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.
More on Technology
Gareth Willey
2 years ago • 3 min read
I've had these five apps on my phone for a long time.
TOP APPS
Who survives spring cleaning?
Relax. Notion is off-limits. This topic is popular.
(I wrote about it 2 years ago, before everyone else did.) So).
These apps are probably new to you. I hope you find a new phone app after reading this.
Outdooractive
ViewRanger is Google Maps for outdoor enthusiasts.
This app has been so important to me as a freedom-loving long-distance walker and hiker.
This app shows nearby trails and right-of-ways on top of an Open Street Map.
Helpful detail and data. Any route's distance,
You can download and follow tons of routes planned by app users.
This has helped me find new routes and places a fellow explorer has tried.
Free with non-intrusive ads. Years passed before I subscribed. Pro costs £2.23/month.
This app is for outdoor lovers.
Google Files
New phones come with bloatware. These rushed apps are frustrating.
We must replace these apps. 2017 was Google's year.
Files is a file manager. It's quick, innovative, and clean. They've given people what they want.
It's easy to organize files, clear space, and clear cache.
I recommend Gallery by Google as a gallery app alternative. It's quick and easy.
Trainline
App for trains, buses, and coaches.
I've used this app for years. It did the basics well when I first used it.
Since then, it's improved. It's constantly adding features to make traveling easier and less stressful.
Split-ticketing helps me save hundreds a year on train fares. This app is only available in the UK and Europe.
This service doesn't link to a third-party site. Their app handles everything.
Not all train and coach companies use this app. All the big names are there, though.
Here's more on the app.
Battlefield: Mobile
Play Store has 478,000 games. Few can turn my phone into a console.
Call of Duty Mobile and Asphalt 8/9 are examples.
Asphalt's loot boxes and ads make it unplayable. Call of Duty opens with a few ads. Close them to play without hassle.
This game uses all your phone's features to provide a high-quality, seamless experience. If my internet connection is good, I never experience lag or glitches.
The gameplay is energizing and intense, just like on consoles. Sometimes I'm too involved. I've thrown my phone in anger. I'm totally absorbed.
Customizability is my favorite. Since phones have limited screen space, we should only have the buttons we need, placed conveniently.
Size, opacity, and position are modifiable. Adjust audio, graphics, and textures. It's customizable.
This game has been on my phone for three years. It began well and has gotten better. When I think the creators can't do more, they do.
If you play, read my tips for winning a Battle Royale.
Lightroom
As a photographer, I believe your best camera is on you. The phone.
2017 was a big year for this app. I've tried many photo-editing apps since then. This always wins.
The app is dull. I've never seen better photo editing on a phone.
Adjusting settings and sliders doesn't damage or compress photos. It's detailed.
This is important for phone photos, which are lower quality than professional ones.
Some tools are behind a £4.49/month paywall. Adobe must charge a subscription fee instead of selling licenses. (I'm still bitter about Creative Cloud's price)
Snapseed is my pick. Lightroom is where I do basic editing before moving to Snapseed. Snapseed review:
These apps are great. They cover basic and complex editing needs while traveling.
Final Reflections
I hope you downloaded one of these. Share your favorite apps. These apps are scarce.
Nick Babich
2 years ago • 4 min read
Is ChatGPT Capable of Generating a Complete Mobile App?
TL;DR: It'll be harder than you think.
Mobile app development is a complicated product design sector. You require broad expertise to create a mobile app. You must write Swift or Java code and consider mobile interactions.
When ChatGPT was released, many were amazed by its capabilities and wondered if it could replace designers and developers. This article will use ChatGPT to answer a specific query.
Can ChatGPT build an entire iOS app?
This post will use ChatGPT to construct an iOS meditation app. Video of the article is available.
App concepts for meditation
After deciding on an app, think about the user experience. What should the app offer?
Let's ask ChatGPT for the answer.
ChatGPT described a solid meditation app with various exercises. Use this list to plan product design. Our first product iteration will have few features. A simple, one-screen software will let users set the timeframe and play music during meditation.
