Blockchain validates transactions with consensus algorithms. Bitcoin and Ethereum use Proof-of-Work, while Polkadot and Cardano use Proof-of-Stake.

Other consensus protocols are used to verify transactions besides these two. This post focuses on Proof-of-Time (PoT), used by Analog, and Proof-of-History (PoH), used by Solana as a hybrid consensus protocol.

PoT and PoH may seem similar to users, but they are actually very different protocols.

Proof-of-Time (PoT)

Analog developed Proof-of-Time (PoT) based on Delegated Proof-of-Stake (DPoS). Users select "delegates" to validate the next block in DPoS. PoT uses a ranking system, and validators stake an equal amount of tokens. Validators also "self-select" themselves via a verifiable random function."

The ranking system gives network validators a performance score, with trustworthy validators with a long history getting higher scores. System also considers validator's fixed stake. PoT's ledger is called "Timechain."

Voting on delegates borrows from DPoS, but there are changes. PoT's first voting stage has validators (or "time electors" putting forward a block to be included in the ledger).

Validators are chosen randomly based on their ranking score and fixed stake. One validator is chosen at a time using a Verifiable Delay Function (VDF).

Validators use a verifiable delay function to determine if they'll propose a Timechain block. If chosen, they validate the transaction and generate a VDF proof before submitting both to other Timechain nodes.

This leads to the second process, where the transaction is passed through 1,000 validators selected using the same method. Each validator checks the transaction to ensure it's valid.

If the transaction passes, validators accept the block, and if over 2/3 accept it, it's added to the Timechain.

Proof-of-History (PoH)

Proof-of-History is a consensus algorithm that proves when a transaction occurred. PoH uses a VDF to verify transactions, like Proof-of-Time. Similar to Proof-of-Work, VDFs use a lot of computing power to calculate but little to verify transactions, similar to (PoW).

This shows users and validators how long a transaction took to verify.

PoH uses VDFs to verify event intervals. This process uses cryptography to prevent determining output from input.

The outputs of one transaction are used as inputs for the next. Timestamps record the inputs' order. This checks if data was created before an event.

PoT vs. PoH

PoT and PoH differ in that:

• PoT uses VDFs to select validators (or time electors), while PoH measures time between events.

• PoH uses a VDF to validate transactions, while PoT uses a ranking system.

• PoT's VDF-elected validators verify transactions proposed by a previous validator. PoH uses a VDF to validate transactions and data.

Conclusion

Both Proof-of-Time (PoT) and Proof-of-History (PoH) validate blockchain transactions differently. PoT uses a ranking system to randomly select validators to verify transactions.

PoH uses a Verifiable Delay Function to validate transactions, verify how much time has passed between two events, and allow validators to quickly verify a transaction without malicious actors knowing the input.

Overview

I'm happy to provide this important update. We've worked on this for a year and a half, so I'm glad to finally write it. We named the application AESIR because we’ve love Norse Mythology. AESIR automates and runs trading strategies.

• Volatility, technical analysis, oscillators, and other signals are currently supported by AESIR.

• Additionally, we enhanced AESIR's ability to create distinctive bespoke signals by allowing it to analyze many indicators and produce a single signal.

• AESIR has a significant social component that allows you to copy the best-performing public setups and use them right away.

Enter your email here to be notified when AEISR launches.

Views on algorithmic trading

First, let me clarify. Anyone who claims algorithmic trading platforms are money-printing plug-and-play devices is a liar. Algorithmic trading platforms are a collection of tools.

A trading algorithm won't make you a competent trader if you lack a trading strategy and yolo your funds without testing. It may hurt your trade. Test and alter your plans to account for market swings, but comprehend market signals and trends.

Status Report

Throughout closed beta testing, we've communicated closely with users to design a platform they want to use.

To celebrate, we're giving you free Aesir Viking NFTs and we cover gas fees.

Why use a trading Algorithm?

• Automating a successful manual approach

• experimenting with and developing solutions that are impossible to execute manually

One AESIR strategy lets you buy any cryptocurrency that rose by more than x% in y seconds.

AESIR can scan an exchange for coins that have gained more than 3% in 5 minutes. It's impossible to manually analyze over 1000 trading pairings every 5 minutes. Auto buy dips or DCA around a Dip

Sneak Preview

Here's the Leaderboard, where you can clone the best public settings.

