Integrity
Write
Loading...
Yogesh Rawal

Yogesh Rawal

3 years ago

Blockchain to solve growing privacy challenges

Most online activity is now public. Businesses collect, store, and use our personal data to improve sales and services.

In 2014, Uber executives and employees were accused of spying on customers using tools like maps. Another incident raised concerns about the use of ‘FaceApp'. The app was created by a small Russian company, and the photos can be used in unexpected ways. The Cambridge Analytica scandal exposed serious privacy issues. The whole incident raised questions about how governments and businesses should handle data. Modern technologies and practices also make it easier to link data to people.

As a result, governments and regulators have taken steps to protect user data. The General Data Protection Regulation (GDPR) was introduced by the EU to address data privacy issues. The law governs how businesses collect and process user data. The Data Protection Bill in India and the General Data Protection Law in Brazil are similar.
Despite the impact these regulations have made on data practices, a lot of distance is yet to cover.

Blockchain's solution

Blockchain may be able to address growing data privacy concerns. The technology protects our personal data by providing security and anonymity. The blockchain uses random strings of numbers called public and private keys to maintain privacy. These keys allow a person to be identified without revealing their identity. Blockchain may be able to ensure data privacy and security in this way. Let's dig deeper.

Financial transactions

Online payments require third-party services like PayPal or Google Pay. Using blockchain can eliminate the need to trust third parties. Users can send payments between peers using their public and private keys without providing personal information to a third-party application. Blockchain will also secure financial data.

Healthcare data

Blockchain technology can give patients more control over their data. There are benefits to doing so. Once the data is recorded on the ledger, patients can keep it secure and only allow authorized access. They can also only give the healthcare provider part of the information needed.

The major challenge

We tried to figure out how blockchain could help solve the growing data privacy issues. However, using blockchain to address privacy concerns has significant drawbacks. Blockchain is not designed for data privacy. A ‘distributed' ledger will be used to store the data. Another issue is the immutability of blockchain. Data entered into the ledger cannot be changed or deleted. It will be impossible to remove personal data from the ledger even if desired.

MIT's Enigma Project aims to solve this. Enigma's ‘Secret Network' allows nodes to process data without seeing it. Decentralized applications can use Secret Network to use encrypted data without revealing it.

Another startup, Oasis Labs, uses blockchain to address data privacy issues. They are working on a system that will allow businesses to protect their customers' data. 

Conclusion

Blockchain technology is already being used. Several governments use blockchain to eliminate centralized servers and improve data security. In this information age, it is vital to safeguard our data. How blockchain can help us in this matter is still unknown as the world explores the technology.

More on Web3 & Crypto

Shan Vernekar

Shan Vernekar

3 years ago

How the Ethereum blockchain's transactions are carried out

Overview

Ethereum blockchain is a network of nodes that validate transactions. Any network node can be queried for blockchain data for free. To write data as a transition requires processing and writing to each network node's storage. Fee is paid in ether and is also called as gas.

We'll examine how user-initiated transactions flow across the network and into the blockchain.

Flow of transactions

  • A user wishes to move some ether from one external account to another. He utilizes a cryptocurrency wallet for this (like Metamask), which is a browser extension.

  • The user enters the desired transfer amount and the external account's address. He has the option to choose the transaction cost he is ready to pay.

  • Wallet makes use of this data, signs it with the user's private key, and writes it to an Ethereum node. Services such as Infura offer APIs that enable writing data to nodes. One of these services is used by Metamask. An example transaction is shown below. Notice the “to” address and value fields.

var rawTxn = {
    nonce: web3.toHex(txnCount),
    gasPrice: web3.toHex(100000000000),
    gasLimit: web3.toHex(140000),
    to: '0x633296baebc20f33ac2e1c1b105d7cd1f6a0718b',
    value: web3.toHex(0),
    data: '0xcc9ab24952616d6100000000000000000000000000000000000000000000000000000000'
};
  • The transaction is written to the target Ethereum node's local TRANSACTION POOL. It informed surrounding nodes of the new transaction, and those nodes reciprocated. Eventually, this transaction is received by and written to each node's local TRANSACTION pool.

