More on Technology
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.
Will Lockett
2 years ago
The world will be changed by this molten salt battery.
Four times the energy density and a fraction of lithium-cost ion's
As the globe abandons fossil fuels, batteries become more important. EVs, solar, wind, tidal, wave, and even local energy grids will use them. We need a battery revolution since our present batteries are big, expensive, and detrimental to the environment. A recent publication describes a battery that solves these problems. But will it be enough?
Sodium-sulfur molten salt battery. It has existed for a long time and uses molten salt as an electrolyte (read more about molten salt batteries here). These batteries are cheaper, safer, and more environmentally friendly because they use less eco-damaging materials, are non-toxic, and are non-flammable.
Previous molten salt batteries used aluminium-sulphur chemistries, which had a low energy density and required high temperatures to keep the salt liquid. This one uses a revolutionary sodium-sulphur chemistry and a room-temperature-melting salt, making it more useful, affordable, and eco-friendly. To investigate this, researchers constructed a button-cell prototype and tested it.
First, the battery was 1,017 mAh/g. This battery is four times as energy dense as high-density lithium-ion batteries (250 mAh/g).
No one knows how much this battery would cost. A more expensive molten-salt battery costs $15 per kWh. Current lithium-ion batteries cost $132/kWh. If this new molten salt battery costs the same as present cells, it will be 90% cheaper.
This room-temperature molten salt battery could be utilized in an EV. Cold-weather heaters just need a modest backup battery.
The ultimate EV battery? If used in a Tesla Model S, you could install four times the capacity with no weight gain, offering a 1,620-mile range. This huge battery pack would cost less than Tesla's. This battery would nearly perfect EVs.
Or would it?
The battery's capacity declined by 50% after 1,000 charge cycles. This means that our hypothetical Model S would suffer this decline after 1.6 million miles, but for more cheap vehicles that use smaller packs, this would be too short. This test cell wasn't supposed to last long, so this is shocking. Future versions of this cell could be modified to live longer.
This affordable and eco-friendly cell is best employed as a grid-storage battery for renewable energy. Its safety and affordable price outweigh its short lifespan. Because this battery is made of easily accessible materials, it may be utilized to boost grid-storage capacity without causing supply chain concerns or EV battery prices to skyrocket.
Researchers are designing a bigger pouch cell (like those in phones and laptops) for this purpose. The battery revolution we need could be near. Let’s just hope it isn’t too late.
Enrique Dans
3 years ago
You may not know about The Merge, yet it could change society
Ethereum is the second-largest cryptocurrency. The Merge, a mid-September event that will convert Ethereum's consensus process from proof-of-work to proof-of-stake if all goes according to plan, will be a game changer.
Why is Ethereum ditching proof-of-work? Because it can. We're talking about a fully functioning, open-source ecosystem with a capacity for evolution that other cryptocurrencies lack, a change that would allow it to scale up its performance from 15 transactions per second to 100,000 as its blockchain is used for more and more things. It would reduce its energy consumption by 99.95%. Vitalik Buterin, the system's founder, would play a less active role due to decentralization, and miners, who validated transactions through proof of work, would be far less important.
Why has this conversion taken so long and been so cautious? Because it involves modifying a core process while it's running to boost its performance. It requires running the new mechanism in test chains on an ever-increasing scale, assessing participant reactions, and checking for issues or restrictions. The last big test was in early June and was successful. All that's left is to converge the mechanism with the Ethereum blockchain to conclude the switch.
What's stopping Bitcoin, the leader in market capitalization and the cryptocurrency that began blockchain's appeal, from doing the same? Satoshi Nakamoto, whoever he or she is, departed from public life long ago, therefore there's no community leadership. Changing it takes a level of consensus that is impossible to achieve without strong leadership, which is why Bitcoin's evolution has been sluggish and conservative, with few modifications.
Secondly, The Merge will balance the consensus mechanism (proof-of-work or proof-of-stake) and the system decentralization or centralization. Proof-of-work prevents double-spending, thus validators must buy hardware. The system works, but it requires a lot of electricity and, as it scales up, tends to re-centralize as validators acquire more hardware and the entire network activity gets focused in a few nodes. Larger operations save more money, which increases profitability and market share. This evolution runs opposed to the concept of decentralization, and some anticipate that any system that uses proof of work as a consensus mechanism will evolve towards centralization, with fewer large firms able to invest in efficient network nodes.
Yet radical bitcoin enthusiasts share an opposite argument. In proof-of-stake, transaction validators put their funds at stake to attest that transactions are valid. The algorithm chooses who validates each transaction, giving more possibilities to nodes that put more coins at stake, which could open the door to centralization and government control.
In both cases, we're talking about long-term changes, but Bitcoin's proof-of-work has been evolving longer and seems to confirm those fears, while proof-of-stake is only employed in coins with a minuscule volume compared to Ethereum and has no predictive value.