As a tiny, self-funded team, we're excited to unveil our product. It's a beta release, so there's still more to accomplish, but we know where we stand.

If this sounds like a project that you might want to learn more about, you can sign up to our newsletter and be notified when AESIR launches.

Useful Links:

Join the Discord | Join our subreddit | Newsletter | Mint Free NFT

The crypto market crashed in June 2022. Bitcoin and other cryptocurrencies hit their lowest prices in over a year, causing market panic. Some believe this crash will benefit future investors.

Before I discuss how this crash might help investors, let's examine why it happened. Inflation in the U.S. reached a 30-year high in 2022 after Russia invaded Ukraine. In response, the U.S. Federal Reserve raised interest rates by 0.5%, the most in almost 20 years. This hurts cryptocurrencies like Bitcoin. Higher interest rates make people less likely to invest in volatile assets like crypto, so many investors sold quickly.

The crypto market collapsed. Bitcoin, Ethereum, and Binance dropped 40%. Other cryptos crashed so hard they were delisted from almost every exchange. Bitcoin peaked in April 2022 at $41,000, but after the May interest rate hike, it crashed to $28,000. Bitcoin investors were worried. Even in bad times, this crash is unprecedented.

Bitcoin wasn't "doomed." Before the crash, LUNA was one of the top 5 cryptos by market cap. LUNA was trading around $80 at the start of May 2022, but after the rate hike?

Less than 1 cent. LUNA lost 99.99% of its value in days and was removed from every crypto exchange. Bitcoin's "crash" isn't as devastating when compared to LUNA.

Many people said Bitcoin is "due" for a LUNA-like crash and that the only reason it hasn't crashed is because it's bigger. Still false. If so, Bitcoin should be worth zero by now. We didn't. Instead, Bitcoin reached 28,000, then 29k, 30k, and 31k before falling to 18k. That's not the world's greatest recovery, but it shows Bitcoin's safety.

Bitcoin isn't falling constantly. It fell because of the initial shock of interest rates, but not further. Now, Bitcoin's value is more likely to rise than fall. Bitcoin's low price also attracts investors. They know what prices Bitcoin can reach with enough hype, and they want to capitalize on low prices before it's too late.

Bitcoin's crash was bad, but in a way it wasn't. To understand, consider 2021. In March 2021, Bitcoin surpassed $60k for the first time. Elon Musk's announcement in May that he would no longer support Bitcoin caused a massive crash in the crypto market. In May 2017, Bitcoin's price hit $29,000. Elon Musk's statement isn't worth more than the Fed raising rates. Many expected this big announcement to kill Bitcoin.

Not so. Bitcoin crashed from $58k to $31k in 2021. Bitcoin fell from $41k to $28k in 2022. This crash is smaller. Bitcoin's price held up despite tensions and stress, proving investors still believe in it. What happened after the initial crash in the past?

Bitcoin fell until mid-July. This is also something we’re not seeing today. After a week, Bitcoin began to improve daily. Bitcoin's price rose after mid-July. Bitcoin's price fluctuated throughout the rest of 2021, but it topped $67k in November. Despite no major changes, the peak occurred after the crash. Elon Musk seemed uninterested in crypto and wasn't likely to change his mind soon. What triggered this peak? Nothing, really. What really happened is that people got over the initial statement. They forgot.

Internet users have goldfish-like attention spans. People quickly forgot the crash's cause and were back investing in crypto months later. Despite the market's setbacks, more crypto investors emerged by the end of 2017. Who gained from these peaks? Bitcoin investors who bought low. Bitcoin not only recovered but also doubled its ROI. It was like a movie, and it shows us what to expect from Bitcoin in the coming months.

The current Bitcoin crash isn't as bad as the last one. LUNA is causing market panic. LUNA and Bitcoin are different cryptocurrencies. LUNA crashed because Terra wasn’t able to keep its peg with the USD. Bitcoin is unanchored. It's one of the most decentralized investments available. LUNA's distrust affected crypto prices, including Bitcoin, but it won't last forever.

This is why Bitcoin will likely rebound in the coming months. In 2022, people will get over the rise in interest rates and the crash of LUNA, just as they did with Elon Musk's crypto stance in 2021. When the world moves on to the next big controversy, Bitcoin's price will soar.

