Security, privacy, and a strategy!

How to manage digital assets in worst-case scenarios is a perennial crypto concern. Since blockchain and bitcoin technology is very new, this hasn't been a major issue. Many early developers are still around, and many groups created around this technology are young and feel they have a lot of life remaining. This is why inheritance and estate planning in crypto should be handled promptly. As cryptocurrency's intrinsic worth rises, many people in the ecosystem are holding on to assets that might represent generational riches. With that much value, it's crucial to have a plan. Creating a solid plan entails several challenges.

• the initial hesitation in coming up with a plan

• The technical obstacles to ensuring the assets' security and privacy

• the passing of assets from a deceased or incompetent person

• Legal experts' lack of comprehension and/or understanding of how to handle and treat cryptocurrency.

This article highlights several challenges, a possible web3-native solution, and how to learn more.

The Challenge of Inheritance:

One of the biggest hurdles to inheritance planning is starting the conversation. As humans, we don't like to think about dying. Early adopters will experience crazy gains as cryptocurrencies become more popular. Creating a plan is crucial if you wish to pass on your riches to loved ones. Without a plan, the technical and legal issues I barely mentioned above would erode value by requiring costly legal fees and/or taxes, and you could lose everything if wallets and assets are not distributed appropriately (associated with the private keys). Raising awareness of the consequences of not having a plan should motivate people to make one.

Controlling Change:

Having an inheritance plan for your digital assets is crucial, but managing the guts and bolts poses a new set of difficulties. Privacy and security provided by maintaining your own wallet provide different issues than traditional finances and assets. Traditional finance is centralized (say a stock brokerage firm). You can assign another person to handle the transfer of your assets. In crypto, asset transfer is reimagined. One may suppose future transaction management is doable, but the user must consent, creating an impossible loop.

• I passed away and must send a transaction to the person I intended to deliver it to.

• I have to confirm or authorize the transaction, but I'm dead.

In crypto, scheduling a future transaction wouldn't function. To transfer the wallet and its contents, we'd need the private keys and/or seed phrase. Minimizing private key exposure is crucial to protecting your crypto from hackers, social engineering, and phishing. People have lost private keys after utilizing Life Hack-type tactics to secure them. People that break and hide their keys, lose them, or make them unreadable won't help with managing and/or transferring. This will require a derived solution.

Legal Challenges and Implications

Unlike routine cryptocurrency transfers and transactions, local laws may require special considerations. Even in the traditional world, estate/inheritance taxes, how assets will be split, and who executes the will must be considered. Many lawyers aren't crypto-savvy, which complicates the matter. There will be many hoops to jump through to safeguard your crypto and traditional assets and give them to loved ones.

Knowing RUFADAA/UFADAA, depending on your state, is vital for Americans. UFADAA offers executors and trustees access to online accounts (which crypto wallets would fall into). RUFADAA was changed to limit access to the executor to protect assets. RUFADAA outlines how digital assets are administered following death and incapacity in the US.

A Succession Solution

Having a will and talking about who would get what is the first step to having a solution, but using a Dad Mans Switch is a perfect tool for such unforeseen circumstances. As long as the switch's controller has control, nothing happens. Losing control of the switch initiates a state transition.

Subway or railway operations are examples. Modern control systems need the conductor to hold a switch to keep the train going. If they can't, the train stops.

Enter Sarcophagus

Sarcophagus is a decentralized dead man's switch built on Ethereum and Arweave. Sarcophagus allows actors to maintain control of their possessions even while physically unable to do so. Using a programmable dead man's switch and dual encryption, anything can be kept and passed on. This covers assets, secrets, seed phrases, and other use cases to provide authority and control back to the user and release trustworthy services from this work. Sarcophagus is built on a decentralized, transparent open source codebase. Sarcophagus is there if you're unprepared.

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

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Tesla Q2 earnings revealed unethical dealings.

As of end of Q2, we have converted approximately 75% of our Bitcoin purchases into fiat currency

That’s OK then, isn’t it?

Elon Musk, Tesla's CEO, is now untrustworthy.

It’s not about infidelity, it’s about doing the right thing

And what can we learn?

The Opening Remark

Musk tweets on his (and Tesla's) future goals.

Don’t worry, I’m not expecting you to read it.

What's crucial?

Tesla will not be selling any Bitcoin

The Situation as It Develops

2021 Tesla spent $1.5 billion on Bitcoin. In 2022, they sold 75% of the ownership for $946 million.

That’s a little bit of a waste of money, right?

Musk predicted the reverse would happen.

What gives? Why would someone say one thing, then do the polar opposite?

The Justification For Change

Tesla's public. They must follow regulations. When a corporation trades, they must record what happens.

At least this keeps Musk some way in line.

We now understand Musk and Tesla's actions.