Structure of information
Information architecture underpins product design. Our app's navigation mechanism should be founded on strong information architecture, so we need to identify our mobile's screens first.
ChatGPT can define our future app's information architecture since we already know it.
ChatGPT uses the more complicated product's structure. When adding features to future versions of our product, keep this information picture in mind.
Color palette
Meditation apps need colors. We want to employ relaxing colors in a meditation app because colors affect how we perceive items. ChatGPT can suggest product colors.
See the hues in person:
Neutral colors dominate the color scheme. Playing with color opacity makes this scheme useful.
Ambiance music
Meditation involves music. Well-chosen music calms the user.
Let ChatGPT make music for us.
ChatGPT can only generate text. It directs us to Spotify or YouTube to look for such stuff and makes precise recommendations.
Fonts
Fonts can impress app users. Round fonts are easier on the eyes and make a meditation app look friendlier.
ChatGPT can suggest app typefaces. I compare two font pairs when making a product. I'll ask ChatGPT for two font pairs.
See the hues in person:
Despite ChatGPT's convincing font pairing arguments, the output is unattractive. The initial combo (Open Sans + Playfair Display) doesn't seem to work well for a mediation app.
Content
Meditation requires the script. Find the correct words and read them calmly and soothingly to help listeners relax and focus on each region of their body to enhance the exercise's effect.
ChatGPT's offerings:
ChatGPT outputs code. My prompt's word script may cause it.
Timer
After fonts, colors, and content, construct functional pieces. Timer is our first functional piece. The meditation will be timed.
Let ChatGPT write Swift timer code (since were building an iOS app, we need to do it using Swift language).
ChatGPT supplied a timer class, initializer, and usage guidelines.
Apple Xcode requires a playground to test this code. Xcode will report issues after we paste the code to the playground.
Fixing them is simple. Just change Timer to another class name (Xcode shows errors because it thinks that we access the properties of the class we’ve created rather than the system class Timer; it happens because both classes have the same name Timer). I titled our class Timero and implemented the project. After this quick patch, ChatGPT's code works.
Can ChatGPT produce a complete app?
Since ChatGPT can help us construct app components, we may question if it can write a full app in one go.
Question ChatGPT:
ChatGPT supplied basic code and instructions. It's unclear if ChatGPT purposely limits output or if my prompt wasn't good enough, but the tool cannot produce an entire app from a single prompt.
However, we can contact ChatGPT for thorough Swift app construction instructions.
We can ask ChatGPT for step-by-step instructions now that we know what to do. Request a basic app layout from ChatGPT.
Copying this code to an Xcode project generates a functioning layout.
Takeaways
ChatGPT may provide step-by-step instructions on how to develop an app for a specific system, and individual steps can be utilized as prompts to ChatGPT. ChatGPT cannot generate the source code for the full program in one go.
The output that ChatGPT produces needs to be examined by a human. The majority of the time, you will need to polish or adjust ChatGPT's output, whether you develop a color scheme or a layout for the iOS app.
ChatGPT is unable to produce media material. Although ChatGPT cannot be used to produce images or sounds, it can assist you build prompts for programs like midjourney or Dalle-2 so that they can provide the appropriate images for you.
Christianlauer
2 years ago • 1 min read
Looker Studio Pro is now generally available, according to Google.
Great News about the new Google Business Intelligence Solution
Google has renamed Data Studio to Looker Studio and Looker Studio Pro.
Now, Google releases Looker Studio Pro. Similar to the move from Data Studio to Looker Studio, Looker Studio Pro is basically what Looker was previously, but both solutions will merge. Google says the Pro edition will acquire new enterprise management features, team collaboration capabilities, and SLAs.
![Dashboard Example in Looker Studio Pro — Image Source: Google[2]](https://storage.googleapis.com/int3grity/posts/m9yb4IqJCm7D/images/ZuJudlWT6GUeTKKNVduA5)
In addition to Google's announcements and sales methods, additional features include:
Looker Studio assets can now have organizational ownership. Customers can link Looker Studio to a Google Cloud project and migrate existing assets once. This provides:
Your users' created Looker Studio assets are all kept in a Google Cloud project.