Bitcoin may recover for another reason. Like controversy, interest rates fluctuate. The Russian invasion caused this inflation. World markets will stabilize, prices will fall, and interest rates will drop.

Next, lower interest rates could boost Bitcoin's price. Eventually, it will happen. The U.S. economy can't sustain such high interest rates. Investors will put every last dollar into Bitcoin if interest rates fall again.

Bitcoin has proven to be a stable investment. This boosts its investment reputation. Even if Ethereum dethrones Bitcoin as crypto king one day (or any other crypto, for that matter). Bitcoin may stay on top of the crypto ladder for a while. We'll have to wait a few months to see if any of this is true.

This post is a summary. Read the full article here.

If you waste time every day, even though you're ambitious, you're not alone.

Many of us could use some new time-management strategies, like these:

Focus on the following three.

You're thinking about everything at once.

You're overpowered.

It's mental. We just have what's in front of us. So savor the moment's beauty.

Prioritize 1-3 things.

To be one of the most productive people you and I know, follow these steps.

Get along with boredom.

Many of us grow bored, sweat, and turn on Netflix.

We shout, "I'm rarely bored!" Look at me! I'm happy.

Shut it, Sally.

You're not making wonderful things for the world. Boredom matters.

If you can sit with it for a second, you'll get insight. Boredom? Breathe.

Go blank.

Then watch your creativity grow.

Check your MacroVision once more.

We don't know what to do with our time, which contributes to time-wasting.

Nobody does, either. Jeff Bezos won't hand-deliver that crap to you.

Daily vision checks are required.

Also:

What are 5 things you'd love to create in the next 5 years?

You're soul-searching. It's food.

Return here regularly, and you'll adore the high you get from doing valuable work.

Improve your thinking.

What's Alex's latest nonsense?

I'm talking about overcoming our own thoughts. Worrying wastes so much time.

Too many of us are assaulted by lies, myths, and insecurity.

Stop letting your worries massage you into a worried coma like a Thai woman.

Optimizing your thoughts requires accepting what you can't control.

It means letting go of unhelpful thoughts and returning to the moment.

Keep your blood sugar level.

I gave up gluten, donuts, and sweets.

This has really boosted my energy.

Blood-sugar-spiking carbs make us irritable and tired.

These day-to-day ups and downs aren't productive. It's crucial.

Know how your diet affects insulin levels. Now I have more energy and can do more without clenching my teeth.

Reduce harmful carbs to boost energy.

Create a focused setting for yourself.

When we optimize the mind, we have more energy and use our time better because we're not tense.

Changing our environment can also help us focus. Disabling alerts is one example.

Too hot makes me procrastinate and irritable.

List five items that hinder your productivity.

You may be amazed at how much you may improve by removing distractions.

Be responsible.

Accountability is a time-saver.

Creating an emotional pull to finish things.

Writing down our goals makes us accountable.

We can engage a coach or work with an accountability partner to feel horrible if we don't show up and finish on time.

‘Hey Jake, I’m going to write 1000 words every day for 30 days — you need to make sure I do.’ ‘Sure thing, Nathan, I’ll be making sure you check in daily with me.’

Tick.

You might also blog about your ambitions to show your dedication.

Now you can't hide when you promised to appear.

Acquire a liking for bravery.

Boldness changes everything.

I sometimes feel lazy and wonder why. If my food and sleep are in order, I should assess my footing.

Most of us live backward. Doubtful. Uncertain. Feelings govern us.

Backfooting isn't living. It's lame, and you'll soon melt. Live boldly now.

Be assertive.

Get disgustingly into everything. Expand.

Even if it's hard, stop being a b*tch.

Those that make Mr. Bold Bear their spirit animal benefit. Save time to maximize your effect.

Research on preventing disease, extending life, and caring for your body from the inside out

Grapefruit and pomegranates aren't on the list, so ignore that. Mostly, I enjoyed the visual, but those fruits are healthful, too.

15 (or 17 if you consider the photo) different foods a day sounds like a lot. If you're not used to it  — it is.

These lists don't aim for perfection. Instead, use this article and the science below to eat more of these foods. If you can eat 5 foods one day and 5 the next, you're doing well. This list should be customized to your requirements and preferences.