  • The miner who finds the following block first adds pending transactions (with a higher gas cost) from the nearby TRANSACTION POOL to the block.

  • The transactions written to the new block are verified by other network nodes.

  • A block is added to the main blockchain after there is consensus and it is determined to be genuine. The local blockchain is updated with the new node by additional nodes as well.

  • Block mining begins again next.

The image above shows how transactions go via the network and what's needed to submit them to the main block chain.

References

ethereum.org/transactions How Ethereum transactions function, their data structure, and how to send them via app. ethereum.org

Faisal Khan

Faisal Khan

2 years ago

4 typical methods of crypto market manipulation

Credit: Getty Images/Cemile Bingol

Market fraud

Due to its decentralized and fragmented character, the crypto market has integrity difficulties.

Cryptocurrencies are an immature sector, therefore market manipulation becomes a bigger issue. Many research have attempted to uncover these abuses. CryptoCompare's newest one highlights some of the industry's most typical scams.

Why are these concerns so common in the crypto market? First, even the largest centralized exchanges remain unregulated due to industry immaturity. A low-liquidity market segment makes an attack more harmful. Finally, market surveillance solutions not implemented reduce transparency.

In CryptoCompare's latest exchange benchmark, 62.4% of assessed exchanges had a market surveillance system, although only 18.1% utilised an external solution. To address market integrity, this measure must improve dramatically. Before discussing the report's malpractices, note that this is not a full list of attacks and hacks.

Clean Trading

An investor buys and sells concurrently to increase the asset's price. Centralized and decentralized exchanges show this misconduct. 23 exchanges have a volume-volatility correlation < 0.1 during the previous 100 days, according to CryptoCompares. In August 2022, Exchange A reported $2.5 trillion in artificial and/or erroneous volume, up from $33.8 billion the month before.

Spoofing

Criminals create and cancel fake orders before they can be filled. Since manipulators can hide in larger trading volumes, larger exchanges have more spoofing. A trader placed a 20.8 BTC ask order at $19,036 when BTC was trading at $19,043. BTC declined 0.13% to $19,018 in a minute. At 18:48, the trader canceled the ask order without filling it.

Front-Running

Most cryptocurrency front-running involves inside trading. Traditional stock markets forbid this. Since most digital asset information is public, this is harder. Retailers could utilize bots to front-run.

CryptoCompare found digital wallets of people who traded like insiders on exchange listings. The figure below shows excess cumulative anomalous returns (CAR) before a coin listing on an exchange.

Finally, LAYERING is a sequence of spoofs in which successive orders are put along a ladder of greater (layering offers) or lower (layering bids) values. The paper concludes with recommendations to mitigate market manipulation. Exchange data transparency, market surveillance, and regulatory oversight could reduce manipulative tactics.

Vitalik

Vitalik

3 years ago

Fairness alternatives to selling below market clearing prices (or community sentiment, or fun)

When a seller has a limited supply of an item in high (or uncertain and possibly high) demand, they frequently set a price far below what "the market will bear." As a result, the item sells out quickly, with lucky buyers being those who tried to buy first. This has happened in the Ethereum ecosystem, particularly with NFT sales and token sales/ICOs. But this phenomenon is much older; concerts and restaurants frequently make similar choices, resulting in fast sell-outs or long lines.

Why do sellers do this? Economists have long wondered. A seller should sell at the market-clearing price if the amount buyers are willing to buy exactly equals the amount the seller has to sell. If the seller is unsure of the market-clearing price, they should sell at auction and let the market decide. So, if you want to sell something below market value, don't do it. It will hurt your sales and it will hurt your customers. The competitions created by non-price-based allocation mechanisms can sometimes have negative externalities that harm third parties, as we will see.

However, the prevalence of below-market-clearing pricing suggests that sellers do it for good reason. And indeed, as decades of research into this topic has shown, there often are. So, is it possible to achieve the same goals with less unfairness, inefficiency, and harm?