When the users who own assets leave your organization, the assets won't be removed.
Using IAM, you may provide each Looker Studio asset in your company project-level permissions.
Other Cloud services can access Looker Studio assets that are owned by a Google Cloud project.
Looker Studio Pro clients may now manage report and data source access at scale using team workspaces.
Google announcing these features for the pro version is fascinating. Both products will likely converge, but Google may only release many features in the premium version in the future. Microsoft with Power BI and its free and premium variants already achieves this.
Sources and Further Readings
Google, Release Notes (2022)
Google, Looker (2022)
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Ethan Siegel
2 years ago • 7 min read
How you view the year will change after using this one-page calendar.
No other calendar is simpler, smaller, and reusable year after year. It works and is used here.
Most of us discard and replace our calendars annually. Each month, we move our calendar ahead another page, thus if we need to know which day of the week corresponds to a given day/month combination, we have to calculate it or flip forward/backward to the corresponding month. Questions like:
What day does this year's American Thanksgiving fall on?
Which months contain a Friday the thirteenth?
When is July 4th? What day of the week?
Alternatively, what day of the week is Christmas?
They're hard to figure out until you switch to the right month or look up all the months.
However, mathematically, the answers to these questions or any question that requires matching the day of the week with the day/month combination in a year are predictable, basic, and easy to work out. If you use this one-page calendar instead of a 12-month calendar, it lasts the whole year and is easy to alter for future years. Let me explain.
The 2023 one-page calendar is above. The days of the month are on the lower left, which works for all months if you know that:
There are 31 days in January, March, May, July, August, October, and December.
All of the months of April, June, September, and November have 30 days.
And depending on the year, February has either 28 days (in non-leap years) or 29 days (in leap years).
If you know this, this calendar makes it easy to match the day/month of the year to the weekday.
Here are some instances. American Thanksgiving is always on the fourth Thursday of November. You'll always know the month and day of the week, but the date—the day in November—changes each year.
On any other calendar, you'd have to flip to November to see when the fourth Thursday is. This one-page calendar only requires:
pick the month of November in the top-right corner to begin.
drag your finger down until Thursday appears,
then turn left and follow the monthly calendar until you reach the fourth Thursday.
It's obvious: 2023 is the 23rd American Thanksgiving. For every month and day-of-the-week combination, start at the month, drag your finger down to the desired day, and then move to the left to see which dates match.
What if you knew the day of the week and the date of the month, but not the month(s)?
A different method using the same one-page calendar gives the answer. Which months have Friday the 13th this year? Just:
begin on the 13th of the month, the day you know you desire,
then swipe right with your finger till Friday appears.
and then work your way up until you can determine which months the specific Friday the 13th falls under.
One Friday the 13th occurred in January 2023, and another will occur in October.
The most typical reason to consult a calendar is when you know the month/day combination but not the day of the week.
Compared to single-month calendars, the one-page calendar excels here. Take July 4th, for instance. Find the weekday here:
beginning on the left on the fourth of the month, as you are aware,
also begin with July, the month of the year you are most familiar with, at the upper right,
you should move your two fingers in the opposite directions till they meet: on a Tuesday in 2023.
That's how you find your selected day/month combination's weekday.
Another example: Christmas. Christmas Day is always December 25th, however unless your conventional calendar is open to December of your particular year, a question like "what day of the week is Christmas?" difficult to answer.
Unlike the one-page calendar!
Remember the left-hand day of the month. Top-right, you see the month. Put two fingers, one from each hand, on the date (25th) and the month (December). Slide the day hand to the right and the month hand downwards until they touch.
They meet on Monday—December 25, 2023.
For 2023, that's fine, but what happens in 2024? Even worse, what if we want to know the day-of-the-week/day/month combo many years from now?
I think the one-page calendar shines here.
Except for the blue months in the upper-right corner of the one-page calendar, everything is the same year after year. The months also change in a consistent fashion.