“Every time you eat or drink, you are either feeding disease or fighting it” -Heather Morgan.

The 15 Foods That You Should Consume Daily and Why:

1. Dark/Red Berries

(blueberries, blackberries, acai, goji, cherries, strawberries, raspberries)

The 2010 Global Burden of Disease Study is the greatest definitive analysis of death and disease risk factors in history. They found the primary cause of both death, disability, and disease inside the United States was diet.

Not eating enough fruit, and specifically berries, was one of the best predictors of disease (1).

What's special about berries? It's their color! Berries have the most antioxidants of any fruit, second only to spices. The American Cancer Society found that those who ate the most berries were less likely to die of cardiovascular disease.

2. Beans

Soybeans, black beans, kidney beans, lentils, split peas, chickpeas.

Beans are one of the most important predictors of survival in older people, according to global research (2).

For every 20 grams (2 tablespoons) of beans consumed daily, the risk of death is reduced by 8%.

Soybeans and soy foods are high in phytoestrogen, which reduces breast and prostate cancer risks. Phytoestrogen blocks the receptors' access to true estrogen, mitigating the effects of weight gain, dairy (high in estrogen), and hormonal fluctuations (3).

3. Nuts

(almonds, walnuts, pecans, pistachios, Brazil nuts, cashews, hazelnuts, macadamia nuts)

Eating a handful of nuts every day reduces the risk of chronic diseases like heart disease and diabetes. Nuts also reduce oxidation, blood sugar, and LDL (bad) cholesterol, improving arterial function (4).

Despite their high-fat content, studies have linked daily nut consumption to a slimmer waistline and a lower risk of obesity (5).

4. Flaxseed

(milled flaxseed)

2013 research found that ground flaxseed had one of the strongest anti-hypertensive effects of any food. A few tablespoons (added to a smoothie or baked goods) lowered blood pressure and stroke risk 23 times more than daily aerobic exercise (6).

Flax shouldn't replace exercise, but its nutritional punch is worth adding to your diet.

5. Other seeds

(chia seeds, hemp seeds, pumpkin seeds, sesame seeds, fennel seeds)

Seeds are high in fiber and omega-3 fats and can be added to most dishes without being noticed.

When eaten with or after a meal, chia seeds moderate blood sugar and reduce inflammatory chemicals in the blood (7). Overall, a great daily addition.

6. Dates

Dates are one of the world's highest sugar foods, with 80% sugar by weight. Pure cake frosting is 60%, maple syrup is 66%, and cotton-candy jelly beans are 70%.

Despite their high sugar content, dates have a low glycemic index, meaning they don't affect blood sugar levels dramatically. They also improve triglyceride and antioxidant stress levels (8).

Dates are a great source of energy and contain high levels of dietary fiber and polyphenols, making 3-10 dates a great way to fight disease, support gut health with prebiotics, and satisfy a sweet tooth (9).

7. Cruciferous Veggies

(broccoli, Brussel sprouts, horseradish, kale, cauliflower, cabbage, boy choy, arugula, radishes, turnip greens)

Cruciferous vegetables contain an active ingredient that makes them disease-fighting powerhouses. Sulforaphane protects our brain, eyesight, against free radicals and environmental hazards, and treats and prevents cancer (10).

Unless you eat raw cruciferous vegetables daily, you won't get enough sulforaphane (and thus, its protective nutritional benefits). Cooking destroys the enzyme needed to create this super-compound.

If you chop broccoli, cauliflower, or turnip greens and let them sit for 45 minutes before cooking them, the enzyme will have had enough time to work its sulforaphane magic, allowing the vegetables to retain the same nutritional value as if eaten raw. Crazy, right? For more on this, see What Chopping Your Vegetables Has to Do with Fighting Cancer.

8. Whole grains

(barley, brown rice, quinoa, oats, millet, popcorn, whole-wheat pasta, wild rice)

Whole-grains are one of the healthiest ways to consume your daily carbs and help maintain healthy gut flora.

This happens when fibre is broken down in the colon and starts a chain reaction, releasing beneficial substances into the bloodstream and reducing the risk of Type 2 Diabetes and inflammation (11).