Musk claimed that Tesla sold bitcoins to maximize cash given the unpredictability of COVID lockdowns in China.

Tesla may buy Bitcoin in the future, he said.

That’s fine then. He’s not knocking the NFT at least.

Tesla has moved investments into cash due to China lockdowns.

That doesn’t explain the 180° though

Musk's Tweet isn't company policy. Therefore, the CEO's change of heart reflects the organization. Look.

That's okay, since

Leaders alter their positions when circumstances change.

Leaders must adapt to their surroundings. This isn't embarrassing; it's a leadership prerequisite.

Yet

The Man

Someone stated if you're not in the office full-time, you need to explain yourself. He doesn't treat his employees like adults.

This is the individual mentioned in the quote.

If Elon was not happy, you knew it. Things could get nasty

also, He fired his helper for requesting a raise.

This public persona isn't good. Without mentioning his disastrous performances on Twitter (pedo dude) or Joe Rogan. This image sums up the odd Podcast appearance:

Which describes the man.

I wouldn’t trust this guy to feed a cat

What we can discover

When Musk's company bet on Bitcoin, what happened?

Exactly what we would expect

The company's position altered without the CEO's awareness. He seems uncaring.

This article is about how something happened, not what happened. Change of thinking requires contrition.

This situation is about a lack of respect- although you might argue that followers on Twitter don’t deserve any

Tesla fans call the sale a great move.

It's absurd.

As you were, then.

Conclusion

Good luck if you gamble.

When they pay off, congrats!

When wrong, admit it.

• You must take chances if you want to succeed.

• Risks don't always pay off.

Mr. Musk lacks insight and charisma to combine these two attributes.

I don’t like him, if you hadn’t figured.

It’s probably all of the cheating.

AI images are like funhouse mirrors.

Google's AI Blog introduced the puppy-slug in the summer of 2015.

Puppy-slug isn't a single image or character. "Puppy-slug" refers to Google's DeepDream's unsettling psychedelia. This tool uses convolutional neural networks to train models to recognize dataset entities. If researchers feed the model millions of dog pictures, the network will learn to recognize a dog.

DeepDream used neural networks to analyze and classify image data as well as generate its own images. DeepDream's early examples were created by training a convolutional network on dog images and asking it to add "dog-ness" to other images. The models analyzed images to find dog-like pixels and modified surrounding pixels to highlight them.

Puppy-slugs and other DeepDream images are ugly. Even when they don't trigger my trypophobia, they give me vertigo when my mind tries to reconcile familiar features and forms in unnatural, physically impossible arrangements. I feel like I've been poisoned by a forbidden mushroom or a noxious toad. I'm a Lovecraft character going mad from extradimensional exposure. They're gross!

Is this really how AIs see the world? This is possibly an even more unsettling topic that DeepDream raises than the blatant abjection of the images.

When these photographs originally circulated online, many friends were startled and scandalized. People imagined a computer's imagination would be literal, accurate, and boring. We didn't expect vivid hallucinations and organic-looking formations.

DeepDream's images didn't really show the machines' imaginations, at least not in the way that scared some people. DeepDream displays data visualizations. DeepDream reveals the "black box" of convolutional network training.

Some of these images look scary because the models don't "know" anything, at least not in the way we do.

These images are the result of advanced algorithms and calculators that compare pixel values. They can spot and reproduce trends from training data, but can't interpret it. If so, they'd know dogs have two eyes and one face per head. If machines can think creatively, they're keeping it quiet.

You could be forgiven for thinking otherwise, given OpenAI's Dall-impressive E's results. From a technological perspective, it's incredible.

Arthur C. Clarke once said, "Any sufficiently advanced technology is indistinguishable from magic." Dall-magic E's requires a lot of math, computer science, processing power, and research. OpenAI did a great job, and we should applaud them.

Dall-E and similar tools match words and phrases to image data to train generative models. Matching text to images requires sorting and defining the images. Untold millions of low-wage data entry workers, content creators optimizing images for SEO, and anyone who has used a Captcha to access a website make these decisions. These people could live and die without receiving credit for their work, even though the project wouldn't exist without them.

This technique produces images that are less like paintings and more like mirrors that reflect our own beliefs and ideals back at us, albeit via a very complex prism. Due to the limitations and biases that these models portray, we must exercise caution when viewing these images.

The issue was succinctly articulated by artist Mimi Onuoha in her piece "On Algorithmic Violence":

As we continue to see the rise of algorithms being used for civic, social, and cultural decision-making, it becomes that much more important that we name the reality that we are seeing. Not because it is exceptional, but because it is ubiquitous. Not because it creates new inequities, but because it has the power to cloak and amplify existing ones. Not because it is on the horizon, but because it is already here.

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.