Each non-leap year has 365 days—one more than a full 52 weeks (which is 364). Since January 1, 2023 began on a Sunday and 2023 has 365 days, we immediately know that December 31, 2023 will conclude on a Sunday (which you can confirm using the one-page calendar) and that January 1, 2024 will begin on a Monday. Then, reorder the months for 2024, taking in mind that February will have 29 days in a leap year.
Please note the differences between 2023 and 2024 month placement. In 2023:
October and January began on the same day of the week.
On the following Monday of the week, May began.
August started on the next day,
then the next weekday marked the start of February, March, and November, respectively.
Unlike June, which starts the following weekday,
While September and December start on the following day of the week,
Lastly, April and July start one extra day later.
Since 2024 is a leap year, February has 29 days, disrupting the rhythm. Month placements change to:
The first day of the week in January, April, and July is the same.
October will begin the following day.
Possibly starting the next weekday,
February and August start on the next weekday,
beginning on the following day of the week between March and November,
beginning the following weekday in June,
and commencing one more day of the week after that, September and December.
Due to the 366-day leap year, 2025 will start two days later than 2024 on January 1st.
Now, looking at the 2025 calendar, you can see that the 2023 pattern of which months start on which days is repeated! The sole variation is a shift of three days-of-the-week ahead because 2023 had one more day (365) than 52 full weeks (364), and 2024 had two more days (366). Again,
On Wednesday this time, January and October begin on the same day of the week.
Although May begins on Thursday,
August begins this Friday.
March, November, and February all begin on a Saturday.
Beginning on a Sunday in June
Beginning on Monday are September and December,
and on Tuesday, April and July begin.
In 2026 and 2027, the year will commence on a Thursday and a Friday, respectively.
We must return to our leap year monthly arrangement in 2028. Yes, January 1, 2028 begins on a Saturday, but February, which begins on a Tuesday three days before January, will have 29 days. Thus:
Start dates for January, April, and July are all Saturdays.
Given that October began on Sunday,
Although May starts on a Monday,
beginning on a Tuesday in February and August,
Beginning on a Wednesday in March and November,
Beginning on Thursday, June
and Friday marks the start of September and December.
This is great because there are only 14 calendar configurations: one for each of the seven non-leap years where January 1st begins on each of the seven days of the week, and one for each of the seven leap years where it begins on each day of the week.
The 2023 calendar will function in 2034, 2045, 2051, 2062, 2073, 2079, 2090, 2102, 2113, and 2119. Except when passing over a non-leap year that ends in 00, like 2100, the repeat time always extends to 12 years or shortens to an extra 6 years.
The pattern is repeated in 2025's calendar in 2031, 2042, 2053, 2059, 2070, 2081, 2087, 2098, 2110, and 2121.
The extra 6-year repeat at the end of the century on the calendar for 2026 will occur in the years 2037, 2043, 2054, 2065, 2071, 2082, 2093, 2099, 2105, and 2122.
The 2027s calendar repeats in 2038, 2049, 2055, 2066, 2077, 2083, 2094, 2100, 2106, and 2117, almost exactly matching the 2026s pattern.
For leap years, the recurrence pattern is every 28 years when not passing a non-leap year ending in 00, or 12 or 40 years when we do. 2024's calendar repeats in 2052, 2080, 2120, 2148, 2176, and 2216; 2028's in 2056, 2084, 2124, 2152, 2180, and 2220.
Knowing January 1st and whether it's a leap year lets you construct a one-page calendar for any year. Try it—you might find it easier than any other alternative!
Anton Franzen
2 years ago • 3 min read
This is the driving force for my use of NFTs, which will completely transform the world.
Its not a fuc*ing fad.
It's not about boring monkeys or photos as nfts; that's just what's been pushed up and made a lot of money. The technology underlying those ridiculous nft photos will one day prove your house and automobile ownership and tell you where your banana came from. Are you ready for web3? Soar!
People don't realize that absolutely anything can and will be part of the blockchain and smart contracts, making them even better. I'll tell you a secret: it will and is happening.
Why?
Why is something blockchain-based a good idea? So let’s speak about cars!