9. Spices

(turmeric, cumin, cinnamon, ginger, saffron, cloves, cardamom, chili powder, nutmeg, coriander)

7% of a person's cells will have DNA damage. This damage is caused by tiny breaks in our DNA caused by factors like free-radical exposure.

Free radicals cause mutations that damage lipids, proteins, and DNA, increasing the risk of disease and cancer. Free radicals are unavoidable because they result from cellular metabolism, but they can be avoided by consuming anti-oxidant and detoxifying foods.

Including spices and herbs like rosemary or ginger in our diet may cut DNA damage by 25%. Yes, this damage can be improved through diet. Turmeric worked better at a lower dose (just a pinch, daily). For maximum free-radical fighting (and anti-inflammatory) effectiveness, use 1.5 tablespoons of similar spices (12).

10. Leafy greens

(spinach, collard greens, lettuce, other salad greens, swiss chard)

Studies show that people who eat more leafy greens perform better on cognitive tests and slow brain aging by a year or two (13).

As we age, blood flow to the brain drops due to a decrease in nitric oxide, which prevents blood vessels from dilatation. Daily consumption of nitrate-rich vegetables like spinach and swiss chard may prevent dementia and Alzheimer's.

11. Fermented foods

(sauerkraut, tempeh, kombucha, plant-based kefir)

Miso, kimchi, and sauerkraut contain probiotics that support gut microbiome.

Probiotics balance the good and bad bacteria in our bodies and offer other benefits. Fermenting fruits and vegetables increases their antioxidant and vitamin content, preventing disease in multiple ways (14).

12. Sea vegetables

(seaweed, nori, dulse flakes)

A population study found that eating one sheet of nori seaweed per day may cut breast cancer risk by more than half (15).

Seaweed and sea vegetables may help moderate estrogen levels in the metabolism, reducing cancer and disease risk.

Sea vegetables make up 30% of the world's edible plants and contain unique phytonutrients. A teaspoon of these super sea-foods on your dinner will help fight disease from the inside out.

13. Water

I'm less concerned about whether you consider water food than whether you drink enough. If this list were ranked by what single item led to the best health outcomes, water would be first.

Research shows that people who drink 5 or more glasses of water per day have a 50% lower risk of dying from heart disease than those who drink 2 or less (16).

Drinking enough water boosts energy, improves skin, mental health, and digestion, and reduces the risk of various health issues, including obesity.

14. Tea

All tea consumption is linked to a lower risk of stroke, heart disease, and early death, with green tea leading for antioxidant content and immediate health benefits.

Green tea leaves may also be able to interfere with each stage of cancer formation, from the growth of the first mutated cell to the spread and progression of cancer in the body. Green tea is a quick and easy way to support your long-term and short-term health (17).

15. Supplemental B12 vitamin

B12, or cobalamin, is a vitamin responsible for cell metabolism. Not getting enough B12 can have serious consequences.

Historically, eating vegetables from untreated soil helped humans maintain their vitamin B12 levels. Due to modern sanitization, our farming soil lacks B12.

B12 is often cited as a problem only for vegetarians and vegans (as animals we eat are given B12 supplements before slaughter), but recent studies have found that plant-based eaters have lower B12 deficiency rates than any other diet (18).

Article Sources:

1. The Global Burden of Disease Study 2010 (GBD 2010)

2. I. Darmadi-Blackberry, M. Wahlqvist, A. Kouris-Blazos, et al. Legumes: the most important dietary predictor of survival in older people of different ethnicities. Asia Pac J Clin Nutr. 2004;13(2):217–20.

3. Guha N, Kwan ML, Quesenberry CP Jr, Weltzien EK, Castillo AL, Caan BJ. Soy isoflavones and risk of cancer recurrence in a cohort of breast cancer survivors: the Life After Cancer Epidemiology study. Breast Cancer Res Treat. 2009 Nov;118(2):395–405.

4. Y. Bao, J. Han, F. B. Hu, E. L. Giovannucci, M. J. Stampfer, W. C. Willett, C. S. Fuchs. Association of nut consumption with total and cause-specific mortality. N. Engl. J. Med. 2013 369(21):2001–2011.

5. V. Vadivel, C. N. Kunyanga, H. K. Biesalski. Health benefits of nut consumption with special reference to body weight control. Nutrition 2012 28(11–12):1089–1097.