Selling at below market-clearing prices has large inefficiencies and negative externalities

An item that is sold at market value or at an auction allows someone who really wants it to pay the high price or bid high in the auction. So, if a seller sells an item below market value, some people will get it and others won't. But the mechanism deciding who gets the item isn't random, and it's not always well correlated with participant desire. It's not always about being the fastest at clicking buttons. Sometimes it means waking up at 2 a.m. (but 11 p.m. or even 2 p.m. elsewhere). Sometimes it's just a "auction by other means" that's more chaotic, less efficient, and has far more negative externalities.

There are many examples of this in the Ethereum ecosystem. Let's start with the 2017 ICO craze. For example, an ICO project would set the price of the token and a hard maximum for how many tokens they are willing to sell, and the sale would start automatically at some point in time. The sale ends when the cap is reached.

So what? In practice, these sales often ended in 30 seconds or less. Everyone would start sending transactions in as soon as (or just before) the sale started, offering higher and higher fees to encourage miners to include their transaction first. Instead of the token seller receiving revenue, miners receive it, and the sale prices out all other applications on-chain.

The most expensive transaction in the BAT sale set a fee of 580,000 gwei, paying a fee of $6,600 to get included in the sale.

Many ICOs after that tried various strategies to avoid these gas price auctions; one ICO notably had a smart contract that checked the transaction's gasprice and rejected it if it exceeded 50 gwei. But that didn't solve the issue. Buyers hoping to game the system sent many transactions hoping one would get through. An auction by another name, clogging the chain even more.

ICOs have recently lost popularity, but NFTs and NFT sales have risen in popularity. But the NFT space didn't learn from 2017; they do fixed-quantity sales just like ICOs (eg. see the mint function on lines 97-108 of this contract here). So what?

That's not the worst; some NFT sales have caused gas price spikes of up to 2000 gwei.

High gas prices from users fighting to get in first by sending higher and higher transaction fees. An auction renamed, pricing out all other applications on-chain for 15 minutes.

So why do sellers sometimes sell below market price?

Selling below market value is nothing new, and many articles, papers, and podcasts have written (and sometimes bitterly complained) about the unwillingness to use auctions or set prices to market-clearing levels.

Many of the arguments are the same for both blockchain (NFTs and ICOs) and non-blockchain examples (popular restaurants and concerts). Fairness and the desire not to exclude the poor, lose fans or create tension by being perceived as greedy are major concerns. The 1986 paper by Kahneman, Knetsch, and Thaler explains how fairness and greed can influence these decisions. I recall that the desire to avoid perceptions of greed was also a major factor in discouraging the use of auction-like mechanisms in 2017.

Aside from fairness concerns, there is the argument that selling out and long lines create a sense of popularity and prestige, making the product more appealing to others. Long lines should have the same effect as high prices in a rational actor model, but this is not the case in reality. This applies to ICOs and NFTs as well as restaurants. Aside from increasing marketing value, some people find the game of grabbing a limited set of opportunities first before everyone else is quite entertaining.

But there are some blockchain-specific factors. One argument for selling ICO tokens below market value (and one that persuaded the OmiseGo team to adopt their capped sale strategy) is community dynamics. The first rule of community sentiment management is to encourage price increases. People are happy if they are "in the green." If the price drops below what the community members paid, they are unhappy and start calling you a scammer, possibly causing a social media cascade where everyone calls you a scammer.

This effect can only be avoided by pricing low enough that post-launch market prices will almost certainly be higher. But how do you do this without creating a rush for the gates that leads to an auction?

Interesting solutions

It's 2021. We have a blockchain. The blockchain is home to a powerful decentralized finance ecosystem, as well as a rapidly expanding set of non-financial tools. The blockchain also allows us to reset social norms. Where decades of economists yelling about "efficiency" failed, blockchains may be able to legitimize new uses of mechanism design. If we could use our more advanced tools to create an approach that more directly solves the problems, with fewer side effects, wouldn't that be better than fiddling with a coarse-grained one-dimensional strategy space of selling at market price versus below market price?