So a new Tesla car is manufactured, and when you buy it, it is bound to an NFT on the blockchain that proves current ownership. The NFT in the smart contract can contain some data about the current owner of the car and some data about the car's status, such as the number of miles driven, the car's overall quality, and so on, as well as a reference to a digital document bound to the NFT that has more information.
Now, 40 years from now, if you want to buy a used automobile, you can scan the car's serial number to view its NFT and see all of its history, each owner, how long they owned it, if it had damages, and more. Since it's on the blockchain, it can't be tampered with.
When you're ready to buy it, the owner posts it for sale, you buy it, and it's sent to your wallet. 5 seconds to change owner, 100% safe and verifiable.
Incorporate insurance logic into the car contract. If you crashed, your car's smart contract would take money from your insurance contract and deposit it in an insurance company wallet.
It's limitless. Your funds may be used by investors to provide insurance as they profit from everyone's investments.
Or suppose all car owners in a country deposit a fixed amount of money into an insurance smart contract that promises if something happens, we'll take care of it. It could be as little as $100-$500 per year, and in a country with 10 million people, maybe 3 million would do that, which would be $500 000 000 in that smart contract and it would be used by the insurance company to invest in assets or take a cut, literally endless possibilities.
Instead of $300 per month, you may pay $300 per year to be covered if something goes wrong, and that may include multiple insurances.
What about your grocery store banana, though?
Yes that too.
You can scan a banana to learn its complete history. You'll be able to see where it was cultivated, every middleman in the supply chain, and hopefully the banana's quality, farm, and ingredients used.
If you want locally decent bananas, you can only buy them, offering you transparency and options. I believe it will be an online marketplace where farmers publish their farms and products for trust and transparency. You might also buy bananas from the farmer.
And? Food security to finish the article. If an order of bananas included a toxin, you could easily track down every banana from the same origin and supply chain and uncover the root cause. This is a tremendous thing that will save lives and have a big impact; did you realize that 1 in 6 Americans gets poisoned by food every year? This could lower the number.
To summarize:
Smart contracts can issue nfts as proof of ownership and include functionality.
Hasan AboulHasan
2 years ago • 2 min read
High attachment products can help you earn money automatically.
Affiliate marketing is a popular online moneymaker. You promote others' products and get commissions. Affiliate marketing requires constant product promotion.
Affiliate marketing can be profitable even without much promotion. Yes, this is Autopilot Money.
How to Pick an Affiliate Program to Generate Income Autonomously
Autopilot moneymaking requires a recurring affiliate marketing program.
Finding the best product and testing it takes a lot of time and effort.
Here are three ways to choose the best service or product to promote:
Find a good attachment-rate product or service.
When choosing a product, ask if you can easily switch to another service. Attachment rate is how much people like a product.
Higher attachment rates mean better Autopilot products.
Consider promoting GetResponse. It's a 33% recurring commission email marketing tool. This means you get 33% of the customer's plan as long as he pays.
GetResponse has a high attachment rate because it's hard to leave and start over with another tool.
2. Pick a good or service with a lot of affiliate assets.
Check if a program has affiliate assets or creatives before joining.
Images and banners to promote the product in your business.
They save time; I look for promotional creatives. Creatives or affiliate assets are website banners or images. This reduces design time.
3. Select a service or item that consumers already adore.
New products are hard to sell. Choosing a trusted company's popular product or service is helpful.
As a beginner, let people buy a product they already love.
Online entrepreneurs and digital marketers love Systeme.io. It offers tools for creating pages, email marketing, funnels, and more. This product guarantees a high ROI.
Make the product known!
Affiliate marketers struggle to get traffic. Using affiliate marketing to make money is easier than you think if you have a solid marketing strategy.
Your plan should include:
1- Publish affiliate-related blog posts and SEO-optimize them
2- Sending new visitors product-related emails
3- Create a product resource page.
4-Review products
5-Make YouTube videos with links in the description.
6- Answering FAQs about your products and services on your blog and Quora.
7- Create an eCourse on how to use this product.
8- Adding Affiliate Banners to Your Website.
With these tips, you can promote your products and make money on autopilot.