As of mid-September, we will have two significant cryptocurrencies, each with a different consensus mechanisms and equally different characteristics: one is intrinsically conservative and used only for economic transactions, while the other has been evolving in open source mode, and can be used for other types of assets, smart contracts, or decentralized finance systems. Some even see it as the foundation of Web3.
Many things could change before September 15, but The Merge is likely to be a turning point. We'll have to follow this closely.
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Claire Berehova
3 years ago
There’s no manual for that
| Kyiv oblast in springtime. Photo by author. |
We’ve been receiving since the war began text messages from the State Emergency Service of Ukraine every few days. They’ve contained information on how to comfort a child and what to do in case of a water outage.
But a question that I struggle to suppress irks within me: How would we know if there really was a threat coming our away? So how can I happily disregard an air raid siren and continue singing to my three-month-old son when I feel like a World War II film became reality? There’s no manual for that.
Along with the anxiety, there’s the guilt that always seems to appear alongside dinner we’re fortunate to still have each evening while brave Ukrainian soldiers are facing serious food insecurity. There’s no manual for how to deal with this guilt.
When it comes to the enemy, there is no manual for how to react to the news of Russian casualties. Every dead Russian soldier weakens Putin, but I also know that many of these men had wives and girlfriends who are now living a nightmare.
So, I felt like I had to start writing my own manual.
The anxiety around the air raid siren? Only with time does it get easier to ignore it, but never completely.
The guilt? All we can do is pray.
That inner conflict? As Russia continues to stun the world with its war crimes, my emotions get less gray — I have to get used to accommodating absurd levels of hatred.
Sadness? It feels a bit more manageable when we laugh, and a little alcohol helps (as it usually does).
Cabin fever? Step outside in the yard when possible. At least the sunshine is becoming more fervent with spring approaching.
Slava Ukraini. Heroyam slava. (Glory to Ukraine. Glory to the heroes.)
Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 1)
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has two very powerful applications:
- Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
- Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.
But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.
Why ZK-SNARKs "should" be hard
Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.
A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.
One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?
Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.
But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.
It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.
see part 2
Davlin Knight
2 years ago
2 pitfalls to stay away from when launching a YouTube channel
You do not want to miss these
Stop! Stop it! Two things to avoid when starting a YouTube channel. Critical. Possible channel-killers Its future revenue.
I'll tell you now, so don't say "I wish I knew."
The Notorious Copyright Allegation
My YouTube channel received a copyright claim before I sold it. This claim was on a one-minute video I thought I'd changed enough to make mine, but the original owner disagreed.
It cost me thousands in ad revenue. Original owner got the profits.
Well, it wasn't your video, you say.
Touché.
I've learned. Sorta
I couldn't stop looking at the video's views. The video got 1,000,000 views without any revenue. I made 4 more similar videos.
If they didn't get copyrighted, I'd be rolling in dough.
You've spent a week editing and are uploading to YouTube. You're thrilled as you stand and stretch your back. You see the video just before publishing.
No way!
The red exclamation point on checks.
Copyright claim!
YouTube lets you publish, but you won't make money.
Sounds fair? Well, it is.
Copyright claims mean you stole someone's work. Song, image, or video clip.
We wouldn't want our content used for money.
The only problem with this is that almost everything belongs to someone else. I doubt some of the biggest creators are sitting down and making their music for their videos. That just seems really excessive when you could make a quick search on YouTube and download a song (I definitely don’t do this because that would be stealing).
So how do you defeat a copyright defense?
Even copyright-free songs on YouTube aren't guaranteed. Some copyrighted songs claim to be free.
Use YouTube's free music library or pay for a subscription to adobe stock, epidemic sound, or artlist.io.
Most of my videos have Nintendo music. Almost all game soundtracks are copyright-free and offer a variety of songs.
Restriction on age
Age restrictions are a must-avoid. A channel dies.
YouTube never suggests age-restricted videos.
Shadow banning means YouTube hides your content from subscribers and non-subscribers.
Keeping your channel family-friendly can help.
I hear you complaining that your channel isn't for kids. I agree. Not everyone has a clean mouth or creates content for minors.
YouTube has changed rapidly in recent years. Focusing on kids. Fewer big creators are using profanity or explicit content in videos. Not YouTube-worthy.
Youtube wants to be family-friendly. A family-friendly movie. It won't promote illegal content. Yes, it allows profanity.
Do I recommend avoiding no-no words in videos? Never. Okay. YouTube's policies are shaky. YouTube uses video content to determine ad suitability.
No joke. If you're serious about becoming a content creator, avoid profanity and inappropriate topics.
If your channel covers 18+ topics, like crime or commentary, censor as much as possible.
YouTube can be like walking on eggshells. You never know what is gonna upset the boss. So play it safe and try to avoid getting on their bad side.
Mr. Beast, Dream, Markplier, Faze Rug, and PewDewPie are popular creators. They maintain it family-friendly while entertaining fans.
You got this.