer sunglasses, but according to The Information, they're "still several years away from release." (I'm interested to see how they compare to Meta and Ray-Bans' true wayfarer-style glasses.)

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.