Begin with the goals. We'll try to cover ICOs, NFTs, and conference tickets (really a type of NFT) all at the same time.

1. Fairness: don't completely exclude low-income people from participation; give them a chance. The goal of token sales is to avoid high initial wealth concentration and have a larger and more diverse initial token holder community.

2. Don’t create races: Avoid situations where many people rush to do the same thing and only a few get in (this is the type of situation that leads to the horrible auctions-by-another-name that we saw above).

3. Don't require precise market knowledge: the mechanism should work even if the seller has no idea how much demand exists.

4. Fun: The process of participating in the sale should be fun and game-like, but not frustrating.

5. Give buyers positive expected returns: in the case of a token (or an NFT), buyers should expect price increases rather than decreases. This requires selling below market value.
Let's start with (1). From Ethereum's perspective, there is a simple solution. Use a tool designed for the job: proof of personhood protocols! Here's one quick idea:

Mechanism 1 Each participant (verified by ID) can buy up to ‘’X’’ tokens at price P, with the option to buy more at an auction.

With the per-person mechanism, buyers can get positive expected returns for the portion sold through the per-person mechanism, and the auction part does not require sellers to understand demand levels. Is it race-free? The number of participants buying through the per-person pool appears to be high. But what if the per-person pool isn't big enough to accommodate everyone?

Make the per-person allocation amount dynamic.

Mechanism 2 Each participant can deposit up to X tokens into a smart contract to declare interest. Last but not least, each buyer receives min(X, N / buyers) tokens, where N is the total sold through the per-person pool (some other amount can also be sold by auction). The buyer gets their deposit back if it exceeds the amount needed to buy their allocation.
No longer is there a race condition based on the number of buyers per person. No matter how high the demand, it's always better to join sooner rather than later.

Here's another idea if you like clever game mechanics with fancy quadratic formulas.

Mechanism 3 Each participant can buy X units at a price P X 2 up to a maximum of C tokens per buyer. C starts low and gradually increases until enough units are sold.

The quantity allocated to each buyer is theoretically optimal, though post-sale transfers will degrade this optimality over time. Mechanisms 2 and 3 appear to meet all of the above objectives. They're not perfect, but they're good starting points.

One more issue. For fixed and limited supply NFTs, the equilibrium purchased quantity per participant may be fractional (in mechanism 2, number of buyers > N, and in mechanism 3, setting C = 1 may already lead to over-subscription). With fractional sales, you can offer lottery tickets: if there are N items available, you have a chance of N/number of buyers of getting the item, otherwise you get a refund. For a conference, groups could bundle their lottery tickets to guarantee a win or a loss. The certainty of getting the item can be auctioned.

The bottom tier of "sponsorships" can be used to sell conference tickets at market rate. You may end up with a sponsor board full of people's faces, but is that okay? After all, John Lilic was on EthCC's sponsor board!

Simply put, if you want to be reliably fair to people, you need an input that explicitly measures people. Authentication protocols do this (and if desired can be combined with zero knowledge proofs to ensure privacy). So we should combine the efficiency of market and auction-based pricing with the equality of proof of personhood mechanics.

Answers to possible questions

Q: Won't people who don't care about your project buy the item and immediately resell it?

A: Not at first. Meta-games take time to appear in practice. If they do, making them untradeable for a while may help mitigate the damage. Using your face to claim that your previous account was hacked and that your identity, including everything in it, should be moved to another account works because proof-of-personhood identities are untradeable.

Q: What if I want to make my item available to a specific community?

A: Instead of ID, use proof of participation tokens linked to community events. Another option, also serving egalitarian and gamification purposes, is to encrypt items within publicly available puzzle solutions.

Q: How do we know they'll accept? Strange new mechanisms have previously been resisted.

A: Having economists write screeds about how they "should" accept a new mechanism that they find strange is difficult (or even "equity"). However, abrupt changes in context effectively reset people's expectations. So the blockchain space is the best place to try this. You could wait for the "metaverse", but it's possible that the best version will run on Ethereum anyway, so start now.