6. D Rodriguez-Leyva, W Weighell, A L Edel,R LaVallee, E Dibrov,R Pinneker, T G Maddaford, B Ramjiawan, M Aliani, R Guzman R, G N Pierce. Potent antihypertensive action of dietary flaxseed in hypertensive patients. Hypertension. 2013 Dec;62(6):1081–9. doi: 10.1161/HYPERTENSIONAHA.113.02094.

7. Vuksan V, Jenkins AL, Dias AG, Lee AS, Jovanovski E, Rogovik AL, Hanna A. Reduction in postprandial glucose excursion and prolongation of satiety: possible explanation of the long-term effects of whole grain Salba (Salvia Hispanica L.). Eur J Clin Nutr. 2010 Apr;64(4):436–8. doi: 10.1038/ejcn.2009.159. Epub 2010 Jan 20. PMID: 20087375.

8. W. Rock, M. Rosenblat, H. Borochov-Neori, N. Volkova, S. Judeinstein, M. Elias, and M. Aviram. Effects of date (Phoenix dactylifera L., Medjool or Hallawi Variety) consumption by healthy subjects on serum glucose and lipid levels and on serum oxidative status: a pilot study. J. Agric. Food. Chem., 57(17):8010{8017, 2009.

9. Eid N, Enani S, Walton G, et al. The impact of date palm fruits and their component polyphenols, on gut microbial ecology, bacterial metabolites and colon cancer cell proliferation. J Nutr Sci. 2014;3:e46.

10. Li Y, Zhang T, Korkaya H, Liu S, Lee HF, Newman B, Yu Y, Clouthier SG, Schwartz SJ, Wicha MS, Sun D. Sulforaphane, a Dietary Component of Broccoli/Broccoli Sprouts, Inhibits Breast Cancer Stem Cells. Clin Cancer Res. 2010 May 1;16(9):2580–90.

11. Lappi J, Kolehmainen M, Mykkänen H, Poutanen K. Do large intestinal events explain the protective effects of whole grain foods against type 2 diabetes? Crit Rev Food Sci Nutr. 2013;53(6):631–40.

12. S. S. Percival, J. P. V. Heuvel, C. J. Nieves, C. Montero, A. J. Migliaccio, J. Meadors. Bioavailability of Herbs and Spices in Humans as Determined by ex vivo Inflammatory Suppression and DNA Strand Breaks. J Am Coll Nutr. 2012 31(4):288–294.

13. Nurk E, Refsum H, Drevon CA, et al. Cognitive performance among the elderly in relation to the intake of plant foods. The Hordaland Health Study. Br J Nutr. 2010;104(8):1190–201.

14. Melini, F.; Melini, V.; Luziatelli, F.; Ficca, A.G.; Ruzzi, M. Health-Promoting Components in Fermented Foods: An Up-to-Date Systematic Review. Nutrients2019, 11, 1189.

15. H. Funahashi, T. Imai, T. Mase, M. Sekiya, K. Yokoi, H. Hayashi, A. Shibata, T. Hayashi, M. Nishikawa, N. Suda, Y. Hibi, Y. Mizuno, K. Tsukamura, A. Hayakawa, S. Tanuma. Seaweed prevents breast cancer? Jpn. J. Cancer Res. 2001 92(5):483–487.

16. Chan J, Knutsen SF, Blix GG, Lee JW, Fraser GE. Water, other fluids, and fatal coronary heart disease: the Adventist Health Study. Am J Epidemiol. 2002 May 1;155(9):827–33. doi: 10.1093/aje/155.9.827. PMID: 11978586.

17. Fujiki H, Imai K, Nakachi K, Shimizu M, Moriwaki H, Suganuma M. Challenging the effectiveness of green tea in primary and tertiary cancer prevention. J Cancer Res Clin Oncol. 2012 Aug;138(8):1259–70.

18. Damayanti, D., Jaceldo-Siegl, K., Beeson, W. L., Fraser, G., Oda, K., & Haddad, E. H. (2018). Foods and Supplements Associated with Vitamin B12Biomarkers among Vegetarian and Non-Vegetarian Participants of the Adventist Health Study-2 (AHS-2) Calibration Study. Nutrients, 10(6), 722. doi:10.3390/nu10060722

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.