You might also like

Protos

Protos

3 years ago

Plagiarism on OpenSea: humans and computers

OpenSea, a non-fungible token (NFT) marketplace, is fighting plagiarism. A new “two-pronged” approach will aim to root out and remove copies of authentic NFTs and changes to its blue tick verified badge system will seek to enhance customer confidence.

According to a blog post, the anti-plagiarism system will use algorithmic detection of “copymints” with human reviewers to keep it in check.

Last year, NFT collectors were duped into buying flipped images of the popular BAYC collection, according to The Verge. The largest NFT marketplace had to remove its delay pay minting service due to an influx of copymints.

80% of NFTs removed by the platform were minted using its lazy minting service, which kept the digital asset off-chain until the first purchase.

NFTs copied from popular collections are opportunistic money-grabs. Right-click, save, and mint the jacked JPEGs that are then flogged as an authentic NFT.

The anti-plagiarism system will scour OpenSea's collections for flipped and rotated images, as well as other undescribed permutations. The lack of detail here may be a deterrent to scammers, or it may reflect the new system's current rudimentary nature.

Thus, human detectors will be needed to verify images flagged by the detection system and help train it to work independently.

“Our long-term goal with this system is two-fold: first, to eliminate all existing copymints on OpenSea, and second, to help prevent new copymints from appearing,” it said.

“We've already started delisting identified copymint collections, and we'll continue to do so over the coming weeks.”

It works for Twitter, why not OpenSea

OpenSea is also changing account verification. Early adopters will be invited to apply for verification if their NFT stack is worth $100 or more. OpenSea plans to give the blue checkmark to people who are active on Twitter and Discord.

This is just the beginning. We are committed to a future where authentic creators can be verified, keeping scammers out.

Also, collections with a lot of hype and sales will get a blue checkmark. For example, a new NFT collection sold by the verified BAYC account will have a blue badge to verify its legitimacy.

New requests will be responded to within seven days, according to OpenSea.

These programs and products help protect creators and collectors while ensuring our community can confidently navigate the world of NFTs.

By elevating authentic content and removing plagiarism, these changes improve trust in the NFT ecosystem, according to OpenSea.

OpenSea is indeed catching up with the digital art economy. Last August, DevianArt upgraded its AI image recognition system to find stolen tokenized art on marketplaces like OpenSea.

It scans all uploaded art and compares it to “public blockchain events” like Ethereum NFTs to detect stolen art.

Victoria Kurichenko

Victoria Kurichenko

3 years ago

Updates From Google For Content Producers What You Should Know Is This

People-first update.

Image credit: Shutterstock. Image edited in Canva

Every Google upgrade causes website owners to panic.

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

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

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

Now, for some (hopefully) exciting news.

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

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

The algorithm generates and analyzes search results, not humans.

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

Google's content update aims to:

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

Isn't it a noble goal?

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

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

Let's first define people-first content.

What does "people-first-content" mean?

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

Like others, I read it from the term.

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

Google gives explicit instructions for creating people-first content.

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

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

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

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

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

  5. Are readers happy after reading your content?

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

As an SEO writer, I'm not scared.

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

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

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

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

This does not imply that SEO is obsolete.

Google:

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

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

  • meeting user needs

  • best practices for SEO

Always read official guidelines, not unsolicited suggestions.

SEO will work till search engines die.

How to use the update

Google said the changes will arrive in August 2022.

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

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

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

Google affirmed plans to extend to other languages.

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

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

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.

A mathematical expression/formula in the Linux codebase, a screenshot by the author

Inbuilt max and min functions can minimize verbose if statements.

Reducing a verbose nested-if with the min function in Neutralinojs, a screenshot by the author

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.

GetWindowRect outputs an LPRECT geometric object, a screenshot by the author

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):

The Git codebase defines a function with logarithmic time complexity, a screenshot by the author

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

A utility function that uses ceil, a screenshot by the author

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.